Handbook of Magnetic Materials Volume 3

Handbook of Magnetic Materials, Volume 3 North-Holland Publishing Company, 1982 Edited by: E.P Wohlfarth ISBN: 978-0-444-86378-2

by kmno4

PREFACE This H a n d b o o k on the Properties of Magnetically Ordered Substances, Ferromagnetic Materials, is intended as a comprehensive work of reference and textbook at the same time. As such it aims to encompass the achievements both of earlier compilations of tables and of earlier monographs. In fact, one aim of those who have helped to prepare this work has been to produce a worthy successor to Bozorth's classical and monumental book on Ferromagnetism, published some 30 years ago. This older book contained a mass of information, some of which is still valuable and which has been used very widely as a work of reference. It also contained in its text a remarkably broad coverage of the scientific and technological background. One man can no longer prepare a work of this nature and the only possibility was to produce several edited volumes containing review articles. The authors of these articles were intended to be those who are still active in research and development and sufficiently devoted to their calling and to their fellow scientists and technologists to be prepared to engage in the heavy tasks facing them. The reader and user of the H a n d b o o k will have to judge as to the success of the choice made. Each author had before him the task of producing a description of material properties in graphical and tabular form in a broad background of discussion of the physics, chemistry, metallurgy, structure and, to a lesser extent, engineering aspects of these properties. In this way, it was hoped to produce the required combined comprehensive work of reference and textbook. The success of the work will be judged perhaps more on the former than on the latter aspect. Ferromagnetic materials are used in remarkably many technological fields, but those engaged on research and development in this fascinating subject often feel themselves as if in strife for superiority against an opposition based on other physical phenomena such as semiconductivity. Let the present H a n d b o o k be a suitable and effective weapon in this strife! The publication of Volumes 1 and 2 took place in 1980 and produced entirely satisfactory results. Many of the articles have already been widely quoted in the scientific literature as giving authoritative accounts of the modern status of the

vi

PREFACE

subject. One book reviewer paid us the compliment of calling the work a champion although with the proviso that the remaining two volumes be published within a reasonable time. The present Volume 3 goes halfway towards this event and contains articles on a variety of subjects. There is a certain degree o f coherence in the topics treated here but this i s not ideal due to the somewhat random arrival of articles. The same will be the case for the remaining Volume 4 as such, although this will then complete the work so as to finally produce a fully coherent account of all aspects of this subject. Three of the authors of Volume 3 are members of the Philips Research Laboratories, Eindhoven and, as already noted in the Preface to Volumes 1 and 2, this organization has been of immense help in making this enterprise possible. The North-Holland Publishing Company has continued to bring its professionalism to bear on this project and Dr. W. Montgomery, in particular, has been of the greatest help with Volume 3. Finally, I would like to thank all the authors of Volume 3 for their co-operation, with the profoundest hope that those of Volume 4 will shortly do likewise! E.P. Wohlfarth

Imperial College

TABLE OF CONTENTS Preface

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

v

T a b l e of C o n t e n t s

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

vii

List of C o n t r i b u t o r s

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

ix

1. M a g n e t i s m a n d M a g n e t i c M a t e r i a l s : H i s t o r i c a l D e v e l o p m e n t s a n d P r e s e n t R o l e in I n d u s t r y a n d T e c h n o l o g y U. E N Z . . . . . . . . . . . . . . . . . . . . . 2. P e r m a n e n t M a g n e t s ; T h e o r y H. Z I J L S T R A . . . . . . . . . . . . . . . . . . 3. T h e S t r u c t u r e a n d P r o p e r t i e s of A l n i c o P e r m a n e n t M a g n e t A l l o y s R.A. McCURRIE . . . . . . . . . . . . . . . . . . 4. O x i d e S p i n e l s S. K R U P I C K A a n d P. N O V A K . . . . . . . . . . . . 5. F u n d a m e n t a l P r o p e r t i e s of H e x a g o n a l F e r r i t e s with M a g n e t o p l u m b i t e Structure H. K O J I M A . . . . . . . . . . . . . . . . . . . 6. P r o p e r t i e s of F e r r o x p l a n a - T y p e H e x a g o n a l F e r r i t e s M. S U G I M O T O . . . . . . . . . . . . . . . . . . 7. H a r d F e r r i t e s a n d P l a s t o f e r r i t e s H. S T J i d ~ L E I N . . . . . . . . . . . . . . . . . . 8. S u l p h o s p i n e l s R.P. V A N S T A P E L E . . . . . . . . . . . . . . . . . 9. T r a n s p o r t P r o p e r t i e s of F e r r o m a g n e t s I.A. CAMPBELL and A. FERT . . . . . . . . . . . .

1 37 107 189

305 393 441 603 747

Author Index

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

805

Subject Index

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

833

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

845

Materials Index

vii

chapter 1 MAGNETISM AND MAGNETIC MATERIALS" HISTORICAL DEVELOPMENTS AND PRESENT ROLE IN INDUSTRY AND TECHNOLOGY

U. ENZ Philips Research Laboratories Eindhoven The Netherlands

Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-Holland Publishing Company, 1982

CONTENTS Introduction 1. F r o m l o d e s t o n e to f e r r i t e : a s u r v e y of t h e h i s t o r y of m a g n e t i s m . . . . . . . . . 2. T h e r o l e of m a g n e t i s m in p r e s e n t - d a y t e c h n o l o g y a n d i n d u s t r y . . . . . . . . . . 3. D e v e l o p m e n t o f s o m e classes of m a g n e t i c m a t e r i a l s . . . . . . . . . . . . . . 3.1. I r o n - s i l i c o n a l l o y s . . . . . . . . . . . . . . . . . . . . . . . . 3.2. F e r r i t e s . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. G a r n e t s . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. P e r m a n e n t m a g n e t s . . . . . . . . . . . . . . . . . . . . . . . 4. T r e n d s in m a g n e t i s m r e s e a r c h a n d t e c h n o l o g y . . . . . . . . . . . . . . . . 4.1. M a g n e t i s m r e s e a r c h b e t w e e n p h y s i c s , c h e m i s t r y a n d e l e c t r o n i c s . . . . . . . . 4.2. T r e n d s in a p p l i e d m a g n e t i s m . . . . . . . . . . . . . . . . . . . . 4.3. O u t l o o k a n d a c k n o w l e d g e m e n t . . . . . . . . . . . . . . . . . : References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

3 3 6 10 10 12 20 24 30 30 31 34 35

Introduction

In this contribution we attempt to trace a few main developments of the history of magnetism and to give an account of the present role of ferromagnetic materials in industry and technology. The treatment of a subject as broad as the present one must necessarily be limited and incomplete; nevertheless, we may give an impression how the large body of knowledge on magnetism accumulated in the past, and how important it is at present. The first section gives a short sketch of some early historical developments and inventions. Such a flash back to history may be useful to place the m o d e r n activities and achievements in a wider context. The next section deals with the role of magnetism and magnetic materials in modern technology, especially in the context of power generation and distribution, telecommunication and data storage. Some statistical figures on the economic significance of magnetic materials are included. The third-section gives a somewhat more detailed account of the development lines~i~f a few selected classes of materials, whereas in the last section an attempt is made to indicate the trends in applied magnetism.

1. F r o m lodestone to ferrite: a survey of the history of m a g n e t i s m

The notion of magnetism dates back to the Ancient World, where magnets were known in the form of lodestone, consisting of the ore magnetite. The name of the ore, and hence that of the whole science of magnetism, is said to be derived from the G r e e k province of Magnesia in Thessaly, where magnetite was found as a natural mineral. It seems very likely that the early observers were fascinated by the attractive and repulsive force between lodestones. Thales of Miletus (624-547 BC) reports that the interaction at a distance between magnets was known before 800 BC. Another, probably m o r e apocryphal account is due to Pliny the Elder, who ascribes the n a m e magnet to its discoverer, the shepherd Magnes "the nails of whose shoes and the tip of whose staff stuck fast in a magnetic field while he pastored his flocks". From such modest beginnings grew the science of magnetism, which may be represented as a tree on whose growing trunk new shoots and branches continuously appeared (see fig. 1). The trunk represents the mag-

4

u. ENZ

netic materials such as metals, alloys or oxides, because history shows that the use and study of materials have been the main sources of discoveries and progress. T h e new branches which developed in the course of time f o r m e d scientific fields in themselves. A brief account of s o m e of these d e v e l o p m e n t s is given in the following pages (Encyclopedia Britannica: Magnetism; see also, Mattis (1965)). Magnets f o u n d their first application in compasses, which were m a d e from a lodestone b u o y a n t on a disc of cork. W e k n o w that the compass was used by Vikings and, of course, by Columbus, but the art of navigation guided by compasses m a y be much older. T h e invention is p r o b a b l y of Italian or A r a b i c origin. T h e earliest extant E u r o p e a n reference to the compass is attributed to the English scholar A l e x a n d e r N e c k a m (died 1217). T h e influence of this simple device was far-reaching in every respect: it m a d e it possible to navigate on the high seas. T h e principle of the compass has r e m a i n e d unchanged, the device is still in full use. T h e invention of the compass is characteristic of m a n y later developments in magnetism: seemingly marginal effects turned out to be very i m p o r t a n t and to have had a t r e m e n d o u s impact on later technological developments. A milestone in the history of magnetism was William Gilbert's De Magnete, electro- high neutroncritical materials spin structures magnetic fields diffr, phenom metals semi- amorphous micromagnetism radiation , magn. M6ssbauer para- alloys cond. mogn. J spin I domains I inductio~ moment ;NI~R ;mogn. gl~ss ~'

;sp;e'Ig° ne i

ro~

I

I I bb,es

leomac netism stellar magnetism

F?Curi~

I Jalloys

I L oxides

Maxwell

~

~-

~

I

Faraday,

A~ere,1 8 0 O r ~ ert' tedr2[lmeognete 1269 Peregrinus de Maricourt 1200 Neckarn describes compass

J J J 800 b ~ r l d

: magnesian stones

Fig. 1. Development of the modern branches of magnetism from a common root. A few names and dates are indicated to mark some of the most crucial moments in this development. The modern fields of magnetism, ranging from basic entities like magnetic fields and particles to more complex ensembles, emanate in quite a straightforward way from a few basic branches. A central position is reserved to the various classes of materials, reflecting the central position of materials in magnetism research.

MAGNETISM AND MAGNETIC MATERIALS

5

Magneticisque Corporibus, et de Magno Magnete Tellure (1600, "Concerning Magnetism, Magnetic Bodies and the Great Magnet Earth") which summarized all the available knowledge of magnetism up to that time, notably that of Petrus Peregrinus de Maricour (1269). In addition Gilbert describes his own experiments: he measured the direction of the magnetic field and its strength around spheres of magnetite with the aid of small compass needles. For this purpose he introduced notions like magnetic poles and lines of force. Gilbert found that the distribution of the magnetic field on the surface of his sphere or terella ("microworld") was much like that of the earth as a whole and concluded that the earth is a giant magnet with its two magnetic poles situated in regions near the geographical poles. This observation made him the founder of geomagnetism. Gilbert's work not only strongly influenced the later development of magnetism, but also contributed to the development of the idea of universal gravitation: it was believed, for some period of time before Newton, that the planets were held in their orbits by magnetic forces in some form or other. Gilbert also discovered that lodestone, when heated to bright red heat, loses its magnetic properties, but regains them on cooling. In this way he anticipated the existence of the Curie temperature. For more than two centuries after Gilbert little progress was made in the understanding of magnetism, and its origin remained a mystery. The early nineteenth century marked the beginning of a series of major contributions. Hans Christian Orsted discovered in 1820 that an electric current flowing in a wire affected a nearby magnet. Andr6 Marie Amp6re established quantitative laws of the magnetic force between electric currents and demonstrated the equivalence of the field of a bar magnet and that of a current-carrying coil. Michael Faraday discovered magnetic induction in 1831, his most celebrated achievement, and introduced the concept of the magnetic field as an independent physical entity. Guided by his feeling for symmetry and harmony he suspected that an influence of magnetic fields on electric conduction should exist as a counterpart to Orsted's magnetic action of currents. After a long period of unsuccessful experiments with static fields and stationary magnets, he discovered the induction effects of changing fields and moving magnets. This line of investigation culminated in Maxwell's equations, establishing the synthesis between electric and magnetic fields. Progress in the understanding of the microscopic origin of magnetism was initiated by Amp6re, who suggested that internal electric currents circulating on a molecular scale were responsible for the magnetic moment of a ferromagnetic material. Amp6re's hypothesis enabled Wilhelm Eduard Weber to explain how a substance may be in an unmagnetized state when the molecular magnets point in random directions, and how they are oriented by the action of an external field. This idea also explained the occurrence of saturation of a magnetic material, a state reached when all elementary magnets are oriented parallel to the applied field. This line of thinking led to the studies of Pierre Curie and Paul Langevin on paramagnetic substances, and also to the work of Pierre Weiss (1907) on ferromagnetic materials. Pierre Curie described the paramagnetic substances as an en-

6

u. ENZ

semble of uncoupled elementary magnetic dipoles subjected to thermal agitation, the orienting action of the external field being counteracted by the thermal agitation. Such a description was also applied successfully to ferromagnetic materials at temperatures higher than the Curie temperature. The modern discipline of critical phenomena is, for the time being, the end point of this branch. Weiss, in turn, postulated the existence of a hypothetical internal magnetic field of great strength in ferromagnets, resulting in a spontaneous magnetization even in the absence of an external field. Amongst his other contributions is the notion of a magnetic domain, a small saturated region inside a ferromagnet, and the notion of domain walls. Weiss's work can be viewed as the starting point of the branch leading to the modern disciplines of micromagnetism and domain theory, and also as the point of departure of N6el's work on interactions, leading to the fields of ferrimagnetism and antiferromagnetism, including the actual disciplines of spin structures and spin glasses. A branch of its own, the study of the magnetic aspects of particles is perhaps a less obvious offshoot from the common source, but it nevertheless forms a very important part of magnetism. Indeed fields like electron spin resonance and nuclear spin resonance, M6ssbauer spectroscopy and structure analysis by neutron diffraction are at the same time indispensable tools and important disciplines of magnetism. The modern disciplines of magnetism as represented at the top of fig. 1 range from the fundamental entities like fields and particles on the left to more complex systems on the right. Critical phenomena, magnetic phase diagrams and spin structures in various materials including spin glasses are important fields of modern research. The classical discipline of domains, domain walls and micromagnetism is still being actively studied, and has even received renewed attention stimulated by the modern investigations on bubbles. The various materials appear in the centre of the three, thus confirming their central role in magnetism. The few materials that are named represent just a very small fraction of the magnetic materials known at the present time. The study of the magnetic properties of materials is the subject of the present handbook, and the present article is intended to give a general introduction to the remaining chapters of this work.

2. The role of magnetism in present-day technology and industry Having outlined the early developments of magnetism as well as the subsequent accumulation of knowledge on magnetic phenomena and materials, we now turn to the description of the role of magnetism in present-day technology and industry. Magnetic materials occupy a key position in many essential areas of interest to society. The most important of these, which depend in an essential way on magnetic materials, are the generation and distribution of electrical power, the storage and processing of information, and of course communication in all its forms, including telephony, radio and television. Apart from these major fields, many other industrial machines and devices, including motors for numerous applications, depend on magnetic materials or magnetic forces. Figure 2 gives a

MAGNETISM AND MAGNETIC MATERIALS

7

Industrally and economicallyrelwant fields of application of matlneticmaterial= Function

Physicaleffect, important parameters

power generators, power transformers magnetic induction, recording heads, medium frequency transformers, inductors, particle accelerator electric motors, small motors with permanentmagnets

Material classes

high induction material, silicon-iron sheet, oriented sheet

Permalloysheet, amorphousmetals, ferrites I ~

[ magnetomotive ~ior~teS~linduction

permanentmagnets, Ticonal, Ferroxdure~ SmCo-magnets

latching devices, levitation (trains) television,radio, resonantband pass filters

self-induction, high Q

ferrites

unidirectional microwavedevices gyrators

ferromagnetic resonance, low damping

garnet crystals, hexagonal ferrites

storageof digital information in cores, plated wires

squarehysteresis loop, fast switching time

l smallparticlesof

massstorage in magnetic tapes, magnetic discs and floppy discs

information storage in magneto-optic stores compact digital massstorage

I square-loop ferrites, plated wires, permalloy

remanenceand coerciveforce of small particles and thin magnetic films

1

3'- Fe203, CrO2, Fe

thin metallic films, Co-based

high Faradayand Kerr effect

amorphous films, MnBi, GdFe

stability and mobility of bubbles

monocrystalline garnet films

Fig. 2. Industrially and economically relevant fields of application of magnetic materials. T h e central column lists the basic physical effects together with the important parameters. T h e left-hand column gives the useful functions and the right-hand one the classes of materials most commonly used to fulfil these functions. The arrows indicate the various interrelations.

8

u. ENZ

survey of the use of magnetic materials in various areas of application. The left-hand column shows the type of application or the function realized with the aid of magnetism. The central column lists the various physical effects and the parameters most relevant to a specific application. The right-hand column displays the classes of materials used to accomplish the various functions. The variety of physical effects, applications and materials is impressive, even in this necessarily incomplete survey. Most of the applications are based on magnetic induction, magnetomotive forces or the specific properties of the hysteresis loop such as squareness or coercive field, but other effects like ferromagnetic resonance or the Faraday effect also find their applications. The useful materials are in general restricted to those classes which are ferromagnetic or ferrimagnetic at room temperature and which possess a sizable saturation magnetization. Although magnetic materials are indispensable for the listed and for many other applications, their role remains to some extent hidden because the ultimate practical function is not associated with magnetism. The public at large is often unaware of the role of magnetism in everyday life. Occasionally one gets the impression that the same holds even for some professionals! The economic impact of magnetism is very considerable. Jacobs (1969) estimates the total value of processed magnetic material produced in the United States in 1967 at about 680 million dollars, which represents about 0.1% of the American gross national product. In 1976 the corresponding amount was 2140 million dollars (Luborsky et al. 1978, Snyderman 1977). These figures apply to magnetic materials as such and do not take into account that magnetic materials are nearly always components of more elaborate products such as electric motors, transformers, loudspeakers, microwave isolators or computer memories. Jacobs estimates that for such products a "multiplication factor" of the order of 15 is appropriate, so that the total economic impact of magnetism was of the order of 1.5% of the American gross national product in 1969. This figure has not changed much since, and probably applies to other economies as well. In table 1 some economic data on magnetic materials are given, split up into various classes of materials to be discussed below. The largest quantities of magnetic material enter the field of electric power generation and distribution, a field which is historically the major application of magnetism. For this function the aim is to reach the highest possible saturation magnetization and the lowest possible total loss, properties which are best met in iron-based alloys such as silicon-iron sheet and grain-oriented sheet. More recently amorphous metals have become competitive for some specific applications in this field. Although power generation and distribution have now achieved the status of well-established and mature technologies, progress towards reduced losses is still going on. As a result the amount of power handled by a transformer of constant size has increased continuously, resulting in the last 40 years in a tenfold increase in power-handling performance. A second area of great and rapidly increasing importance is that of magnetic materials for information storage and processing. The amount of material involved in these fields is much smaller, but their economical significance is larger

MAGNETISM AND MAGNETIC MATERIALS TABLE 1 Annual magnetic materials market in millions of dollars (not corrected for inflation) 196%1968 US Electrical steel Magnetic recording tapes Magnetic discs and drums Soft ferrites (communication, entertainment and professional) Square-loop ferrites Permanent magnets

World (17

1976-1977 US

World 07

180(27

4400)

180(27

45007

1300(3/

100(~)

900(37

3000(37

110(2) 55(2) 55(27

130 70(67

535(4)

1 5 0 (3,6)

1979-1980 US

World 07

148 57(7) 170(5)

600(4) 960(5)

(1/Western world including Japan. (2)Jacobs (1969). (3)Luborski et al. (1978). (4)De Bruyn and Verlinde (1980). (s)Hornsveld (1980). (6)Snijderman (1977). (7)Electronics, 3, Jan. 1980.

than that of electrical steels. T h e leading e c o n o m i c position was taken over by information storage about ten years ago. A m o n g s t information-storing materials, magnetic tapes and discs are the most i m p o r t a n t groups. T a p e and disc techniques are both based on the same physical principle, the association of a bit of information with the direction of the magnetization in a small area of the material. T h e merits of this storage principle are simplicity, p e r m a n e n c e (or non-volatility) of information, and a high information density per unit surface of the (film-like) material. T h e progress of these techniques has been entirely directed towards higher information densities and thus towards lower prices per bit of information, and further progress in this direction is expected. Square-loop ferrites or bubble d o m a i n m e m o r i e s are also based on the association of inf o r m a t i o n with the direction of the magnetization in the material, in the f o r m e r case in a small sintered core, in the latter case in a single domain, a bubble, which is able to m o v e in a single-crystal film. Magnetic cores have been the basic m e t h o d of information storage in c o m p u t e r s for m o r e than 25 years, but have now r e a c h e d a level of saturation, which is i m p o s e d by the limitations of handling ever smaller (and faster) cores. T h e bubble d o m a i n memories, on the o t h e r hand, are in full d e v e l o p m e n t and m a y find a p e r m a n e n t position in the hierarchy of information storage. N u m e r o u s other magnetic information storage principles have been p r o p o s e d and realized, including thin permalloy films and permalloyplated wire, but their total e c o n o m i c impact has r e m a i n e d small. C o m m u n i c a t i o n is the third i m p o r t a n t field of application of magnetic materials. This field includes telephony, radio and television broadcasting and receivers, and radar, all of which techniques use m e d i u m to very high frequencies. D u e to their

10

u. ENZ

high resistivity and consequently low eddy-current losses, ferrites are the best suited materials for communication. In telephony the medium frequency channel filters are based on resonant circuits using high-O ferrite cores, one of the first applications of ferrites and the standard technique till now. Every broadcast receiver contains many ferrite parts, such as inductors, deflection units, line transformers and antenna rods.

3. Development of some classes of magnetic materials

In this section the development of a few selected classes of magnetic materials is described. These case histories relate to iron-silicon alloys, ferrites, garnets and permanent magnets. The emphasis will be on the chronology of events, the improvement of performance and the technical relevance.

3.1. Iron-silicon alloys Electrical grade steel is the magnetic material produced in the largest quantities of all; hundreds of thousands of tons are annually needed by the electrical industry. The bulk of this material is used for the generation and distribution of electrical energy and for motors. High magnetic induction and low losses are of prime importance in these applications. Alloys of iron and silicon meet the above conditions well and therefore take a prominent position with the product category of electrical steels. Here we confine ourselves to some historical remarks and to give some recent figures on silicon-iron alloys. The starting point of the development of silicon-iron alloys of suitable quality is marked by the work of Barrett et al. (1900). These authors found that the addition of about 3% of silicon in iron increased the electrical resistance and reduced the coercive force as compared to unalloyed iron. The slight reduction in saturation magnetization due to silicon was far outweighted by the improvement in the other properties. Some years later, in 1903, the industrial production of these alloys started in Germany and in the U n i t e d States. The promotion and subsequent improvement of this technique is, to a considerable extent, the merit of Gumlich and Goerens (1912). The material was used in the form of hot rolled polycrystalline sheets having random grain orientation. Due to the higher permeability and the reduced hysteresis and eddy-current losses, iron-silicon sheet replaced the conventional materials within a few years, in spite of the initial difficulties of production and the higher price, and was used in this form for about three decades. However, these random oriented materials were still imperfect because saturation was only reached by applying magnetic fields well above the coercive field, which limits the useful maximum induction to about 10 kG. The hysteresis loops of single crystals or of well oriented samples, on the other hand, are nearly rectangular. Fields slightly higher than the coercive field are therefore sufficient to drive the core close to saturation. The useful maximum induction is thus higher,

MAGNETISM AND MAGNETIC MATERIALS

ll

reaching 15 to 1 7 k G (1.5 to 1.7Wb/m 2) (fig. 3). An ideal transformer would consist of single crystal sheets oriented such that a closed rectangular flux path along [100] directions, the preferential directions, results. Progress towards this goal was achieved by Goss (1935) who showed that grain oriented sheets can be obtained by certain cold rolling and annealing procedures. This so called Goss texture is characterized by crystallites having their [110] planes oriented parallel to the plane of the sheet, with common [100] direction in this plane. The magnetic properties of such materials are characterized by coercive fields around 0.1 Oe and maximum permeabilities up to 70.000 (fig. 3). Data obtained by Williams and Shockley (1949) on a oriented single crystal frame of high purily 3.85% silicon iron with limbs parallel to [100] directions are included in fig. 3 for comparison. The coercive field of this single crystal was as low as 0.028 Oe (2.2 A/m) and the maximum permeability exceeded 10 6. Grain orientation contributed to a further decrease of the magnetic core losses. Loss figures dropped to about 0.6 Watt per kg at 60 cycles and an induction of 10 kG (1 Wb/m 2) for commercial grade oriented silicon-iron sheet. An additional advantage was that maximum induction up to 17 kG (1.7 Wb/m 2) became practical. Another more recent step towards higher quality is related to even more perfect crystalline orientation combined with the introduction of a controlled tensile stress in the sheet (Taguchi et al. 1974). The composition of the material remained unchanged i.e. the silicon content is still around 3%. The tensile stress is introduced by a surface coating consisting of a glass film and an inorganic film applied on both surfaces of the sheet. This procedure leads, by magnetoelastic

Magnetization (kG) 18

Br.=17 kG

~kO

t

'°r i/ill'

l I

-0.2

0

0.2

I

I

I

0.L

0.6

Magnetic field (Oe)

Fig. 3. Static hysteresis loops of grain oriented silicon-iron sheet (Goss texture). For comparison the loop of a single crystal (broken line, Williams and Shockley 1949) is shown (after Tehble and Craik 1969).

12

U. E N Z

interactions, to improved properties of the hysteresis loop and thus to still lower magnetic losses. The improvement of the quality of electrical grade steel since 1880 is shown in fig. 4. In a time span of 100 years the core loss decreased from 8 W/kg to about 0.4 W/kg for an induction of 10 k G and a frequency of 60 Hz. The innovations described above clearly show up as marked steps: the introduction of silicon-iron alloys after 1900, causing the loss figure to drop from 8 to 2 W/kg and also the use of grain-oriented material in the late thirties. The latter innovation enabled higher induction ratings: new branches with maximum induction of 15 kG and 1 7 k G appear after 1940. The dramatic increase of the power handled by a transformer of equal size is also shown. co. e toss ( W a t t / k g )

transforrnator power { MVA)

6 4.

17 kG 15kG

2

1000

! 10 kG

1 0.8 0.6

I ' /t

o.4

/ 0.2

50

//

If

188o

1900

1920

194.0

I

/

I I

1960

I

1980

2000 year

Fig. 4. Core loss of electrical grade steel (after Luborsky et al. 1978). Since 1880 the core loss decreased from 8 W / k g to 0 . 4 W / k g at an induction of 1 0 k G and a frequency of 6 0 H z . T h e introduction of textured sheet around 1940 led to the use of higher m a x i m u m induction (up to 17 k G (1.7 Wb/m2)). T h e broken line shows the increase in power handled by a transformer of constant size.

3.2. Ferrites Ferrites are mixed oxides of the general chemical composition MeOFe203, where Me represents a divalent metal ion such as Ni, Mn or Zn. The crystallographic structure of ferrites, and also that of the closely related ore magnetite (FeOFe203) is the spinel structure. Ferrites can therefore be seen as direct descendants of magnetite (see fig. 1). Many simple or mixed ferrites are magnetic at room temperature, but due to their ferrimagnetic character the saturation magnetization is only a fraction of that of iron. The outstanding property of ferrites, which makes them suitable for many applications, is their high electrical resistivity as compared to that of metals. Their specific resistivity ranges from 102 to 101° f~ cm, which is up to 15 orders of magnitude higher than that of iron. In most high frequency applications of ferrites eddy currents are therefore absent or negligibly small, whereas at such frequencies eddy currents are the main drawback of

MAGNETISM A N D M A G N E T I C M A T E R I A L S

13

metals, even in laminated form. Such intrinsic properties make the ferrites indispensable materials in telecommunications and in the electronics industry, where frequencies in the range of 109 to 1011Hz have to be handled. The potential usefulness of magnetic oxides for high frequency applications was realized as early as 1909 by S. Hilpert, who investigated the magnetic properties Of various oxides including some simple ferrites. In 1915 the crystallographic structure of ferrites, which had remained unknown until then, was determined independently by W.H. Bragg in England and S. Nishikawa in Japan. Contributions to the understanding of the chemistry of ferrites were also made by Forestier (1928) in France. All of this early work remained without a direct follow-up; at that time there was apparently no technological need yet for such materials. The situation remained unchanged until 1933, when Snoek of the Philips Research Laboratories started a systematic investigation (Snoek 1936) into the magnetic properties of oxides. In the same period of time ferrites were independently investigated by Takai (1937) in Japan. Snoek's working hypothesis in his search for high permeability materials was to look for cubic oxides which, for symmetry reasons, could be expected to have a low crystalline anisotropy. Simultaneously he aimed at finding materials with low magnetostriction values to minimize the adverse effects of the unavoidable internal stresses present in polycrystalline materials. Snoek's approach turned out to be fruitful: he found suitable materials in the form of mixed spinels of the type (MeZn)Fe204, where Me is a metal of the group Cu, Mg, Ni or Mn. Permeabilities up to 4000 were reached (Snoek 1947). Snoek's achievement may again have remained of more academic interest, but this time there was a clear demand for magnetic materials from the telephone industry, which felt the need to improve the load coils of their long-distance lines and to use bandpass filters based on low-loss magnetic materials. Ferrite inductors proved to be well suited for these purposes, and so ferrites and telephone technology developed in close cooperation. Six (1952) was the inventive and leading promotor of this development, which did not, however, proceed without a great deal of effort from chemists, physicists and electrical engineers, who cooperated in achieving adequate material properties and practical technical designs. Before 1948, when most of this work was done, little was known about the cause of the low saturation magnetization of ferrites or of the origin of their anisotropy. This changed when N6el (1948), who had already explained the behaviour of antiferromagnets, introduced his concept of partially compensated antiferromagnetism, which he called ferrimagnetism. The essential point of N6el's explanation is the antiparallel orientation of the spins of the ions in the two sublattices, octahedral and tetrahedral, of the spinel structure. N6el's model revealed directly the cause of the low saturation of ferrites. The work of Verwey and Heilman (1947) on the distribution of the various ions over these lattice sites was undoubtedly of great help. N6el's model was directly verified by neutron diffraction work done by Shull et al. (1951) only a few years after the invention of this powerful method of analysis. Further proof was derived from a study of the temperature dependence of the saturation magnetization in some spinel ferrites

14

u. ENZ

(Gorter et al. 1953). A n o t h e r fundamental mechanism, ferromagnetic resonance, was extensively studied in ferrites (Snoek 1947) shortly after its discovery by Griffiths (1946). The main difficulty encountered in the early use of ferrites was their high level of magnetic losses and disaccommodation. It was found that even in the absence of eddy currents there were still appreciable residual losses, which prevented the design of high quality resonance circuits. It is now well known that quite a large number of electronic and ionic relaxation processes can cause magnetic aftereffects in magnetic materials subjected to alternating fields. These processes are the main cause of the losses in magnetic cores. Snoek (1947) tried to minimize these after-effects by controlling the presence of relaxing ions with the aid of special sintering procedures in suitable oxidizing or reducing atmospheres. A n important insight concerning the use of ferrites in resonant filter circuits was that the relevant quantity to be considered is the ratio between the loss factor tan6 and the initial permeability/x rather than tan~ as such. This ratio can be controlled by introducing air gaps in the magnetic circuits. Therefore a high initial permeability is as important as a low loss factor. A reduced loss level in the ferrite material made it possible to reduce the physical size of the inductors, a successful development vizualized in fig. 5. Ferrite cores having about equal quality factors are shown in a sequence ranging from 1946 to 1974. The volume of the inductors was reduced by a factor of 32 during this time span. Compared with an air coil of

Fig. 5. Development of pot cores between 1946 and 1974. Reduction of the loss level of ferrite materials led to the reduction of the physical size of these components, all of which fulfil the same technical function. The quality factor Q of the ferrite components remained, as indicated, about constant during this time span. An air coil and a Fernico coil of much lower quality, representing the state of the art in 1936 and 1939, are shown for comparison. The total reduction in volume is nearly a factor of 400.

MAGNETISM AND MAGNETIC MATERIALS

15

much lower quality representing the state of the art in 1936, the reduction in volume is nearly a factor of 400. Similar, albeit less spectacular progress was also made in another ferrite application, i.e., that in power transformers where a high saturation induction and low hysteresis losses are of principal importance (see fig. 6). The total losses are shown to be reduced by a factor of three, while the maximum usable inductance nearly doubled in the indicated period of time. This type of material, a high saturation MnZn ferrite, is at present finding increasing application in switched-mode power supplies for small to medium power levels. loss P (Watt cm-3)

\

0.2

Induction 8 (kG)

"°"3c'3c5 ...---tt

I

"~..3c8 2

0.1

J

1950

L

i

1960

1970

0

1980 year

Fig. 6. Reduction of loss factor and increase of usable maximum induction of ferrite cores for power applications from 1950 to 1980.

A new and rather unexpected application of ferrites emerged with the invention of the gyrator, a non-reciprocal network element. The impedance of signals passing through such an element in the forward direction differs from that in the backward direction. The gyrator was conceived by Tellegen (1948) on theoretical grounds as a possible but not yet realized network element. Hogan (1952) was the first to realize a non-reciprocal microwave device consisting of a ferrite-loaded waveguide. The physical effect on which the device is based is analogous to the well-known Faraday effect, i.e., the rotation of the plane of polarization of a light wave passing through a magnetized body. One form of the non-reciprocal device thus consists of a circular wave-guide carrying a central ferrite rod magnetized along its axis. If the rotation of the plane of polarization of the microwave equals 45 ° and coupling in or out also occurs with an offset angle of 45 ° the microwaves pass through the device in the forward direction while propagation in the backward direction is suppressed. A similar device functions as a microwave switch (see fig. 7) controlled by the bias field. Other devices based on this principle, which have found wide application in microwave technology, are circulators, resonance isolators and power limiters. The discovery that some polycrystalline spinel ferrites can have a rectangular hysteresis loop and therefore can be used as computer memory elements was of paramount importance for computer technology. Until 1970 nearly all main-frame

16

U. E N Z

Rectangular waveguide Cylindrical waveguide'-k~" ~ IX Rectangular ~ ~..,/', waveguide -x~.r~.~ ~ ,.~1"~,, !/

". L~ ~ I t ', , "':."l'-'~4"-"

]

I I I L___ I

Fig. 7. Microwave switch based on the rotation of the plane of polarization of microwaves propagating along the magnetized ferrite rod in the central cylindrical part of the device.

Fig. 8. Core array of a ferrite core m e m o r y in 3D organization showing word, bit and sense lines. T h e ferrite core matrix is shown together with the preceding storage technology, based on electron tubes, and the succeeding technology, the semiconductor memory.

MAGNETISM AND MAGNETIC MATERIALS

17

computer memories consisted of ferrite cores, so that it is fair to say that the whole computer development was closely connected with the development of the ferrite core memory. A r o u n d 1968 the yearly,world production of ferrite cores was about 2 x 10 l° cores (Jacobs 1969). J.W. Forrester and W.N. Papion, both at that time at MIT, are generally considered to be the inventors of the principle of coincident current selection of a core (Forrester 1951). The first square-loop cores consisted of nickel-iron alloys, the switching speed of which suffered from an inherent limitation due to eddy currents. Both Forrester and Rajchman (1952) suggested the use of non-metallic cores to avoid this shortcoming. At about the same time, Albers-Schoenberg (1954) observed the square-loop properties of some ferrite compositions. A link with system requirements was immediately made. This revolutionary challenge materialized in Whirlwind I, the first experimental computer based on a ferrite core memory, built at the Lincoln laboratory at MIT in 1953. Figure 8 shows a wired ferrite core matrix consisting of 1024 ferrite cores. A stack of such matrix planes forms the memory. Two individual cores are shown in fig. 9. Ferrites also p l a y e d an unexpected role in particle accelerators constructed to study elementary particles (Brockman et al. 1969). The operation of these large

Fig. 9. Two individual ferrite memory cores (20 mil and 14 mil) are shown on the wings of a fly.

18

U. E N Z

machines is based on accelerating units consisting of large transformers designed as resonance cavities. These elements accelerate the charged particles (protons) by feeding energy into the particle beam circulating in the machine. The stations act in such a way that the particle beam represents the secondary winding of the transformers. During one acceleration sequence the increasing frequency has to be followed by controlling the self-induction of the core of the transformer with the aid of a bias field. Again, the demand for low losses, especially low eddy current losses, favoured ferrites above other materials for this application, and so ferrites entered this field as essential elements and played a continued role in the subsequent stages of the development of these machines. Figure 10 shows an acceleration unit of the alternating gradient synchrotron in Brookhaven. The synchrotron contains 12 of such cavities, and each unit Contains about 500 kg of ferrite.

Fig. 10. Accelerator unit of the alternating gradient synchrotron at Brookhaven, containing a hollow cylindrical ferrite core assembled from a large number of rings. The total weight of the core is about 500 kg (after Brockman et al. 1969).

Apart from these few examples of specific implementations of ferrites we recall that the bulk of ferrite material is used in telecommunication and consumer applications, with roughly equal turnover in these two fields. The main consumer products are television and radio sets, in which such parts as line transformers, deflection coils, tuners and rod antennas contain ferrite materials. About 0.7 kg of ferrite enters a black-and-white television set, and about 2 kg a colour set. Figure 11 gives an impression of the diversity of ferrite products for such applications.

MAGNETISM AND MAGNETIC MATERIALS

19

Fig. 11. Various ferrite componentsas used in radio and televisionsets.

Hand in hand with the implementation of ferrites and with the tailoring and perfection of their technically relevant parameters, the investigation of their fundamental properties continued, resulting in a considerable deepening of the understanding of their chemical and physical properties. The main lines of investigation concerned: (a) crystal structures, chemical miscibility regions and preferential site occupation of the various ions in the spinel lattice; (b) the experimental determination of data relating to spontaneous magnetization, Curie temperature, anisotropy and magnetostriction constants; (c) micromagnetic properties such as domain walls and domain configuration in polycrysta!line and monocrystalline materials; (d) the dynamics of the magnetization process, and damping and resonance phenomena; and (e) the theoretical description, discussion and understanding of these properties in atomic terms, i.e., the arrangement of the ionic magnetic moments in sublattices, the quantum mechanics of magnetic interactions between localized moments, the spin-orbit interaction and dipole-dipole interaction as a cause of anisotropy. These methods of studying the properties of ferrites have acquired ~he status of a scientific standard, i.e., a paradigm, which has since been applied to many other materials. Garnets and hexagonal ferrites are examples of materials of industrial importance discovered and investigated along such lines. Other compounds of as yet more academic interest include sulphospinels and rare-earth chalcogenides.

20

U. ENZ

3.3. Garnets

The prototype of the family of garnets is the compound Mn3A12Si3012, a mineral and esteemed gemstone occurring in nature. The crystal structure of garnets is cubic with three different types of sublattices occupied by the three metals of the above compound. The garnets existing in nature often contain other ions as well and are in most cases non-magnetic. It is interesting to note that it was precisely the ferrimagnetic properties, discovered by Pauthenet (1956) and Bertaut et al. (1956) of some synthetic rare-earth iron garnets that attracted attention and opened up a new field of research in magnetism. Since then, a wealth of scientific and technological information on garnets has been produced. For more than two decades, publications on garnets have been appearing at a rate of about 200 papers a year, so that garnets and especially yttrium iron garnet (YIG), are now amongst the best known magnetic materials. One may agree with J.H. van Vleck who compared the role of Y I G for magneticians to that of the fruit fly to geneticists. Pioneering work on the chemical, crystallographic and magnetic properties of garnet was done by Geller et al. (1957), while Pauthenet (1957) investigated the magnetism of mixed rare-earth iron garnets, Re3FesO12, some of which were found to have compensation temperatures of the magnetization. These findings demonstrated directly their ferrimagnetic character and indicated that the magnetic moment of the rare-earth sublattice is oriented oppositely to the resulting moment of the two iron sublattices. The total magnetization of garnets is therefore relatively low as compared with that of magnetic metals or ferrites. The Curie temperatures, dominated by the iron-iron interaction, are of the order of 300°C, reflecting the same type of interaction mechanisms as those active in ferrites. Because the magnetization of garnets is lower than that of ferrites, garnets have not found bulk applications competing with ferrites, such as in transformers, coils, etc. One of the outstanding properties of YIG, which was discovered by Spencer et al. (1956) and Dillon (1957) shortly after the publication of the first papers on garnets, is its extremely low ferromagnetic resonance linewidth. Values of the linewidth A H of some oersteds were then measured, but subsequent improvements of crystal quality and purity yielded figures as low as A H = 0 . 1 0 e (8 A/m) at 10 MHz for carefully polished samples of Y I G (LeCraw et al. 1958). These exceptional resonance properties made Y I G very useful as a microwave device material, with loss figures one or two orders of magnitude lower than those of corresponding spinel ferrites. Moreover, Y I G also proved to have acoustic losses lower than quartz, thus opening up prospects for magneto-acoustic devices such as adjustable delay lines. Small amounts of rare-earth ions substituted into Y I G produced a dramatic increase in both anisotropy and linewidths. Such substituted materials were ideal objects on which to study the fundamentals of anisotropy (Kittel 1959) and relaxation processes (Dillon 1962, Teale et al. 1962), studies which contributed considerably to progress in the understanding of these mechanisms.

MAGNETISM AND MAGNETIC MATERIALS

21

Garnets are also outstanding in their optical properties: Y I G shows a low optical absorption in the range of visible light, so that layers up to several microns thick are transparent. With the aid of the magneto-optical Faraday effect, domain structures can be directly observed (Dillon 1958). Y I G m o r e o v e r exhibits a "window" of extremely low optical absorption in the infrared region. Optical absorption coefficients as low as c~ = 0.03 cm -1 for wavelengths between A = 1.2 ~ m and A = 4.4 p~m have been observed. The Faraday rotation of some garnets is large enough to m a k e the material suitable for magneto-optical devices such as light modulators and magneto-optical memories. In particular, garnets containing bismuth show a very high specific Faraday rotation, e.g., 0 = 3°/~m at A = 0.5 ~m for Y2.6Bi0.4Fe4Oa2 (Robertson et al. 1973). Bismuth-doped garnets have also proved to be suitable for use as fast switching magneto-optical display components (Hill et al. 1978). The non-magnetic yttrium aluminium garnet (YAG), was found to be an excellent laser host (Geusic et al. 1964). Garnets, especially Si-doped Y I G , are also interesting for their photomagnetic properties, i.e., the light-induced change of magnetic properties as a consequence of a light-stimulated redistribution of electrons or Fe 2+ ions (see Teale et al. 1967, Enz et al. 1971). Even greater prominence was achieved by the granets in their application as the leading magnetic bubble device material. Two basic contributions, both m a d e by Bobeck, opened up this new field. The first was the invention of the principle of high-density information storage with the aid of bubble domains (Bobeck 1967); the second was his observation of a growth-induced uniaxial anisotropy energy in garnets (Bobeck et al. 1970). B o b e c k ' s basic idea was to associate a bit of information, a digital one or zero, with the presence or absence of a bubble at some defined location and time. Bubbles are cylindrical domains of reversed magnetization occurring in nearly magnetized thin films having a sufficiently large uniaxial anisotropy. The dimensions of bubbles are mainly determined by the length l = trw/47rM2s, a material constant depending on the specific Bloch wall energy O-w and the saturation magnetization Ms. By controlling the magnetization of the garnet material the bubble diameters can be adjusted in a wide range from submicron size to tens of microns. The first observation of stable bubbles, which were in fact submicron bubbles, was made by Kooy et al. in 1960 in the hexagonal material BaFe120~9, a material with a rather high magnetization and a large uniaxial anisotropy. D u e to the microscopic dimensions of the bubbles, the packing density of the bubbles and thus the density of information can be very high; values of 1 0 6 bits cm -2 have been achieved, and densities higher than 1 0 7 bits c m -2 a r e considered to be attainable in the future. An extensive review of the physical and chemical properties of garnets has been given by Wang (1973) and a survey of garnet materials for bubble devices has been published by Nielsen (1976). The advent of bubble domain devices stimulated work in the field of crystal growth, both of bulk garnet crystals and of thin monocrystalline films grown by liquid phase epitaxy, known as the L P E method. Flux-grown bulk crystals were

22

U. E N Z

first prepared by Remeika in 1956, mainly for the purpose of studying fundamental properties. This art developed rapidly and the growth of large crystals of high perfection was finally mastered (Tolksdorf et al. 1978). L P E growth experienced a similar evolution, starting with the work of Shick et al. 1971, who grew films suitable for bubble devices. This method of preparation, which is an extension of flux growth, has now become the standard method of growing bubble device films. The growth procedure is as follows: a carefully polished wafer of a non-magnetic garnet crystal is immersed in a liquid consisting of a flux and the dissolved garnet. If the lattice misfit is controlled, the magnetic garnet grows isostructurally and without dislocations on the substrate. The films made in this way meet high standards of quality and reproducibility: composition and film thickness can be controlled within narrow limits and the remaining level of defects is low, which is reflected in the low values of the coercive fields achieved. Figure 12 shows bubbles and stripe domains in a Y G d T m epitaxial garnet film as observed with the aid of the Faraday effect. Figure 13 shows an overlay Y-bar structure of a shift register as processed on a garnet film (Bobeck and Della Torre 1975). A second scientific discipline which was greatly stimulated by the success of bubbles is that of the dynamics of domain walls and bubbles. Domain wall motion

U •

•

•

• •

•

•

•

•

..

i •

•

Fig. 12. Bubbles and stripe domains in a Y G d T m epitaxial garnet film 7 Ixm thick. The bias field is near to the run-out field. The bubble diameter is about 7 ixm (after Bobeck and Della Torre 1975).

MAGNETISM AND MAGNETIC MATERIALS

23

Fig. 13. Bubbles moving in a Y-bar pattern of a bubble shift register. Some propagation loops and the bubble generator (heavy black square) are shown (after Bobeck and Della Torre 1975).

has been studied in the past in the context of magnetization processes of magnetic bodies caused by domain wall displacements. A detailed understanding of the dynamic wall properties had not been reached along such lines owing to the extreme complexity of the process. This situation changed when perfect monocrystalline layers of garnets for bubble devices became available, which made it possible to study the motion of domain walls and bubbles by direct optical observation. As a result of this development, the body of experimental data on wall dynamics has greatly increased and the theoretical understanding of the mechanisms involved has deepened considerably. Amongst the new results is the insight that there is an upper limit to the velocity of a domain wall, a velocity limit which also marks a limit to the speed, i.e., the data rate of bubble devices. Extended reviews on the subject of wall and bubble dynamics have been published by Malozemoff and Slonczewski (1980) and also by de Leeuw et al. (1980).

24

U. ENZ

3.4. Permanent magnets

Permanent magnets, i.e., the magnesian stones, marked the beginning of magnetism. It is interesting to observe that, at present, permanent magnets are still being investigated, improved and increasingly applied. They are essential to modern life as components of a wide variety of electromechanical and electronic devices. It has been estimated that the average home contains more than fifty permanent magnets and every car uses an average about eight of them. The applications of permanent magnets range from loudspeakers, small electric motors and generators, door latches and toys, to ore separators, water filters, electric watches and microwave tubes. The function of a permanent magnet in these and other applications is to generate a magnetic field in an air gap of a magnet system. The air gap may either be fixed to accommodate moving electric conductors which exert external forces, a function performed by loudspeakers and electric motors, or it may be variable as it is in movable armatures on which the magnet exerts the force. The latter application is found in door latches, relays, telephone sets, magnetic levitation and contactless couplings between rotating shafts. Another typical application of permanent magnets is the alignment of an object by exerting a magnetic torque on it, as in a compass. A special application is found in electron tubes where permanent magnets are used for controlling the orbits of electron beams or for focussing them. Table 2 shows a number of functions performed by permanent magnets together with the corresponding applications. The four functions described cover the main applications of permanent magnets; they include the conversion of electrical into mechanical energy and vice versa, and the exertion of mechanical forces on material bodies and on moving charge carriers. Figures 14 and 15 give an impression of two of the most common applications of permanent magnets, the loudspeaker and the small motor (after Zijlstra 1976). The early development of permanent magnet materials proceeded entirely by trial and error. Nevertheless 100 years ago bar and horseshoe magnets made from TABLE 2 Typical functions and applications of permanent magnets with some examples of machines, devices and components (after Zijlstra 1974) Function

Application

Conversion of electrical into mechanical energy and vice versa

Small electric motors, dynamos, loudspeakers, microphones, eddy-current brakes, speedometers, magnetos

Exerting a force on a ferromagnetically soft body

Relays, couplings, bearings, clutches, magnetic chucks and clamps, separators (extraction of iron impurities, concentration of ores)

Alignment with respect to a field

Positioning mechanisms (e.g. stepping motors), compasses, some ammeters

Exerting a force on moving charge carriers

Magnetrons, travelling-wave tubes, some cathode-ray tubes, Hall plate

MAGNETISM AND MAGNETIC MATERIALS

25

Fig. 14. Cut-away view of a loudspeaker containing a Ferroxdure ring.

Fig. 15. Cut-away view of a windscreen wiper. The stator field is provided by two Ferroxdure segments.

26

U. ENZ

carbon steel were well known and widely used. Since then an unparallelled development has taken place; new permanent magnet materials have been discovered and the existing ones improved. The foundations for the scientific understanding of permanent magnets have also been laid in this period. The relevant figure of merit expressing the quality of a permanent magnet is its maximum energy product (BH).... This figure describes the ability of a permanent magnet to withstand the influence of a counteracting magnetic field. Moreover the energy product is a measure of the useful magnetic flux that can be produced by the magnet in a given volume. Figure 16 shows the magnetic flux density B plotted as a function of the magnetic field H, i.e., the well-known hysteresis loop. The shaded area represents the (BH)max product; the optimum working point of the loop is that which defines the largest area. As an illustration of the achievements of the past, the energy product is plotted in fig. 17 as a function of time, starting in 1880. Since then, the (BH)max values have increased by a factor of more than 100. This great achievement was not realized by improving a single material, but rather by the discovery of new classes of material. Each new finding was followed by a period of technological improvement, which in turn was followed by a new discovery. The figure gives the top values reached in any year. The sequence starts with carbon steels and tungsten steels at the end of the last century and is continued with cobalt-containing steels around 1920. A major advance in magnetic materials was made in 1932, when the development of the Alnico magnets started with Mishima's AINiFe alloy (Mishima 1932). In the illustration the various members of this family are indicated as Tic II, Tic G (Jonas et al. 1941) etc. The coercive force of Alnico magnets was essentially doubled as compared with earlier materials; these magnets were the first to be truly p e r m a n e n t under adverse conditions such as stray fields, shock and elevated temperature. The magnetic and mechanical hardness of the Alnico alloy is due to

Fig. 16. Hysteresis loop showing the optimum working point of a permanent magnet. The hatched rectangle represents the maximum energy product of the material.

MAGNETISM AND MAGNETIC MATERIALS

27

(BHlrnax (MG Oe) 100

// / /

50

/

20

(Sin, Pr) Cos (.1/ Sm C o 5 / ~

10 5 // 2

//

/

oFxd 330

tlTic lI

//M is~j.I, el* FxdlO0

1

0.5 0.2

,/ I W-steel C-steel

0.1 i

i

i

i

/

I

1880 1900 1920 19~0 1960 1980 = year Fig. 17. Development of the maximum energy products of permanent magnets between 1880 and 1980. Most data are due to Van den Broek and Stuijts (1977). 7

a thermal treatment leading to the precipitation of a second phase in a finely dispersed form. This development culminated with Ticonal XX, an Alnico alloy hardened in the presence of a magnetic field which leads to the precipitation of oriented second-phase particles of elongated shape (fig. 18). The maximum energy product reached was about 11 M G O e (90 kJm -3) (Fast a n d r e Jong 19591)/. The next breakthrough in the development of high energy product materials was made with rare-earth transition metal compounds. The systematic investigation of the physical and magnetic properties of these alloys and compounds started around 1960 at Bell Laboratories (Nesbitt et al. 1961). However it was Strnat who realized the potential of these compounds for high energy-product magnets and vigorously promoted their development (Strnat et al. 1966). In 1969, Das of the Raytheon Company announced that he had made a magnet having an energy product of 20 M G O e (160 kJm -3) by sintering SmCos. Even higher values, up to 35 M G O e (280 kJm-3), were recently reported to have been obtained in a related material of the formula (RE)2(CoFe)17 (Wheeler report, 1979)*. This quasi-binary intermetallic phase was again prepared by sintering. It is interesting * Wheeler Associates, Inc., 1979, Rare Earth-Cobalt permanent magnets, Elizabethtown, Kentucky, USA.

28

U. ENZ

Fig. 18. Micrograph of Ticonal XX (after De Vos, thesis, Delft, 1966). to note in fig. 17, that the energy product, plotted as a function of time, follows an approximately linear dependence throughout the period reported. The material quoted last yields the top value of the energy product reached up till now. It is possible to reach still higher values of (BH)max? Rathenau (1974) discussed this 1 2 question in detail and showed that the limit of (BH)max is given by ~Bs for any material, provided the coercive field and the anisotropy can be made strong enough. The saturation magnetization of iron or iron cobalt alloys is high enough to allow for a further increase of (BH)max by a factor of four. In addition to the materials discussed, which follow a straight line, fig. 17 also contains materials indicated as Fxd 100 and Fxd 300. The energy products of these materials fall clearly below the general trend. They are typical representatives of the family of low cost permanent magnet materials having a medium energy product, the hexagonal oxides. If we plot the price per unit energy product of various materials (fig. 19) we observe another systematic correlation, the continuous progress made in improving the economy of permanent magnets. In this plot the hexagonal oxides occupy a leading position and are the end point of a long development. The importance of ferrimagnetic hexagonal oxides for permanent magnets was first pointed out in 1952 by Went et al. A detailed account of these magnetically hard materials, called Ferroxdure, and their history has been given recently by Van den Broek and Stuijts (1977). The opinion expressed at the time of discovery was that these new materials were of great economic importance. That opinion has been fully confirmed: the total world production of magnetically hard f e r r i t e s - which, in composition and crystal structure, all belong

MAGNETISM A N D M A G N E T I C M A T E R I A L S

l

100

29

T S'mCo5

50 price per unit of energy 20

' P t Co I Tic xx /

C-steel

•___. W.-steel •~ ,~,~ Co-steel

10 Q

%

5

Tic ff X

2

Tic

1

0.5

Tic GG

\NPZFxd 100 \ \ \ \ ~ F x d 330 \

0.2 0.1

1800 '90 1900 '10

'20

'30

%0 '50

'60 '70 '80 '9 2 = year

0

Fig. 19. Price per unit of energy product (after Rathenau 1974). to the same g r o u p - is now estimated at about 100,000 tonnes a year (1980), with a value of some 400 million dollars. Figure 20 shows how these ferrites have acquired an ever increasing share of the world production of p e r m a n e n t magnets, measured in tonnes per annum. C o m p a r e d with other materials for p e r m a n e n t magnets, Ferroxdure is characterized by an exceptionally high coercivity, combined with a r e m a n e n c e which, though not very high, is valuable for practical purposes. With such a material it became possible to produce magnets of shapes such that would have almost completely demagnetized themselves if made of a different material. Typical shapes were flat ring magnets, magnetized perpendicular to the plane of the ring, or transversely magnetized rods with m a n y north and south poles closely adjacent to each other. Ferroxdure is also highly resistant to external demagnetizing fields, as encountered in D C motors, for example. These novel properties were exploited on a large scale, e.g., for making flat loudspeakers and compact D C motors (see figs. 14 and 15). The great economic success of Ferroxdure is due in the first place, however, to the low price per unit of available magnetic energy (fig. 19). The material is therefore mainly used not so much as a technical i m p r o v e m e n t but m o r e as a substitute for m o r e expensive components, such as Ticonal magnets in loudspeakers or stator coils of windscreen-wiper motors. Ferroxdure is inexpensive because it does not contain any rare material such as nickel or cobalt, and it is relatively easy to manufacture: it is only necessary to "mix a few cheap oxides" and to " b a k e them to the right shape". Finally, Ferroxdure - an oxide - has a high electrical resistivity, so that there are

30

U. ENZ

)roduction (kt) 100

tot 20

10

//~lloys

5

I

L

I

I

I

I

L

I

1900 '10 '20 '30 '/.0 '50 '60 '70 '80 year Fig. 20. Estimate of the world production of permanent magnets (after Rathenau 1974). hardly any eddy-current losses. This is an important advantage in radio-frequency applications and also in certain types of electric motors. A disadvantage is the relatively high temperature coefficient of the remanence and the coercivity. This makes the material less suitable for certain professional applications. In 1954 the material was substantially improved by orienting the crystallites (Stuijts et al. 1954, 1955). In isotropic material the magnetic moments of the crystallites, in zero field after saturation, are randomly distributed over a hemisphere. In anisotropic Ferroxdure, on the other hand, which is the material now most widely used, the c-axes and hence the moments after saturation are approximately parallel. Consequently the remanence is about twice as great and (BH)max is about four times higher. At the time it was a surprise that the attempts to produce crystal-oriented Ferroxdure were so successful. It was feared, quite reasonably, that the orientation of the crystallites, achieved with much difficulty in the compacted product, would be lost during sintering. The result exceeded all expectations: the texture was not only preserved but was even greatly improved.

4. Trends in magnetism research and technology

4.1. Magnetism research between physics, chemistry and electronics On studying the ways to progress in magnetism one observes that magnetism research has an interdisciplinary character and depends in an essential way on the

MAGNETISM AND MAGNETIC MATERIALS

31

cooperation of scientists and engineers working in fields quite different from each other. The various disciplines relevant for magnetism research range from fundamental theoretical physics through chemistry to electric and electronic engineering. The cooperation of these disciplines is of such a type that the preparation and chemical or crystallographical study of new materials may stimulate physical work, or alternatively that the discovery of a physical effect in one material may stimulate the search for other classes of material showing analogous effects. A similar mutual relation is observed between engineering efforts facing material problems and basic material studies concentrating on the relevant critical parameters. Last but not least, and most commonly recognized, the discovery of new materials or of new physical effects may stimulate new engineering applications. This special character of magnetism research has consequences for the organization of research and development laboratories. An organizational structure concentrating the various disciplines in multidisciplinary units or groups is probably the most adequate form. Indeed, the study of the case histories of m a j o r innovations seems to show that those research laboratories which have such an organization are most likely to produce outstanding results. This applies equally for university laboratories organized as "material centers", government institutes and industrial laboratories. In the last category the multidisciplinary approach has an even stronger weight as engineering aspects are included. Examples of research successes obtained by the cooperation of experts in different disciplines are easily at hand. In fact some have already been described in this chapter. The early industrialization of ferrites is an example in which chemistry, crystallography, physics and telecommunication technology were equally indispensable for success. Other examples are the discovery of garnets, the invention of the gyrator or the development of bubble devices. In all cases the study of materials played a central role. Some remarks concerning the growth of magnetism research may be made here. Before the second world war only few laboratories were active in this field, and with some famous exceptions, magnetism was not usually a subject of research at universities. Since then the n u m b e r of laboratories occupied with magnetism has largely increased. In particular many new or existing university institutes turned to studies in this field. As a consequence the n u m b e r of investigations has much increased and more and more detailed studies of materials were made. The industrial laboratories, on the other hand, did not much grow in n u m b e r or size, so that their share, especially concerning fundamental studies, has diminished. The few government or national research centers which were traditionally active in magnetism research maintained their position and continued their important role.

4.2. Trends in applied magnetism In this outlook into the future of applied magnetism we try to indicate some trends which are discernable at this m o m e n t and which will probably be of importance for some time to come (see, Wijn 1976). We have seen that magnetic materials

32

U. ENZ

are used for a wide variety of different functions such as transformers, various types of inductive elements or m e m o r y cores. C o m m o n to most of these applications is the use of materials prepared separately in bulk form. The processed material is then assembled into the magnetic device as a separate part. Since some years, however, there seems to be a tendency towards the use of materials as an integrated part of the device. In m a n y cases the magnetic material is present in the form of a thin layer, having a monocrystalline, polycrystalline or amorphous structure. The layers are often structured or shaped by methods known from integrated circuit technology. The purpose is to reach a miniaturization also in the case of magnetic materials and to give it its shape in situ. Modification or control of the local compositions and the local magnetic properties of a thin film, e.g., by means of ion implantation, is another aspect of the tendency described here. A second development is aimed at the control of the position and displacement of individual domain walls in monocrystalline or oriented polycrystalline layers. The bubble devices are a good example for this tendency. Such devices depend, apart from a successful miniaturization, in an essential way on the mastering of the material properties, the material perfection and the internal stress distribution. Some examples of these tendencies in device development will now be given, starting with the magnetoresistive reading heads used in magnetic recording. Reading of the information recorded on a magnetic tape is usually achieved by picking up the stray flux passing the air gap of an inductive reading head. T h e electric signal induced in the windings of the head is proportional to the rate of change of the flux. In the magnetoresistive reading head proposed some time ago (Hunt 1971), the flux itself is measured with the aid of the magnetoresistive effect in a thin film of Permalloy. The effect depends on the angle 0 between the direction of the current flowing through the film and the direction of the magnetization. The latter is modulated by the stray flux of the tape. To obtain a linear characteristic the equilibrium angle 0 should be 45 °. An elegant solution is achieved in the so-called " B a r b e r pole configuration" (Kuijk et al. 1975) in which the direction of the current flow is forced into the desired direction with the aid of parallel conductor strips (see fig. 21).

i Ni'Fe

// z - - current flow

Fig. 21. Magnetoresistive reading head based on the "Barberpole configuration". The magnetization of the NiFe film is parallel to the vector M, the current is forced, by conducting bars, into a direction parallel to the vector I. The optimum angle 0 is 45° (after Kuijk et al. 1975).

MAGNETISM AND MAGNETIC MATERIALS

33

Closely related to this example are the thin film integrated recording heads of the inductive variety. Here the emphasis is on reading and writing many tracks on the tape or disc simultaneously. Accordingly the heads are made in large number in integrated form by a batch process using thin film and photolithographic techniques (Romankiw 1970). In combination with solid state integrated circuits a new and very attractive approach of magnetic recording becomes feasible in such a way (fig. 22). A similar development toward miniaturization can be observed with inductors. The L-chip, a miniaturized self inductance based on multiple coils printed on ferrite substrates, is being developed at present. The second main trend, the control of magnetic domain walls and domain structures at a micromagnetic level is manifest in bubble domain devices and domain control in Fe-Si sheet. Both fields have already been discussed in the present survey. Also thermomagnetic recording can be viewed as an example of this line. The basic idea of this storage principle has been proposed long ago (Mayer 1958), but new interest has arisen recently (Berkowitz and Meiklejohn 1975). The information is stored in small regions of reversed magnetization in a thin magnetic film. Unlike the situation with bubbles, these domains remain fixed. Reversal of the magnetization is achieved by reducing locally the coercive force of the film by heating with the aid of a focussed light beam. The information is read by using the Faraday effect. The bits of information are accessed by mechanical motion. Film materials include GdFe, MnBi and garnet films. The

Fig. 22. Array of integrated recording heads shown in a fabrication stage prior to cutting off the front part. The individual heads carry 6 windings (courtesy of W.F. Druyvesteyn, Philips Research Laboratories).

34

U. ENZ

large Faraday effect of some substituted garnets is also used in a different type of device, proposed recently (Hill 1980), the integrated light modulation matrix. The matrix consists of isolated islands etched from a garnet film (fig. 23), which can be switched individually by a cross bar system. The switching of an island occurs by a single Bloch wall, and is initiated by local heating of the island. These examples sufficiently demonstrate the trend mentioned and show that magnetic materials provide an environment in which rather naturally we can build and control certain kinds of objects having dimensions in the micron or submicron range, a region which is generally not readily accessible. The examples also show that applied magnetism is still very much alive.

~ranspareniresis]Gnce,J

q

d

'

I

subsirate

y-bus

Fig. 23. Light modulating matrix based on switching cells of iron garnet single crystal films, with x-y addressed resistance network (after Hill 1980).

4.3. Outlook and acknowledgement In this contribution we have sketched the early historical lines leading to the present edifice of magnetism, and indicated its importance for modern industry and society as a whole. Some material classes received more detailed attention in both the way they developed and their achievements. These materials represent only a very small fraction of those which have been studied. Moreover, many achievements in the explanation of material properties and their theoretical understanding have hardly been touched upon. In this context we note that the amount of knowledge and detailed information on the properties of magnetic

MAGNETISM AND MAGNETIC MATERIALS

35

m a t e r i a l s has a c c u m u l a t e d t o s u c h a d e g r e e , t h a t it is b e c o m i n g i n c r e a s i n g l y difficult t o k e e p sight o n t h e w h o l e of i n f o r m a t i o n . P e r h a p s it is w o r t h w h i l e t o c o n s i d e r t h e f e a s i b i l i t y of t h e i n s t a l l a t i o n of a d a t a b a n k c o n t a i n i n g i n f o r m a t i o n o n magnetic materials. T h e a u t h o r w o u l d l i k e to t h a n k P r o f . G . W . R a t h e n a u , P r o f . H . P . J . W i j n , D r . R . P . v . S t a p e l e , D r . D . J . B r e e d a n d D r . P . F . B o n g e r s of this l a b o r a t o r y , f o r a d v i c e a n d c r i t i c a l r e a d i n g of t h e m a n u s c r i p t of this c o n t r i b u t i o n .

References Albers-Schoenberg, E., 1954, J.A.P. 25, 152. Barrett, W.F., W. Brown and R.A. Hadfield, 1900, Sci. Trans. Roy. Dublin Soc. 7, 67. Berkowitz, A.E. and W.H. Meiklejohn, 1975, IEEE-MAG 11,997. Bertaut, F. and F. Forrat, 1956, C.R. Acad. Sc. 242, 382. Bobeck, A.H., 1967, Bell Syst. Tech. J. 46, 1901. Bobeck, A.H. and E. Della Torre, 1975, Magnetic Bubbles (North-Holland, Amsterdam). Bobeck, A.H., E.G. Spencer, L.G. van Uitert, S.C. Abrahams, R.L. Barnes, W.H. Grodkiewicz, R.C. Sherwood, P.H. Schmidt, D.H. Smith and E.M. Waiters, 1970, Appl. Phys. Lett. 17, 131. Bragg, W.H., 1915, Phil. Mag. 30, 305. Brockmann, F.G., H. van der Heide and M.W. Louwerse, 1969, Philips Tech. R. 30, 323. Das, D.K., 1969, IEEE-MAG 5, 214. De Bruyn, R. and G.J. Verlinde, 1980, Philips Elcoma Division, Eindhoven, private communication. Dillon, J.F., 1957, Phys. Rev. 105, 759. Dillon, J.F., 1958, J.A.P. 29, 539. Dillon, J.F., 1962, Phys. Rev. 127, 1495. Enz, U., R. Metselaar and P.J. Rijnierse, 1971, J. de Phys. 32, C1-703. Fast, J.D. and J.J. de Jong, 1959, J. de Phys. Radium 20, 371. Forestier, H., 1928, Ann. de Chim. 10e srr. 9, 316. Forrester, J.W., 1951, J.A.P. 22, 44. Geller, S. and M.A. Gilleo, 1957, Acta Cryst. 10, 239. Geusic, J.E., H.M. Marcos and L.G. van Uitert, 1964, Appl. Phys. Lett. 4, 182. Gorter, E.W. and J.A. Schulkes, 1953, Phys. Rev. 90, 487. Goss, N.P., 1935, Trans. Am. Soc. Metals, 23, 511.

Griffiths, J.H.E., 1946, Nature, 158, 670. Gumlich, E. and P. Goerens, 1912, Trans. Farad. Soc. 8, 98. Hill, B., 1980, IEEE-ED 27, 1825. Hill, B. and K.P. Schmidt, 1978, Philips J. Res. 33, 211. Hilpert, S., 1909, Ber. Deutsch. Chem. Ges. Bd 2, 42, 2248. Hogan, C.L., 1952, Bell Syst. Tech. J. 31, 1. Hornsveld, L., 1980, Philips Elcoma Division, private communication. Hunt, R.P, 1971, IEEE-MAG 7, 150. Jacobs, I.S., 1969, J.A.P. 40, 917. Jonas, B. and H.J. Meerkamp van Embden, 1941, Philips Tech. Rev. 6, 8. Kittel, C., 1959, Phys. Rev. Lett. 3, 169. Kooy, C. and U. Enz, 1960, Philips Res. Rep. 15, 7. Kuijk, K.E., W.J. van Gestel and F.W. Gorter, 1975, IEEE-MAG 11, 1215. LeGraw, R.C., E.G. Spencer and C.S. Porter, 1958, Phys. Rev. 110, 1311. Leeuw, F.H. de, R. van den Doel and U. Enz, 1980, Rept. Progr. Phys. 43, 689. Luborsky, F.E., P.G. Frischmann and L.A. Johnson, 1978, J. Magn. Mag. Mat. 8, 318. Malozemoff, A.P. and J.C. Slonczewski, 1979, Physics of magnetic domain walls in bubble materials (Academic Press, New York). Mattis, D.C., 1965, Theory of Magnetism (Harper and Row, New York). Mayer, L., 1958, J.A.P. 29, 1454. Mishima, T., 1932, Iron Age, 130, 346. N6el, L., 1948, Ann. de Phys. 3, 137. Nesbitt, E.A., H.J. Williams, J.H. Wernick and R.C. Sherwood, 1961, J.A.P. 32, 342 S. Nielsen, J.W., 1976, IEEE-MAG 12, 327. Nishikawa, S., 1915, Proc. Tokyo Math. Phys. Soc. 8, 199. Pauthenet, R., 1956, C.R. Acad. Sc. 242, 1859. Pauthenet, R., 1957, Thesis, Grenoble, France.

36

U. ENZ

Rajchman, J.A., 1952, RCA Rev. 13, 183. Rathenau, G.W., 1974, Proc. 3rd Eur. Conf. on Hard Magn. Mat., Amsterdam (Bond voor Materialenkennis, P.O. Box 9321, Den Haag, The Netherlands) p. 7. Remeika, J.P., 1956, J. Am. Chem. Soc. 78, 4259. Robertson, J.M., S.W. Wittekoek, Th.J.A. Popma and P.F. Bongers, 1973, Appl. Phys. 2, 219. Romankiw, L.T., I.M. Croll and M. Hatzakis, 1970, IEEE-MAG 6, 597. Shick, L.K. and J.W. Nielsen, 1971, J.A.P. 42, 1554. Shull, C.G., E.O. Wollan and W.C. Koeler, 1951, Phys. Rev. 84, 912. Six, W., 1952, Philips Tech. Rev. 13, 301. Snoek, J.L., 1936, Physica, 3, 463. Snoek, J.L., 1947, New Devel. in Ferromagn. Materials (Elsevier, Amsterdam). Snyderman, N., 1977, Electronics News, 28 November. Spencer, E.G., R.C. LeCraw and F. Reggia, 1956, Proc. IRE 44, 790. Strnat, KJ., G.J. Hoffer, W. Ostertag and I.C. Olson, 1966, J.A.P. 37, 1252. Stuijts, A.L., G.W. Rathenau and G.H. Weber, 1954/1955, Philips Tech. Rev. 16, 141. Taguchi, S., T. Yamamoto and A. Sakakura, 1974, IEEE-MAG 10, 123. Takai, T., 1937, J. Electrochem. Japan, 5, 411.

Teale, R.W. and D.W. Temple, 1967, Phys. Rev. Lett. 19, 904. Teale, R.W. and Tweedale K., 1962, Phys. Lett. 1,298. Tebble, R.S. and D.J. Craik, 1969, Magnetic Materials (Wiley, London) 520. Tellegen, B.D.H., 1948, Philips Res. Rep. 3, 81. Tolksdorf, W. and F. Welz, 1978, Crystal growth of magnetic garnets from high temperature solutions, in Crystals Vol. 1 (Springer, Berlin). Van den Broek, C.A.M. and A.L. Stuijts, 1977, Philips Techn. Rev. 37, 157. Verwey, E.J.W. and E.L. Heilmann, 1947, J. Chem. Phys. 15, 174. Vos, K.J. de, 1966, Thesis, Delft. Wang, F.Y., 1973, in: Treatise on Materials Science and Technology, ed., H. Herman (Academic Press, New York) 279. Weiss, P., 1907, J. Phys. 6, 661. Went, JJ., G.W. Rathenau, E.W. Gorter and G.W. van Oosterhout, 1951/1952, Philips Techn. Rev. 13, 194. Wijn, H.P.J., 1970, Proc. Int. Conf. Ferrites, Kyoto. Wijn, H.P.J., 1976, Physics in Industry (Pergamon, Oxford) 69. Williams, H.J. and W. Shockley, 1949, Phys. Rev. 75, 178. Zijlstra, H., 1974, Philips Tech. Rev. 34, 193. Zijlstra, H., 1976, Physics in Technology (May), 98.

chapter 2 PERMANENT MAGNETS; THEORY

H. ZlJLSTRA Philips Research Laboratories Eindhoven The Netherlands

Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-HollandPublishing Company, 1982 37

CONTENTS 1. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. G e n e r a l p r o p e r t i e s a n d a p p l i c a t i o n s . . . . . . . . . . . . . . . . 1.2. T h e h y s t e r e s i s l o o p . . . . . . . . . . . . . . . . . . . . . 2. Suitability criteria for a p p l i c a t i o n s . . . . . . . . . . . . . . . . . . 2.1. T h e e n e r g y p r o d u c t . . . . . . . . . . . . . . . . . . . . . 2.2. T h e m a g n e t i c free e n e r g y . . . . . . . . . . . . . . . . . . . 3. M a g n e t i c a n i s o t r o p y . . . . . . . . . . . . . . . . . . . . . . 3.1. A n i s o t r o p y field a n d coercivity a s s o c i a t e d w i t h m a g n e t i c a n i s o t r o p y . . . . . 3.2. S h a p e a n i s o t r o p y . . . . . . . . . . . . . . . . . . . . . . 3.3. M a g n e t o c r y s t a l l i n e a n i s o t r o p y . . . . . . . . . . . . . . . . . . 4. F i n e p a r t i c l e s . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Critical r a d i u s for s i n g l e - d o m a i n particles . . . . . . . . . . . . . . 4.2. B r o w n ' s p a r a d o x . . . . . . . . . . . . . . . . . . . . . . 5. C o e r c i v i t y a s s o c i a t e d w i t h s h a p e a n i s o t r o p y . . . . . . . . . . . . . . 5.1. P r o l a t e s p h e r o i d . . . . . . . . . . . . . . . . . . . . . . 5.2. C h a i n of s p h e r e s . . . . . . . . . . . . . . . . . . . . . . 6. C o e r c i v i t y a s s o c i a t e d with m a g n e t o c r y s t a l l i n e a n i s o t r o p y . . . . . . . . . . 6.1. M a g n e t i z a t i o n r e v e r s a l by d o m a i n wall p r o c e s s e s f o r / * 0 / / A > Js . . . . . . 6.2. T h e 180 ° d o m a i n wall . . . . . . . . . . . . . . . . . . . . 6.2.1. E n e r g y a n d w i d t h of a 180 ° d o m a i n wall . . . . . . . . . . . . 6.2.2. T h e e x c h a n g e e n e r g y coefficient A . . . . . . . . . . . . . . 6.3. I n t e r a c t i o n of d o m a i n walls w i t h cavities a n d n o n - f e r r o m a g n e t i c i n c l u s i o n s 6.3.1. D o m a i n - w a l l p i n n i n g at l a r g e i n c l u s i o n s . . . . . . . . . . . . 6.3.2. N u c l e a t i o n of r e v e r s e d o m a i n s at l a r g e i n c l u s i o n s . . . . . . . . . 6.3.3. D o m a i n - w a l l p i n n i n g at small i n c l u s i o n s . . . . . . . . . . . . 6.4. D o m a i n - w a l l n u c l e a t i o n at surface defects . . . . . . . . . . . . . 6.5. I n t e r a c t i o n of d o m a i n walls w i t h the crystal lattice . . . . . . . . . . 6.5.1. W a l l p i n n i n g at r e g i o n s w i t h d e v i a t i n g K and A . . . . . . . . . 6.5.2. P i n n i n g of a d o m a i n wall by an a n t i p h a s e b o u n d a r y . . . . . . . . 6.5.3. N u c l e a t i o n of a d o m a i n wall at an a n t i p h a s e b o u n d a r y . . . . . . . 6.5.4. T h i n - w a l l c o e r c i v i t y in a perfect crystal . . . . . . . . . . . . 6.5.5. P a r t i a l wall p i n n i n g at d i s c r e t e sites . . . . . . . . . . . . . 7. I n f l u e n c e of t e m p e r a t u r e . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

39 39 4O 42 42 46 49 49 52 53 55 55 6O 6O 60 64 66 66 67 67 69 74 76 78 78 80 81 81 88 93 94 98 100 104

1. Introduction

1.1. General properties and applications The appearance of permanent-magnet materials such as alnico (Jonas et al. 1941) and hexaferrite (Went et al. 1951) with much better properties than materials previously in use was followed by a great increase in the applications of the permanent magnet. Compared with electromagnets (including power supplies) permanent magnets offer the advantage of a larger ratio of the useful magnetic field volume to the volume of the magnet system. Their usefulness is of course particularly apparent where a constant magnetic field is required. As is widely known, the constancy of the externally generated field is related to the magnetic "hardness" of the material, that is to say the extent to which the material retains its magnetization in opposing fields. In this way the p o l a r i z a t i o n - a n d therefore the external f i e l d - of a p e r m a n e n t magnet is maintained. A particular example of an opposing field is the internal field of the poles of the magnet itself. In this case the demagnetizing action is again unable to destroy the polarization of the magnet. The present increasing interest in the further development of hard magnetic materials is explained in part by the growing demand for miniaturization in modern technology. The problem of heat dissipation is inseparable from miniaturization, and the substitution of permanent magnets for electromagnets obviously goes a long way towards solving that problem. To ensure the most effective development it is desirable to start by investigating the likely applications of permanent magnets. The next step is to decide on the criteria that indicate suitability for these applications. These criteria can then provide a pattern for the production of tailor-made magnetic materials. This calls for insight into the effects that variation of such properties as remanence and coercivity has on the suitability of the materials for a particular application, and it also requires knowledge of the physical background. This will be the main subject of the present chapter. Table 1 lists various machines, devices and components in which permanent magnets are nowadays used. The classification is based on four principles: - m e c h a n i c a l energy is converted into electrical energy (or vice versa) in the magnetic field; - t h e permanent magnet exerts a force on a ferromagnetically soft body; 39

40

H. ZIJLSTRA

TABLE 1 Examples of machines, devices and components using permanent magnets, classified by four functions which the magnet can perform. Function

Application

Conversion of electrical in'~o mechanical energy and vice versa

Small electric motors, dynamos, loudspeakers, microphone% eddy-current brakes, speedometers, magnetos

Exerting a force on a ferromagneticaUy soft body

Relays, couplings, bearings, clutches, magnetic chucks and clamps, separators (extraction of iron impurities, concentration of ores)

Alignment with respect to a field

Positioning mechanisms (e.g., stepping motors), compasses, some ammeters

Exerting a force on moving charge carriers

Magnetrons, travelling-wave cathode-ray tubes, Hall plates

tubes,

some

- t h e permanent magnet is subjected to a directional force exerted by a magnetic field; - t h e permanent magnet exerts a force on moving charge carriers, e.g., a beam of electrons in a vacuum. In sections 2.1 and 2.2 the two main suitability criteria are discussed which together cover almost the entire field of applications. They are the maximum energy product and the maximum change in the magnetic free energy. Applications not covered by these criteria can be found among the positioning mechanisms in table 1. Apart from the fact that the existing applications provide an incentive to search for better magnetic materials, the converse is of course equally true: better magnets lead to applications that had not previously been thought of or did not seem feasible.

1.2. The hysteresis loop Permanent magnet materials are characterized by high coercivities and high remanent magnetizations. Before proceeding with the discussion of the structural parameters that determine the hard magnetic properties, we must first define the parameters that are generally used to specify the magnetic properties of permanent magnets. We employ the International System of Units (SI) in which the magnetic flux density B is expressed as either B =/~o(H + M ) , or

B =/~oH + J ,

PERMANENT MAGNETS; THEORY

41

where M and J are are the local material contributions to the flux density, respectively called magnetization and magnetic polarization, and H is the con: tribution from all other sources and is called magnetic field strength. The quantities H and M are measured in A m -1 (1 A m -1 = 4~r x 10 - 3 0 e ) . The quantities B and J are measured in Vsm -2 or tesla (1 T = 10 4 Gauss). The vacuum permeability ~0 is equal to 47r x 10 -7 V s A -1 m -t (or Hm-1). Both expressions for B will be used in this chapter. Although magnetic polarization is the official n a m e for J it will often be called magnetization. If the magnetization M or J of a p e r m a n e n t magnet material is plotted as a function of the applied field H a hysteresis loop is obtained in which the magnetization is not a unique function of H, but depends on the direction and magnitude of previously applied fields. A typical hysteresis loop is shown in fig. 1. The initial magnetization curve starting at the origin is obtained when the material is in a thermally demagnetized state. If the m a x i m u m applied field H m is sufficient to saturate the material the loop is referred to as a saturation loop. When the applied field is reduced the magnetization decreases to the r e m a n e n t magnetization J,, which is generally less than the saturation magnetization Js. In an efficient p e r m a n e n t magnet material Jr is usually 0.8-1.0Js. If the material is subjected to a demagnetizing field (i.e. a negative applied field H ) the magnetization is gradually reduced and at a critical field - H = jHc the magnetization is zero. This critical field jHc is known as the magnetization coercivity and is defined as the reverse field required to reduce the net magnetization of the material to zero in the presence of the field. The latter qualifying statement is necessary because if the field is r e m o v e d the specimen may return to a small positive r e m a n e n t magnetization J; < Jr. Instead of J we can plot the magnetic

/Z jHc k

/]I//] .,11] /

Fig. 1. Saturation hysteresis loop for magnetic flux density B as a function of H (drawn) and for magnetization J as a function of H with initial magnetization curve (dashed).

42

H. ZIJLSTRA

flux density B = / x 0 H + J as a function of H (drawn line in fig. 1). We then obtain the flux hysteresis loop with remanence Br = Jr and with a smaller value of the coercivity which is here called the flux coercivity ~Hc. Note that by these definitions the coercivities are positive numbers quantifying negative field strengths. It should be emphasized that the coercivities jHc and BHc are assumed to correspond to demagnetization of the saturated material, though we shall see later that permanent magnet materials are rarely if ever absolutely saturated even in exceptionally high fields. Unless otherwise stated, it can usually be safely assumed that the values of Hc quoted in the various scientific journals, books and papers refer to the "saturation" values as defined above. In the following the prefix J will be omitted when jH~ is discussed.

2. Suitability criteria for applications 2.1. The energy product

The extent to which a material will be suitable for applications in which electrical energy plays a part (the first groups in table 1) depends on the amount of magnetic flux linkage per metre squared and the maximum opposing field that can be tolerated without loss of polarization. The product of the flux density B and the associated opposing field H, referred to as the energy product, is a useful measure of the performance of a particular magnet, since it is proportional to the potential energy of the field in the air gap. It is useful only, however, when the magnet is not disturbed by fields from another source. To determine the energy product it is of course necessary to have information about the hysteresis loop of the material (fig. 2). A permanent magnet that is subject only to the influence of its own field will be in a state represented by a working point in the second (or the fourth) quadrant of the hysteresis loop. In these quadrants the field is opposed to the flux density, and is referred to as the demagnetizing field. It can be shown quite generally that the occurrence of a magnetic field outside the permanent magnet does in fact relate to a field inside the magnet with B and B

Fig. 2. Part of a magnetic hysteresis loop for magnetic flux density B; the shaded area is equal to the maximum energy product (BH)....

PERMANENT MAGNETS; THEORY

43

/ - / i n opposition. To do this, we have to apply Maxwell's equations to a situation in which there are no electric currents (apart from the circular currents on an atomic scale, which are the carriers of the magnetization of the material). The magnetic field strength H then satisfies curl H = O, and for the flux density B we always have div B = 0. For a permanent magnet of finite dimensions we may therefore deduce (Brown 1962a)

fn(H.

B ) d V = 0,

(2.1)

where the integration is performed over the complete space R. If this integral is written as the sum of the integral over the volume (Rrnagn) of the permanent magnet and the integral over the rest of the complete space (Rrest), then

~Rmagn (/~r B)

dV

= --fRrest(H- B) dV.

Assuming that the space Rrest is " e m p t y " , i.e., contains no magnetic substances, then the flux density there is given by B =/x0H. The right-hand side of the last equation is then negative, which is possible only if B and H inside the magnet are of opposite sense or at least include an obtuse angle at least somewhere. This result is not affected if Rrest contains soft magnetic material in which B and H always have the same direction. It can also be shown directly from what we have said above why the product is a good criterion of quality for the applications considered in this section. If we assume that any field present in soft magnetic material is negligible, we may write:

BH

fRmagn(lt.B)dV=-tXo f nrestH2dV.

(2.2)

The right-hand side of this equation is twice the potential energy of the field outside the magnet (i.e. in the air gap). This is proportional to H • B. The exact location of the operating p o i n t - a n d hence the value of the energy p r o d u c t - d e p e n d s on the relative dimensions of the magnet and the magnetic circuit in which it is used. In the limiting cases of an infinitely long needle of a closed circuit ( H = 0) or of an infinitely extensive plate (B = 0) the energy product is equal to zero; then there

44

H. Z I J L S T R A

is no external field. Between these two extremes a situation exists in which the energy product has its maximum magnitude. In the case of the needle-shaped magnet the demagnetizing field is very weak and the working point is close to the point Br in fig. 2. The value of the flux density at this point is the remanence. If the magnet is made shorter and thicker, the working point then moves along the loop in the direction of the point sHe, which it reaches if the magnet is given the form of a thin plate magnetized perpendicular to its plane. The demagnetizing field then has its maximum value and exactly compensates the magnetization. In a properly dimensioned design the energy product will thus assume a maximum value, ( B H ) .... which is determined solely by the material used. The suitability criterion sought has thus been found. The product can be represented by the area of the shaded rectangle in fig. 2; its magnitude is equal to twice the total potential energy of the field produced outside the magnet divided by the volume of the magnet. The higher the remanence, the greater the coercive force and the more convex the hysteresis loop, the greater is the value of the product. For an ideal magnet, i.e., a magnet that maintains the saturation value Js of its polarization in spite of the presence of an opposing field H, the hysteresis loop in the second quadrant is formed by a straight line going from the point where H = 0, i.e., where B = Br = Js, to the point where - H = BHc = Js/l~o. The maximum energy product is then given by: 1 (BH)max = 4/x~ j 2 .

(2.3)

To reach this maximum it is sufficient if the magnet maintains its saturation until the opposing field reaches the value -½JJl~o. A further improvement in the energy product is then only possible with materials that have a higher saturation value J~. The highest known saturation value at room temperature is shown by an FeCo alloy (2.4 T); from this value the theoretical energy product could be as much as 1150 kJm -3 (144 MGOe). However, the coercive force of this alloy is very low, which makes it unsuitable for permanent magnets. Figure 3 shows the improvements achieved in maximum energy products over the years, the record values being indicated on a logarithmic scale. It is interesting to note how closely the curve approximates to an exponential development. Once the material and thus the hysteresis loop and the (BH)max value are given, the magnet system has to be designed to make optimum use of the material parameters. Very schematically this is done as follows: Consider a permanent magnet system as drawn in fig. 4. The magnet has a length Im and cross-sectional area Sin. The air gap has a length Ig and crosssectional area Sg. The pole pieces are assumed to have infinite permeability ( H = 0 at finite B). The fields H and B are assumed to be uniform in the magnet body and in the air gap. For simplicity the field spread outside the magnet and the air gap is taken to be zero, although this is certainly not true in the given arrangement. We then have from flux continuity BmSm = - B g S g ,

PERMANENT MAGNETS; THEORY I00C k Jim 3 50C

45

// /

/

j11

20C (BH)mox 100

,

50

j

~10

zt ~

20 10 //

5

/

/

/

//

1 I

880 19'00 1920 19 0,960 1 80 Fig. 3. Historical trend of the maximum energy product (BH)mx achieved experimentally since the year 1880; (1) carbon steel, (2) tungsten steel, (3) cobalt steel, (4) Fe-Ni-AI alloy, (5) 'Ticonal II', (6) 'Ticonal G', (7) 'Ticonal GG', (8) 'Ticonal XX' (laboratory value, Luteijn and de Vos 1956), (9) SmCos, (10) (Sin, Pr)Co5 (laboratory value, Martin and Benz 1971), (11) Sm2(Co0.85Fe0.11Mn0.04)17 (laboratory value, Ojima et al. 1977). The energy in MGOe is found by dividing the value in kJm -3 by 7.96.

1 Ig

s/[ Fig. 4. Permanent magnet system with pole pieces. S m and Sg are the cross-sectional areas of the magnet and the air gap respectively, and Im and lg their respective lengths.

46

H. ZIJLSTRA

and, since no currents are present, Hmlm - G i g = O,

where the positive direction for H and B is taken to the right. From these equations it is easily found that H m = Hglg/Im,

and B m = - tzoHgSg/ Sm B m / H m = - tZoSglm / Smlg .

The latter expression shows that the reluctance of the system and hence the working point of the magnet is entirely determined by the dimensional ratios of the yoke. Allowance for finite permeability of the pole pieces and for flux leakage can be made by factors o~ (resistance factor) and /3 (leakage factor) so that the equations for magnetomotoric force and the flux in the air gap are written as HgLg = otHmLm,

BgSg = - /3BmSm .

For good designs c~ may have values between 0.7 and 0.95 and/3 between 0.1 and 0.8. Detailed discussions of these factors have been published by Edwards (1962) and by Schiller and Brinkmann (1970). 2.2. T h e m a g n e t i c free energy

In applications involving clamping ability, lifting power or pull of the magnet (ponderomotive force, the second category in table 1) the working point is also in the second quadrant of the hysteresis loop. Whereas in the previous group of applications it was the location of the working point that mattered, the important thing now is how the working point moves. If, for example, the application is of a cyclical nature, it is usually necessary for the working point to "stay well on the loop" during the cyclical motion, so that good reversibility is important. The amount of mechanical work spent in going anticlockwise round part of the loop and completely recovered on going back again is used as a criterion for measuring the performance of a magnet system for applications of this type. In these applications there is generally a particular configuration of permanent magnets and magnetizable objects, which are capable of relative movement. Leaving aside the work required to overcome friction, the mechanical work required to produce an isothermal change in the configuration is equal to the increase in its magnetic free energy. Conversely, a decrease in the magnetic free energy will result in the same amount of mechanical work becoming available.

PERMANENT MAGNETS; THEORY

47

According to the first law of thermodynamics (conservation of energy) a system in which a reversible process takes place can be described by the equation TdS

+ dA = dU.

The term T dS, the product of the absolute temperature T of the system and the change of its entropy S, is equal to the amount of heat supplied to the system from the environment. In addition the environment performs on the system an amount of mechanical work dA, taken as positive. This sign convention for the mechanical work performed is employed for systems in which magnetic effects occur. Both amounts of energy are spent on the increment d U of the internal energy of the system. The free energy F of the system is defined by F=U-TS.

It follows from these two relations that dF = dA- S dT. If the state of the system changes isothermally (i.e. d T = 0), then dF = dA. In a system that contains magnetic material the main problem is to find the correct expression for the mechanical work. The criterion used for the suitability of a magnetic material for applications of the type we are now considering is the maximum possible reversible change of its magnetic free energy. This value is usually calculated per unit volume of the magnet. The mechanical work d A associated with an infinitesimal change of the configuration is equal to dA

½f_

(H. dS - S . d H ) d V, magn

where the integration is performed over the part Rmagn of the space occupied by the material. T o derive this expression for the mechanical work, let us imagine a number of bodies of various magnetizations arranged in a particular configuration. We assume that the bodies are situated in each other's magnetic field and that their temperature remains constant. A slight change in the configuration causes a change in the fields and hence in the polarizations. For each body the increase in the magnetic free energy consists of a quantity dFp, connected with the build-up of the polarization in the material, and a quantity of interaction energy dF~, since in a field H a piece of material with the polarization vector J possesses the potential energy, - ( J • H). For the body considered we can now write: d F = dFp+ d E = H . d d - d ( J - H ) .

48

H. ZIJLSTRA

T o find the change in the free energy of the whole system we must perform a summation over all the bodies. The contributions from the interaction energy would then be counted twice, but putting a factor 1 in front of them corrects for this. The total increase in the free energy is therefore dFsystem = E

dVp+½E

dFi,

where both summations are made over all the bodies. Using the above expressions for dFp and dF~ and applying the expression d F = d A for isothermal changes, we obtain the required expression for the mechanical work, calculated per unit volume of the material. W e should note here that the energy change H - d J is positive, because the structure of the material offers a certain resistance to the change of the polarization. The interaction energy, - ( J • H ) , has a minus sign because it is customary to take this energy by definition equal to zero for two bodies that are an infinite distance apart. If the polarization vector in the expression for the mechanical work is replaced by the equivalent quantity B -/~0H, then, after integration, d A = ½fu

( H . dB - B . dH) d V. magi

T o evaluate this integral it is necessary to bear in mind that during a change in the configuration the working point moves along the hysteresis loop in the second quadrant from P to Q (fig. 5). It is then found that the work d A is equal to the area of the sector O P Q . One configuration (point P) cannot move farther to the right than point Br, where H is zero, and therefore the magnetic circuit must be closed. The other configuration (point Q) cannot m o v e farther to the left than the point BHc, where B and the force exerted are zero. W h e r e possible, cyclical processes will be carried out in such a way that the working region in the second quadrant extends to the vertical axis (Br). T h e magnetic circuit there is closed, which corresponds to a state of lowest energy. In general the material chosen for

B/ P

Br

S Fig. 5. Part of a B hysteresis curve in the second quadrant. The area of the sector OPQ represents the change in magnetic free energy when the working point moves from P to Q.

PERMANENT MAGNETS; THEORY

49

these applications is one in which the working point can move reversibly from remanence over the greatest possible extent of the hysteresis loop. For an ideal magnet, where the complete (linear) hysteresis branch in the second quadrant is transversed reversibly, the maximum mechanical work made available per unit volume during a change of configuration is given by: ½B~BH~ = (1/2/Xo)J 2 • It will be evident t h a t the magnet must be capable of maintaining its saturation polarization Js until the opposing field reaches the value -JJtxo. This imposes a stronger requirement on the coercivity than when the magnet is used for static field generation. The hexaferrite materials with their (for that time) high coercivity of the order of 3 x 10SAm -a ( ~ 4 k O e ) made many of these dynamic applications possible. Today there are many materials with much higher coercivities, notably the rare-earth alloys, whose coercivities are of the order of 106 A m -1 (104 Oe).

3. Magnetic anisotropy

3.1. Anisotropy field and coercivity associated with magnetic anisotropy Consider a single-crystal sphere of a material with uniaxial magnetic anisotropy, uniformly magnetized to saturation parallel to the easy axis of magnetization. We assume that changes in the magnetization occur by a uniform or coherent rotation of the magnetization Ms and that the anisotropy energy density is given by Wk = K sin 2 q~, where ~0 is the angle between the easy axis and the magnetization vector. In the presence of a f i e l d / - / a l o n g the easy axis we assume that the magnetization vector is rotated through an angle ~p as shown in fig. 6. In this state the total magnetic energy is 1 2 W = g/x0Ms + K sin 2 q~ +/x0HMs(1 - cos q~).

Note that the first term, which is the magnetostatic energy of the magnetized sphere, is independent of the angle q~ because the demagnetization factor of the sphere is isotropic and equal to ½. For a minimum in the energy W corresponding to a stable position of the magnetization vector we require dW d~ - 0

and

d2W > 0. d~ 2

Thus q~ = 0 is a stable position of Ms when

H. ZIJLSTRA

50

easy

axis

Ms

Fig. 6. Uniaxial crystal with easy axis for the magnetization.

H > -2K/IxoMs. However, if the field H 0.1781J~/~0, in which case the two-domain state shown in fig. 11(b) has a lower energy than the uniformly magnetized state provided that the particle radius

58

H. ZIJLSTRA

R > Rc2, where /x0A ~/: /x0K Rc2= 56.129 ( J~s ) ( --77-+ Js 1.5708)

1/2

Note that when R > Rc2 the two-domain state has a lower energy than the uniformly magnetized state even when the material has a low magnetocrystalline anisotropy density. When K = 0, R c l = 1.2562Rc0 and Rc2 = 13.7965Rc0 ; when K = 0.1781J~//z0, Rcl = ~ and Rc2 = 14.5576Rc0 ; when K = 0.1627J~/Iz0, Rca = Rc2 = 14.5Rc0. and R c j R c 0 as functions of the parameter Graphs of the ratio R c l / R c o are shown in fig. 12. The calculations of the critical radius made by Kittel (1949) are also shown for comparison. Kittel's calculations are based on a comparison of the approximate energy of a two-domain sphere having a plane wall through the centre with the energy of a x = txoK/J~

102

two doma ~s

b

10

curling

1o.2

lo-~---~ x =.uo K/J~

10

Fig. 12. Ratios of upper bounds beyond which magnetization curling occurs, Rcl (curve a) or the two-domain state has the lowest energy, Rc2 (curve b), both with respect to the lower bound Rc0, below which the uniform state is stable, as a function of the reduced magnetocrystalline anisotropy x = t.LoK/J~. T h e critical radius separating uniform from non-uniform behaviour (Kittel's approximation) is also given as its ratio with Rc0 (curve c).

PERMANENTMAGNETS;THEORY

59

uniformly magnetized sphere. H e finds the latter to have lowest energy when #0A 1/2 /z0K 1/2

RRc~ or R > R c 2 are not necessarily non-uniformly magnetized. Although the latter particles can be uniformly magnetized, the energy of that state is higher than that for the non-uniform state. Thus the uniformly magnetized state may persist if there is an energy barrier between this and the non-uniform state. This is true for a perfect single crystal in which the nucleation of a domain wall requires a finite energy for nucleation (see section 4.2). It is also possible for particles with R < R c 0 to contain domain walls provided they contain lattice defects where the domain wall energy is lower than that in the surrounding matrix. The coercivity is determined by the height of the nucleation energy barrier and hence by the presence of lattice defects and the particular magnetic spin structure of the material (see section 6.5.3). The presence of superficial features, such as scratches and sharp edges, may also influence the coercivity owing to the associated local demagnetizing fields, which may assist domain wall nucleation (see section 6.4). The coercivity can also be determined by domain wall pinning at the lattice defect (see section 6.5.2). The behaviour of the sphere for radii between Rc0 and Rcl or Rc2 is unknown, but it cannot be excluded that the magnetization alternates from the uniform to the non-uniform states. The region between Rc0 and Rcl or Rc2 is associated with the upper and lower bounds to the magnetostatic energy of the non-uniform states (Brown 1962b). If this energy is zero as is indeed the case for a cylindrical bar which demagnetizes by the curling mode, the calculation is exact, and Rc0 and Rc~ coincide and therefore correspond to a single critical rod radius (Frei et al. 1957) (see also section 5.1).

60

H. ZIJLSTRA

4.2. Brown's paradox For high anisotropy a supercritical (R > Rc2) sphere has the non-uniform multidomain mode as the lowest energy state. However, if the particle happens to be in a uniform state it cannot spontaneously transform to the lower energy state. For this a wall has to be nucleated, which means that one or several spins must start rotating. Consider one particular spin. It is subjected to an effective field H which is composed of H = HA + Hw+ Ha+ He, H A is the anisotropy field; Hw is the Weiss field, accounting for the exchange interaction between the spin and its neighbours; Ha is the demagnetizing field; He is the externally applied field. For instability of the spin it is required that

where

- (Ha + He) > HA + H w .

Now Hw is of the order of 10 9 A m -1 which far outweighs any practical value that Ha or He could reach. The conclusion is that the uniform magnetization is maintained under all circumstances and that when - H e > HA the magnetization reverses by uniform rotation. The coercivity of a spherical crystal is thus always H~=Ha, which is in obvious contradiction with experiment (see table 2). This inconsistency which is referred to as "Brown's paradox" (Shtrikman and Treves 1960) is solved by considering that lattice defects are able to reduce Hw considerably and even reverse it locally. Also HA can be influenced by a defect as the symmetry of the crystal is disturbed locally. Finally sharp edges and scratches can locally increase Ha. These matters are discussed in more detail in sections 6.4 and 6.5.

5. Coercivity associated with shape anisotropy

5.1. Prolate spheroid From calculations using micromagnetic theory Frei et al. (1957) and Aharoni and Shtrikman (1958) have shown that magnetization reversal of a prolate spheroid may occur by three basic mechanisms. These are:

PERMANENT MAGNETS; THEORY

61

(a) Uniform rotation of the magnetization for which the coercivity is equal to the anisotropy field Ho = HA = !

/Xo

(N. - N)J~,

(5.1)

where N~ and N]I are the demagnetization factors perpendicular and parallel to the major axis of the spheroid (see also sections 3.1 and 3.2). (b) Magnetization curling (see figs. l l ( a ) and 13(a)) for which the coercivity is Hc=k

Js 1 2/Zo p2,

(5.2)

where p = R/Ro, R is the minor half axis of the spheroid, R0 is a fundamental length defined by R0 = (47rtxoA/J2)1/2 and A is the exchange energy coefficient as discussed in sections 4.1 and 6.2.1. The factor k depends on the axial ratio of the spheroid and is equal to 1.08 for the infinitely long spheroid or the infinite cylinder. For the sphere k = 1.39. However, a sphere will rotate its magnetization uniformly under any applied field. Therefore its coercivity is zero. The sphere can perform a transition in zero applied field from the uniformly magnetized state to a non-uniform one by the curling process under its own demagnetizing field. The condition for this is

Js > 1 . 3 9 Js 1 3tZo 2/Xo p 2,

(5.3)

where the left-hand member is the self-demagnetizing field of the sphere and the

£1

b

c

Fig. 13. Demagnetization modes of the infinite cylinder: (a) curling; (b) twisting; (c) buckling.

62

H.' ZIJLSTRA

right-hand member follows from eq. (5.2) with k = 1.39. This is rewritten as p2 > 2.09, or

/ lzoA \ 1/2

R > 5.121--=~/

which is about the result obtained by Brown (1969) for the critical radius of a sphere (see section 4.1). It is interesting to note the similarity between the quantity R0 and the thickness of a domain wall. As discussed in section 6.2.1, the wall thickness 6 is determined by the exchange energy competing with the anisotropy energy, so that 3 c~ ~/--A/K. In the present discussion we deal with a balance between exchange energy and magnetostatic self-demagnetization energy, the latter being proportional to J2/iXo. If we substitute this for K in 6 we obtain

{ l~oA "ll/2 6 oc\ j2 ] o:Ro. (c) Magnetization buckling. This mechanism of magnetization change is shown in fig. 13(c) and is degenerate with magnetization twisting (fig. 13(b)) as first described by Kondorsky (1952). Both of these mechanisms are nearly degenerate with uniform rotation of the magnetization of an infinite cylinder with R < R0 and represent a higher energy barrier than curling does for R > R0. This is illustrated in fig. 14 where the coercivities of an infinite cylinder due to these mechanisms is shown as a function of R/Ro. The buckling and twisting mechanisms will be ignored in the present discussion. When the magnetization changes by uniform rotation the associated anisotropy energy is entirely of magnetostatic origin, whereas for magnetization curling the associated energy is entirely due to changes in the ferromagnetic exchange energy. In the latter case there is no magnetic flux leakage from the surface of the spheroid so that the magnetostatic energy is zero. This result implies that for the curling mode the coercivity is independent of the particle packing density. For the uniform rotation of the magnetization the coercivity depends on the particle packing density p (p is the ratio of the volume occupied by the particles compared with the total volume of the specimen) i.e., for a system of parallel infinite cylinders Hc = ~

1

/-/xo

Js(1 - p ) .

(5.4)

For a derivation of this result see Compaan and Zijlstra (1962). Thus in any assembly of particles the hysteretic behaviour will be determined by the magnetization reversal mechanism which has the lowest coercivity (see fig. 14). In all the above cases the particles remain uniformly magnetized until the reverse field

PERMANENT MAGNETS; THEORY

63

2 Uniform r o t a t i o n

Buckling or twisting 0.2

HC/HA

l

o,

Curling

0.05

0.02 ~- R / R o

0.01 0.2

I 0.5

i 1

i 2

t 5

10

20

50

Fig. 14. R e d u c e d coercivity He/HA due to various demagnetization m o d e s of the infinite cylinder as a function of reduced radius R/Ro.

nucleates an instability in the magnetization, which is then reversed either by a sudden uniform rotation or a curling of the magnetization. In this case the nucleation field is the same as the coercivity and the hysteresis loops are all symmetrical and rectangular. Which mechanism of magnetization reversal occurs depends on both R and p. The uniform rotation mode changes to the curling mode for a system of parallel infinite cylinders when R e > I ~~13.6 ( ~ 2A ) ,

(5.5)

which is obtained by putting Hc of eq. (5.4) greater than Hc of eq. (5.2). The critical radius for an isolated cylinder is / i,~oA \ l/2

Rc = 3.68~---f{-2)

.

If we assume that for iron A = 2 x 10-'1 Jm -1 (Kittel 1949) and Js = 2 T, the critical radius for an isolated infinite cylinder is 9 x 10-9m. For an assembly of iron cylinders with a packing density p = 2 (as it occurs for example in alnico 5) Rc ~ 16 x 10-9 m. The measured coercivity Hc for alnico 5 is about 5.5 X 104 A m -1.

64

H. ZIJLSTRA

F r o m measurements with a torque m a g n e t o m e t e r the anisotropy field H A -~ 2 x 105Am -1. The latter value is the coercivity which would be expected for uniform rotation of the magnetization. According to measurements m a d e by D e Jong et al. (1958) the rod diameters in alnico 5 are about 3 x 10 -8 m, which is too close to the calculated critical diameter to determine whether the difference between HA and Hc is due to curling or to the fact that the elongated particles are not regular in shape. More convincing evidence in support of the above theory has been provided by Luborsky and Morelock (1964) who measured the coercivities of Fe and FeCo whiskers of various diameters. The coercivities varied from 4 x 104Am -1 to 25 × 10 4 A m -1 for whisker diameters in the range 65 nm to 5 nm and are in very good agreement with the theoretical curve for the curling mechanism. For whiskers with larger diameters the experimental results deviate from the theoretical curve, due presumably to the presence of a finite magnetocrystalline anisotropy energy and to the non-circular cross section of the whiskers.

5.2. Chain of spheres The appearance of electrodeposited particles in a mercury cathode, as observed by Paine et al. (1955), inspired Jacobs and Bean (1955) to investigate theoretically the hysteretic properties of a chain of ferromagnetic spheres, consisting of an intrinsically isotropic material. The spheres touch each other but have only magnetostatic interaction. Two mechanisms of reversal are considered: (a) symmetric fanning, and (b) parallel rotation.

a

b

c

Fig. 15. Demagnetization modes of the chain of spheres: (a) symmetric fanning; (b) parallel rotation. For comparison the uniform rotation mode of the prolate spheroid of the same dimensional ratio is also indicated (c).

PERMANENT MAGNETS; THEORY

65

The coercivities of these models are compared with those of prolate spheroids of the same length-to-diameter ratio. The three models are shown in fig. 15. The symmetric fanning appears not to provide the lowest energy barrier owing to end effects that have been ignored. Taking these into account leads to a modified fanning process, called asymmetric fanning. The results of the calculations for a system of non-interacting elongated particles oriented at random are given for the various mechanisms mentioned as a function of the length-to-diameter ratio (fig. 16). The experimental points refer to samples consisting of electrodeposited elongated particles (Paine et al. 1955) with diameters lying between 14 and 18 nm. Coercivities are in good agreement with the asymmetric fanning model. However, this might be a fortuitous agreement, since the experimental spheres have certainly more than a point-like contact, and possibily exchange interaction between the spheres has to be reckoned with. The mechanism must then be something between symmetrical fanning and magnetization buckling as described in section 5.1.

a

b 0

T I

I

I

~- Elongation

Fig. 16. Coercivity of fine-particle iron oriented at random as a function of particle elongation. Chain of spheres model: (a) parallel rotation; (b) symmetric fanning; (c) asymmetric fanning. Prolate spheroid model: (d) uniform rotation. The points refer to experiments (Jacobs and Bean 1955).

66

H. ZIJLSTRA

The magnetization reversal in elongated particles has been thoroughly analyzed theoretically by Aharoni (1966).

6. Coercivity associated with magnetocrystalline anisotropy 6.1. Magnetization reversal by domain wall processes for tXoHA > Js The fundamental requirements for magnetization reversal by domain wall processes are: (a) The nucleation of a domain wall (or a reverse domain) by a nucleation field Ha which may be either positive or negative, though for high coercivities we require Ha to be large and negative.

Hn

~H

IHnl>lHpl

b

J Hp

Hn

~H

J

IHnl 0 parallel spins have minimum energy, resulting in ferromagnetic coupling. We suppose an angular gradient d~/dx to be present along the x-axis. The coupling energy between spins i and j can then be written as (d~'~ 2 Wi] = J S 2 ~ 2 COS2 a \ ~ X ] '

where sc is the distance between the spins, A is the angle between their connecting line and the x-axis, and the moduli of the spin vectors are assumed equal. In the same way as in the previous section these energy contributions are added for the various spin pairs in a crystallographic unit cell. We then find for the exchange energy density, 2 J S 2 {d~o'~ 2 bcc: We = - - 7 - ',~X ] '

4JS z {d~o"~2

fcc:

We = - - 7 - - \d--x-x) '

SC:

JS 2 {dq~'~2 we = --a- \ ~ x x j , JS22~/ 2 [ d~o'~2

hcp: W e -

a

k~xx] "

Expansion by a factor a of the vertical axis divides the coefficient of (dq~/dx) 2 by

74

H. ZIJLSTRA

the same factor a, as only the cell volume increases by this factor and the rest remains the same. The coefficients thus derived are usually written as A, e.g., by N6el and Kittel, or as C = 2A by Brown. They are associated with the Curie t e m p e r a t u r e Tc and can be determined by calorimetry, spin-wave resonance m e a s u r e m e n t s or t e m p e r a t u r e dependence of magnetization. A difficulty is that the models discussed here are based on nearest neighbour interaction, although there is much experimental evidence that interactions at a longer range cannot be ignored. Therefore determination of A will seldom be better than an indication of the order of magnitude. Using the approximate relation A~105~ZTc,

(SI),

with A in J/m, ~ the nearest neighbour distance in meters and Tc the Curie temperature in Kelvin, fulfills most requirements in the present context. In cgs units we have A in erg/cm, ~ in cm and Tc in Kelvin, for which the relation becomes A ~ 106~2Tc,

(cgs).

6.3. Interaction of domain walls with cavities and non-ferromagnetic inclusions Consider an array of non-ferromagnetic spheres on a simple cubic lattice as shown in fig. 25, and assume that the spheres have a radius p and occupy a fraction a of

radius p

0 © ©

0 0

) d

0

) t

Domain Wall

Fig. 25. Cubic array of spherical cavities interacting with a rigid domain wall.

PERMANENT

MAGNETS; THEORY

75

the total volume of the material. The n u m b e r n of spheres per unit volume is

3 n = 0, 4 . / r p 3 ,

so that the n u m b e r of spheres which are intersected by a (100) plane is given by /./2/3= { 3 ~ 2/3 0,2/3 \4~r/ p2 " The distance d between the centres of the spheres on any (100) plane is given by /4,B-'~ 1/3

If we assume that a (100) plane of these spheres is intersected by a domain wall and that the wall m a x i m u m pinning force per sphere is fm, the m a x i m u m pinning force on the wall is F = r~ .~2/3g Jm

•

If the wall is m o v e d through an infinitesimally small distance dx in the presence of an external field H, the change in magnetostatic energy is 2J~H dx. The total change in energy is d W = n2/3fm dx + 2J~H d x . T h e wall will actually m o v e if d W / d x 6, so that the wall can be regarded as a plane of zero thickness. When a sphere is intersected by a planar domain wall, which is also assumed to be rigid, the pinning force is due to the change in the wall energy which occurs because an area ~rp2 is r e m o v e d when the wall intersects a sphere through a diameter. However, it should be appreciated that the pinning force is a m a x i m u m at the edge of the sphere where the rate of change of the wall energy with position d y / d x is a maximum. For a sphere of radius p the area of intersection with a plane domain wall changes at a m a x i m u m rate of 2~p so that the m a x i m u m pinning force fm per sphere is f~ = 2~-py.

76

H. Z I J L S T R A

Hence the coercivity for a simple cubic lattice of these spheres is given by _

He=

3 )2/3 ~-y _

4~r

_

_

^

2/3

pJs 'x

"

(6.8)

Unfortunately the above result does not agree with the experimental values for ferromagnetic materials which contain dispersions of non-ferromagnetic particles, principally because the effect of the magnetostatic energy due to the surface poles has been omitted. When the spheres, each of volume V, are not intersected by a domain wall the magnetostatic energy is 1 2 m = g/toMs V,

but when they are intersected across their major diameters the above magnetostatic energy is reduced by a factor of about 2 (N6el 1944b). This magnetostatic energy variation may not be negligible in comparison with the change in the domain wall energy. Furthermore the assumption that the domain walls are rigid is unrealistic and makes the model strongly dependent on the shape of the inclusions. 6.3.1. D o m a i n - w a l l p i n n i n g at large inclusions

N6el (1944b) has extended Kersten's theory and has developed a theory of the coercivity of an array of identical non-ferromagnetic spheres which includes the effects of their magnetostatic energies. The resulting expressions for the coercivities depend on the size of the inclusions compared with the width 6 of the domain wall. We consider large inclusions first (p >>6). Consider a non-ferromagnetic sphere in a uniformly magnetized material. The associated magnetostatic energy of the sphere due to the magnetic charges on its surface is W m = l g/x0Ms47rp/3. 2 3

When the sphere is intersected by a plane domain wall through its centre the above magnetostatic energy is reduced by a factor of about 2, i.e., AW m

. # 2s P 9171"[.ZoIVl

3•

A rigid wall moving through the crystal will have minimum energy when it intersects the spherical hole just through the centre. The force required to move it away from the centre is

f = d(Wm+ W~) dx where W~ is the contribution of the wall energy to the total energy. N6el (1944b) has numerically calculated the energy Wm as a function of wall position x and the

PERMANENT MAGNETS; T H E O R Y

77

maximum value of its derivative with respect to x, d Wm')

dx

= 0.600 j2p2,

,/max

/~0

which maximum is attained when the wall is just tangent to the sphere• With eqs. (6.7) and (6.8) we then find for the rigid wall pinned by a cubic array of spheres He = 0 385o:2/3(0 3Ms+ •

\ "

"rr'y "~

(6.9)

/xopMs]"

Note that the magnetostatic term is independent of sphere radius and that the wall energy term is inversely proportional to p. There is a critical radius pc, below which the surface energy term is dominant, and thus Kerstens theory becomes applicable. Above pe the magnetostatic term is dominant and N6eI's theory must be applied. The critical radius is pe ~

~o~/Y~

•

This value is exactly the same as that derived by Kittel (1949) for the radius below which a ferromagnetic sphere is uniformly magnetized in its lowest state (see section 4.1). In order to test the validity of eq. (6.9) we substitute the parameter values of a typical rare-earth magnet and of iron (see table 4). We then obtain for the rare-earth magnet, with a = 0 . 1 and p = 1 0 - 6 m , H e ~ 1 0 4 A m -1, which is by several orders of magnitude too low as compared with experiment. The coercivity of these magnets is obviously not determined by wall pinning at large inclusions• More likely models are discussed in sections 6.3.3 and 6.5. For iron with the same dispersion of inclusions we find He ~ 105 Am -1, which is far too high. A possible explanation for the latter discrepancy is discussed in the next section.

TABLE 4 Intrinsic properties (order of magnitude) of a typical hard magnetic material (lanthanide-cobalt alloy) and a soft magnetic material (iron). La--Co Anisotropy field HA 107 Anisotropy constant K 5 × 106 Saturation magnetization Js 1 Saturation magnetization Ms 106 Exchange parameter A 10-11 Wall energy 3' 5 x 1 0 -2 Wall thickness 6 5 x 10 -9

Fe

(SI)

La-Co

Fe

(cgs)

5 × 104 5 × 104 2 2 × 106 10-11 5 x 1 0 -3 5 x 10-8

(Am -1) (Jm -3) (T) (Am -1) (Jm -1) (Jm -2) (m)

10s 5 × 107 103

5 x 102 5 x 105 2 × 103

(Oe) (erg cm -3) (erg Oe -1 cm -3)

10-6 10-6 50 5 5 × 10-7 5 × 10 -6

(erg cm -1) (erg cm -2) (cm)

78

H. ZIJLSTRA

Fig. 26. Spherical cavity in a ferromagnetic crystal with reverse-domain spikes. The arrows indicate the domain magnetization. Concentrations of surface charges are indicated by their respective signs.

6.3.2. Nucleation of reverse domains at large inclusions If the spherical cavity is larger than the critical radius it becomes energetically favourable to provide it with a pair of reverse domain spikes as shown in fig. 26. The (dominant) magnetostatic energy is then appreciably reduced at the expense of some wall energy. The latter energy becomes less important the larger the sphere. Therefore in the magnetized crystal reverse domains may occur spontaneously at non-ferromagnetic inclusions or cavities. N6el (1944b) has shown that these reverse domains expand indefinitely when the applied field H = -H~, where Hc = 1.23y/tzopMs.

(6.10)

For the same two examples of the previous section (table 4) we calculate the nucleation coercivity at an inclusion of radius p = 10-6m and find Hc(La-Co) 5 × 104Am -1 and H c ( F e ) ~ 103 A m -1. The nucleation at an inclusion in a hard magnetic material is thus relatively easyl Inclusions of cavities should therefore be avoided or indefinite expansion of a nucleated domain should be prevented by some pinning mechanism. The spike formation at a cavity is analogous to the formation of reverse domain spikes at the flat end face of a long magnetized crystal, where as mentioned in section 6.4 the local demagnetizing field is Hd = -½Ms (see also fig. 29). 6.3.3. Domain-wall pinning at small inclusions If the inclusions are small (p ~ ~), the pinning force is due to the change in the energy of a wall which occurs when part of its volume is occupied by nonferromagnetic inclusions. Consider a spherical cavity of volume V and radius p in the magnetized crystal. If this is located inside a wall the wall energy is reduced by the following quantities: (a) (b)

exchange energy

We = a ( dq~'~2 \ d x ] V; magnetocrystalline anisotropy energy

WK = K V s i n 2 ~ .

The inhomogeneous magnetization requires a correction Wn of the order which may be neglected here since p ~ 6.

p2/t~2,

PERMANENT MAGNETS; THEORY

79

The presence of the sphere adds a certain amount of magnetostatic energy, calculated by N6el (1944b) to be (c)

2_ 2//dq~ 2] g Wa = _~/x0Ms2[1-25P \ dx ] J '

where the second term is due to the inhomogeneous magnetization with angular gradient dq~/dx. Outside the wall the magnetization is uniform and oriented along the easy axis. Hence the energies WK and We are zero and

1 2 Wd = gtx0Ms V. The difference in energy between the two situations: sphere outside wall and sphere inside wall then is

[

A W = - / K sin 2 ~0 + A

-~

dq~ 2

or using eqs. (6.3) and (6.5),

A W

=

-

[

2K +

75

B21 V sin 2 q~.

Under the present approximations, K > / x 0 M ~ and p ~ B, we may ignore the second term and find A W = -2KV

sin 2 q~.

The pinning force (using eq. (6.3) for the relation between ~0 and x) is f-

d(zX dxW ) _ 4 K V 3 / K~ sin 2 p cos p .

This is maximum for cos 2 ~ = ½so that with eq. (6.5)

sV5 K V Im-- ~ - - 'TT~-Substituting this result into eq. (6.7) we find the coercivity due to a cubic array of spheres with radius p ~ 8 as 2 K a2/3 V 1 Hc = 0.47-----0-~s p 28 = 1.95/-/1 ~ ol 2/s , where H a = 2K/~oMs, the anisotropy field.

(6.11)

80

H. ZIJLSTRA

The numerical factor of 1.95 depends on the geometry of the inclusions and their distribution, but is expected to be of the same order of magnitude for a variety of probable inclusion shapes and distributions. Using the parameters of the two examples mentioned in section 6.3.1 (table 4), we find for a dispersion of inclusions with a radius of 10 -9 m, occupying 0.1 of the material Volume H c ( L a - C o ) ~ 106Am -1 and H c ( F e ) ~ 5 0 0 A m -1. Both orders of magnitude agree well with experiment, which suggests that pinning at small inclusions might be an explanation for the observed coercivities. For this pinning mechanism it is assumed that the wall is rigid and moves through a cubic array of spheres (see fig. 25). A non-rigid wall in a random distribution of spheres is able to arrange itself so that it contains a maximum number of inclusions. The latter, a more likely picture of a pinned wall is expected to obey eq. (6.11) as well.

6.4. Domain-wall nucleation at surface defects Domain-wall nucleation may occur at surface defects such as pits, protrusions, scratches or sharp edges, where the magnetization reversal is assisted by the locally increased demagnetizing fields (Shtrikman and Treves 1960). Consider, for example, a surface defect such as a pit (fig. 27) in the form of a truncated cone with an apex semi-angle ~b, base radius r± and face radius r2. It can be shown (Zijlstra 1967) that the axial demagnetizing field Ha at the apex point P is Ha = 1Ms sin 2 q5 cos ~b ln(rl/r2).

,,//I////////////l z

\

\

Fig. 27. Surface defect.

PERMANENT MAGNETS; THEORY

81

At an infinitely sharp point, i.e., when r2 = 0, the demagnetizing field at the point P is infinite. However, as pointed out by Aharoni (1962), this is physically unrealistic since a point cannot be sharper than the atomic radius --~10-1° m. For a conical pit with a base radius of 1 p~m and sin 2 ~p cos ~b = 0.4 (i.e. ~b ~ 60 °) Ha ~ 1.8Ms. Similar demagnetizing field concentrations arise at sharp corners and edges and at the bottom of cracks and scratches. Although they are appreciably stronger than the overall demagnetizing field of a magnetized body and perfectly capable of explaining the persistence of reverse domains in soft magnetic materials (De Blois and Bean 1959) they are not sufficient to account for nucleation of reverse domains in hard magnetic crystals. However, there is experimental evidence that sharp edges do play a role in nucleating reverse domains, as demonstrated by the following experiments on SmCo5 and related compounds. Becker (1969) has measured a coercivity of 8.3kAm -1 (105 Oe) on a YCo5 powder made by mechanical grinding. Subsequent treatment in a chemical polishing solution increased the coercivity to 266 kAm -1 (3340 Oe). Becker attributed the increase to the rounding off of the initially sharp edges of the powder particles, which he observed by microscope. Ermolenko et al. (1973) prepared a single-crystal sphere of 8mCo5.3 of about 2 mm diameter. After chemical polishing the sphere had a coercivity of 460 kAm -1 (5800 Oe). Scratching the sphere reduced the coercivity to practically zero (Shur 1973) and subsequent polishing restored it again. The influence on the nature of the hysteresis loop was shown by Zijlstra (1974) who compared the hysteresis loops of two single particles taken from a ground SmCo5 powder before and after annealing (fig. 28). The coercivity of the particle as ground appeared to be determined by easy nucleation and subsequent pinning of domain walls. For the annealed particle the nucleation proved much less easy. The annealing process may have removed internal defects which also have their influence on the hysteresis. However, McCurrie and Willmore (1979) have ~hown that a similar behaviour is obtained when the particles are smoothed by chemical polishing rather than by heat treatment. A special case is the long body with a flat end face. The local demagnetization factor equals ½ at this end face, although the average demagnetization factor approaches zero for longitudinal magnetization. The associated superficial demagnetizing field may give rise to homogeneous nucleation of reverse domains as shown in fig. 29. 6.5. Interaction of domain walls with the crystal lattice 6.5.1. Wall pinning at regions with deviating K and A The nucleation of domain walls at regions with reduced K has been treated by Aharoni (1960, 1962) and Brown (1963) using micromagnetic theory, but although a nucleation field Hn of the order of one tenth of the anisotropy field HA could be derived, their model was not able to explain the many orders of magnitude

H. ZIJLSTRA

82

r~

e..

""

O

,-

©

E

o~

~E

E

r.~

r~

O

=2 o

PERMANENT MAGNETS; THEORY

83

/

/ a

Fig. 29. End surface of a magnetized body. (a) The body in cross section. Reverse-domain spikes penetrate from the surface into the body (schematic). The arrows indicate the domain magnetization. (b) Micrograph of a Sm2Co17single-crystal surface with the spikes seen from above. reduction of Hn with respect to HA f o u n d experimentally. Calculations of the pinning of d o m a i n walls at regions with r e d u c e d K and A were m o r e successfully carried out by A h a r o n i (1960), Mitzek and S e m y a n n i k o v (1969), Hilzinger (1977) and Craik and Hill (1974). W e will discuss the p r o b l e m on the basis of the t h e o r y by Friedberg and Paul (1975) of d o m a i n wall pinning at a planar defect region. Consider the crystal shown in fig. 30 in which there are three distinct regions a, b and c defined by a f r o m - ~ to Xl , b f r o m xl to x2, c from x2 to + ~ . Their magnetic properties J, K and A are identified by subscripts i = a, b and c where

Ja=Jc¢Jb, A a = A~ ¢ A b ,

g . = K ~ gu.

84

H. ZIJLSTRA Z

I

I

x

,/

c ,¸ , /

b

I a

,

\

I X2

I I Xl

Fig. 30. Domain wall distributed in three zones a, b and c of the ferromagnetic crystal.

The easy axis of the uniaxial crystal is along the z-axis; the planar defect is in the yz plane. A field H is applied along the z-axis. A 180 ° domain wall parallel to the planar defect has an energy per unit area of

f~[Ai\{d~2 d x ] + Ki sin 2 ~ - H J / c o s ~ ] dx,

Y = -~ L

(6.12)

where ~ is the angle between the magnetization vector and the z direction, and the subscript i applies to the appropriate region where the wall is located. Minimizing Y by variational calculus and integrating Euler's equations in the three regions yields the following three equations: - A i ( d ~ ' ~ 2 + Ki sin 2 ~ - HJ~ cos ~p = C~, \dx]

(6.13)

for i = a, b and c, where C~ are constants to be determined by the boundary conditions. Imposing the conditions ~ ( - ~ ) = 0 and ~p(+~)--~- and noting that d~/dx = 0 at x = _+0%determines Ca = -HJa and Cc = HJa. The'continuum approach inherent in micromagnetic methods requires continuity of ~ at the interfaces at xl and x2, where ~ has the values ~1 and q2 respectively. Stability of the wall requires zero torque everywhere and thus minimum local energy density. This requirement implies continuity of A d~/dx at the interfaces xl and x2, which can be seen from the following argument. Consider the interface of xl and a narrow zone of width Ax on either side (fig. 31). The value of z~x is so small that dq/dx may be taken as constant in each zone. The energy content of this slab is then (to a first approximation) A T = A a (~Pl - ~0a)2 ~. ( K a sin 2 f~l -- HJa c o s ~/)1) A x

Ax

+ Ab (~Pb-- ~)2 4- (Kb sin 2 ~p~-- HJb cos ~1) Ax. Ax

PERMANENT MAGNETS; THEORY

85

i i [ I

i I

i

1

I I

I I

×

Fig. 31. Orientation angle ~0as a function of distance x near the interface between zone a and zone b. Minimizing this with respect to q~l with fixed values of ~0a,~b and Ax and subsequently letting Ax approach to zero, yields

A.(~x) = Ab(~-~-~X)b at x= Xl. The difference ~ b - ~Oahas a fixed value for fixed Ax, since it determines the local exchange energy density. This must be equal to the anisotropy energy density, which is fixed by ~1 lying between ~0, and q~b,which interval can be taken arbitrarily small. Continuity of q~ and A d~p/dx at the interfaces xl and x2 produces four equations from which dq~/dx and Cb are eliminated to give a relation between q~ and ~02 with coefficients expressed in the parameters A, K, J and H : H(AaJ~ - A J b ) ]2

[cos ~, + ~ -

A--/~uJ -

[cos

H ( A a J , - AbJb) ]2

~,2 ~ 2(--X~Ka- A---~3]

(6.14)

2HAaJa - O. AaKa - AbKb

This equation describes a hyperbola shown in fig. 32. Only the upper right hand branch applies to our model. For H = 0 this curve degenerates to its asymptote cos ~j = cos ¢2. The width of the defect determines which point of the curve represents the actual situation. Narrower defects shift the point to the right. In the small-deviations approximation, A a ~ . A b , K a ~ K b and Ja-~Jb, eq. (6.14) can be written as

7)/t-x-+-k-)j = -4h

/(A_k- ,,÷) +

,

-

[cos

K,12I (6.15)

86

H. ZIJLSTRA cos %

J cos "P2 -p

\ \\

Fig. 32. The hyperbola (cos ¢1 + p)2 _ (cos ~2 + p)2_ Q = 0.

w h e r e A A = A b - - Aa, A K = Kb = K a , A J = J b - - J a and h = H/HA with H A = 2KJJa, the anisotropy field of the undisturbed crystal. T h e relation b e t w e e n go1, go2 and the width x 2 - xl of the defect is calculated by integrating eq. (6.13) for i = b:

f

x: dx = f~i2 dgo [A~ sin z go - ~

Cb 1-1/2 ' cos go - AbJ

(6.16)

dX 1

with -- AaKa sin2 gol -- ~H (AbJb -- AaJa) cos ~1 - H AAabJ Cb - AbKb Ab

H o w e v e r , this integral cannot be solved analytically and has to be approximated. First consider the case H = 0. F r o m eq. (6.14) we see that cos: go1= cos 2 go2,which means that for finite width of the defect go1 = ~ ' - ~ 2 and the wall is located symmetrically with respect to the defect (see fig. 33). Since the width of the defect is not specified this m e a n s that in zero field a wall finds an equilibrium position at a defect of any size different f r o m zero; there is no critical size for defects of this kind. M o r e o v e r this m e a n s that a field, h o w e v e r small, is n e e d e d to detach the wall f r o m the defect. N o w assume that the width D of the defect is small c o m p a r e d to the wall width 6 defined by eq. (6.5). T h e angular gradient dgo/dx m a y then be assumed constant inside the defect. F r o m eq. (6.4) in section 6.2.1 we see that d_~_~= 4 K b dx ~ sin ~ ,

PERMANENT MAGNETS; THEORY "it-- --

--

--

87

[

0 . . . . .

I

XI

X2

--

~ X

Fig. 33. Orientation angle ~0 as a function of x of a pinned d o m a i n wall in zero field (drawn line) and

in a small positive applied field (dotted line). w h e r e we take for ~0 the average value 1(~1 + ~pz). Integrating this gives

(Abl Kb) 112 D

=

x2 -

Xl =

sin

(6.17)

l ( ~ o I -it- ~D2) (~2}2 - - ~ 0 1 ) "

N o w suppose that a small field H ~ HA is applied. F r o m eq. (6.15) we see that in the small-field, small-deviations a p p r o x i m a t i o n

COS2 ~1 -- COS2 ~2 =

-4h

/?A ~

+T

"

T h e small-defect-width a p p r o x i m a t i o n w h e r e ~92~'~-~1 allows cos 2 q~l - cos 2 ~2 ~ (~02- ~pl) sin(~j + ~2), so that by substituting this into eq. (6.17) we find

h-

7r D / A A

AK\

~- 6b t--A---+--K--) sin(qh + ¢2)sinl(qh+ ~2).

(6.18)

L o o k i n g at fig. 33 we see that u n d e r increasing field h the wall will shift to the right thus steadily decreasing the average angle of orientation ~p inside the defect. Starting from ~p = ~-/2, the position at H = 0, we see that the angular function of eq. (6.18) starts at zero and increases to a m a x i m u m of the o r d e r o n e at a certain critical value of h. F u r t h e r increase of h will give no solutions for ~1 and ~2 so that no stable wall will exist. W e identify this critical field with the unpinning field or coercive force (6.19)

88

H. ZIJLSTRA

The minus sign in eq. (6.18) implies that pinning occurs only if the form between brackets in eq. (6.19) is negative, i.e., the wall energy inside the defect is lower than if the defect were not present. If the form in brackets is positive a wall will be repelled, and the defect will form a barrier rather than a trap. It should be noted that eq. (6.19) is valid only in the small-field, small-deviations, small-defect-width approximation. If deviations become larger the symmetry in AA and AK will be lost. In particular a substantial lowering of A will contract most of the wall inside the defect so that the condition 6 >> D is no longer satisfied. This particular situation is discussed in secion 6.5.2. In the small-deviations approximation ~b may be replaed by 6a, the wall thickness in the undisturbed crystal. Note that hc falls within the small-field approximation as a direct consequence of the small-defect-width, small-deviations approximation. In this approximation a deviation of J has no influence on he. In the case where D >> ~b the wall will be almost entirely within the defect region at H = 0. With field increasing from zero we deal with a wall penetrating from region b into region c, i.e., a wall pinned by a phase boundary. Using eq. (6.13) with i = b, we impose boundary conditions ~ = 0 and d~/dx = 0 for the far left-hand end of the wall, which yields Cb = -HJb. Similarly we find with q~(+~) = 7r and d p / d x ( + ~ ) = 0 in eq. (6.13) with i = c the integration constant Cc = HJa, recalling that region c has the s a m e properties as region a. Eliminating d~o/dx from these equations we find H=

(KaAa - KbAb) sin 2 q?2 (AaJa - AbJb) COS q~2+ (AaJa -{-AbJb) '

which in the small-deviations approximation becomes

(AA/A + AK/K) sin 2 ~2 H = ½Ha(b) 2 + (AA/A + AJ/J)(1 + cos ¢2)" Looking at fig. 33 we expect that the highest rate of energy change will be found at about ¢2 = ~-/2, so that the coercivity becomes _

hc

He

HA(b)~

AK\ ~-A--+--K--)'

1/AA

(6.20)

which is the pinning force exerted upon a wall that penetrates from a phase with low A and K into a phase with high A and K. In a material as SmCo5 with HA = 2.5 x 1 0 7 A m -1 (300 kOe) this pinning mechanism could account for a coercivity of the order of 1 0 6 A m i (~104 Oe) with a 10% variation in A and K.

6.5.2. Pinning of a domain wall by an antiphase boundary This section treats a theoretical model of the interaction of a plane domain wall with a certain type of plane lattice defect, namely the antiphase boundary (APB). The A P B occurs in ordered crystals where the atomic order on either side of the

PERMANENT MAGNETS; THEORY

89

I

X X X I0 0 0 I~ I~ I~III'IX'XI'X ~ X I

x x × f×?×?×?×

~x~x~×~?x?x?×? x I

APB Fig. 34. Ferromagnetic ordered crystal with magnetically active antiphase boundary (APB). A P B is opposite in phase. This is clarified in fig. 34 for a two-dimensional binary crystal consisting of A atoms (circles) and B atoms (crosses). The crystal lattice is continuous, but on the right-hand side of the defect B atoms occupy what would have been A sites without the presence of the APB, and vice versa. Suppose now that only the A atoms carry a magnetic m o m e n t and that these are coupled ferromagnetically in the undisturbed crystal. However, across the A P B the much shorter A - A distance might give rise to antiferromagnetic coupling, thus dividing the crystal into two ferromagnetic parts which, in the lowest state and zero field, are antiparallel as indicated in fig. 34. It has been suggested by Zijlstra (1966) that such magnetically active A P B s are responsible for the easy nucleation of reverse domains in MnA1 crystals. On the other hand it was expected that moving domain walls would encounter strong pinning, which was indeed found to exist in MnA1 crystals (Zijlstra and Haanstra 1966). Consider a magnetic domain wall as described in section 6.2.1 with its plane parallel to an A P B as described above. T h e orientation angle of the magnetization is 0 at x = - ~ and ~r at x = + ~ . The A P B is located at x = 0 and coincides with the y z plane. The ferromagnet has uniaxial anisotropy with the z-axis as easy axis. The energy densities due to anisotropy and to exchange interaction are described by eqs. (6.1) and (6.2), respectively. T h e coefficients K and A are assumed to be the same throughout the crystal, except for the APB. The situation at the A P B is described as two layers of atoms, at a distance ~, one belonging to the left-hand side of the crystal and the other to the right-hand side. The coupling energy density between these two adjacent lattice planes, is different from the coupling energy density in the undisturbed crystal owing to shorter A - A distance and is given by At w~ = g ~ - [1 - c o s ( ~ , 2 - ~ , ) ] ,

(6.21)

where pl is the orientation of the left-hand layer and ~2 that of the right-hand layer. The coefficient A ' is different from A and can be negative, in which case antiparallel coupling across the A P B is favoured. The structure of the wall in an arbitrary position with respect to the A P B is shown in fig. 35 by the orientation

90

H. Z I J L S T R A

J

0

-×

Fig. 35. Orientation angle p as a function of distance x normal to a domain wall pinned at APB.

angle q~ as a function of x. T h e wall energy per unit area can then be written as 3' = 2X/)-K(1 - cos q~,) + 2 X / ~ ( 1

+ cos q~2)

+ (A'/sc)[1 - cos(~2 - ~01)] nt- ½K~(sin 2 ~, + sin 2 (P2).

(6.22)

T h e first two terms follow by integrating eq. (6.6) from 0 to ~1 and f r o m q~2 to ~, respectively. T h e third term is the exchange coupling energy in the slab of thickness ~ at the A P B and the last term accounts for the anisotropy energy in the same slab. N o w approximating to continuous magnetization with the A P B as a mathematical plane of zero thickness (~: ~ 0) where the j u m p in p is concentrated, we can ignore the anisotropy energy term and write (omitting constant terms) 3' = x/)-g

2(cos q~2- cos ~1) - r/cos(r/2

-- ~1)

(6.23)

where the coefficient r / = A'/~X/--A-K can take values f r o m -oo to 0 for antiparallel coupling, and f r o m 0 to +o0 for parallel coupling across the A P B . F o r r / ~ oo the difference between q~l and q~2 vanishes and we have the undisturbed wall with 3' = 4X/A--K following from eq. (6.22). Using standard differential calculus with respect to the two variables ~pl and q~2 we find for r / > 1 stability at cos qh = l/r/ and cos ~0z = - l / r / , i.e., the wall is pinned with its centre coinciding with the A P B . F o r r / < 1 the wall collapses into the A P B with q~l = 0 and ~2 = ~r. Such a d e g e n e r a t e d wall will still be called a wall here. T h e energy of the pinned wall follows f r o m eq. (6.22) with the a p p r o p r i a t e values of cos ~01 and cos q~2 substituted as

y = 4 ( 1 - 1/2r/)N/)--K,

for

and T=2r/X/A--K,

for

r/ 1

PERMANENT MAGNETS; THEORY

91

-5

I

1'0

"-5

--10

Fig. 36. Energy ~/of domain wall pinned at A P B in zero field as a function of the coupling p a r a m e t e r ~7 across the APB.

These relations are shown in fig. 36. N o t e that there is no discontinuity at r / = 1, neither in value, nor in slope. Since we have chosen the uniformly magnetized state with q~l = ~02 = 0 as the g r o u n d state with zero energy, the wall e n e r g y goes to - ~ when ~ / ~ - ~ . This m e a n s that eventually the pinning b e c o m e s infinitely strong. T h e d o m a i n wall is thus pinned at the A P B for any value of r/ in zero field. To calculate the field that must be applied to detach the wall, we first have to see h o w the pinned wall behaves in an applied field.

Energy of a pinned wall in an applied field. Consider a part of a wall stretching f r o m x = - w where q~ = 0, to x = 0 w h e r e q~ = ~00. T h e angle ~0 is kept fixed and the wall e n e r g y is calculated as a function of the f i e l d / - / a p p l i e d along the positive z direction. T h e energy of this partial wall is Y(~o, H ) =

F[

K sin e ~ + HJ(1 - cos ~ ) + A [ d~'~2]

\ d x ] J dx,

(6.24)

where J is the saturation magnetization and the o t h e r symbols are as m e n t i o n e d before. With variational calculus we find the condition for m i n i m u m energy to be

d2~p

2 K sin ~ cos ~ + H J sin ~p - 2 A ~

= 0,

which states that the t o r q u e is zero everywhere. Multiplication by dq~/dx and integration f r o m - ~ to 0 give

92

H. ZIJLSTRA

{dq~ ,~2 K sin 2 q~0+ HJ(1 - cos q~0)= A \d-x-x] " Substituting this into eq. (6.24) and switching f r o m x to ¢ as variable we have Y(q~o, h) = 2 ~/ A K

(1 - -

fO~°

COS 2 ~ - -

2h cos q~ + 2h) u2 d~o

= -2{[cos 2 Po + 2(h + 1) cos q~0+ 2h + 1] 1/2- 2(h + 1) 1/2 + h ln[(cos 2 ~o + 2(h + 1) cos q~o+ 2h + 1) 1/2 + cos ¢o + h + 1] - h In[2(h + 1) 1/2+ h + 2]}, where h

=

(6.25)

H/HA, and HA = 2 K / J is the anisotropy field.

Detachment of a pinned wall. Consider the wall in zero field symmetrically pinned at x = 0 with q~2= ~" - qh. A field applied along the z axis will rotate ~Pl and q~2 towards 0, i.e., the centre of the wall will be shifted from x = 0 to the right in fig. 35. If the field is varied f r o m zero to increasing positive values, the force exerted on the wall will increase, at first being in equilibrium with the rate of change of wall energy. But as the latter quantity reaches a m a x i m u m a further increase of the field detaches the wall from its pinning site and makes it travel to infinity. T h e total energy of the wall when pinned is

3' : 3'(~1, h)+ 3'(¢2, h ) - n V ~

cos(~2- ~1),

where 7(qh, h) follows from eq. (6.25) with qh substituted for q~0, and 7(qh, h) follows by substituting 7r - q~2 for ~0 and - h for h. T h e m i n i m u m of 3' with respect 1

0.5

\

\

0.2

0.1

\

\

0.05

\

\

0.02

\

0.01 0.1

0.2

0.5

1

2 _

F i g . 37. R e d u c e d

c o e r c i v i t y h0 =

5 ~

Ho/HA d u e

10

20

50

100

r]

to pinning at APB

a s a f u n c t i o n o f 7.

PERMANENT MAGNETS; THEORY

93

to the independent variables ~01 and ~02 is sought and the critical value h~ of h where this extreme ceases to be a minimum is determined. This critical value h~ is identified with the unpinning field or the coercivity and its relation with r/ is shown in fig. 37. The curve applies only to positive values of ~7. At negative 7/ the zero field values of q~l and ~2 are 0 and ~-, respectively, and it would take a stronger field than h = 1 to detach the wall. However, at h = 1 uniform rotation occurs and the whole concept of wall detachment becomes irrelevant. 6.5.3. Nucleation of a domain wall at an antiphase boundary Consider the crystal of fig. 34 with the coupling p a r a m e t e r ~7 at its A P B smaller than zero. If a strong positive field is applied a situation occurs as depicted in fig. 38(a). This is a m o r e or less saturated state which is stable, though not always of the lowest energy, for all positive values of h including zero. If a counter field of increasing strength is applied tO this state there is a critical value hc of - h at which the symmetric configuration becomes unstable and a wall is emitted from the defect, leaving the defect itself with an antiparallel magnetization orientation as given in fig. 38(b). The relation between the critical field hc and the coupling constant is calculated in the following. Consider the configuration of fig. 38(a) in a field h. Near the A P B there are two partial domain walls separated by an angle (~;2-~pl). The energy of this configuration is T = Y(~I, h ) + T(q~2, h ) - 7/N/A--K cos(~2 - ~1), where ~/ is a negative n u m b e r and Y(q~l, h) and 7(q~2, h) are given by eq. (6.25) with @1 and q~2 respectively substituted for ~P0. For equilibrium the partial derivatives of y with respect to the independent variables ~/91and q~2 must be zero. Since in equilibrium q)l --@2 for symmetry reasons, these two conditions reduce to one: ~

2(1 - cos 2 q~l- 2h cos ~pl+ 2h) 1/2+ ~ sin 2q~1 = 0.

(6.26) q~

q01

-~ x

r

a Fig. 38. (a) Magnetization orientation near A P B after saturation in a strong positive field. (b) Wall emitted from A P B by a negative field moves to the right, leaving the A P B in antiparallel configuration.

94

H. Z I J L S T R A

The value of q~a in the remanent state (h = 0) is given by cos ¢~ = 1

for

0 > 7 > -1

cosqh=-l/7

for

7> ~2. W e e s t i m a t e the wall r e s o n a n c e f r e q u e n c y . T h e e n e r g y as a f u n c t i o n of wall position x is, to a first approximation,

[2X\ 2

3'(x) = a3"o~--~.-) + (1 - a)3'0 ,

(7.6)

a n a l o g o u s to eq. (7.3) b u t n o w with half the lattice p a r a m e t e r ~: as the excursion for which 3' has the value 3'0. W i t h 6 = 10 -9 m, ~ = 3 x 10 -20 m, 3'0 = 10 -2 J m -2 a n d a = 0.1 we calculate, using eqs. (7.2), (7.4) a n d (7.6), that w ~ 3 x 10 22s -1 or 1-'~'1012S 1. T h e activation e n e r g y for the excitation is

A E = a3"oS, which has to b e smaller t h a n 10-29J to p e r m i t m o r e t h a n o n e excitation per second. W i t h the a s s u m e d values for a a n d 3'0 this gives a m a x i m u m value for the wall area i n v o l v e d of S = 10-27 m 2 , which is by two orders of m a g n i t u d e m o r e t h a n ~2 a n d thus c o n s i s t e n t with o u r p r e s u p p o s i t i o n . T h e c o n c l u s i o n is that in materials with thin wall coercivity t h e r m a l excitations m a y well occur that give rise to wall creep. Such creep has b e e n observed, a.o., by B a r b a r a a n d U e h a r a (1976) a n d H u n t e r a n d T a y l o r (1977). E g a m i (1973) has w r i t t e n an extensive theoretical t r e a t m e n t of the creep of thin walls, taking into a c c o u n t b o t h t u n n e l l i n g a n d t h e r m a l excitation.

References Aharoni, A. and S. Shtrikman, 1978, Phys. Rev. 109, 1522. Aharoni, A., 1960, Phys. Rev. 119, 127. Aharoni, A., 1966, Phys. Stat. Sol. 16, 3. Aharoni, A., 1962, Rev. Mod. Phys. 34, 227. Barbara, B., B. B6cle, R. Lemaire and D. Paccard, 1971, J. Physique, C1-1971, 299. Barbara, B. and M. Uehara, 1977, Physica (Netherlands) 86-88 B + C, 1477, (Proc. Int. Conf. Magn., Amsterdam, 1976). Becket, J.J., 1969, IEEE Trans. Magn. MAG-5, 211. Berkowitz, A.E., J.A. Lahut, I.S. Jacobs, L.M.

Levinson and D.W. Forrester, 1975, Phys. Rev. Lett. 34, 594. Brouha, M. and K.H.J. Buschow, 1975, IEEE Trans. Magn. MAG-11, 1358. Brown Jr., W.F., 1957, Phys. Rev. 105, 1479. Brown Jr., W.F., 1962a, Magnetostatic Principles in Ferromagnetism (North-Holland, Amsterdam). Brown Jr., W.F., 1962b, J. Phys. Soc. Japan, 17, Suppl. B-I, 540. Brown Jr., W.F., 1963, Micromagnetics (Interscience/Wiley, New York).

PERMANENT MAGNETS; THEORY Brown Jr., W.F., 1965, in: Fluctuation Phenomena in Solids, ed., R.E. Burgess (Academic Press, New York) p. 37. Brown Jr., W.F., 1969, Ann. New York Acad. Sci. 147, 463. Brown Jr., W.F., 1979, IEEE Trans. Magn. MAG-15, 1196. Buschow, K.H.J. and M. Brouha, 1975, AIP Conf. Proc. 29, 618. Compaan, K. and H. Zijlstra, 1962, Phys. Rev. 126, 1722. Craik, D.J. and E. Hill, 1974, Phys. Lett. 48A, 157. De Blois, R.W. and C.P. Bean, 1959, J. Appl. Phys. 30, 225S. De Jong, J.J., J.M.G. Smeets and H.B. Haanstra, 1958, J. Appl. Phys. 29, 297. De Vos, K.J., 1966, Thesis Tech. Univ. Delft. D6ring, W., 1948, Z. Naturf. 3a, 373. Edwards, A., 1962, Magnet Design and Selection of Material, in: Permanent Magnets, ed., D. Hadfield (Iliffe, London) p. 191. Egami, T. 1973, Phys. Status Solidi (13) 57, 211. Egami, T. and C.D. Graham Jr., 1971, J. Appl. Phys. 42, 1299. Ermolenko, A.S., A.V. Korolev and Y.S. Shur, 1973, Proc. Int. Conf. on Magn., Moskow, 1973, Vol. I(2), p. 236. Frei, E.H., S. Shtrikman and D. Treves, 1957, Phys. Rev. 106, 446. Friedberg, R. and D.I. Paul, 1975, Phys. Rev. Lett. 34, 1234. Hilzinger, H.R., 1977, Appl. Phys. 12, 253. Hilzinger, H.R. and H. Kronmfiller, 1972, Phys. Status Solidi (B) 54, 593. Hilzinger, H.R. and H. Kronmfiller, 1973, Phys. Status Solidi (B) 59, 71. Hilzinger, H.R. and H. Kronmfiller, 1976, J. Magn. Magn. Mat. 2, 11. Hunter, J. and K.N.R. Taylor, 1977, Physica (Netherlands) 86-88 B + C (1), 161 0aroc. Int. Conf. Magn., Amsterdam, 1976). Jacobs, I.S. and C.P. Bean, 1955, Phys. Rev. 100, 1060. Jonas, B. and H.J. Meerkamp van Embden, 1941, Philips Tech. Rev. 6, 8. Kersten, M., 1943, Phys. Z. 44, 63. Kittel, C., 1949, Rev. Mod. Phys. 21, 541. Kondorsky, E., 1952, Dokl. Akad. Nauk SSSR, 80, 197 and 82, 365. Lapworth, A.J. and J.P. Jakubovics, 1974, Proc. 3rd. Eur. Conf. on Hard Magn. Mat., Amsterdam, 1974, p. 174. Lilley, B.A., 1950, Phil. Mag. 41, 792.

105

Luborsky, F.E. and C.R. Morelock, 1964, J. Appl. Phys. 35, 2055. Luteijn, A.I. and K.J. de Vos, 1956, Philips Res. Rep. 11, 489. McCurrie, R.A. and L.E. Willmore, 1979, J. Appl. Phys. 50, 3560. Margenau, H. and G.M. Murphy, 1956, The Mathematics of Physics and Chemistry (2nd ed.) (Van Nostrand, Princeton) p. 198. Martin, D.L. and M.G. Benz, 1971, Cobalt No. 50, 11. Meiklejohn, W.H. and C.P. Bean, 1957, Phys. Rev. 105, 904. Mildrum, H., A.E. Ray and K. Strnat, 1970, Proc. 8th Rare Earth Research Conf., Reno, 1970, p. 21. Mitzek, A.I. and S.S. Semyannikov, 1969, Soviet Physics-Solid State 11, 899. N6el, L., 1944a, Cahiers de Physique, No. 25, 1. N6el, L., 1944b, Cahiers de Physique, No. 25, 21. N6el, L., 1954, J. Phys. Radium 15, 225. Ojima, T., S. Tomizawa, T. Yoneyma and T. Hori, 1977, Japan J. Appl. Phys. 16, 671. Paine, T.O., L.I. Mendelsohn and F.E. Luborsky, 1955, Phys. Rev. 100, 1055. Schiller, K. and K. Brinkmann, 1970, Dauermagnete (Springer, Berlin) p. 74. Shtrikman, S. and D. Treves, 1960, J. Appl. Phys. 31, 72 S. Shur, Y.S., 1973, private communication. Stoner, E.C. and E.P. Wohlfarth, 1948, Phil. Trans. Roy. Soc. (London) 240A, 599. Street, R. and J.C. Woolley, 1949, Proc. Roy. Soc. (London) A62, 562. Van den Broek, J.J. and H. Zijlstra, 1971, IEEE Trans. Magn. MAG-7, 226. Van Landuyt, J, G. van Tendeloo, J.J. van den Broek, H. Donkersloot and H. Zijlstra, 1978, IEEE Trans. Magn. MAG-14, 679. Weiner, J.H., 1973, IEEE Trans. Magn. MAG9, 602. Went, J.J., G.W. Rathenau, E.W. Gorter and G.W. van Oosterhout, 1951/52, Philips Tech. Rev. 13, 194. Zijlstra, H., 1966, Z. Angew. Phys. 21, 6. Zijlstra, H., 1967, Experimental Methods in Magnetism, Vol. I (North-Holland, Amsterdam) p. 135. Zijlstra, H., 1970a, IEEE Trans. Magn. MAG-6, 179. Zijlstra, H., 1970b, J. Appl. Phys. 41, 4881. Zijlstra, H., 1974, Philips Tech. Rev. 34, 193. Zijlstra, H. and H.B. Haanstra, 1966, J. Appl. Phys. 37, 2853:

chapter 3 THE STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS

R.A. McCURRIE School of Materials Science and Technology University of Bradford Bradford, W Yorks BD7 1DP UK

Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-Holland Publishing Company, 1982 107

CONTENTS 1, Isotropic alnicos 1-4 . . . . . . . . . . . . . . . . . . . . . . 1.1. Fe2NiA1 and the isotropic alnicos 1-4 . . . . . . . . . . . . . . . 1.2. Microstructure and origin of the coercivity in Fe2NiA1 and the isotropic alnicos 1-4 . . . . . . . . . . . . . . . . . . . . . . . . 2, Anisotropic alnicos 5 and 6 . . . . . . . . . . . . . . . . . . . . 2.1. Thermomagnetic treatment of anisotropic alnico 5 . . . . . . . . . . 2.2. Cyclic heat treatment of alnico 5 . . . . . . . . . . . . . . . . 2.3. Anisotropic cast alnico 5 with grain orientation (alnico 5 D G or alnico 5-7) . 2.4. Shape anisotropy of alnico 5 and alnico 5 D G (alnico 5-7) . . . . . . . . 2.5. Magnetostriction of alnico 5 and alnico 5 D G (alnico 5-7) . . . . . . . 2.6. Microstructures of alnico 5 alloys . . . . . . . . . . . . . . . . 2.7. Alnico 6 . . . . . . . . . . . . . . . . . . . . . . . . . 3. Anisotropic alnicos 8 and 9 . . . . . . . . . . . . . . . . . . . . 3.1. Thermomagnetic treatment of anisotropic alnico 8 . . . . . . . . . . 3.2. Extra high coercivity alnico 8 . . . . . . . . . . . . . . . . . 3.3, Anisotropic alnico 9 with fully columnar grains . . . . . . . . . . . 3.4. Shape anisotropy of alnicos 8 and 9 . . . . . . . . . . . . . . . 3.5. Microstructures of alnicos 8 and 9 . . . . . . . . . . . . . . . . 4. M6ssbauer spectroscopy of alnicos 5 and 8 . . . . . . . . . . . . . . 5. Sintered alnicos . . . . . . . . . . . . . . . . . . . . . . . . 6. Moulded, pressed or bonded alnico magnets . . . . . . . . . . . . . . 7. Effects of thermomagnetic treatment on the magnetic properties of alnicos 5-9 7.1. Factors controlling development of am particle shape anisotropy . . . . . 7.2. Relationship between the preferred or easy direction of magnetization and the direction of the applied field during thermomagnetic treatment 7.3. Dependence of the magnetic properties on the direction of the applied field during thermomagnetic treatment . . . . . . . . . . . . . . 8. Effects of cobalt on' the magnetic properties of the alnicos . . . . . . . . . 9. Effects of titanium on the magnetic properties of the alnicos (mainly 6, 8 and 9) . . . . . . . . . . . . . . . . . . . . . . . 10. Dependence of the magnetic properties on the angle between the direction of measurement and the preferred or easy axis of magnetization . . . . . . . 11. Relationship between magnetic properties and crystallographic texture . . . . . 12. Effects of particle misalignment on the rcmanence and coercivity of the anisotropic field-treated alnicos . . . . . . . . . . . . . . . . . . . . . . 12.1. Remanence . . . . . . . . . . . . . . . . . . . . . . . 12.2. Coercivity . . . . . . . . . . . . . . . . . . . . . . . . 108

111 111 113 121 121 129 129 131 133 134 137 137 137 141 142 145 146 148 148 149 149 149 151 151 154 155 158 161 161 161 163

13. Determination of the optimum volume fraction of the F e - C o rich particles 14. Interpretation of the magnetic properties in terms of the Stoner-Wohlfarth theory of hysteresis in single domain particles . . . . . . . . . . . . . . . . 15. Interpretation of the magnetic properties in terms of magnetization reversal by the curling mechanism . . . . . . . . . . . . . . . . . . . . 16. Magnetostatic interaction domains in alnicos . . . . . . . . . . . . . . 17. Comparison of the N6el-Zijlstra and Cahn theories of magnetic annealing in alnico alloys . . . . . . . . . . . . . . . . . . . . . . . . 17.1. N6el-Zijlstra theory . . . . . . . . . . . . . . . . . . . . 17.2. Cahn's theory . . . . . . . . . . . . . . . . . . . . . . 17.3. Discussion of the N6el-Zijlstra and Cahn theories . . . . . . . . . . 18. Rotational hysteresis . . . . . . . . . . . . . . . . . . . . . . 19. Anhysteretic magnetization . . . . . . . . . . . . . . . . . . . . 20. Magnetic viscosity . . . . . . . . . . . . . . . . . . . . . . . 21. Temperature dependence of magnetic properties . . . . . . . . . . . . 22. Dynamic excitation (AC magnetization) . . . . . . . . . . . . . . . 23. Prospects for impi-ovement in the magnetic properties . . . . . . . . . . 24. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

109

164 166 169 170 171 172 173 174 177 179 179 181 181 181 182 184

1. Isotropic alnicos 1-4

1.i. Fe2NiAl and the isotropic alnicos 1-4 The alnicos are an important group of p e r m a n e n t magnet alloys. They contain Fe, Co, Ni and A1 with minor additions of Cu and Ti. The first m e m b e r s of the series, which do not contain cobalt, were discovered by Mishima (1932) and are known as the Mishima alloys. They have a composition in the range 55-63% Fe, 25-30% Ni and 12-15% A1, an energy product of ~ 8 kJm -3 and a coercivity of 4.8 x 1 0 4 A m which is m o r e than twice the coercivity of the magnet steels which were available in 1931. Because of their commercial importance the alnico alloys have been studied in great detail by m a n y researchers. Burgers and Snoek (1935) found that when an alloy containing 59% F e - 28% N i - 1 3 % A1 was slowly cooled at a controlled rate from 1200°C to 700°C the coercivity rose to a m a x i m u m of about 48 k A m 1 (600 Oe) as the cooling time was extended and then decreased to about 16 k A m -~ (200 Oe) as the cooling time was prolonged. X-ray investigation showed that in the o p t i m u m high coercivity state a precipitation reaction had occurred. F r o m m e a s u r e m e n t s of the internal demagnetization coefficient Snoek (1938, 1939) suggested that the alloys were heterogeneous and that in the optimum high coercivity state there were two ferromagnetic phases a~ and c~2. The phase segregation process in Fe2NiAI has been investigated by Sucksmith (1939) who measured the magnetization versus t e m p e r a t u r e curves of the single and two-phase alloy. The latter was formed by quenching from 800°C and the magnetization versus t e m p e r a t u r e curve showed a dip at 450°C which indicated that the alloy was indeed two-phase. Sucksmith (1939) found that the phase segregation occurred according to the reaction: 3.25 FesoNi25A125~ Fe9sNizsAlz5 + 2.25 Fe30Ni35A13s, and that the saturation magnetizations of the two phases are, respectively 2 1 2 J T -1 kg -1 (212emu/g or 212erg Oe -1 g-a) and 6 1 J T 1 kg 1(61emu/g or 6 1 e r g O e -1 g-l). Since the densities of the two phases were not known the saturation magnetic polarizations in teslas (T) could not be determined. Details of the o p t i m u m composition and heat treatment of these isotropic iii

112

R.A. M c C U R R I E

Fe-Ni-A1 alloys have been given by Betteridge (1939). The best properties were obtained for an alloy containing 59.5% F e - 2 7 . 6 % Ni and 12.9% A1 which had been quenched at 28°Cs I from the single phase state at l l00°C and then tempered for 4 hours at 650°C. This treatment gave a coercivity BHc = 4 1 k A m - 1 ( 5 1 5 O e ) and a maximum energy product ( B H ) m ~ = 1 0 . 8 k J m -3 (1.35 x 106G Oe). The coercivity was shown to depend very critically on the A1 content while the remanence depended more on the Ni content. Betteridge (1939) also investigated the effects of adding Cu to the Fe-Ni-A1 alloys and found a Cu addition of 3.5% increased (BH)max to 12kJm -3 (1.5 x 1 0 6 G O e ) after quenching from above 950°C and tempering at 550°C. The Cu addition increased the rate of precipitation so that the Fe-Ni-A1-Cu alloys required more rapid cooling or quenching. The effects of elastic stress on the precipitation and magnetic properties of Fe-Ni-A1 alloys with additions of Cu and Ti have been investigated by Yermolenko and Korolyov (1970) who obtained improved optimum permanent magnet properties of ( B H ) m a x = 16.8 k J m -3, BHc = 63 kAm 1 and Br = 0.67 T. The permanent magnet alloys with compositions close to Fe2NiA1 are usually prepared commercially by cooling from above 1250°C at an approximately controlled rate. Rapidly cooled castings can be improved by annealing at 600°C for several hours. These alloys, which usually have small additions of Cu, are known as alni or alnico 3, in spite of the fact that they contain no cobalt; they are still produced in small quantities. Betteridge (1939), Zumbusch (1942a) and others also found that the magnetic properties of the Fe-Ni-A1 alloys could be significantly improved by the addition of cobalt as shown in fig. 1. The increase in remanence follows the increase in the saturation magnetic polarization of the alloys while the larger relative increase in the coercivity BHo can be attributed to an increase in the difference between the

100 -

1"Or

20 Br

~ 80- 0"8I

16

~6o -,-°= ~.6

12 "J

,ff

BH(max)

g 8

40 -

0-4 f

20 -

0.2

0

--0

0

E

I

-r Ill

4

5

10 15 Wt % Cobalt

20

25

Fig. 1. Dependence of coercivity, remanence and energy product on cobalt content (after Zumbusch 1942b).

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 113 saturation magnetic polarization of the F e - C o rich precipitate particles and the Ni-A1 rich matrix. The addition of cobalt has the further beneficial effect of raising the Curie temperature. The cobalt-containing alloys are produced by controlled cooling from above !250°C and subsequent annealing for several hours in the range 600-650°C. Since cobalt decreases the rate of precipitation of the c~1 and ~2 phases it was found essential to add small quantities of copper (Betteridge 1939) and to reduce both the nickel and aluminium contents as the cobalt content was increased. It was also shown (Betteridge 1939, Edwards 1957) that the magnetic properties of these isotropic alloys (alnicos 1, 2, 3 and 4) could be significantly improved by the addition of 4-5% Ti provided that the cobalt content was increased to 17-20%. These extra high BHc isotropic alnicos (alnico 2) have coercivities in the range 60-72 kAm 2 compared with 36-56 kAm -1 for the isotropic alnicos 1, 2, 3 and 4. The energy product of the high coercivity form of isotropic alnico 2 is also slightly higher. Although the Ti addition reduces the remanence this is more than compensated by the much higher coercivities. Details of the optimum composition and heat treatments of the isotropic alnicos have been given by Betteridge (1939) and Edwards (1957). The magnetic properties and compositions of the alnicos 1-4 are summarized in table 1 and typical demagnetization B - H curves are shown in fig. 2.

0.8 0.6

lib

>2

0"4

u) "0 X -I m

0.2 u.

I1

60

I

50

/

!

I

I

I

I

40 30 20 Applied field,H (kAm-1)

I

10

0

0

Fig. 2. Demagnetization curves for isotropic alnicos 1, 2, 3 and 4.

1.2. Microstructure and origin of the coercivity in Fe2NiAl and the isotropic alnicos 1--4 The compositions of the alnicos are complex and the F e - N i - A I system is the only one for which the phase diagram has been investigated in detail. Bradley and Taylor (1938a, b) and Bradley, (1949a, b, 1951, 1952) established the positions of the phase boundaries and the general metallurgical behaviour of the Fe-Ni-A1 system and showed that the alloys with potentially interesting permanent magnet properties lay close to the line from Fe to NiA1 and were centered round the

114

R.A. M c C U R R I E

~

_'2

~

t--

©

,q.

tt~

t--

e., ©

©

©

c~
34% Co and a Ti content > 5 % Ti. For alnico 8 alloys with 34-40% Co and 5-8% Ti, Wyrwich (1963), Stfiblein (1963), Planchard et al. (1964b), Bronner et al. (1966a, b) and Vallier et al, (1967), Livshitz et al. (1970a) have shown that coercivities BHc --~ 176 kAm -1 and energy products up to ~48 kJm -3 can be obtained. Bronner et al. (1966a, b) found that the energy product of 48 kJm -3 was constant up to about 45% Co. Wright (1970) and Bronner et al. (1970a) have shown that the addition of niobium as well as titanium also has beneficial effects on the magnetic properties of alnicos 5, 6, 8 and 9, though alnico 5-7 should contain a small addition of niobium only. Typical compositions and magnetic properties of alnico 8 alloys are given in table 5. Koch et al. (1959) found that for the alloy 35.5% Fe, 34% Co, 14.5% Ni, 7% A1, 4% Cu, 5% Ti, the homogeneous bcc ce phase is stable only above about 1250°C and that between 1250°C and 845°C it decomposed to form another bcc c~ phase and an fcc y phase with lattice parameter, a0 = 0.365nm. In the range 845-800°C, the c~ phase decomposes spinodally to form a bcc F e - C o rich al phase and a bcc Ni-A1 rich a2 phase. A small amount of the y phase is also present at this stage but below 800°C this transforms by an apparently diffusionless reaction to another bcc phase, c~v with lattice parameter 0.359 nm. Ritzow (1963) suggested that the difficulties encountered in controlling the heat treatment of the high Ti alloys is probably due to the fact that the Curie temperature is practically in the y region (see section 9) so that the isothermal thermomagnetic treatment temperature is very critical. Julien and Jones (1965a, b)

S T R U C F U R E A N D P R O P E R T I E S OF A L N I C O P E R M A N E N T M A G N E T A L L O Y S

139

TABLE 5 High coercivity field-treated anisotropic alnico 8 alloys. Composition Fe

Ni

A1

Co

Cu

Ti

Nb

B, (T)

BHc (kAm -l)

(BH)max (Jm -3)

40.8

14.6

6.9

28.5

3

4.2

2

0.95

97

40

35

14.9

7

34

4.5

5

-

0.96

103

41

34.5

14.3

6,9

34

3.8

5.5

1

0,88

117

41

36

14

7,5

34

3

5

0.5

0.93

119

46 48

35

13

7.5

34

3

6

1.5

0.83

/ ' 150

29.5

14

7.5

38

3

8

-

0.74

167

48

35.5

14

7.5

34

3

4.5

1.5

0.8

162

48

33

15

7.5

34

3

7

0.5 Hf

0.8

154

49

N.B. 1 T = 10 4 G ; 1 A m -~ = (4:7/1000) Oe; 1 Jm -3 = 40~ GOe.

have shown that if an alloy of alnico 8 with 32% Co and 6.5% Ti is held at 900°C for about 15 rain the 3' phase is produced which lowers the (BH)max product by 50% compared with the same alloy which had not been annealed at 900°C, They also found that the tendency to precipitate the 3' phase was increased when the Cu content was increased (a similar effect was observed in alnico 5) while the Ti suppressed its formation. The homogenization temperature was just below the melting point. If alnico 8 alloys are cooled too slowly the appearance of the 3' phase results in a deterioration in magnetic properties which manifests itself in a concave demagnetization curve just as occurs in alnico 5 (see fig. 18). Such concave demagnetization curves can be synthesised from three normal demagnetization curves. The effects of the a~ phase on the hysteresis loops have also been discussed by Julien and Jones (1965b). In view of the tendency of Ticontaining alnico 8 alloys to form the fcc Y phase their heat treatment must be Carefully controlled in order to obtain optimum magnetic properties. This inevitably increases the cost of their p r o d u c t i o n - though this is largely due to the high cobalt content. The kinetics of the a ~ 3, transformation in alnico 8 (and alnico 5) alloys have also been investigated by Planchard et al. (1964a, 1965, 1966a). A study of the influence of cobalt on the c~ ~ 3, transformation has been made by Marcon et al. (1971) who showed that for alnicos containing more than 28% Co it is practically impossible to avoid the precipitation of the deleterious y phase during thermomagnetic treatment unless appropriate amounts of a-stabilizing elements such as silicon or titanium are added. A typical heat treatment for alnico 8 alloys is as follows. After controlled

140

R.A. McCURRIE

1"2

Alnico 5

1.0

0.8 ~ m 0.6 O "O

0"4 x

_= I.I.

0"2

t

0

60

50

40 30 20 10 Applied field,H (kAm-1.)

0

Fig. 18. Demagnetization curve for alnico 5 showing deleterious effect of the presence of the o~ fcc phase on the shape of the curve.

(BH) max (k Jrn-3) 80 60 40 //

/I

¢I

~

//

1.2

/I

,

/ i/./

1-4

i

1I

//

1"0 ~ "

ii

0"8

m ¢n c

0.6 ¢~ qD X

0.4 0.2 !

160

140

120 100 80 Applied field, H

60 40 CkAm-1)

I

20

0

Fig. 19. Demagnetization curve for alnicos 8, 9 and 5-7. The latter two curves are given for comparison. The alloy 8(b), which has the highest coercivity is also known as sermalloy A1 (Bronner et al. 1966b). c o o l i n g f r o m a b o v e 1250°C, t h e a l l o y is h e a t t r e a t e d f o r a f e w m i n u t e s at a b o u t 820°C in a s a t u r a t i n g m a g n e t i c field ( ~ 3 0 0 k A m -1) a n d t e m p e r e d f o r a b o u t 6 h at 650°C f o l l o w e d by a b o u t 24 h at 550°C.

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 141 A typical B - H demagnetization curve for alnico 8 is shown in fig. 19, the compositions and magnetic properties of various alnico 8 alloys are given in table 5.

3.2. Extra high coercivity alnico 8 A higher coercivity field-treated random grain form of alnico 8 can be produced by increasing the cobalt and titanium contents still further to 37-40% Co and 7-8% Ti. Sometimes a little (0.5 to 1.5%) of the titanium is replaced by niobium. The maximum coercivity of these extra high coercivity alnico 8 alloys is about 180 kAm -1 which is higher than that of any other alnico. The production and properties of extra high coercivity alnico 8 alloys have been described and investigated by Wyrwich (1963), Planchard et al. (1964b, 1966b), Bronner et al. (1966a, b), Vallier et al. (1967) and Bronner et al. (1970a). Planchard et al. (1964b) and Bronner et al. (1966a) studied the dependence of the magnetic properties on the Ni, Ti, A1 and Cu content for alloys containing 40% Co. Planchard et al. (1964b) obtained a maximum coercivity BHc = 161 kAm -1 with Br = 0.71 T and (BH)m~ = 44 kJm -3, for an alloy containing 27.5% F e - 4 0 % C o - 14% N i - 8 % A 1 - 7 . 5 % T i - 3 % Cu. The alloy was homogenized at 1250°C for 1 h and then heat treated isothermally for 5 minutes at 810°C in a magnetic field of 336 kAm -1. After this treatment the alloy was annealed for 6 h at 650°C and then for 24 h at 550°C. In a later investigation Bronner et al. (1966b) developed an alloy containing 29.5% F e - 3 8 % C o - 1 4 % N i - 7 . 5 % A 1 - 8 % T i - 3 % Cu with a coercivity BHo = 168 kAm -I with Br = 0.74 T and (BH)max = 48 kJm -3. These properties were obtained by homogenization at 1250°C in a neutral or reducing atmosphere followed by cooling in compressed air to 600°C in order to avoid the precipitation of the deleterious 3, phase. The alloy was then isothermally annealed for a few minutes at 820°C in a magnetic field ~336 kAm 1 and then tempered for 6 h at 640°C and finally for 24 h at 550°C. This alloy, which is an extra high coercivity alnico 8, is also known as sermalloy A1. Apart from its high coercivity and energy product, sermalloy A1 has high useful recoil energy (a maximum Erec ~ 20 kJm -3) and a high Curie temPerature Tc = 874°C so that it is very stable under demagnetizing conditions and at temperatures up to about 550°C. An alloy, with almost identical properties to sermalloy A~, also known as hycomax IV has also been developed by Harrison and Wright (1967). A typical demagnetization curve for this special alnico 8 alloy (A1) is shown in fig. 19. Koch et al. (1957) investigated the effectiveness of Ti and Nb additions in increasing the coercivity of alnico 8 alloys and concluded that Ti was more effective. However, Bronner et al. (1970a) and Bronner (1970) found that the addition of Nb (0.5-2.0%) to alnico 8 alloys containing 4.5-6.5% Ti could be beneficial. For example the alloy 35.5% F e - 34% C o - 14% N i - 7.5% A 1 - 4.5% T i - 3 % C u - 1 . 5 % Nb B H c = 1 6 2 k A m -1, B r = 0 . 8 T and (BH)max=48kJm -3. Bronner (1970) reported that the addition of hafnium was also beneficial and found that the alloy 33% F e - 3 4 % C o - 15% N i - 7.5% A 1 - 7% T i - 3% Cu with 0.5% Hf had a coercivity td-/c = 154 k A m -1, a Br = 0.8 T and a (BH)m~ = 49 kJm -3.

142

R.A. McCURRIE

Similar investigations of extra high coercivity alnico 8 alloys have been made by Livshitz et al. (1970a) who used a wide variety of thermomagnetic and tempering treatments. They obtained magnetic properties in the ranges Hc = 160-176 kAm -1, Br = 0.65-0.75 T and (BH)m~x = 36-44 kJm -3 for alloys containing 38% Co and 8.0-8.5% Ti after optimum thermomagnetic and tempering treatments. The compositions and magnetic properties of some typical extra high coercivity alnico 8 alloys are given in table 5. A simplified heat treatment, using continuous cooling, rather than isothermal heat treatment in a magnetic field (240 kAm -1) for alnico 8 alloys has been developed by Wright (1970). He showed that by cooling alloys with compositions in the range 34-35% Co, 14-15% Ni, 6.8-7.2% A1, 5-5.4% Ti, 0.8-1.1% Nb, 3 - 4 % Cu, balance Fe from 1250°C (at average rates of 2, 1.2, and 0.6°Cs -I from 1200-600°C) in a magnetic field of 240 kAm 1 followed by tempering for 4 h at 640°C and then for 16h at 570°C, magnetic properties better than Br = 0.85 T BHc = l l 2 k A m -~ and (BH)max = 36kJm -3 can be obtained. Wright (1970) also showed that if 0.25% S is added to the alloys, magnets with columnar crystals can be produced by casting in a mould with heated sides and chilled at the end faces. For these columnar magnets typical properties are, Br = 1.03 T, BHc = 118 kAm -~, and (BH)max = 58 kJm -3. Columnar alnico 8 alloys i.e. alnico 9 alloys are discussed in section 3.3.

3.3. Anisotropic alnico 9 with fully columnar grains Alnico 9 is produced by the columnar crystallization of alnico 8. Unfortunately, the high Ti content of the latter reduces the grain size (Luteijn and De Vos 1956) so that columnar crystallization of alnico 8 is difficult. Luteijn and De Vos (1956) succeeded in producing a grain oriented alnico 9 magnet by using special techniques. For the alloy containing 35% Fe, 34% Co, 15% Ni, 7% A1, 5% Ti and 4% Cu by weight, they obtained a magnet with Br = 1.18 T, BHc =- 105 kAm -1 and (BH)max = 88 kJm -3. These very high values were obtained by using very pure starting materials and isothermal heat treatment parallel to the [100] axis of the columnar grains. The demagnetization curves for the alloy are shown in fig. 19. Gould (1964), Makino and Kimura (1965), Wittig (1966) and Harrison and Wright (1967) have shown that these difficulties in producing fully columnar alnico 9 magnets can be overcome by the addition of small quantities of S, Se or Te. Alnico 9 can be prepared as follows. After melting an alnico 8 alloy with a small addition of S, Se or Te (sometimes two of these elements are added) the fully columnar structure is obtained by casting the alloy in a heated or exothermic mould in which the end faces are chilled so that grains with (100) axes grow perpendicularly to the chilled surfaces. The alloy is then solution treated at 1250°C cooled at a controlled rate and heat treated in a saturating magnetic field (~300 kAm -1) for a few minutes at about 820°C and finally given a two-stage tempering treatment for several hours at 650°C and at 550°C. The grain structure of a fully columnar alnico 9 magnet is shown in fig. 20.

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 143

Fig. 20. Grain structure of fully columnar alnico 9 (Gould 1964) (magnification: ~2x).

The production of columnar alnico 9 has also been described and investigated by Fahlenbrach and Stfiblein (1964), Naastepad (1966), Harrison (1966), Hoffmann and Stfiblein (1966, 1967, 1970), Palmer and Shaw (1969), Dean and Mason (1969), Hoffmann and Pant (1970) and Pant (1974). Hoffmann and Pant (1970) produced magnets (containing 7.7% Ti) with coercivities up to a m a x i m u m of Uric = 1 7 1 k A m -1, iHc = 1 7 9 k A m -l, B r = 0 . 8 7 T and (BH)max = 7 7 k J m -3. They also produced a magnet (containing 7.1% Ti) with an energy product (BH)max = 98 kJm -3 in combination with ~Hc = 136 k A m -1, i S c ~ 138 k A m -~ and Br = 1.03 T. Pant (1974) produced alnico 9 magnets having diameters ~ 1 5 - 8 0 m m with a columnar crystallization length of ~120 m m for which (BH)max ~ 90 kJm -3 (with BHo = 150 k A m -1) and (BH)max ~ 80 k J m -3 (with BHc ~ 160 kAm-1). Although the coercivity of alnico 9 is nearly the same as that of alnico 8 the higher energy product is due to the increased remanence parallel to the columnar axis i.e. [100]. The improved properties of alnico 9 parallel to the columnar axis are of course achieved at the expense of those perpendicular to the columnar axis but in many applications this is not a serious disadvantage. Demagnetization curves for alnicos, 8 and 9 are shown in fig. 19 from which it can be seen that the magnetic properties of alnico 9 are considerably better than those for alnico 8; the m a x i m u m energy products for alnico 9 are typically in the range 60-75 kJm -3. The higher energy products of alnicos 8 and 9 compared with alnico 5-7 are, unfortunately, obtained at the expense of a reduced remanence. T h e relationship between the magnetic properties and the crystal textures of alnico 9 alloys have been investigated by Higuchi and Miyamoto (1970) and D u r a n d - C h a r r e et al. (1978). T h e latter used Schulz's (1949) X-ray diffraction method and found that the observed metallurgical texture could be correlated with the solidification rates. Grain growth by solid state recrystallization in various alnico 9 alloys has been

144

R.A. M c C U R R I E

investigated by Wright and Ogden (1964) but although some large crystals were grown the technique was not considered to be very successful. The dependence of the magnetic properties of columnar alnico 9 on the angle between the columnar axis and the direction of thermomagnetic treatment, and the angle of measurement is discussed in section 7.3. The development and chronology of alnico magnets are shown in fig. 21 (Cronk 1966). The best magnetic properties are of course obtained for single crystal alnicos. Naastepad (1966) showed that a single crystal containing 35 wt % Fe, 34.8% Co, 14.9% Ni, 7.5% A1, 5.4% Ti and 2.4% Cu had a coercivity 8He of 122kAm -1 and an energy product (BH)max of 107kJm -3. The latter energy product is the highest yet reported for any alnico. A summary of the magnetic properties and compositions of columnar alnico 9 alloys is given in table 6. 120 Alnicos DG -- Directed grain MC - Monocrystal

100 ¢0 I

E

-~

MC9

MC5

80

5-7 x

60

5DG

E

.,p m

40

2

20

II I I 1940 1950 Calendar year

o

1930

!

I

1960

1970

Fig. 21. Development and chronology of alnico magnets (after Cronk 1966),

TABLE 6 Compositions and magnetic properties of anisotropic field-treated alnico 9 columnar alloys. Composition Fe

Ni

A1

Co

Cu

Ti

Nb

Others

26.1

14.7

6.8

40.3

2.9

8,2

-

35.2 35 36.1 29

14.8 15 14.5 14

7 7 7 7

33.1 34 34 38.9

4.5 4 3 3,5

5.5 5 5.2 7.1

-

35

14.9

7.5

34.8

2.4

5.4

-

0.77 Te O.22 S 0.22 S 0,2S 0.45 S 0.05 C -

N.B. 1 T

=

10 4

G; 1 A m -1 = (4~'/1000) Oe; 1 Jm -3 = 40~r GOe.

Br (T)

BEe (kAm -1)

(BH)max (kJm -3)

0.895

160

67

1.095 1,18 1.11 1.03

123 104.5 129 136

83.5 87.5 91.5 97

1.15

121

106

STRUCTURE

AND PROPERTIES

OF ALNICO PERMANENT

MAGNET

ALLOYS

145

3.4. Shape anisotropy of alnicos 8 and 9 The effects of varying the cobalt and titanium contents on the induced shape anisotropy constant K. of alnico alloys have been studied by Takeuchi and Iwama (1976) (see also section 2.4). They found that for an alnico 8 alloy (29.5% F e - 39% C o - 14% N i - 7% A1- 7.5% T i - 3% Cu) Ku = 2.4 × 105 Jm -3 and a magnetocrystalline anisotropy constant K1 = 0.26 x 105 Jm -3, thus confirming that the anisotropy and hence the coercivity of alnico alloys is due predominantly to the shape anisotropy of the individual Fe-Co rich particles. The induced anisotropy constant K. was of course measured on single crystal specimens in which the individual particles were almost fully aligned by the thermomagnetic treatment. TABLE 7

Compositions of single crystal alnicos. Specimen No.

Fe

1

51.4

2

Ni

Al

Co

Cu

Ti

14

7.7

23.9

3

0

47.9

14.4

7.9

26

2.5

1.3

3

43.5

14

7.6

29

2.9

3

4

29.5

14

7

39

3

7.5

TABLE 8

Apparent anisotropy constants Ku and K,] ( x 104 J m -3) determined by torque measurements, volume fraction, p, particle diameter d, elongation l/d intrinsic coercivity iHc and flux coercivity BHc (K" = Ku/p) (Takeuchi and Iwama 1976). Specimen No.

Ti (wt % )

Ku (104Jm -3)

p

d (nm)

lid

inc (kAm-1)

BH¢ (kAm-1)

K" ( 1 0 4 j m 3)

1

0

15.6

0.68

44

4-5

57

-

22.9

2

1.3

16.1

0.67

42

6-7

59

-

24

3

3.0

17.3

0.63

37

8-12

67

-

27.5

4

7.5

24.2

0.46 ~

30

30-50

167

-

52.6

Alnico 5*

0.0

15.2

0.67

40

4-6

-

53

22.7

Alnico 8*

5.0

23

0.54

30

13-16

-

114

42.6

Alnico 8"*

7.5

-

-

20

30-35

-

147

-

*Sergeyev and Bulygina (1970) and **Granovsky et al. (1967). N.B. 1 T = 104 G ; 1 A m -1 = (47r/1000) O e ; 1 J m -3 = 40~" G O e .

146

R.A. McCURRIE

This is clearly shown by the electron micrographs obtained by Takeuchi and Iwama (1976). Their value of Ku = 2.4 x 105 Jm -3 is in very good agreement with that obtained by Sergeyev and Bulygina (1970) who found a Ku = 2.3 x 105 Jm -3 for an alnico 8 alloy containing 26.5% F e - 40% C o - 1 4 % N i - 7.5% A 1 - 7.5% T i - 4 . 5 % Cu. The alloy was homogenized at 1240°C, cooled to 800°C at 5°Cs -1 and then annealed for about 12 rain at 820°C in a magnetic field of 160 kAm -1 after which the alloy was tempered for 5 h at 650°C and 20 h at 560°C. The compositions and properties of the alloys used in the above investigations are summarized in tables 7 and 8. The high coercivities of alnico 8 (and alnico 9) can be attributed to the increased shape anisotropy energy resulting from the high cobalt content and the addition of titanium. The effects of cobalt and titanium contents on the magnetic properties are discussed in sections 8 and 9 respectively.

3.5. Microstructures of.alnicos 8 and 9 Replication electron micrographs of the highly oriented microstructure of an alnico 8 alloy were obtained by De Vos (1966, 1969). Typical microstructures in planes parallel and perpendicular to the thermomagnetic field direction are shown in figs. 22(a) and (b). The regular distribution of the precipitated particles in both orientations is characteristic of a system in which phase separation has occurred by spinodal decomposition. From measurements on the electron micrographs the average dimensional length to diameter ratio 1/d is >10 and from the application of quantitative metallography (Hilliard 1962, 1967, 1968, Hilliard and Cahn 1961, Underwood 1970, 1973, Saltykov 1970) the volume fraction of the particles is ~0.65. Although the volume fraction of the particles is comparable to that of the other alnicos there is a marked increase in the dimensional ratio, degree of particle alignment and particle perfection; all of these factors contribute to the increased coercivity of the alnico 8 alloys compared with alnico 5 alloys. Since alnico 9 alloys have similar compositions to the alnico 8 alloys (alnico 9 is simply a columnar crystallized alnico 8) it may be assumed that the microstructures are similar to those of alnico 8. The microstructures of alnico 8 alloys have also been investigated by Bronner et al. (1967), Granovsky et al. (1967), Pfeiffer (1969), Mason et al. (1970), Livshitz et al. (1970b), Iwama et al. (1970) and Takeuchi and Iwama (1976). From the electron micrographs obtained by the above authors it can be seen that the F e - C o rich particles have length to diameter ratios l/d in the range 10-50 where l ~ 400-1000 nm and d is in the range 20-40 nm. The application of quantitative metallography to the electron micrographs shows that the volume fraction of the F e - C o rich particles is ~0.65. Although the volume fraction of the particles in alnico 8 is comparable to that in the other alnicos, there is a marked increase in the elongation (l/d), the degree of particle alignment and particle perfection; all of these factors contribute to the increased coercivity of alnico 8 alloys compared with alnico 5 alloys. By using X-ray electron diffraction Pashkov et al. (1969) measured the lattice parameters of the bcc a~ and a2 phases in three alnico 8 alloys containing

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS

147

Fig. 22. Electron micrograpti of the al + ~2 structure of alnico 8 after an isothermal heat treatment at 800°C for 9 min; (a) in a plane parallel to the direction of the applied field during heat treatment, (b) in a plane perpendicular to the field direction (magnification 45500 ×) (after De Vos 1966).

TABLE 9 Lattice parameters of the bcc oq and c~2 phases in alnico 8 alloys (A). c~1 phase (Fe-Co) Alnico 8

a

c

35% Co, 5% Ti

2.909

2.873

40% Co, 7% Ti

2.909

42% Co, 8% Ti

2.915

c~2 phase (Ni-A1) c/a

a

c

c/a

0.99

2.855

2.873

1.006

2.872

0.987

2.850

2.872

1.008

2.872

0.985

2.852

2.872

1.007

148

R.A. McCURRIE

respectively, 35, 40, 42% Co and 5, 7, and 8% Ti; their results are shown in table 9, from which it can be seen that both the eel and O~2 phases are very slightly tetragonal with c/a < 1 and c/a > 1 respectively.

4. M6ssbauer spectroscopy of alnicos 5 and 8

From M6ssbauer spectroscopy measurements on alnico 5, Shtrikman and Treves (1966) have concluded that in the optimum permanent magnet state, the alloy consists of two phases one of which is an Fe-rich ferromagnetic phase and the other is a Ni and Cu rich paramagnetic phase. M6ssbauer measurements on alnico 8 made by Albanese et al. (1970) show that 7-8% of the total Fe content is paramagnetic. From the quadrupole splitting of the M6ssbauer spectra it was also concluded that the two phases have a small tetragonal distortion in agreement with the X-ray work of Bulygina and Sergeyev (1969). Van Wieringen and Rensen (1966) also detected the presence of Fe in both the al and Og2 phases. They have also shown that after continuous cooling of alnico 5 all the Fe atoms have a ferromagnetic environment suggesting that both the c~1 and O~2 phases are ferromagnetic, whereas after tempering (Ho = 50 kAm -1) 5% of the total iron content is in a non-ferromagnetic phase. The M6ssbauer spectra of alnico 5 and alnico 8, particularly the latter, have also been investigated in detail by Makarov et al. (1967), Belova et al. (1969), Povitsky et al. (1970), Belozersky et al. (1971) and Makarov et al. (1972). A short review of M6ssbauer measurements on the alnicos has been published by Schwartz (1976).

5. Sintered alnicos

The alnico alloys whether isotropic or anisotropic can also be made by mixing suitably fine metal powders, pressing to a green compact followed by a sintering heat treatment at about 1250-1350°C to produce a homogeneous solid with low porosity. The solid compact is then given a heat treatment appropriate to the particular composition. The resulting magnetic properties of the sintered alloys are comparable, though slightly inferior, to those of the cast alloys. The energy product for anisotropic sintered magnets may sometimes be as much as 20% lower than that for the cast magnets but for isotropic cast magnets the difference is usually smaller than this. A comparison of the magnetic properties of various sintered and cast alnicos has been given by Bronner et al. (1970b). Typical demagnetization curves for four sintered alnicos are shown in fig. 23. The advantage of the sintering process is that very small magnets of intricate shape can be made which is not possible or very expensive by the usual casting and grinding process. However, sintered alnicos have a very small share of the market. The production and magnetic properties of sintered alnicos have been discussed by Schiller (1968), Schiller and Brinkmann (1970) and Heck (1974).

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 149 - 1-2

Sinteredalnicos/~~

1.0

6

0.8~ 0.6

D'4

(D "0

I,I.

D.2 n 70

0 60

50

40

30

20

10

0

Applied field, H (kAm-1) Fig. 23. Typical B-H demagnetization curves for sintered alnicos 2, 5, 6 and 8.

6. Moulded, pressed or bonded alnico m a g n e t s

Alnico alloys can be milled to fine powders without a marked deterioration in their magnetic properties. If the powders are then bonded into a thermosetting resin they can be accurately pressed or moulded to the required magnet shape. The properties of the bonded magnets are inferior (Dehler 1942, Heck 1974) to those of the cast or sintered magnets. This is due to the fact that the volume fraction of the powder cannot exceed about 60% so that there is a corresponding reduction in the remanence.

7. Effects of t h e r m o m a g n e t i c t r e a t m e n t on the magnetic properties of alnicos 5 - 9

7.1. Factors controlling development of Ol 1 particle shape anisotropy The factors which control the development of the magnetic anisotropy of alnico 5 during thermomagnetic treatment have been studied in detail by Zijlstra (19601962) following a suggestion made by N6el (1947b). H e found that the rate of elongation of the particles is related to the difference between the decrease in the magnetic free energy of the particles in the magnetic field and the simultaneous increase in the interfacial or surface free energy. The equilibrium value of the elongation is high when the magnetic free energy is large compared with the interfacial free energy between the particles and the matrix. Since the former is measured as energy per unit volume and thus independent of particle size and the

150

R.A. McCURRIE

latter is a surface energy and hence inversely proportional to the particle size, the particles will always become considerably elongated when they are sufficiently large. The efficacy of the thermomagnetic treatment on alnico 5 can be attributed to the particularly low value of the interfacial energy or surface free e n e r g y typically this is ~10-3Jm -2 (1 erg cm-2). This enables the particles to become elongated when they are still small enough to display single domain behaviour and thus to form a magnet with high shape anisotropy together with a high coercivity. Zijlstra (1961) suggested that the same reasoning leads to the conclusion that the Mishima alloy Fe2NiAI, which is usually not considered to respond to magnetic annealing owing to its much larger interfacial free energy, may be expected to do so only when the particles are large enough. He verified this conclusion by heat treating a specimen of Fe2NiA1 in a magnetic field for two weeks at 725°C during which it developed a uniaxial magnetic anisotropy of 4.5 x 10 4 Jm 3 which is of the same order of magnitude as that observed in alnico 5. This Fe2NiA1 alloy did not, however, have a high coercivity because after the long thermomagnetic treatment the particles were too large to be single domains. Thus it appears that the function of the cobalt in the alnico alloys, apart from increasing the saturation magnetic polarization and the Curie temperature, is to decrease the interfacial free energy between the Fe-Co rich particles and the Ni-A1 rich matrix and hence to enable the alloys to respond to thermomagnetic treatment with a resulting improvement in their magnetic properties. If the magnetic field is applied only during the cooling over the narrow temperature range 840-790°C with subsequent tempering at 600°C without an applied field, the resulting magnetic properties are only slightly inferior to alloys which have been given the full thermomagnetic treatment. If the field is applied only below 790°C the anisotropy is less than half that of the fully thermomagnetically treated specimens. If the specimen is cooled to 790°C in the presence of the field and then allowed to cool with the field off, the maximum energy product is lower than the value obtained by quenching the alloy from 790°C. The decrease is due presumably to a partial destruction of the shape anisotropy by inhomogeneous demagnetizing fields and thermal fluctuations. The most effective temperature range for the particle elongation and alignment in a magnetic field is therefore 840°C to 790°C; the lower limit is particularly critical. Nesbitt and Williams (1957) suggested that in the temperature range 850-790°C only nucleation takes place, while particle growth occurs at 600°C. However, Zijlstra's (1960-1962) and De Vos' (1966, 1969) experiments showed that in the field cooling treatment the final particle shape is attained in the very first stage (i.e. in the range 850-790°C) and that subsequent heat treatments did not alter the shape or size of the particles. As was mentioned earlier tempering at 600°C increases the difference in the saturation magnetic polarization between the c~1 (Fe-Co rich) and c~2 (Ni-A1 rich) phases and leads to an increase in the coercivity and remanence.

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 151

7.2. Relationship between the preferred or easy direction of magnetization and the direction of the applied field during thermomagnetic treatment The relationship between the orientation of the particles and the direction of the magnetic field during heat treatment has been investigated by Heidenreich and Nesbitt (1952). They found that the orientation of the particles is not strictly bound to the (100) directions, but could be forced into other directions by the thermomagnetic treatment. In a later paper Nesbitt and Heidenreich (1952a) deduced from magnetic torque measurements that the magnetic anisotropy of alnico 5 was a maximum when the magnetic field was directed along a (100) direction of a single crystal sample during the thermomagnetic treatment. If the field was applied in another direction the anisotropy was lower and the preferred direction of magnetization appeared to lie between the field direction and the nearest (100) direction. Similar results were obtained by Hoselitz and McCaig (1951) but they found that the preferred direction of magnetization was closer to the [100] direction than was indicated by the experiments of Heidenreich and Nesbitt (1952). These differences may be attributable to difference in the magnitudes of the applied fields which were chosen for the thermomagnetic treatments. In another series of experiments McCaig (1953) found that the uniaxial anisotropy of alnico 5 was approximately 105 Jm 3 and that for normal cooling rates (~l.4°Cs -1) and angles less than about 45 ° between the crystal and field directions, the easy direction of magnetization was close to the columnar axis. However, for faster cooling rates, larger angles and less than optimum heat treatments the easy direction of magnetization may be closer to the field direction with a correspondingly lower value of the anisotropy coefficient. An extensive investigation has also been made by Yermolenko et al. (1964) who found that when the thermomagnetic field was parallel to the [100] direction the O/1 (Fe-Co) particles were elongated parallel to this direction but for other angles between the applied field and the [100] direction, the axes of elongation of the particles were not parallel to the field direction. They concluded in contrast to the theory proposed by N6el (1947b) and later developed by Zijlstra (1960-1962) that the axes of elongation are not entirely determined by the minimization of the magnetic and interface energies of the particles in the thermomagnetic field but that their shapes and orientations are partly determined by their elastic energies. It should be mentioned that Yermolenko et al. (1964) used isothermal heat treatment in a magnetic field (720 kAm 1) but this enabled them to study the microstructures of the alloy at different stages in the formation and growth of the particles.

7.3. Dependence of the magnetic properties of the alnicos on the direction of the applied field during thermomagnetic treatment The dependence of the magnetic properties of columnar and single crystal alnico 5 (and alnico 6) on grain orientation and the direction of the thermomagnetic field have been investigated in detail by Ebeling and Burr (1953). They found that the

152

R.A. McCURRIE

best magnetic properties are obtained when the direction of the thermomagnetic field is as close as possible to the [100] direction in the single crystals or to the long axis of the columnar single crystals- i.e., approximately parallel to the [100] direction. When the thermomagnetic field was applied at other angles to [100] or to the [100] columnar axis the maximum energy product decreased according to the cosine of the angle between the thermomagnetic field direction and the [100] or the [100] columnar axis:

(BH)max(O)=

(BH)max(0)cos 0.

The variation of (BH)max with the angle 0 for various sintered single crystals of alnico 5 is shown in fig. 24. From measurements of the energy products of single crystal alnico 5 (51 wt % F e - 24% C o - 14% N i - 8% A 1 - 3% Cu) after heat treatment in a magnetic field parallel to the directions [100], [110] and [111] Zijlstra (1956) showed that the energy product could be expressed as a power series of the direction cosines/31,/32 and/33 measured with respect to the cube axes of the crystal. This was used to calculate the energy product for polycrystalline alnico 5 as a function of crystal orientation. The columnar texture of the magnet was represented by assuming that there was a constant density of [100] axes inside a cone of revolution around the measuring direction which enclosed an angle 2,/. By averaging the above power series for (BH)max Zijlstra obtained an expression for (BH)max in terms of r/. The energy product was shown to decrease almost linearly from 60.8 kJm -3 for ~7 = 0° to 40 kJm -3 for r / = 45 °. The calculated value of the energy product for a

50-

0

~3o

\cosO

"--"20

0

I 0

I

I 30

I

I 60

90

Angle 0 °

Fig. 24. Dependence of (BH)max energy product on the angle between the field applied during thermomagnetic treatment and the [100] preferred or easy axis of magnetization (after Ebeling and Burr 1953).

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS

153

polycrystalline alnico 5 magnet (i.e. one for which ~/= 180 °) was 39.2 kJm -3 which was in good agreement with experiment and suggests that the analysis was essentially correct. An expression for the energy product as a function of ~/ was also developed for magnets in which the crystals are radially oriented in a plane perpendicular to the magnet axis. Magnets with this texture are significantly better than those with randomly oriented grains. The magnetic properties of equiaxed and columnar alnico 5 have been investigated in detail by Makino et al. (1963) and Makino and Kimura (1965). They measured the demagnetization curves parallel and perpendicular to the columnar axis (a) as a function of the angle 0 between the columnar axis and the direction of the 'thermomagnetic field', and (b) as a function of the angle 0' (0' = 90 - 0) between the direction of measurement perpendicular to the columnar axis and the direction of the thermomagnetic field. The results of these measurements are shown in fig. 25 from which it can be seen that the maximum coercivity (58 kAm-1), remanence (1.35 T) and energy product (64 kJm -3) are obtained when the 'thermomagnetic field' is applied parallel to the columnar axis. For the measurements in the direction perpendicular to the columnar axis the maximum coercivity (50kAm-1), remanence (1.32 T) and energy product (42 kJm -3) are obtained when the thermomagnetic field is parallel to the direction of measurement, i.e., perpendicular to the columnar axis. Although the maximum energy product for (b) of 42 kJm -3 is lower than that of 64 kJm -3 for (a) the fact that such a high value was obtained for (b) is an important result because it provides further evidence for the theory that - 1-4

~

0=0¢

I

60

50

1

40 30 Applied field, H

.

20

2

10

(kAm-1}

0

Fig. 25. B - H demagnetization curves measured in the direction M of the columnar axis after heat treatment in a magnetic field at an angle 0 to the columnar axis c (after Makino and Kimura 1965 and Makino et al. 1963).

154

R.A. McCURRIE

15

45

~"~'I0

.

[010] . H ~ ~ . , . 4 ~...Ku " ~

/

/

ool 0~ 0

30

e.ol, I

1 15

I

I 30

I

I 0 45

Angle [30

Fig. 26. Variations of uniaxial anisotropy constant Ku and its direction o~ with direction/9 of the heat treatment field H.

the preferred direction of magnetization is largely determined by the direction of the thermomagnetic field (N6el 1947(b), Zijlstra 1960, 1961) and that crystallographic anisotropy is of secondary importance. Zijlstra (1960, 1961) has shown by experiments on Fe2NiA1 that the time for which the alloy is subjected to the thermomagnetic field treatment is also of fundamental importance in determining the results. (The theories of the effects of thermomagnetic treatment of the alnicos are discussed in section 17.) Iwama et al. (1976) measured the anisotropy constant Ku of single crystal alnico 5 after cooling in a magnetic field at angles 0 °, 15°, 30 ° and 45 ° to the [100] direction. The results are shown in fig. 26; Ko decreased from 15.6× 104Jm -3 parallel to the [100] direction to 4.5 x 104 Jm s at 45 ° to [100]. Figure 26 also shows the variation of the angle a between the preferred axis of Ku and the [100] direction as a function of the angle/3 between the direction of the heat treatment field and the [100] direction. It can be seen that only when /3 = 45 ° does the preferred direction of magnetization (i.e. the Ku axis) follow that of the heat treatment field, i.e., a 2 4 5 °. At lower values of /3 the Ku axis lies between the direction of the heat treatment field and the [100] direction. These results are in good agreement with those obtained by McCaig (1953).

8. Effects of cobalt on the magnetic properties of the alnicos

The addition of cobalt to both the isotropic and anisotropic alnicos has several beneficial effects. In the isotropic alloys it increases the saturation magnetic

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 155 polarization Js and hence the remanence Jr. Since the cobalt is precipitated in the c~1 phase particles (i.e. the F e - C o rich phase) this increases the difference between the magnetic polarizations of the al and a2 phases and hence increases the coercivity due to the resulting increase in the shape anisotropy. The same improvements are also observed in the anisotropic alnicos 5-9 but in these alloys the cobalt content is in the range 23-40%. The high cobalt content also increases the Curie temperature Tc which has the beneficial effect of increasing the sensitivity (of the alnicos 5-9) to magnetic annealing. This is due to the fact that the spinodal decomposition temperature Ts is then further below Tc so that the magnetic polarization of the particles at Tc is higher, and therefore increases the elongation of the particles in the magnetic field direction because their magnetic free energy is thereby lowered. Cahn (1963) has shown the magnetic energy is proportional to the square of the rate of change of the saturation magnetic polarization with composition i.e. (OJs/Oc)2 and that the latter is very large when the spinodal decomposition temperature is close to the Curie temperature. Thus heat treatment in a magnetic field is expected to be most effective when T~ is close to but lower than To. According to Zijlstra (1960, 1961) the high cobalt content also decreases the interfacial energy ,,/between the F e - C o rich c~i phase and the Ni-A1 rich a2 phase so that the increase in the total surface energy which results from the particle elongation is reduced. N6el (1947b) and Zijlstra (1960, 1961) have suggested that the sensitivity of alnico alloys is proportional to (A J)2~3, where AJ is the difference between the saturation magnetic polarizations of the F e - C o rich c~ phase and the Ni-A1 rich a2 phase. Thus when AJ is high and 3' low the rate of elongation of the particles in the thermomagnetic field is high. This results in an increase in the coercivity, the remanence and the energy product parallel to the direction of the applied field. From tables 2, 3, 5, and 6 it can be seen that there is a substantial improvement in BHc, Br and (BH),nax in the cobalt containing alloys compared with the original F e - N i - A I alloy (table t). Unfortunately the increased cobalt content, particularly in the anisotropic alnicos 5-9, favours the precipitation of the magnetically deleterious fcc phase so that more carefully controlled cooling through the range 1200°C to 850°C is required. Detailed investigations of the effects of cobalt on the magnetic properties of the alnicos have been made by many authors, see e.g., Betteridge (1939), Jellinghaus (1943), Zumbusch (1942a, b), Bronner et al. (1966a-1970). According to Wyrwich (1963) the best magnetic properties are obtained with a cobalt content -~38%.

9. Effects of titanium on the magnetic properties of the alnicos (mainly 6, 8 and 9) The effects of titanium additions on the magnetic properties of the alnico 8 are summarized in fig. 27 from which it can be seen that titanium increases the coercivity and the energy product and the time required to form the undesirable fcc 3, phase at 1050°C, though there is unfortunately a rapid decrease in the remanence with increasing Ti content (Vallier et al. 1967). Similar results were obtained by Iwama et al. (1970) who also showed that the Curie temperature of

156

R.A. M c C U R R I E oO. 120

m

1 " 1 --

O O

1"0--

~" E

4~,16

3C

®

0-9 - ~

3 E

Br

12 0

0

o

toO'8

2

= 8

C

E

[~'mlc

c

0"7-

1 ® E

0 . 6 [-

0

I--

2

4 6 Wt % Ti

8

I

[0

Fig. 27. Effects of titanium additions on the magnetic properties of alnico 8 (41% F e - 3 4 % C o - 15% N i - 7% A I - 3% Cu) (after Vallier et al. 1967).

the Ni-A1 rich OL2 phase decreased linearly with increasing Ti content as shown in fig. 28 from which it can be seen that if the alnico 8 alloy containing more than 5% Ti is annealed at 600°C the Curie temperature falls below room temperature. This increases the coercivity because in normal use (~20°C) the F e - C o rich

6 0 0 I-

.

~,AnneaEed

o

for 48hr at T C

I "~

0 "~_

0.200

0

I

I

I

I

2

4

6

8

Wt % titanium Fig. 28. Variations of Curie temperature of the Ni-AI rich o~2 phase with Ti content for alnico specimens annealed at various temperatures (after Iwama et al. 1970).

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 157 particles are then surrounded by a non-ferromagnetic matrix and are not therefore in exchange contact so that the difference between the saturation magnetic polarizations of the F e - C o rich al phase and the Ni-AI rich ~2 phase is as large as possible; the latter therefore increases the shape anisotropy energy of the particles and hence the coercivity. The effects of Ti additions on the magnetic properties of various thermomagnetically treated alnico single crystals have been investigated by Takeuchi and Iwama (1976). They measured the anisotropy coefficient Ku, the volume fraction of the F e - C o rich particles, p, the particle diameter d, the elongation l/d and the intrinsic coercivity iHc. Their results are summarized in tables 7 and 8. The latter includes results obtained by Sergeyev and Bulygina (1970) and Granovsky et al. (1967) for comparison. These results show that the anisotropy Ku (and K ' , the anisotropy per unit volume of the F e - C o rich particles), the particle elongation l/d and the coercivity increase as the Ti content increases. The increase in coercivity is also accompanied by a decrease in the volume fraction p and the particle diameter d. If we can assume that the coercivity dependence on the packing fraction is given by, He(p) = He(0)(1 - p ) , an increase in Hc is to be expected if p decreases. The increase in the coercivity due to the titanium addition can also be partly attributed to an increase in the elastic and surface energy associated with the spinodal decomposition which increases the smoothness, perfection and regularity of the particle s p a c i n g - s e e e.g. electron micrographs of alnico 8 (fig. 22(a), (b)) obtained by De Vos (1966, 1969), and those obtained by Granovsky et al. (1967) and Takeuchi and Iwama (1976). While Ti inhibits the a ~ y transformation Vallier et al. (1967) have shown that it restricts the temperature ranges for homogenization and thermomagnetic treatment so th~it the choice of the heat treatment schedule is critical. De Vos (1966, 1969) has suggested that the necessity to give titanium containing alnicos an isothermal anneal in a magnetic field is due to the fact that the Ti 2+ ion has a large radius and a low rate of diffusion so that longer times are required for the phase separation and particle elongation to occur. Marcon et al. (1971) have shown, for alnicos containing more than 28% Co, that it is practically impossible to avoid the precipitation of the deleterious y phase during thermomagnetic treatment unless appropriate amounts of a-stabilizing elements such as silicon or titanium are added. Unfortunately titanium inhibits the formation of the columnar grain structure. However, Gould (1964), McCaig (1964) and Harrison and Wright (1967) have shown that the addition of small quantities of sulphur, selenium or tellurium facilitates the formation and growth of columnar grains. Thus the addition of titanium to the alnicos, although beneficial, means that much more careful control of the composition and heat treatment of the alloys is required. It is for this reason and the higher cobalt content that the high coercivity alnicos 8 and 9 are generally more expensive than the other alnicos. The effects of additions of Ti, S, Nb, and other elements on the magnetic and metallurgical properties of the

158

R.A. McCURRIE

alnicos have been investigated by Clegg (1966, 1970), Palmer and Shaw (1969), Higuchi (1966), Hoffmann and St/iblein (1970) and Wright (1970).

10. Dependence of the magnetic properties on the angle between the direction of measurement and the preferred or easy axis of magnetization The variation of the coercivity with angle 0 to the preferred axis in alnico 9 and ticonal 900 (single crystal) has been measured by McCurrie and Jackson (1980) who observed small maxima at 0 = 60 ° followed by a rapid decrease to zero at 90 ° (fig. 29). According to Shtrikman and Treves (1959) the reduced coercivity hc as a function of the angle of m e a s u r e m e n t 0 and the reduced radius for infinitely long cyclindrical rods with shape anisotropy only is given by Hc hc = 2XMs- $2[(1 _

1.08(1- 1.08S 2) ( 1 - 2.16S -2) sin 2 0] 1/2'

1.08S_2)2

where S = R/Ro (Ro = (4"n't.zoA/JZs)1/2) and 0 is the angle between the easy axis of magnetization (i.e., the axis of the cylinder) and the direction of m e a s u r e m e n t of He. Comparison of the results shown in fig. 29 with the theoretical curves obtained from the above relation shown in fig. 30 suggests that the observed angular variation of Hc in these alloys is due to magnetization reversal by the curling mechanism. The coercivities of alnico 9 and ticona1900 are - 0 . 2 5 H A (HA is the anisotropy field) which are in good agreement with the values to be expected if the magnetization reverses by curling (Shtrikman and Treves 1959). The angular variation of the r e m a n e n c e coercivity Hr (Hr is the reverse field required to reduce the r e m a n e n c e to zero) showed even m o r e pronounced maxima at 0 ~ 80 ° followed by a rapid decrease to zero at 0 ~ 90 °. Unfortunately no detailed theory of the variation of Hr with 0 is available for comparison, though Kneller (1966, 1969) has suggested that Hr(O)/Hc(O) varies between the limits:

1 (0 = 0 °) Dx. Thus in a given field H the stable positions of the magnetization vector are those which correspond to the minima of eq. (2). The solutions, for various values of the field and the angle 0, have been tabulated by Stoner and Wohlfarth (1948) who have also plotted several representative hysteresis loops notably those for 0 = 0, 45 ° and 90 °. For a survey of the results the reader is referred to Zijlstra, (chapter 2 in this handbook). One of the most important conclusions from the Stoner-Wohlfarth theory is that the coercivity of an aligned assembly of identical non-interacting (i.e., infinitely dilute) single domain particles with uniaxial shape anisotropy is Hc = (D: - D x ) M s ,

i.e., the coercivity is directly proportional to the saturation magnetization and to the difference in the demagnetization factors perpendicular and parallel to the easy axis. For a randomly orientated array of such particles the coercivity is reduced to Hc = 0.479(Dz - D x ) M s . The dependence of ( D z - Dx) on the degree of elongation, i.e., the ratio of the lengths of the x- and z-axes of the particle, is shown in fig. 38. It has already been mentioned in section 1.2 that in view of the complex microstructures and particle shapes in the isotropic alnicos 1-4 it is not possible to give a quantitative comparison or interpretation of their magnetic properties in terms of the StonerWohlfarth (1948) theory though their magnetic properties can be understood Ms

H

Fig. 37. Relationship between the applied field, easy axis and magnetization vector in a prolate ellipsoidal single domain particle with uniaxial shape anisotropy.

168

R.A. M c C U R R I E

0.5 0"4

Dz

~0-3 I

N

0'2

Dx

0"1 0

1

I

I

2

3

I

I

4 5 Dimensional

I

I

6 7 8 ratio m = a / b

I

I

9

10

Fig. 38. Difference (Dz- Dx) between demagnetization factors perpendicular and parallel to the preferred axis of magnetization as a function of the particle elongation or dimensional ratio m = a/b, where a is the semi-major and b the semi-minor axis of the prolate ellipsoid of revolution.

qualitatively. In any case in the alnicos 1-4 both the al and a2 phases are ferromagnetic so that magnetization changes by domain wall movement may also occur.

From the electron micrographs of alnico 5 and alnico 5-7, the precipitated F e - C o rich particles are rod-like (i.e., they approximate to prolate ellipsoids of revolution) and have dimensions ~150 nm long and ~40 nm in diameter. From fig. 38 the corresponding value of Dz - Dx is ~0.5 and hence if we take the saturation magnetization of the particles Ms = 1.7x 106Am -1 which is considerably larger than the observed value of 60 kAm -1. Although the particles are not fully aligned this is insufficient to account for the difference in the two values. Since the coercivity depends on the presence of demagnetizing fields it is clear that particle interactions cannot be neglected. Many authors (see e.g., N6el 1947a, Compaan and Zijlstra 1962) suggest that the effects of particle interactions on the coercivity are best described by the relation

He(p)= H o ( O ) ( 1 - p ) , where He(p) is the coercivity for a particle packing fraction p and He(0) is the coercivity for a packing fraction of zero. Thus if the effects of particle interactions are included the coercivity of a fully aligned array of single domain particles with uniaxial shape anisotropy is Ho= (1-p)(Dz -Dx)Ms,

(3)

or

Hc = (1 - p ) ( D z - Dx)M's/p, where M'~ is the average saturation magnetization of the alloy. The packing factor

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 169 p is usually in the range 0.6-0.7 and (Dz-D~) approaches 0.5 so that the theoretical value of Hc ~ 300 kAm -~. Thus even if particle interaction effects are included there is still a very significant difference between the theoretical and observed coercivities (-~60 kAm-1). Baran (1959) has derived a more general expression for the coercivity of a fully aligned array of particles which takes account of the reduction in coercivity due to particle interactions and the possibility that the matrix is also ferromagnetic, viz. Hc = p(1

-

p)(Dz

-

Dx)(MI

-

M2)2/M's,

(4)

where p is the volume fraction of the most strongly ferromagnetic phase, M1 and M2 the saturation magnetizations of this phase and the matrix phase respectively, M's the overall saturation magnetization of the alloy and Dz and Dx are the demagnetization factors Of the particles perpendicular and parallel to the axis of elongation respectively. For the maximum coercivity it is clear from eq. (4) that the difference M 1 - M 2 should be as" large as possible. If it is assumed that the alloy is fully heat treated, i.e., sufficient time has been allowed for all the Fe and Co atoms to diffuse to the precipitated particles, then the matrix saturation magnetization M2 ~ 0 and the saturation magnetization of the Fe--Co rich particles M1 = Ms = M's/p, so that eq. (4) reduces to eq. (3). From the electron micrographs of alnico 8 shown in figs. 22(a) and (b) (De Vos 1966, 1969) the F e - C o rich particles are very long rods and approximate to prolate ellipsoids of revolution with length to diameter ratios l/d ~-16 corresponding to D z - D~--~ 0.5. Quantitative metallography shows that the volume fraction of the F e - C o rich particles p ~ 0.65. Since there is a very high degree of particle alignment we may calculate the coercivity from eq. (1). If Ms is taken to be at least equal to the value for pure iron viz. 1.7 MAre -1 (the saturation magnetization for Fe-30% Co is about 10% higher than that of pure iron) the theoretical coercivity as derived from eq. (3) is ~300 kAm -1 which compares very favourably with the highest experimental value of 180 kAm -~ for alnico 8. The discrepancy between the observed value of the coercivity and that calculated according to the Stoner-Wohlfarth (1948) theory suggest that the assumption that changes in the magnetization occur by coherent rotation is invalid (see Zijlstra, chapter 2 in this handbook).

15. Interpretation of the magnetic properties in terms of magnetization reversal by the curling mechanism According to calculations by Kondorsky (1952a), Brown (1957, 1963, 1969), Frei et al. (1957) and Aharoni and Shtrikman (1958) magnetization reversal by coherent rotation in infinitely long cylinders with shape anisotropy only, should occur only when the cylinder radius R is less than a critical radius R0 = (4zrA)llZ/Izaol2Ms where A is the exchange constant,/z0 is the magnetic constant 4~- × 10 -7 H m -1 and Ms the saturation magnetization. Above this radius magnetization reversal occurs by the curling mechanism (apart from a very small range of radii for which magnetization

170

R.A. McCURRIE

reversal occurs by a process known as buckling). According to Aharoni and Shtrikman (1958) the dependence of the coercivity on the cylinder radius R is given by Hc = 1.08(Ro/R )ZMs/2 ,

(5)

where it is of course assumed that D z - Dx has its maximum value of 0.5 for an infinitely long cylinder. The curling mechanism is discussed in chapter 2 of this handbook by Zijlstra who has also included a diagram showing the configuration of the magnetic Spins during the reversal process. From measurements on the electron micrographs of alnico 8 obtained by De Vos (1966, 1969) (see figs. 22(a) and (b)) the particles have radii ~15 nm. Although the particles are obviously not infinitely long cylinders their length to diameter ratio l/d ~ 16 so that assuming magnetization reversals occur by curling we may estimate the coercivity from eq. (5) from which we find that Hc ~ 2.4 × 105 A m -1 (McCurrie and Jackson 1980). The highest observed flux coercivity for alnico 8 BHo ~ 1.8 × 105 A m -1 (this is slightly less than the intrinsic coercivity He) so that the theoretical and observed coercivities are in reasonable agreement. When the magnetization reversal occurs entirely by curling there are no particle interaction effects so that the coercivity is independent of the packing fraction p. However, the appearance of magnetostatic interaction domains (discussed below) during demagnetization suggests that some interparticle interaction does occur. From measurements of the angular variation of the coercivity and rotational hysteresis in columnar and single crystal alnico 9 (see sections 10 and 18) McCurrie and Jackson (1980) have concluded that magnetization reversal does occur by the curling mechanism and that the quantitative results are in reasonable agreement with those predicted on the basis of the theory proposed by Shtrikman and Treves (1959).

16. Magnetostatic interaction domains in alnicos Magnetization reversal in the alnicos is further complicated by the formation of magnetostatic interaction domains which are due to interparticle interactions. Although it is well established that the alnicos contain single domain particles, macroscopic surface domain structures known as magnetostatic interaction domains, can sometimes be observed by the Bitter colloid technique, as shown by Nesbitt and Williams (1950), Bates (1955), Bates and Martin (1955), Kussmann and Wollenberger (1956), Schulze (1956), Andr/i (1956), Kronenberg and Tenzer (1958), Bates et al. (1962) and Iwama (1968). This apparently contradictory observation can be explained as follows. Consider the demagnetization process of an alnico magnet. As the magnetization of the particles is gradually reversed we should expect that as a result of the long-range interaction fields, particles in a particular region which have already reversed their magnetization will tend to assist the reversal of those in adjacent regions. Thus in the demagnetized state, when just half the total magnetization has been reversed, the magnet is effectively

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 171

Fig. 39. Magnetostatic interaction domains in alnico 5 (Bates et al. 1962). divided up into a domain structure as shown in fig. 39. At the boundaries between the various regions or interaction domains there are stray magnetic fields and gradients which attract the colloidal particles and so delineate the domain structure. These boundaries are of course quite different from the conventional Bloch-Lifshitz walls (Kittel 1949, Kittel and Galt 1956). Similar magnetostatic interaction domains have also been observed on elongated single domain magnets by Craik and Isaac (1960). For detailed discussions of magnetostatic interaction domains and the mechanism of their formation the reader is referred to the papers by Craik and Lane (1967, 1969). The effects of particle interactions have also been discussed by Wohlfarth (1955).

17. Comparison of the N6ei-Zijlstra and Cahn theories of magnetic annealing in alnico alloys The improvements in the magnetic properties of alnico alloys by heat treatment in a magnetic field were first observed in alnico 5 (see section 2) but the following discussion also includes the effects which are observed when alnicos 6, 8 and 9 are given an isothermal heat treatment in a magnetic field.

172

R.A. McCURRIE

17.1. Ndel-Zijlstra theory In the theory of magnetic annealing proposed by N6el (1947b) and later developed by Zijlstra (1960-1962) the spinodal decomposition at high temperatures results in the formation of very small spherical particles and is considered to be complete before the elongation of the particles begins. If the decomposition takes place in a magnetic field the spherical particles develop into ellipsoids with their axes of elongation parallel to the applied field thereby reducing their total magnetic free energy. During the thermomagnetic treatment the particles increase their size and elongation very rapidly because at high temperatures the rate of atomic diffusion is high. The applied field should of course be sufficient to saturate the Fe-Co rich particles in order to achieve the maximum possible alignment during the relatively short thermomagnetic heat treatment. The relevant counteracting energies are the interfacial energy F~ between the a~ and a2 phases and the difference in the magnetostatic energy Fm between the decomposition waves parallel and perpendicular to the applied field. During the elongation of the particles there is arl increase in the interfacial energy but this is accompanied by a larger reduction in the magnetic energy of the particles in the applied field. Thus the elongation is energetically favourable when the ratio Fm/Fs is large. In the N6el-Zijlstra theory F~ is defined as the product of the interface tension and the amount of interface per unit volume. Thus the ratio Fm/Fs will increase in a coarsening structure so that the interfacial free energy is of great importance in determining the efficacy of magnetic annealing. According to Zijlstra (1960-1962) the rates of elongation and coarsening of the particles are proportional to the square of the difference in the saturation magnetic polarizations of the OgI and a2 phases (AJs)2 and inversely proportional to the interfacial energy Y, i.e., the efficacy of the thermomagnetic treatment is proportional to (AJs)2/T. This theory explains why thermomagnetic treatment is most effective in alnico alloys with a high cobalt content (i.e. alnicos 5-9) which raises the Curie temperature and AJs and lowers the interfacial energy Y. From measurements on alnico 5 Zijlstra (1960) concluded that 3' ~0.1 Jm -2, a result which confirms an earlier suggestion by Kittel et al. (1950) who also suggested that since the interfacial energy is small the particles should develop a shape anisotropy in order to minimize their magnetic energy in the applied field. Thus according to the N6el-Zijlstra theory the axes of elongation of the particles should be parallel to the applied field irrespective of its orientation relative to particular crystallographic directions in the alloy. This conclusion suggests that the shape anisotropy for finite annealing time at a given temperature should give the same result for both polycrystalline and single crystal specimens. However, Zijlstra's (1960) experiments show that the anisotropy of the single crystal specimens is considerably larger than that for the polycrystalline specimens. Zijlstra (1960) suggested that this difference could be due to a contribution from magnetocrystalline anisotropy, but the magnitude of the difference makes this unlikely.

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 173 17.2. C a h n ' s theory

The spinodal decomposition of the alnico alloys into two phases al and Ol2 occurs because it is accompanied by a reduction in the total free energy FT of the alloy. The effect of the magnetic field in producing elongated particles with their axes of elongation parallel to the field direction has been investigated theoretically by Cahn (1963). He suggested that the effect of the magnetic field is to suppress the spinodal decomposition waves along the magnetic field direction and that this is due to the difference in the magnetic energy Fm of the spinodal waves parallel and perpendicular to the field direction which favours the formation of long rods parallel to the field direction. In the absence of the magnetic field the spinodally decomposed system consists of three mutually perpendicular spinodal decomposition waves, i.e., a cubic array of isotropic particles. Cahn (1963) stated that the two main sources of anisotropy are the magnetic and elastic energies. The former favours compositional waves parallel to the internal field direction while the latter favours compositional waves parallel to particular crystallographic directions. Waves parallel to the (100) directions in the {100} planes in cubic crystals are favoured when 2C44- Cl1+

C12>0

,

where the Cii coefficients are elastic energy constants from the stress tensor. If the anisotropy in the magnetic energy is much larger than the anisotropy in the elastic energy then the geometry of the decomposition will be independent of the crystallographic orientation so that the axes of elongation of the particles will be parallel to the applied field direction. However, if the anisotropy in the elastic energy predominates then the axes of elongation of the particles will be parallel to the crystallographic direction which minimizes the elastic energy. When the elastic and magnetic anisotropy energies are of comparable magnitude the axes of elongation of the particles lie between the field direction and the nearest (100) direction. In particular if the applied field is parallel to a (100) direction then the axes of elongation of the particles are parallel to the chosen (100) direction. Cahn (1963) also suggested that for a solid solution with a composition fluctuation ( x - x 0 ) where x0 is the average composition, the anisotropy in the magnetic energy is proportional to (OJs/Ox) 2 where Js is the saturation magnetic polarization of the precipitated particles. The quantity (OJs/Ox) 2 is expected to vary rapidly with temperature and to be very large near the Curie temperature, To, so that thermomagnetic treatment will be most effective when the spinodal decomposition temperature T is at, or just below, the Curie temperature. If the alloy is cooled to lower temperatures the effectiveness of the field diminishes rapidly. The anisotropy in the elastic energy depends on two factors: (1) it is proportional to (d In a / d x ) 2 where 'a' is the stress-free lattice parameter, and (2) it is proportional to the variation in the elastic energy coefficient with crystallographic direction; the latter can be approximated by Ay = ]71100]- 71111][. Cahn

174

R.A. McCURRIE

(1963) estimated that the elastic energy is much greater than the magnetic energy except near the Curie temperature. Thus according to Cahn's (1963) theory a large ratio of Fm/F-r favours the elongation of the particles when they are heat treated in a magnetic field. The shape of the particles is established during the first stages of the decomposition and the magnetic shape anisotropy can be further increased only by a subsequent increase in their saturation magnetic polarization by diffusion of atoms between the two phases al and a2 without thereby changing their shape, though their wavelength is increased by this process.

17.3. Discussion of the Ndel-Zijlstra and Cahn theories Electron micrographs of alnico 8 (De Vos 1966, 1969) which had been given an isothermal heat treatment in a magnetic field show that even in the initial stages of the spinodal decomposition the three (100) decomposition waves are developed which have practically the same wavelength, a result which disagrees with Cahn (1963) who suggested that the (100) decomposition waves perpendicular to the magnetic field direction are suppressed from the beginning of the spinodal decomposition. De Vos's (1966, 1969) electron micrographs of alnico 8 also show that elongated Fe-Co rich particles with their axes of elongation parallel to the (100} directions develop even in the absence of an applied field; this result is also in disagreement with Cahn's (1963) theoretical predictions. According to the discussion in section 7.2 of the relationship between the field direction and the preferred direction of magnetization Heidenreich and Nesbitt (1952) and Nesbitt and Heidenreich (1952a, b) found that when the field direction was parallel to a principal crystallographic direction, i.e., [100], [110] or [111], the easy or preferred direction of magnetization is parallel to the field direction. However, Heidenreich and Nesbitt (1952), Nesbitt and Heidenreich (1952a, b), Hoselitz and McCaig (1951), McCaig (1953) and Yermolenko et al. (1964) showed that when the thermomagnetic field is applied at an angle to a (100) direction, the direction of easy magnetization lies between the field direction and the chosen (100) direction. The above authors also found that the magnetic anisotropy (at room temperature) has a maximum value when the field is parallel to a (100) direction. Thus from the results presented in section 7.2 and the short summary of these given above there is strong evidence that in addition to the magnetic and interracial energies the anisotropy of elastic energy has some effect in determining the orientation of the elongated Fe-Co rich particles during thermomagnetic treatment. This conclusion is also supported by the microstructural observations made by De Vos (1966, 1969). Although Cahn's (1963) suggestion that the anisotropy of the elastic energy is important in determining the nature of the spinodal decomposition waves does not agree with the electron microscopic observations of De Vos (1966, 1969) it is clear that the orientation of the particles is affected by the anisotropy of the elastic energy. The experiments performed by Zijlstra (1960-1962) and De Vos (1966, 1969) show that the Ndel-Zijlstra theory of thermomagnetic treatment or magnetic annealing is in better agreement with the experimental results than that

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS

175

proposed by Cahn (1963). Strong support for this conclusion is provided by the following three experiments carried out by Zijlstra (1960-1962): (1) A specimen of alnico 5 (51% Fe, 24% Co, 14% Ni, 8% A1 and 3% Cu by weight) was heat treated in a magnetic field of 128 kAm -1 parallel to the [100] direction for 7 h at 748°C and subsequently a part of the same specimen was annealed for 24h at the same temperature with the field parallel to the [010] direction. A part of this specimen was then annealed for a further 24 h at 748°C. Electron micrographs of each of the three thermomagnetic treatments (actually thermal magnetic anneals) are shown in figs. 40(a), (b) and (c) from which it can be seen that when the alloy is annealed in a field perpendicular to the initial field direction, the particles become elongated in the new field direction thus reducing their magnetic free energy, in agreement with the N6el-Zijlstra theory. The electron micrographs shown in figs. 41(a) and (b) also confirm that in the initial stages of the phase separation the Fe-Co rich particles are spherical (fig. 41(a)) and that they are elongated by heat treatment in the magnetic field-the direction of elongation being parallel to the field direction as shown in fig. 41(b). (2) A polycrystalline specimen (disk) of alnico 5 with the same composition as that given above was heat treated in a non-inductively wound furnace for 7 h at

i~

a

b t

i~ i~

C ....!

Fig. 40. Microscopical demonstration of crossed-field annealing of a single crystal: (a) after heat treatment for 7 hours at 748°C with field along the [100] direction; (b) after subsequent heat treatment for 24 hours at 748°C with field along the [010] direction; (c) after final heat treatment for 24 hours at 748°C with field along the [010] direction. All three micrographs are made of the (001) plane (after Zijlstra 1960).

176

R.A. McCURRIE

a

I

b

2pm Fig. 41. (a) Electron micrograph of an alnico showing that in the initial stages of the phase separation the Fe-Co rich particles are spherical. (b) Electron micrograph after heat treatment in a magnetic field. The direction of elongation of the Fe-Co rich particles is parallel to the direction of the field (after Zijlstra 1962).

755°C in the absence of an applied field. After this treatment the specimen was shown to be isotropic but when it was subsequently heat treated in a magnetic field of 6 4 0 k A m -t at the same t e m p e r a t u r e it became anisotropic with an anisotropy energy approximately equal to that of a polycrystalline alnico 5 specimen which had been given a m o r e conventional thermomagnetic heat treatment, i.e., Ku ~ 8 x 104 Jm -3. (3) A specimen of polycrystalline Mishima alloy, Fe2NiA1, which is not usually considered to respond to thermomagnetic treatment was heat treated in a field of 640 k A m -1 for 2 weeks at 725°C after which it became magnetically anisotropic with an anisotropy energy K ~ 6 × 104 Jm73 which is comparable to that of alnico 5. After this treatment, however, the particles are too large to be single domains so that the coercivity is correspondingly low ~10 k A m -1 parallel to the preferred direction, i.e., the field direction. None of the above three results is to be expected according to the theory proposed by Cahn (1963). However, it should be emphasized that Zijlstra's (1960-1962) results were obtained by heat treatment times much longer than those used in commercial practice so that it seems likely for shorter thermomagnetic heat treatments (e.g. in cooling of alnico 5) that the orientation of the axes of

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS

177

elongation are partly determined by the anisotropy in the elastic energy but there now seems to be little doubt that the N6el-Zijlstra theory of the thermomagnetic treatment of the alnicos is in good general agreement with the experimental results.

18. Rotational hysteresis The rotational hysteresis energy W~(H) in a field is defined as the energy required to rotate the specimen through 360 °, i.e., Wr(H)

= f~'~ F(O) dO.

It can also be conveniently obtained by measuring the area enclosed by the 360 ° clockwise torque curve and the 360 ° anticlockwise torque curve (McCurrie and Jackson 1980); the rotational hysteresis energy W~(H) is equal to half this area, i.e.,

W~CH)= ½

Fc(O) dO +

/'Ac(O) dO , JO

where Fc(0) and FAt(0) are the torque curves in a given field for clockwise and anticlockwise rotation in the applied field. The clockwise and anticlockwise torque curves corresponding to the maximum value of Wr(H) for single crystal alnico 9 are shown in fig. 42. McCurrie and Jackson (1980) have measured the rotational hysteresis energies of alnico 9 and single crystal alnico 9 as a function of the applied field and their results are shown in fig. 43. Note the very rapid variation in W~(H) for applied fields close to the coercivity. From the value of the rotational hysteresis integrals, defined by

j~ where Wr(H) is the rotational hysteresis energy observed in a field H, R can therefore be obtained from the area under the Wr(H)/Js vs 1/H curve (Bean and Meiklejohn 1956, Jacobs and Luborsky 1957, Luborsky 1961, Luborsky and Morelock 1964). McCurrie and Jackson (1980) have concluded that magnetization reversal in alnico 9 and ticonal 900 occurs by curling. This conclusion is also supported by their measurements of the angular variation of the coercivity discussed in section 10. The rotational hysteresis energy of single crystal alnico 8 as a function of the applied field has also been measured by Livshitz et al. (1970c). They also observed a very sharp peak in the rotational hysteresis energy but in contrast to the results obtained by McCurrie and Jackson (1980) they observed a smaller peak in a higher applied f i e l d - about 2.5 times the field corresponding to the first sharp peak.

178

R.A. M c C U R R I E

1"00 I Ha= 188 kAm -1

0'751-

H c = 138 kAm -1

0"50 I

E 0.25

.-j

Acw w

0

90

270

12( Angle 0 °

0

~0.25

~0-50

Ticonal 9 0 0 (100) plane

- 0-75

-1.00 uFig. 42. Torque curves showing rotational hysteresis in a single crystal of alnico 9 (ticonal 900) in an applied field of 188 k A m -1 (McCurrie and Jackson 1980). T h e rotational hysteresis energy Wr(H)can be determined by halving the area enclosed between the two curves: C W - c l o c k w i s e rotation; A C W anticlockwise rotation.

2"0

E

1.5 • Ticonal 9 0 0

1.0

0-5

0 .P~ 0

2

I , ~--..-.-~ 4 6 8 H ~'105Am -1)

I 10

Fig. 43. Variation of rotational hysteresis energy of columnar alnico 9 and single crystal alnico 9 (ticonal 900) with applied field (McCurrie and Jackson 1980).

STRUCTURE AND PROPERTIES OF ALNICO PERMANENT MAGNET ALLOYS 179

19. Anhysteretic magnetization The anhysteretic magnetization of a ferromagnetic material is the magnetization which results from the application of a static field H and a superimposed alternating field Ha > H which is gradually reduced to zero while the static field H is still on. The anhysteretic magnetization c u r v e - s o m e t i m e s referred to as the ideal magnetization c u r v e - r i s e s much more steeply than the conventional curve and if the specimen has a low or zero external demagnetization factor the initial slope of the anhysteretic magnetization curve is known as the anhysteretic susceptibility Ka. A simple general theory of anhysteretic magnetization curves has been presented by Ndel (1943) and N6el et al. (1943) but for a short review the reader is referred to Kneller (1969). The reciprocal K21 is known as the internal demagnetization factor. Dussler (1927) has shown that the geometrical demagnetization factor Dg of open magnetic circuits also depends on the structural details of the material. The demagnetizing field HD for a uniformly magnetized ellipsoid is given by HD = D g M ,

but for non-uniformly magnetized particles such as occur in the alnicos it has been found by experiment that Ka 1 = D,

where

D > Og.

The difference D i = AD = D - D g has been attributed to internal interaction effects arising from the structure of the materials. Unfortunately, Di is not a constant, characteristic of the material, but also depends on Dg as one would expect since the shape and structural effects are due fundamentally to magnetostatic interactions. Bulgakov (1950) found that for alnico 5 that the values of Di parallel and perpendicular to the preferred axis of magnetization were respectively 0.02 and 0.4. Similar measurements were also made by Gould and McCaig (1954) on alnico 5 who obtained values of 0.01 and 0.5 for D~. They suggested that the precipitated particles were oriented parallel to the thermomagnetic field and separated by a non-ferromagnetic matrix, but they stressed that their measurements of D~ did not enable them to make any really firm conclusions.

20. Magnetic viscosity In all the above discussions of coercivity theory it has been assumed that after saturation of a ferromagnetic material in the forward direction the demagnetization curve represents instantaneous and stable values of B or M as a function of the reverse applied field H. However, if a steady reverse field less than the coercivity is applied after

180

R.A. M c C U R R I E

saturation, the magnetization decreases with time t after the application of the field H. This time dependent change of the magnetization in an applied field is known as magnetic viscosity. The magnetic viscosity of cast alnico 2 (54% Fe, 18% Ni, 12% Co, 10% A1, 6% Cu) as measured by Street and Woolley (1949) is shown in fig. 44. Measurements on the same alloy which had been heat treated at 1250°C for 20 minutes and then allowed to cool at about 2°C per second gave similar results to the cast alloy. According to Street and Woolley (1949) the magnetic polarization at time t is given by the empirical relation

J=C-Slnt, where C is a constant and S is a parameter which depends on the temperature T and the applied field H. Since a similar effect also occurs when the applied field is positive, the phenomenon of magnetic viscosity is a general property of all ferromagnetic materials, though its presence is not always readily observable. The above equation suggests that the magnetization reversal by the field H involves the thermally activated surmounting of energy barriers in the material. For further details on the magnetic viscosity in the alnicos the reader is referred to the papers by Bulgakov and Kondorsky (1949), Street and Woolley (1949, 1950, 1956), Street et al. (1952a, b), Phillips et al. (1954) and Barbier (1954).

0"20 _

Alnico

2

~

523°K

0-15

-ff + M '3+ giving ~,,l+~,3+c~2Iv-to.5 -tvx2.5 '~.J4 , 3+ M2+~[]~/3 .± . .~.4 12/3 leading to so-called y - M ~ O 3 defect sesquioxide phase, etc.). The basic binary spinel types are listed in table 2a together with relevant cations and their ionic radii. Additional spinel types derived by substitutions of the basic ones are listed in table 2b. It is seen from tables 2a and 2b that practically any cation with radius within the limits 0.4 to = 1 ~ may be incorporated into the spinel structure and most of them can occur in both octahedral and tetrahedral positions. The smallest cations with valency />4, however, are found in the tetrahedral coordination only, while the large monovalent cations occurring mainly in 6-1 spinels are confined to the octahedral sites. Besides the geometrical factors, the distribution of cations among A and B positions is influenced by many others, as briefly discussed in section 1.5. The interstices available for cations in the spinel structure have radii RA = (u - ~)aX/5- r(O>);

R , = (~- u ) a - r(O2-).

(2)

In table 3, these are compared with corresponding ionic radii as listed in table 2, using the experimental values for a and u. The agreement is satisfactory though a small but rather systematic contraction of the ionic radii, up to a few percent, is observed. On the other hand, a comparison of experimental a and u values with the calculated ones based on the eq. (1) (table 4), where the ionic radii from table 2 are inserted for RA, RB, shows that this contraction concerns the lattice

195

O X I D E SP1NELS

5

J oo

c5 + • eq

0 "0

.x. ~

~

+

~

•

~

c~

.. spinel and olivine-->phenacite transformation, respectively. The thermodynamic relations among olivine, spinel and phenacite structures in silicates and germanates are discussed by Navrotsky (1973a, b, 1974, 1975), Navrotsky and Hughes (1976) and Reinen (1968). The AG values for both groups of oxides are shown in fig. 6. With large cations, e.g., large divalent cations (Ca 2*, Ba 2+, etc.) in M2+M~>O4, the spinel structure becomes also unstable and other structures (hexagonal) appear. The mutual relations to spinel have not yet been established. Hitherto no attention was paid to the chemical stability of the oxide spinels against the oxidizing or reducing influence of the atmosphere. This may be justified if the incorporated cations have fixed valencies that cannot be changed

OXIDE SPINELS

F .

.

.

.

.

199

.

i~Geq [co~Geq jn2Geq I L

. . . . .

,Fe~SJO~ iI A+~'

•

'

. . . . . 1 ' N~S~Oj ' Z ISjO ; , , ylic%j ', ,In92vq ', l'J I'---~---~' ' , f ~ ~ ',n~2sJq', . . . . .

J

L

. . . . .

3

I

L. . . . F . . . . .

"

31

I

z~Geq! L . . . . .

A

Temperature Fig. 5. Phase relations between spinel, olivine and phenacite; after Navrotsky (1973). i

i

i

i

,

,

Hg 16

14

~9

~8

I

-I0

I

-8

-6

I

-4

I

I

-2

0

Germanates a G ~kcaL/moLJ Fig. 6. Gibbs free energy of transformation olivine-spinel in germanates and silicates; after Navrotsky and Hughes (1976).

200

S. KRUPICKA AND P. NOV/~d~ TABLE 6 Valencies and ground states of 3d" ions. Number of 3d electrons

Valency

0

1+ 2+ 3+ 4+ 5+ Ground term

1

2

3

4

5

6

7

8

9

10

Cr Mn Fe

Mn Fe Co

Fe Co

Co Ni

Cu

Cu Zn

Ti V

V Cr Mn

Ni

Sc Ti V

Ti V Cr

1S

2D

3F

4F

69

58

5D

4F

3F

2D

IS

within wide limits of the oxygen pressure. In the case of transition metal ions, however, this certainly is not a plausible approach, because these ions usually exist in several valency states (see tables 2a and 6). As a consequence the thermodynamic stability has then to be considered for both the crystal and gaseous phases in mutual contact. This leads to definite deviations from chemical stoichiometry of the ideal spinel depending on both the temperature T and the partial oxygen pressure Poz. If this deviation exceeds some critical value (depending on T and po~) the spinel structure may become unstable. The situation is illustrated in figs. 7 and 8. Note that in air the transition metal oxides with spinel structure melt often incongruently, which makes it difficult to prepare single crystals of an arbitrary composition from their own melt. Also the fact that at a given temperature the spinel of a definite composition is in thermodynamical

i

~~'~4~

600

hematite[I o.o 5 3

1400

1200

,pc]

1000

Fig. 7. Phase diagram for system Fe-O (Tretyakov 1967); projection into temperatureiequilibrium pressure of oxygen plane is shown. The heavy lines define the borders of the stability regions of the respective phases. The thin lines are the lines of constant 3' in the formula Fe304+~.

OXIDE

201

SP1NELS

•~

.~~z / o~ " * _

°O~ 0 , reflects the spatial distribution of the electronic cloud (EibschLitz et al. 1966). In the presence of the Jahn-Teller ions (see section 1.6) the local symmetry may be tetragonal in both types of sites. This symmetry splits both the E doublets and T triplets. The latter is split similarly as in a trigonal field, i.e., into a doublet and a singlet. If the symmetry is orthorhombic, the T level is additionally split so that only singlets appear. Note that due to partial disorder (inverse spinels, solid solutions) the local fields often possess fluctuating components with lower symmetries. In early work on d-level splitting in insulators only the effect of electrostatic crystal field was considered. This leads among others to the conservation of the centre of gravity of the split d-levels which makes it easy to determine the crystal field stabilization in terms of 10 Dq (Dunitz and Orgel 1957, McClure 1957). This was frequently used in evaluating the relative preferences of cations for A and B positions in spinels (section 1.5). It appeared, however, that this simple picture is inadequate because it entirely neglects the covalency whose effect has been shown to be of comparable magnitude. Due to covalent mixing of states the centre of gravity of 3d levels is generally shifted upwards, while the energy of the (p, s) valency band is lowered (fig. 10). As a consequence, a contribution to the stabilization energy appears which is difficult to estimate (Goodenough 1963, Blasse 1964).

204

S. KRUPICKA A N D P. NOV/kK

e-,

..,.d ©

~

cq

t.-,

.t::l

II

II

~D

° ° ~', t"q ¢q

¢q

I

I

[

II

II

,...,

t'q

-'T I

E

I

I

I

I

I

I

©

v~

.% +

©.--,

+

+

+

O

~D

% re)

o

I

0"5

~

+

OXIDE SPINELS

205

[~ ~

~.~

t"q

r.i

dd

Z ~5 ~

t"¢3

r¢3

.~

,~

~5

206

S. KRUPICKA AND P. NOV~J( TABLE 8 Trigonal field splitting of energy levels of Cr 3+ and Fe 2+ ions. Parameters v, v' are defined in the usual way: v = (t2gA] Vtrigltzga) - (t2gE[Vtriglt2gE); I)' = (t2gE] VtriglegE). The splitting of the ground state triplet T2g of Fe 2+ is ~v, while for Cr3+ the splitting of 4T 1 is ~'~'I/9+ /)t and that of 47"2is -~v/2 (excited states). Ion Cr3+ Cr 3+ Cr3+ Fe z+

Spinel MgA1204 ZnGa204 Li0.sGazsO4 GeFezO4

o (cm-1)

v' (crn 1)

Ref.

- 200 -650 -400 - 1145

- 1700 -1100 2400

1 2 3 4

1. Wood, D.L. et al., 1968, J. Chem. Phys. 48, 5255. 2. Kahan, M.H. and R.M. Macfarlane, 1971, J. Chem. Phys. 54, 5197. 3. Szymczak, H. et al., 1975, J. Phys. C8, 3937. 4. Eibsch/itz, H. et al., 1966, Phys. Rev. 151, 245.

2p 2s

without covaLency

~¢ith covatenoy

Fig. 10. Effect of the covalency on the energy levels of transition metal oxide (schematically). A p r o m i s i n g d i r e c t m e t h o d f o r d e t e r m i n i n g t h e r e l a t i v e p o s i t i o n s of t h e d l e v e l s in A a n d B sites of f e r r i m a g n e t i c spinels s e e m s to b e t h e p h o t o e m i s s i o n m e t h o d c o m b i n e d w i t h t h e m e a s u r e m e n t of e l e c t r o n spin p o l a r i z a t i o n ( A l v a r a d o et al. 1975, 1977).

1.5. C r y s t a l energy, c a t i o n distribution a n d site p r e f e r e n c e s T h e far l a r g e s t c o n t r i b u t i o n to t h e crystal e n e r g y in o x i d e spinels is t h e C o u l o m b e n e r g y of t h e c h a r g e d i o n s ( M a d e l u n g e n e r g y ) :

OXIDE SP1NELS

207 (4)

Ec = -(e2/a)AM,

where e is the charge of electron, a the lattice p a r a m e t e r and AM the Madelung constant. AM m a y be expressed as a function of the mean electric charge qA of the cations in A positions and of the oxygen p a r a m e t e r u. It was calculated by several authors (De Boer et al. 1950, Gorter 1954, D e l o r m e 1958, T h o m p s o n and Grimes 1977b) with slightly differing results. H e r e we give the formula based on the generalized Ewald method used by T h o m p s o n and Grimes (1977b): AM = AM(qA, U) = 139.8 + 1186A, -- 648332, --(10.82 + 412.2A, - 1903A ])qA + 2.609q~,

(5)

where au = u - 0 . 3 7 5 . The dependence of AM on qA for different values of the oxygen p a r a m e t e r u is given in fig. 11. With increasing AM the stability of the spinel increases. Therefore, owing to its dependence on qA, the Coulomb energy will generally play an important role in the equilibrium distribution of cations among A and B positions, even though in some cases other energy contributions may become important. The Born repulsion energy is difficult to estimate in a direct way and it is usually deduced from the simple oxide data (Miller 1959). The polarization energy appears as a consequence of the deformation of the spherical electron cloud of ions in the local electric field in the crystal. A t t e m p t s to calculate it in the classical way lead apparently to an overestimation (Smit et al. 1962, Smit 1968), so that only qualitative conclusions are usually used (Goodenough 1963). In the quantum mechanical picture it is difficult to distinguish this effect f r o m

o~

138LL

o

\pS \

i

0.3F5 0.3F8 0.381

134

- "

0,384 0.38F 0,390

130 -

2 % Fig. 11. Dependence of Madelung constant on the average ionic charge qA of A-site ions for several values of the parameter u.

208

S. KRUPICKA AND P. NOV.Ad(

covalency. The last relevant contribution is the ligand field energy treated in the preceding paragraph. As already mentioned in section 1.2, the spinels may have various degrees of inversion, according to the formula MaM~-a [M>aM~+a]04. If the energy difference for two limiting cases 6 = 0, 8 = 1 is not very large, we expect the distribution of cations to be random at high temperatures (i.e. 6 = ½) due to the prevailing influence of the entropy term - T S in the free energy. When the temperature is lowered, the spinel tends to be more or less normal or inverse depending on the sign and amount of energy connected with the interchange of cations M, M' in different sublattices. The equilibrium distribution is determined by the minimum of the Gibbs free energy, i.e., dG dH d6 - d ~

dS T~=0.

(6)

If we restrict ourselves to the configurational entropy of cations and supposing total randomization in both sublattices, S may be approximated by S = Nk[-8

In 8 + 2 ( 6 - 1) l n ( 1 - 8 ) - (8 + 1) 1n(6 + 1)].

(7)

Defining further AP = d H / d 6 we find

8(1 +

6) _ exp(-AP/RT)

(l - 8) 2

(8)

which determines the equilibrium value 6 at the temperature T. Generally, Ap depends on 8 and frequently a linear expression A p = 14o + 1-116

(9)

is being used to describe the experimental results (fig. 12). Here, H0 and H0 +/-/1 may be interpreted as energies connected with the interchange of ions M, M' from different sublattices in the case of completely inverse and normal distribution, respectively. It may be shown that the linear dependence (9) is obtained when the short-range interactions between pairs of ions are considered (Driesens 1968). Sometimes, an entropy term - T S o is added to the exponent in eq. (8) (Driesens 1968, Reznickiy 1977). The representative values of /-/0, H1 are given in table 9. When Ap ~< 5 kcal/mol, a mixed type spinel is usually observed; otherwise the energy difference between normal and inverse structure is sufficient to attain the one o r the other in practically pure form. The achievement of the equilibrium depends on the rate of cation migration. As this is a thermally activated process, the time constant changes exponentially with temperature and if T ~< 500 K, the

OXIDE SPINEI~

209

o.J +8

o

Ng Fe20~

o

0

0.2

I

FO0

J

f

~

I

900

~

o

1100

13~00 r ~

Fig. 12. Dependence of the degree of inversion 6 on temperature. Data for MgFeaO4 are taken from Pauthenet and Bochirol (1951) (A), Kriessman and Harrison (1956) (rT), Mozzi and Paladino (1963) (©) and Faller and Birchenall (1970) (+), those for MnFe204 are from Jirfik and Vratislav (1974). The full lines correspond to formulae (8) and (9) with Ho, H1 given in table 9. For MnFe204 also the time t, necessary for establishing the equilibrium distribution of ions at given temperature, is shown.

•m i g r a t i o n b e c o m e s t o o slow to allow any o b s e r v a b l e c h a n g e in cation d i s t r i b u t i o n . S o m e t i m e s , t h e t e m p e r a t u r e d e p e n d e n c e of t h e m i g r a t i o n r a t e is so s t e e p that, d u e to t e c h n i c a l r e a s o n s , t h e 6 v a l u e s can b e v a r i e d o n l y in n a r r o w limits. This is t h e case, e.g., of t h e M n - F e spinels (Simgovfi a n d Simga 1974). T h e ~ v a l u e s a r e usually d e t e r m i n e d by diffraction m e t h o d s ( B e r t a u t 1951, Jirfik a n d V r a t i s l a v 1974), m e a s u r e m e n t s of t h e s p o n t a n e o u s m a g n e t i z a t i o n ( P a u t h e n e t a n d B o c h i r o l 1951), o r by M 6 s s b a u e r effect ( S a w a t z k i et al. 1969). It is i m p o r t a n t to r e a l i z e t h a t t h e e n e r g y A P c o n c e r n s t h e crystal as a whole. T h e m a i n c o n t r i b u t i o n s to A P c o m e f r o m t h e M a d e l u n g e n e r g y (4), B o r n r e p u l s i o n e n e r g y ,

S. KRUPICKA AND P. NOV~K

210

TABLE 9 Values of H0 and H1 for some spinels. Spinel MgFe204 MnFe204 MgMn204 NiMn204

T (K) 573-1473 603-1443 T < 1050 298-1213

g 0.1 < 0.763< 0.78 < 0.74
--MB(O)/MA(O) and/3 > --MA(O)/MB(O). In other regions of the (c~/3) plane the simple theory predicts one or both sublattices to be unsaturated (partly or fully disordered). This conclusion has proved to be not correct due to the oversimplifications included in the model: (1) only two sublattices were considered instead of 6 (six cations in the primitive cell), and (2) the magnetic moments in each sublattice were a priori assumed to be parallel. The removal of the restriction (1) by Yafet and Kittel (1952) led to the so-called triangular arrangement (fig. 18(b)) in which the spins in one of the sublattices (say B) are canted and divided into two groups B1, B2 with opposite canting angles; the corresponding sublattice magnetization MB = MB1 + MB2 is then antiparallel to the spins in the other sublattice A. This configuration should have replaced the Ndel solution with one sublattice unsaturated. As shown by Kaplan (1960) and Kaplan

OXIDE SPINELS

223

/'4B

Ns

"K "~5

~g Of

c~p = i

/

~ y~///~/////////,, .

/

/

Paramagnetic region

Subtattice B unsaturated

Fig. 19. Division of (aft) plane into regions with different magnetic behaviour. For the ordered regions the type of the M ( T ) dependence is indicated. et al. (1961), h o w e v e r , it d o e s not r e p r e s e n t a state with m i n i m u m e x c h a n g e e n e r g y in cubic spinels, w h e r e o t h e r m o r e c o m p l e x c o n f i g u r a t i o n s of t h e spiral t y p e p o s s e s s i n g l o w e r e n e r g y exist (fig. 20). In t h e i r t h e o r e t i c a l study, which is u p to n o w t h e m o s t c o m p l e t e o n e c o n c e r n i n g t h e g r o u n d s t a t e m a g n e t i c c o n f i g u r a t i o n in spinels within t h e classical limit, e v e n r e s t r i c t i o n (2) was r e m o v e d . O n t h e o t h e r h a n d t h e A - A i n t e r a c t i o n s w e r e n e g l e c t e d a n d only n e a r e s t n e i g h b o u r inter-

U

8/9 2 o E

4

6

8

~I/E ' .......... I

10

12

14

,

EL Ua I

-20

K,TTEC

-60

-

80

LOWER BOUND

~

~

~

'

~

~

~

~

Fig. 20. Dependence of the normalized energy ~ = E / J ~ S A S B N of various spin configurations in spinel on the parameter u = 4JBBSB/3JABSA; after Kaplan et al. (1961).

224

S. KRUPICKA AND P. NOVfid(

actions were taken into account. They also found an improved criterion for the stability of the N6el configuration as expressed by the critical value uo = ~ of a single parameter u = 4JBBSB/3JABSA describing the relative strength of the B-B and A - B interactions. For u t> u0 the collinear structure is expected to change continuously into a ferrimagnetic spiral (fig. 18(d)). Nevertheless, the Yafet-Kittel type configurations may become stable in tetragonally deformed spinels (Mn304, CuCr204). Note that in this case 5 generally different exchange integrals between nearest neighbour cations have to be considered (including JAA which is usually taken ~0). Even the collinear ferrimagnet may become canted under the influence of a strong magnetic field whose torque is sufficient to compete with the exchange torques. The effect was theoretically studied in the molecular field approximation (Tyablikov 1956, Schl6mann 1960) and it was found that two critical fields Ha = n ( M B - MA), /-/2 = n(MB + MA) exist so that the overall magnetization M is constant and equal to ]MB- MA] for H < Ha and equals MA + M~3 for H > H2. In the intermediate region M linearly increases with H. As the molecular fields are rather high for most of the ferrimagnetic spinels, this effect is expected to become observable only in the region of the compensation point, i.e., when MA --~MB.

2.3. Magnetic ordering: experiment The results included in this section are mostly based on direct neutron diffraction determinations of the magnetic structure and completed by magnetic measurements.

2.3.1. Spinels with one magnetic sublattice only If only the A sublattice is occupied by magnetic ions, an antiferromagnetic arrangement appears in all known cases. As JAA is small, the corresponding N6el temperature, TN, is l o w (table 17). Two sublattices A1, A2 with mutually antiparallel spin alignment were found to be identical with the crystallographical ones (section 1.1) (Roth 1964). The situation for spinels with magnetic ions in the B sublattice only is more complex. As pointed out by Anderson (1956) the octahedral sublattice possesses a peculiar topology which prevents a long range order to be stabilized by nearest neighbour (n.n.) antiferromagnetic interactions only. Hence the interactions between more distant ions have to be considered. A number of different arrangements may then appear as discussed by Plumier (1969), Aiyama (1966), Akino and Motizuki (1971) and Akino (1974). The complexity may be somewhat reduced if the symmetry of the crystal structure is lowered either by the cooperative Jahn-Teller effect or due to the magnetic interactions. Note that large single ion anisotropy of some ions (Co >, Fe E+, Ni 2+) may strongly influence the resulting magnetic structure; this is believed to be the case, e.g., for normal 4-2 spinels G e 4+ [M2+]O42-, M = Fe, Co, Ni (Plumier 1969). In few cases the ferromagnetic ordering occurs. Only typical examples with magnetic ions in B sublattice together with the relevant data are listed in table 18.

O X I D E SPINELS

225

T A B L E 17 Spinels with magnetic ions in the A sublattice only. The A - A interactions seem to be enlarged by the presence of the transition metal ions Co 3+, Rh 3+ in the B sublattice even though their spin is zero. Spinel

Tr~ (K)

Mn2+Al~+O4 * Mn2+Rh~+O4 Fe2+A13+O4* . Co2+Al3+O4 * Co 2+Rh 32+O4 Co2+Coz3+O4 Ni2+Rh3+O4 CuZ+Rh~+O4

6 15 8 4 27 46 18 25

~ga(K)

-25

- 30 -50 -20 -70

Ref. 1 2 1 1 3 2 2, 3 2

* 5 to 15% inverse spinel. 1. W.L. Roth, 1964, J. Phys. Rad. 25, 507. 2. G. Blasse, 1963, Philips Res. Rep. 18, 383. 3. G. Blasse and D.J. Schipper, 1963, Phys. Lett. 5, 300.

T A B L E 18 Spinels with the magnetic ions in the B sublattice only.

Spinel Mg2+[Cr~+]O4

Crystallographic structure

cubic at 10 K, weakly tetragonal at 4.2 K cubic at 77 K, Mg2+ [ V 3 + ] 0 4 tetragonal at 4.2 K tetragonal Zn 2+[Mn 3+]O4 cubic Zn2+[Fe3+]O4 cubic Gen+[Fe~+]O4 Ge 4+[Ni2+]O4 cubic 4+ cubic C u + [NI•2+ 1/2Mn3/2]O4 Cu +rM~2+ cubic [ N 1/2Mn 4+ 3/2J10 4

Magnetic structure

TN or Tc (K)

Ref.

complex antiferromagnet

-350

14

1

antiferromagnet

-750

45

1

antiferromagnet complex antiferromagnet antiferromagnet antiferromagnet ferromagnett ferromagnet

-450 -50 - 15 -6 -20 -75

200* 9 10-11 15 150 57

2 3 4 4, 5 6 6

* Different N6el temperature TN = 50 K was reported in ref. (7). t Magnetic moments of Ni 2+ antiparallel to the Mn 4+ moments. 1. 2. 3. 4. 5. 6. 7.

~9a (K)

Plumier, R., Theses, Paris 1968. Aiyama, Y., 1966, J. Phys. Soc. Jap. 21, 1684. K6nig U. et al., 1970, Solid State Commun. 8, 759. Blasse, G. and J.F. Fast, 1963, Philips Res. Rep. 18, 393. Bertaut, E.F. et al., 1964, J. Phys. (France) 25, 516. Blasse, G., 1966, J. Phys. Chem. Solids 27, 383. Gerard, A. and M. Wautelet, 1973, Phys. Status Solidi a16, 395.

226

S. K R U P I C K A A N D P. N O V i ~ K

2.3.2. Spinels with magnetic ions in both subIattices The A - B interaction was always found to be antiferromagnetic. For many inverse or almost inverse ferrospinels this interaction is predicted to be strong (table 14b) and, accordingly, a collinear ferrimagnetism is expected to appear (section 2.2). This was confirmed experimentally-representative data are given in table 19. T A B L E 19 Examples of spinels with the collinear ferrimagnetic spin arrangement. riB(A) System

nB(B)

nB

theor,

neutrons

theor,

neutrons

theor,

neutrons

experiment

Fe3+ [Fe3+Fe2+]O4

5

5

9

9

4

4

4.03-4.2

Fe3+[Ni2+Fe3+]O4

5

5

7

5 (Fe 2.3 (Ni3+) 2÷)

2

2.3

2.22-2.40

Fe3+ [Li~.sFe~]O4

5

-

7.5

-

2.5

-

2.6

Mn0.98Fez0204*

5

4.99

9.74

9.72

4.74

4.73

4.52-4.84

* Partially inverse spinel with 6 = 0.13 (see Jir~ik, Z. and J. Zajf~ek, 1978, Czech. J. Phys. B28, 1315). A s s u m e d ionic distribution M n 2+ 3+ [Mn o. 3+13Fe3+ 2+13] 04. 0.85Feo.z5 1.74Feo.

When the A - B interaction becomes comparable with one (or both) of the intra-sublattice interactions the collinear structure is destabilized and complicated structures with canted spins are observed. Spiral structures were reported in several chromites and Yafet-Kittel-like structures in manganites, vanadates and some chromites (see table 20). In some of these compounds transitions between various spin arrangements have been observed. Note that the non-collinear structures may be also very sensitive to substitutions (Vratislav et al. 1977). T A B L E 20 Examples of spinels with the non-collinear spin structure. nB exp.

Low temperature magnetic structure

2.54

-1.88

Y-K-like structure in the B sublattice

1

2.52 (B1) 2.8 (B2)

1.02

-2.28

spiral in both A and B sublattices

2

2.44

5.88

3.44

0.2

spiral in the B sublattice

3

4.24

2.2

Y - K structure in the 13 sublattice

3

System

riB(A)

nB(B)

Mn304

4.34

3.64 (B1) 3.25 (Bz)

MnCr204

4.3

CoCr204

MnV204

nB N6el

-2.04

-2.74

1. Jensen, G.B. and O.V. Nielsen, 1974, J. Phys. C7, 409. 2. Vratislav, S. et al., 1977, J. Mag. Magn. Mat. 5, 41. 3. Plumier, R., 1968, Thesis, Paris.

Ref.

OXIDE SPINELS

227

A special group is formed by the inverse 4-2 spinels, examples being the titanates M2+[Ti4+M2+]O2 or stannates M2+[Sn4+M2+]O2- (for summary of experimental data see Landolt-B6rnstein 1970). In these compounds the spin moments are compensated at 0 K as far as the arrangement is strictly collinear. Nevertheless, finite magnetic moments may appear due to the unequal orbital contribution of the M 2+ ions in A and B positions. The measurements on ulv6spinel Fe2TiO4 indicate further a possibility of a weak ferromagnetic moment to appear due to a small canting of spins (Ishikawa et al. 1971).

2.3.3. The effect of diamagnetic substitutions In principle, diamagnetic ions may enter either one of the sublattices only, or both, depending on the relative site preferences of the ions present. The diamagnetic substitutions in A sublattice probably represent the most clear-cut case, the Zn substituted ferrites being a well known example. Because of JAA = 0 only the A - B interactions are effectively weakened. If the number of substituted ions is not too high, however, (usually up to 30 or 40%) the overall ferrimagnetic arrangement is not destroyed for T ~ 0 K even though some loosely bound spins may become locally canted or disordered at higher temperatures T < Tc. For larger substitutions the A - B interactions may become comparable to, or even weaker than the B - B interactions. In this way the collinear ferrimagnets often change to canted ones. Both local canting and long-range non-collinear structures were reported (e.g. Piekoszewski et al. 1977, Zhilyiakov and Naiden 1977 and the references therein), the interpretation of experimental results being, however, often controversial. Finally, above a certain critical concentration of diamagnetic ions both sublattices are practically decoupled and only the B sublattice becomes magnetically ordered (usually antiferromagnetically). While the diamagnetic substitution as a rule lowers the ferrimagnetic Curie temperature, the saturated magnetic moment at 0 K may increase. This is shown for Zn substituted ferrites in fig. 21. If the ferrimagnetic order could be retained even when approaching ZnFe204 the magnetic moment at 0 K should increase steadily up to the limit 10/ZB per molecule; the breakdown in the vicinity of 50% substitution may be interpreted in terms of spin canting mentioned above. For a more detailed description the statistical methods (Gilleo 1958, 1960, Rosencwaig 1970) originally developed for diamagnetically substituted garnets, may be used. Diamagnetic substitution in the B sublattice weaken both A - B and B-B interactions simultaneously and hence the collinear ferrimagnetic structure need not be so strongly affected, only Tc is always decreased. The examples often quoted are the A1 substituted ferrites (for experimental data see Landolt-B6rnstein 1970). As the net magnetization in simple ferrites is parallel to the sublattice magnetization MB, the B substitutions lower the saturated magnetic moment and a compensation point (M = 0) may appear. Note that the change in JBB/JAB and MA/MB ratios generally modify the form of the M versus T curve (see section 2.3.4). The lowering of the sublattice magnetic moments found in some neutron diffraction experiments (e.g. K6nig et al. 1969) may be due to the local spin canting.

S. KRUPICKA AND P. N O V ~ K

228

, , / 10

na

..-i~~

..>?.~C';" .-'S:"~JS:"

M

8

o~'g""" ~ o

o~ ' ' ; ' "

o~ . ~ - ' ~ o

% , /o.:>~o/o..~/

°\

\o

co

6

%

",o.

%

Ni"

\

- -

ob

o

ot~

oi~

MFe204

2

o.8

~.o

x

ZnFe204

Fig. 21. Dependence of the saturated magnetic moments of ZnxMl-xFe204 ferrites on x. Data are taken from Gorter (1954) (©) and Sobotta and Voitl~inder (1963) (+).

~"'+'°'~.o.~. X = '0 50 ~ O's

o' experi'men~al + at 90° K o a~ RT

o.. u

%\

J

emulg I 40 i.

o~ %

0--'°-oooQ "O,o\ ° \

so ~ + ° - o . o 0.50

\

%

½

"13.0

0

I

\

,or-----+.. "%. \ ~o4 }I,_ U.O,~/ ,~o,~°--o0.60 % \ \1 ~ ~'0 + ~0~0..~ o

0~0 ~o. o

-----÷000.00.75

'~" 0.~.0 ~ ~

"o,.~

o-~.o.~ ~O_o~O.~

0~--O--o.._o~2oZll ~--+o-o-o-o-o.o_o_o_o:oO~Oo~-/[ + o-o-o-o-o-o~ ~'~'O~o -,0 ~__._~_ ,~ o..O>° / -~-o........... -/ I .._...~.

_

x =/.00

-20 ~ + ' ° ~ 0 ~ 0 ~ 0 " 0 ~ 0

0

0.2

0.4

~_...o/

I

~°~

0.6

0.8

%

1,0

Fig. 22. Temperature dependence of the saturated magnetization of NiFe2-xVxO4 sYstem, after Blasse and Gorter (1962).

OXIDE SPINELS

229

2.3.4. Temperature and field dependences The constraint of antiparallel orientation of the sublattice magnetizations reduces the freedom of the individual m o m e n t s in a collinear ferrimagnet which results in deviations from the normal statistical behaviour as expressed by the Brillouin type t e m p e r a t u r e dependences of MA and MB. The same is of course true for the overall magnetization M = MB -- MA for which the different characteristic types of M = M ( T ) curves were predicted by the N6el theory (see fig. 19). All of these types were found experimentally. In fig. 22 the curves for the system of V substituted nickel ferrites are shown; all 3 types of M ( T ) dependence appear when the V content is gradually increased. A lot of neutron diffraction, M6ssbauer and N M R data are available concerning also the t e m p e r a t u r e course of i

1.0

1.0

-o "-, ~'o

~"

-,.\

0.8

~ % o

MB/M8 (0) 0.8

\~ xo

,xo 0.6

0.6

0.4

0.4

0.2

0.2 i

I

i

o12 o,~ o'6 o.8

~0

't 012 o'.~ o'.6 o18 1.o

7.0

r/rc i

1.0

Msms(# 0.8

-° ~'~o~

",oN,° o\

0.6

k o~ ~\°~ o

0.4

"~"b~'o

0.2

~o

o'.2 o'.4 o16 o.'8

,.o r/re

Fig, 23. Comparison ot experimental and theoretical temperature dependencies of Ms, MA and MB for the Li ferrite (Prince 1965). Full curves were obtained by taking the biquadratic exchange into account. Dashed lines correspond to the simple N6el model with the zero intra-sublattice exchange. Good agreement of the N6el model with the experimental Ms(T) may be also achieved if appropriate intra-sublattice interactions are assumed. Then, however, calculated Ma(T) and MB(T) for 0.4~ T/Tc ~ 0.9 are considerably smaller than those determined directly by neutrons (Prince 1964).

230

S. KRUPICKA AND P. N O V ~ K

individual sublattice magnetization (K6nig et al. 1969, Sawatzki et al. 1969, Prince 1964, Yasuoka 1962). Note that their interpretation in terms of molecular field coefficients usually leads to an overestimation of JAA; this difficulty may be removed, however, when biquadratic exchange is taken into account (see fig. 23). In spinels with non-collinear magnetic structure the canting angle represents the necessary additional degree of freedom for the system of magnetic moments to make their statistical behaviour Brillouin-like (within the limits of molecular field theories). For this it is irrelevant whether the non-collinearity is due to competing exchange interactions or induced by a strong external magnetic field. It holds also for all canted structures that the canting angle depends on the applied magnetic field, even for T ~ 0 K. As a consequence the net magnetization increases with increasing magnetic field even when technical saturation has been reached. This behaviour was experimentally found for many ferrimagnetic spinels possessing non-collinear magnetic structures, such as manganites, chromites and others, including systems with diamagnetic substitutions. Examples are given in fig. 24. Jacobs (1959) analyzed the data assuming a triangular spin configuration. He found for this special case that the increase of saturation magnetization at low temperatures may be related to the molecular field coefficient n/3 for the B-B interaction by the simple equation

AM

=

HintS.

(16)

The behaviour in the paramagnetic region was found to be similar in all ferrimagnetic spinels, and corresponds to the predictions of the N6el theory (eq.

(]4)). 560

[

.

.

.

520 L/" ° ~ ° - - ° - ,~.

.

.

.

°-- °~°~°~°--°

Mn Fe2 0,;

,7F°K

24O 200

za

160 _~/,~.... ~ ~

Zx

~'

~

z~ . . . . - - z a

4.2OK

(Mnj/c,'Aq

120 -I 80

a

[]

o

u~d u~

4.2 K

2'0 ~'o ~'o 8'0 ~'oo ~o ~4o (koe)

Fig. 24. Dependence of the magnetization on an applied magnetic field for three spinel systems (Jacobs 1959, 1960). While there certainly exists a non-collinear spin arrangement in Mn[FeCr]O4 and Mn[Cr2]O4, the spin structure of MnFe204 is not yet unambiguously determined.

OXIDE SPINELS

231

2.4. S p i n w a v e s

The simplest quantum mechanical approach to the ferrimagnetism in spinels uses the two sublattice model (Kaplan and Kittel 1953). As a consequence two magnon b r a n c h e s - o n e acoustical and one o p t i c a l - a r e obtained. An important result of this model is that for small values of the wave vector k, the energy of the acoustical magnons is quadratic function of k, E = if0 + ~ k 2 ,

(17)

with _ 2JAAS 2 + 4JBBS~ - I I J A B S A S B a2 ' 16ISA - 2SB[ where a is the lattice constant, JAA, JBB and JAB are the exchange integrals. The dispersion relation (17) yields the well known r 3/2 dependence of magnetization and specific heat at low temperatures M(T)/M(O)

~- 1 - ~'(3/2)0 3/2 ,

(18)

C~ -~ ( 1 5 / 4 ) k B [ M (O)/ ge~p.B];',(5/2)O 3/2 ,

with 0 = [g~dM(O)]3/2kBr/(4~), M (O) = Nola.B(gASa -- 2gBSB), ge~ = ( g A S A - g B S B ) / I S A - SBI ,

kB is the Boltzmann's constant, gA, gB are the g factors of magnetic ions in A and B sublattices respectively, No is the number of A cations, and ~'(x) is the Riemann ~" function. More sophisticated spin wave calculations in spinels (Kaplan 1958, Kowalewski 1962, Glasser and Milford 1963) take into account that there are six sublattices of cations (section 1.1). Accordingly six magnon branches appear. The quadratic form (17) of the dispersion relation for acoustical magnons still applies and therefore both magnetization and the specific heat should follow the r 3/2 dependence at low temperatures. Experimentally most attention was directed towards magnetite Fe304 where magnon dispersion curves were determined by several authors (Watanabe and Brockhouse 1962, Torrie 1967, G r o u p e de diffussion des neutrons 1970) (fig. 25) using neutron scattering. Some experimental data are also available for M n - F e (Wegener et al. 1974, Scheerlinck et al. 1974), Co (Teh et al. 1974) and Li (Wanic 1972) ferrites. By fitting the spin wave theory to these experiments the exchange

232

S. KRUPICKA AND P. NOV~K 120

~

,

L

,

,

,

,

,

E

/~0v]

1o0 ~

90

* /-+~

50

/

40 %

20

o

-

o .+

o/+

30

10 4

(5)a.a(6)

0/4-

/

I

/ 0.2

&

o'6

o18

a__Eo[ool]

2IF

Fig. 25. Dispersion curves of spin waves in magnetite (six branches). Data taken from Groupe de diffusion des neutrons (1971) (+) and Watanabe and Brockhouse (1962) (©). integrals may be estimated. Both the sign and the magnitude of the inter-sublattice exchange integral obtained by such procedure agree with the expected ones (compare tables 14, 16). The same cannot be said about the intra-sublattice integrals-e.g, the ferromagnetic B-B coupling and rather large values of JAg were found in Fe304. Such contradictory results may be connected either with approximations made in the spin wave calculations (consideration of only isotropic bilinear exchange between nearest neighbours, introduction of effective exchange integrals etc.) or with insufficiency of the G o o d e n o u g h - K a n a m o r i rules. The T 3/2 dependence of the magnetization and specific heat predicted by the spin wave theory was observed in several ferrite systems (Kouvel 1956, Heeger and Houston 1964). An example of the results obtained is shown in fig. 26. Several authors reported the observation of spin wave resonance in single crystal (Ivanov et al. 1972, Baszynski and Frait 1976, Sim~ovfi et al. 1976) and polycrystalline (Gilbart and Suran 1975) spinel ferrite thin films. From the resonance fields the value of constant @ in eq. (17) may be determined. This procedure is somewhat obscured by the unclear way in which the spins are pinned at the surfaces.

OXIDE SP1NELS

233 T(K)

.~

50

(Mc/s) ~

o

100

158

200

'

'

'

800

1ooo

2400

250

3200

4000

r ½ (K3,~) Fig. 26. Temperature dependence of the Mn55 NMR frequency ~ in MnFe204 (Heeger and Houston 1964). ~, is propotional to the sublattice magnetization.

3. Magnetic properties 3.1. A n i s o t r o p y a n d magnetostriction 3.1.1. Introductory r e m a r k s The anisotropy constants are usually defined with respect to the free energy F of the system. For cubic symmetry,

(20)

F = Fo + K l s + K2p + K3s 2 + . • • ,

where 2 2 S = 0/la2-1-

2 2 2 2. 0/10/3"}- 0 / 2 0 : 3 ,

~2 2~2 p = tXl0/2~ 3 ,

a l , 0/2, 0/3 are the direction cosines of magnetization, and K1, K2, K 3 . . . are the familiar anisotropy constants. In addition, expressions corresponding to the tetragonal symmetry and sometimes-also to the orthorhombic one may be relevant to spinels,

F = Fo+ K l a n + K z a ~ + K3(a4+ 0 / 4 ) + . . .

(tetragonal),

(21) F = Fo + K l a ~ + K ~ ( a ~ - 0/~) + . • •

(orthorhombic).

There are several complications connected with such definitions of anisotropy constants. First, as a rule, the anisotropy is determined from measurements at constant temperature and external stress so that the experimentally determined K 1 , / £ 2 . . . refer to the Gibbs potential and not to the Helmholtz free energy. The difference between the two sets of constants is due to the magnetostriction. The

234

S. K R U P I O K A

AND

P. N O V / i d ~

detailed analysis as well as the formulae connecting Ki and /£~ are given, e.g., by Carr (1966). For cubic crystals, /£1 =

K1

+ h2(Cll - -

C12) - - 2 h 2 c 4 4 - 3hoh3(C~l + 2 c 1 2 ) -}- " • " ,

(22)

g 2 = K 2 - 3 h l h 4 ( C l l - c12) - 1 2 h 2 h s c 4 4 + • • • ,

where Cll, c12, c44 are the elastic constants and coefficients hi characterize the magnetoelastic coupling. To define hi the Gibbs free energy G is to be expanded in powers of the stress tensor 0-,

(23)

G=Go-A~-½~g~,

g being the elastic compliance tensor. The components of the tensor A are further written as series in powers of m , Ai~ = h0 + hl(O~ 2

- -

1) +

h3s +

h4(o¢ 4 +

2s/3

- 13) + "

",

(24) A i j = h2ofio~j + hsoqce].

The last two formulae yield the definition of the hi. The magnetostriction e in a direction specified by the direction cosines /31, /32, /33 is related to the tensor A through the relation e = ~'~ Aij/3i/3j.

(25)

/,j

Combining eqs. (24) and (25) the connection between the parameters hi, the commonly used magnetostriction constants A100, Aln is established, 3-100= 2 h i 3 ;

/~111= 2h2/3 .

h2

and

(26)

One point to note in eq. (22) is the t e r m - 3 h o h 3 ( c n + 2 c 1 2 ) which corresponds to the contribution of the isotropic strain. This correction depends upon the choice of the unstrained volume, in particular it vanishes if the state of zero volume stress is defined by setting h0 = 0. Some authors take as unstrained volume the volume of a hypothetical crystal with magnetic interactions switched off. Isotropic strain term may then contribute substantially to anisotropy, e.g., for synthetic magnetite Birss (1964) estimated this contribution to be - 2 8 % . The disadvantages of such an approach are: (i) constant h0 may be estimated only indirectly; (ii) it is difficult to determine h 3 with sufficient precision. It seems therefore more convenient to refer the free energy to the volume of the real (magnetized) crystal, in which case the contribution of the isotropic strain vanishes identically. The contribution of the anisotropic strain to magnetocrystalline anisotropy of spinels is, with few exceptions, small. The relevant data for several spinels are given in table 21.

OXIDE SPINELS

235

TABLE 21 Magnetostrictive contribution AK~ to the first anisotropy constant. Temperature (K)

K1 x 10-5 (erg/cm3)

Fe304

300

- 1.1

Li0.sFe2.504

300

-0.9

0.004

300 77

-0.7 5.8

0.053 52

System

(disordered) NiFe204 TiFe204

AK1x 10 s (erg/cm3) - 0.24

The second complication in defining the anisotropy constants is connected with the possible dependence of the magnitude of magnetization on its direction with respect to the crystallographic axes (anisotropic magnetization). Effectively it leads to the dependence of anisotropy constants on external magnetic f i e l d - for a corresponding analysis see, e.g., Aubert (1968). Up to now the experimental results in spinels were analyzed without taking this contribution into account. Finally, note that in the presence of the relaxation effects (section 3.3) the anisotropy measured by static methods generally differs from the one determined by FMR. In the following two subsections the microscopic origin of the anisotropy and magnetostriction will be discussed. A survey of the experimental data will be given in the Appendix.

3.1.2. Microscopic origin: anisotropy The dominant source of the magnetocrystalline anisotropy in spinels is to be sought in the interplay of the ligand field, spin-orbit coupling and the exchange interaction of the magnetic ions. The magnetic dipole-dipole energy may also contribute in tetragonal or orthorhombic spinels. In most cases the single ion model (Yosida and Tachiki 1957, Wolf 1957) is sufficient to describe semiquantitatively the magnitude and temperature dependences of the anisotropy constants K1, K2. In this model the magnetic ions contribute additively to the macroscopic anisotropy effects; their interactions are approximated by effective fields (ligand and exchange) and the anisotropy appears as a result of the dependence o f their individual energy levels on the direction of magnetization. T o deduce the low lying levels (i.e. those which may be thermally populated) the properly chosen effective Hamiltonian is usually used. For ions with orbitally non-degenerate ground states this reduces to the familiar form of the spin Hamiltonian (S ~spin--orbit coupling). The effect of higher order terms is indicated by weak lines.

OXIDE SPINELS

237

with the macroscopic description put forward in section 3.1.1 (i.e. with /(i corresponding to the Gibbs free energy) the terms depending on strains must be added to the Hamiltonian (see section 3.1.3, eq. (30)). Note that averaging over inequivalent sites must be performed when calculating ki(T). In the cases where the Hamiltonian (27) applies the contribution to the cubic first anisotropy constant is (with the F term neglected): kI(T) = at(y) + 7[DE/(kT)]t(y),

(29)

where y = exp[-glzBHex/(kT)], r(y) and t(y) are functions depending on S (Wolf 1957), and 3/ is a constant which equals 4 for ~"--- [111] (four non-equivalent axes) and - ~ for ~--- [100] (three non-equivalent axes). The latter may be, e.g., the case in the presence of the local Jahn-Teller distortions. For T ~ 0

k~(O) = -½S(S - 1)(S - 1)(S - ~)a + 23,S(S - ½)(S - ~)D2/(glXBHex), so that for ions with $ 4 3 the a term does not contribute to anisotropy. The temperature dependence (29) may be fitted to the experimental curve KI(T) to evaluate the constants a, D, gHex (see figs. 28(a) and (b)). On the other hand these values may be compared with those deduced from an independent experiment (most often E P R in doped diamagnetic crystals) or estimated on the basis of the ligand field theory. In many ferrimagnetic spinels, in particular ferrites, the first term in eq. (29) was found to predominate (Yosida and Tachiki 1957, Wolf 1957). The second term becomes important if either S ~~10 5. For lower concentrations of cation vacancies the activation energy is increased from the usual value ~1 eV to ~ 2 eV indicating a more difficult diffusion mechanism. In Ni-Co (Perthel 1962, Glaz et al. 1980), N i - F e - C o ferrites (Michalk 1968) and N i - Z n - C o ferrites (Michalowski 1965) similar effects appear. The induced anisotropy is usually lowered due to fluctuations in the local symmetry which primarily concerns the G term. In table 25 the room temperature values of G and F found for the system CoxNi0.46_xZn0.29Fe22504+ 7 after magnetic anneal at 350°C are compared with those reported for CoxFe3-xO4. Let us note that the coexistence of more kinds of ions yields possibilities for new anisotropic configurations to appear. In Co substituted Li0.sFe2.504 a substantial reduction of the induced anisotropy was observed when the B sublattice becomes ordered (lvanova et al. 1979). In spinels containing both Co 2+ and Co 3+ ions in octahedral sites a preferential T A B L E 25 Constants of induced anisotropy in Co containing ferrites. System CoxFe3-xO4 CoxNi0.a6-xZn0.29Fez2504+~

F (105 erg/cm 3)

G(105 erg/cm 3)

Ref.

101 x 2 0.06 + 100 x 2

92.5 x 7x

1 2

1. Penoyer, R.F. and L.R. Bickford Jr., 1957, Phys. Rev. 108, 271. 2. Michalowsky, L., 1965, Phys. Status Solidi 8, 543.

252

S. KRUPII)KA AND P. N O V ~

occupation of certain positions by Co 2+ may be achieved by the electron transfer between Co 2+ and Co 3+ ions. If the concentration of Co ions on equivalent sites is sufficient for a direct electron exchange Co2+ ~,~-Co3+, the activation energy is low ~ 0 . t e V . This is, e.g., case of cobalt rich C o - F e and C o - F e - N i spinels investigated by Iizuka and Iida (1966)- see figs. 37(a) and ( b ) - or Co 3+ containing Co ferrite (Marais et al. 1970). Low temperature torque m e a s u r e m e n t s would be necessary here to get the full frozen-in induced anisotropy. More often the spinels with low concentration of both Co 2+ and Co 3+ are quoted in the literature (Sixtus 1960, Marais and Merceron 1959, Mizushima 1965). The Co ions are then separated by many other ions, e.g. Fe 3+, so that the electron transfer involves also these ions as intermediary. This results in rather high activation energy up to ~0.6 eV. r

,

,

,

,

J

i

,

i

-o-o- be¢ore rec~ucUon -×-x- al~er ~ o

20

°d,, \°i

15

x

10

~

.\ ,,

'

!

~Z

×

o /

0

~ttl,~.,,.

0.'2

0.'4

O.6

0.8

1.0 X

Fig. 37. The dependence of induced anisotropy on the composition in the system CoxFe3-xO4(Iizuka and Iida 1966). The reduction decreases the concentration of Co3+ ions.

N i - F e and other iron rich spinels

Induced anisotropy and various after-effects were studied in several systems containing Fe 2+ ions usually simultaneously with cation vacancies. Typical examples are iron rich Ni and Mg ferrites including magnetite (Motzke 1962, 1964, G e r b e r and Elbinger 1964, Wagner 1961). In pure magnetite with a slight oxygen excess an induced anisotropy of G type was observed (Knowles 1964) possessing a relaxation time ~ 2 0 s at room t e m p e r a t u r e . This is compatible with the preferential occupation of certain octahedral positions by vacancies. The magnitude and temperature dependence of G may be brought into reasonable agreement with the mechanism of a vacancy dipole-dipole contribution (eq. 34). In a m o r e recent study (Kronm/iller et al. 1974) the corresponding after-effect was shown to be composed of two processes which were attributed to different distributions of Fe 2+ and Fe 3+ around the vacancy. Only recently Brtining and Semmelhack (1979) have also reported F ¢ 0 and directly proportional to the cation vacancy concen-

OXIDE SPINELS

253

tration in their magnetite single crystal. The ratio F / G was practically independent of vacancy concentration ( F / G = ½). In mixed spinels, particularly Ni-Fe and Mg-Fe ferrites, the relaxation spectrum corresponds to two distinct magnetic annealing processes (fig. 38). One of them (observable around room temperature) is similar to that discussed above; in addition to the G term it possesses also an F term proportional to p x ( 2 - x ) , x and p denoting the concentration of Ni 2+ (or Mg 2+) ions and vacancies, respectively. This indicates the active role of vacancy-Ni 2+ pair ordering. The other process with the annealing temperature -300°C was usually found to be of pure F type with F proportional to x2(2- x) 2. It does not depend on p. This points to an ion pair ordering while the role of vacancies is believed to be similar as previously discussed for Co 2+ substituted magnetite, i.e., they increase the diffusion rate and lower the annealing temperature. For historical reasons these processes are usually denoted as III (lower temperature process) and I in the literature. An additional effect (II) lying in the region between I and III and reported in some papers was shown to be due to cobalt impurities. The magnetic annealing spectra of Mn-Fe spinels are a little more complicated (fig. 39) and were discussed, e.g., by Krupi~ka and Vilim (1957), Krupi~ka (1962), Marais and Merceron (1965) and Braginski and Merceron (1962). In particular, an additional effect labeled as IV with lower activation energy was observed below room temperature. It was ascribed to vacancies forming some complexes, e.g., with Mn 3+ and Fe 2+ ions. A similarly positioned induced anisotropy effect was observed in Ti or Sn substituted magnetite and ferrites (Knowles and Rankin 1971, Knowles 1974) where formation of some Me 4+ containing complexes (e.g. Ti4+-Fe 2+ pairs) may influence both the vacancy migration rate and the resulting induced anisotropy. For Ti substituted magnetite the corresponding anisotropy was found to be of G type (Knowles 1974). Let us note that by properly adjusting the concentration of Ti 4÷, Fe 2+ and cation vacancies the effect III may be suppressed so that practically only IV remains (fig. 40); this is important for the ferrite materials design.

1000

f

"~ 800

i

/

~ 1. In spite of a large amount of existing experimental data only few of them which have been obtained on well defined single crystals may be used to draw quan-

262

S. KRUPI(~KA AND P. NOVfid~

TABLE 28 Crystallograplaic and electrical conductivity data for vanadium spinels (after Rogers 1967 and Rogers et al. 1967).

Formula Mn[V2]O4 Fe[V2]O4

Mg[V2]O4 Zn[V2]O4 Li[V;]04

Lattice constant (A)

V-V separation (A)

Activation energy of electrical conductivity (eV)

8.522 8.454 8.418 8.410 -

3.014 2.990 2.974 2.973 2.91

0.37 0.25 0.18" 0.16 metallic*

* single crystal. titative conclusions about the n u m b e r of carriers, their mobility, activation energies etc. The other ones, particularly those related to polycrystalline samples, are to be taken with caution and may be explored mainly in a qualitative way. The discussion of the electronic transfer will be limited to conductivity and Seebeck effect. The evaluation of the Hall mobility is usually difficult due to a large contribution of the spontaneous magnetization for which no reliable theory seems to be available. Moreover, it has been argued that in the case of small polaron hopping which probably is the predominant transport mechanism in ferrites and related spinels no simple relation exists between Hall and drift mobilities (Adler 1968). It is usually admitted that the drift mobility is rather low, ~0.1 to 1 c m W - l s -1 for magnetite and much lower (10 -4 to 10-Scm2V-Is 1) for compositions approaching the stoichiometric ferrites (Klinger and Samochvalov 1977). As a rule, these values are deduced from conductivity or Seebeck effect measurements on the basis of some model, and no reliable independent method has been used for their determination. Even the magnetoresistance experiments though occasionally reported in the literature have not been interpreted from the point of view of electrical transport mechanisms (for a review see, e.g., Svirina 1970). M a g n e t i t e a n d substituted magnetite

The log o- versus T -1 plots for magnetite covering a broad t e m p e r a t u r e region are shown in figs. 45a and 45b. The Hall coefficient and mobility are displayed in fig. 46. At elevated temperatures (1500 K > T ~> Tc = 858 K) magnetite exhibits a semiconductive behaviour with thermally activated conductivity, which may be fitted (Parker and Tinsley 1976) by the formula: ~r = A T -~ e x p ( - q / k T ) ,

(41)

with A = 490 f~-lcm-lK and q = (99-+3)× 10 3eV. Note that eq. (41) can also explain the m a x i m u m in cr versus T observed at ~1100 K. In the vicinity of Tc (usually somewhat below) o- begins to depart from eq. (41); in a certain tem-

OXIDE SPINELS 103

.

.

.

.

102 ooooo-O--o~ o~ o~. 10~

263

250 ~ - p ~

.

"-O~ojO

~ 200

0.0~ 0

~(858K)

. . . . . .

I ~ 1oo~5°r o

O,lS eVJ" X

I0-'

I

. 50

i Lo~/ ternperef;ure transition

10-2

o

°"~t

' 4o0 . .800 ...

12oo (K)00',6

10-3 o

104

\o

10 -5

°~o

10-6 10-7 0

,

,

i2

14

f.o3e~,~o.. /6

18

20 loao/r

22

24

(K-')

Fig. 45a. Conductivity vs temperature for a single crystal of Fe304 (Miles et al. 1957).

-200 I

-205

"-•-210

~o

\2

o...-

o

-215

~o o

-220 o

-225

[! \ '%/ ?

-230

/

'°

o

-235

NO

~°,,o 4 i

r~

2

- ~ o - o - o . ~

3

4

-240

1ooo/T (K-~) Fig. 45b. Resistivity vs temperature for several specimens of magnetite (Parker and Tinsley 1976); (1) Stoichiometric single crystal, (2) oxygen defficient polycrystalline specimen Fe300.3988, (3) stoichiometric polycrystalline specimen, (4) single crystal according to Smith (1952).

264

S. KRUPICKA AND P. NOV/~K

10~ & i0 ~ (cmalc)

///

10 1

o~

bo

rv

1o-1 lo-2 10-3 O_ o

104 0.50

--0 I

t

I

I

I

i

i

i

E

~u 0.20

(cm2/VS)o 1o o~ 0.05

["

0-. 4 I

0.02 2

I

[

I

IO00/T (K 4) Fig. 46. Ordinary Hall coefficient R0 and Hall mobility/zH vs temperature (Siemons 1970).

perature interval it behaves metal-like with negative temperature coefficient and in the vicinity of room temperature it passes a new maximum. At Tv = 119 K magnetite undergoes a phase transition (the Verwey transition ) accompanied by a sudden decrease of conductivity of about two orders of magnitude. Below this it behaves like a semiconductor with a temperature dependent activation energy, at least down to ~10 K. Attempts have been made (fig. 47) to fit the or versus T dependence in this region to Mott's formula; o" = A e x p ( - B / T W 4 ) ,

(42)

derived for variable range hopping (Mott 1969). It was early recognized (Verwey and Haayman 1941) that the transition in magnetite at 119 K is connected with some kind of electronic charge ordering and a model was proposed for it based on regular arrangement of Fe 2+ and Fe > ions in rows parallel to [110] and [110] directions, respectively (Verwey ordering). The more recent models, partly based on new neutron diffraction, NMR and M6ssbauer data either abandon the presumption of definite ionic valencies (Cullen and Callen 1973) or correspond to more sophisticated ordering schemes of Fe 2+

OXIDE

265

SPINELS

~

T(K) n

2

n

I

I

n

I

o0%0

0

%%

o

.t%o

-2

"to

%

E

o

,o, %

t~ -6

'oo

c3

oI

-8

q

-10

o

-12 %

-14

~o

\%%o OoooO

O.2

Oi3

0 .'4

0'e 05 T@ (K)@

Fig. 47. log cr as a function of T -1/4 for Fe304 single crystal, after Drabble et al. (1971).

and Fe 3+ (Hargrove and Kfindig 1970, Fujii et al. 1975, Shirane et al. 1975, Iida et al. 1976-1978, Umemura and Iida 1979). These models assign the low temperature phase rather as monoclinic than orthorhombic. It is clear that any model explaining the electronic conductivity in magnetite also has to explain (or at least to be compatible with) the Verwey transition and vice versa. It must also account for the anisotropy of o- below this transition (Chikazumi 1975, Mizushima et al. 1978). The common feature of recent models of conduction in magnetite is the splitting of electronic 3d 6 levels of Fe2+(B) in the ordered phase by an energy gap of ~0.1 eV; only states below this gap are populated at 0 K because the number of Fe 2+ is half the number of the octahedral sites. The electronic charge transport is then effectuated by carriers either created by thermal activation across the gap or introduced by impurity atoms or oxygen non-stoichiometry. The separated levels are usually supposed to form some kind of narrow subbands that overlap above the Verwey transition. In the simplest case a tight-binding scheme combined with Coulomb repulsion was used which leads to a Hubbard-type Hamiltonian for description of the situation (Cullen and Callen 1970, 1973, Fazekas 1972). More refined theories include also polaronic effects (electron-phonon interaction) and other short-range energy contributions, included spin correlation and exchange effects (Haubenreisser 1961, Klinger 1975, Klinger and Samochvalov 1977 and ref. therein, Buchenau 1975).

266

S. K R U P I C K A A N D P. N O V A K

Due to the polarization effect upon their surroundings the electrons are usually supposed to be not entirely free to move below the transition and their transfer is described as a polaron hopping process, perhaps except at the lowest temperatures ( Tc the Fe z+ valency states may appear also in the A sublattice which may play a role in changing the character of the conduction process. The effect of small substitution or oxygen non-stoichiometry is twofold: The ordered phase becomes imperfect which lowers the temperature of the Verwey transition and makes it disappear for a certain critical impurity concentration. Besides, the ratio [Fe2+]/[Fe3+] is changed which introduces carriers into one of the split subbands (holes into the lower filled band or electrons into the empty higher one depending on the kind of impurity). In fig. 48 the thermopower versus temperature is plotted for single crystals with various degrees of oxidation. The

"~l

40

-40g

~"

-oi ~/,~ l

•

•

I

...

-

Ill

I,IIII

~-~,~

•

"

C

_,of \O.o/ o/ -200

/

'

"o

eo

s2o

1so

200

2~o

80

I2o

T(K)

Fig. 48. Absolute thermoelectric power vs temperature; after Kuipers (1978). (a) Experimental data for various magnetite single crystals. T h e lines are only meant as a guide to the eye. T h e vacancy concentration decreases from A to E. (b) Calculated values according the model of Kuipers and Brabers (1976), T denotes the cation vacancy concentration per formula unit.

OXIDE SPINELS t

,

i

267

,

,~ x : 8 . 1 0 -3 x x=3xlO v

-3

×=O

+ x' = 10 -4

0

~: : 1 0

"a

o x : 4 x l O -4 ,,?

\;:4T2g(4G) 6A1(6S) ~ *ra(4G) 6A 1(6S) ~ *r2(4G) 6A1(65)---)4E, 4Al(4G ) 6Alg(68) ~ 4Eg, 4Alg(4G) 6Alg(6S)-~ 4T2g(4D) 6A1(65) --~4T2(4D)

Site B B A A m B B A

Oscillator strength 2× 2× 8x 1.6 x 3.2 × 2x 1x 6x

10-5 10-5 10-5 10-4 10-s 10-s 10 -4 10-s

Region above 2 e V The spectra in this region are ascribed to charge transfer transitions, the most probable mechanism being the intersublattice transfer (Blazey 1974, Scott et al. 1975, Wittkoek et al. 1975), e.g.,

282

S. KRUPICKA AND P. NOVSd~ (Fe 3+) + [Fe 3+] + hu -+ (Fe 4+) 5~ [Fe2+]

(see fig. 60). Other possibilities are biexciton transitions, i.e., simultaneous crystal field transitions in both sublattices with AStor= 0 (Blazey 1974, Krinchik et al. 1977) or charge transfer between 02- and Fe 3+ (fig. 60). But the oscillator strengths depending on Fe 3+ concentration and the fact that the diamagnetic dilution in any sublattice influences all absorptions (Krinchik et al. 1979) indicate the first model involving [Fe3+]-(Fe 3+) pairs is correct. At still higher energies (above 3-4 eV) also orbital promotion ( 3 d ~ 4s) or interband (2p ~ 4s) transitions become important.

Magnetooptical effects Unfortunately there are only scarce experimental data on spinels which can be directly compared with the above conclusions. One of them is the Li ferrite, studied by Malakhovsky et al. (1974) and Vigfiovsk~ et al. (1979, 1980a, b). The other ones are Mn-Fe spinels including magnetite, systematically investigated by Simga et al. (1979, 1980), and Ni and Co ferrites studied, e.g., by Kahn et al. (1969), Westwood and Sadler (1971), Krinchik et al. (1977, 1979) and Khrebtov et al. (1978). On the other hand, the assignment of various transitions can be often supported and completed on the basis of the magnetooptical data. They include the Faraday rotation - mainly in the near infrared (up to 1 eV) and both polar and transversal Kerr rotations above l e V . Actually, many of the references given above are partly or fully devoted to the magnetooptical studies. Sometimes also the reflectance circular dichroism has been examined from which both Faraday and Kerr rotations may be calculated (see, e.g., Ahrenkiel et al. 1974a, 1975). All magnetooptical effects are intimately related to the off-diagonal elements of the dielectric tensor function; both diagonal and off-diagonal elements are complex so that besides the index of refraction and absorption coefficient two additional independent measurements are necessary for determining the whole dielectric function (e.g. Kerr rotation and Kerr elipticity). Examples of the magnetooptical spectra of Li0.sFe2.504 and some other simple ferrites as compared with those of YIG are given in figs. 64(a) and (b). The spectral dependences are similar but the sign of rotation in spinel ferrites opposes that in YIG due to the opposite mutual orientation of sublattice and total magnetizations in both types of materials. As the magnetooptical effects depend on both diagonal and off-diagonal elements of the dielectric tensor function their strengths (magnetooptical activity) generally does not simply correspond to the oscillator strengths of the underlying optical transition. In order to obtain large magnetooptic effects the transition has also to be highly circularly polarized. An example of strong magnetooptical activity are spinels containing Co 2+ in A positions (Ahrenkiel et al. 1974b). This has been ascribed to the crystal field transitions 4A2(F)--+ 4T2(F ) and 4A2(F)--+ 4TI(P ) of CO2+(A). In fig. 65 the spectral dependence of the reflectance circular dichroism for some of such spinels measured on polycrystalline layers are shown.

OXIDE SPINELS

283

200 Io/°

.o.o.t_e.o-m-- o----re.

,,:,~.~"

~gFe, o~

,%0

E

-200

-400 c_

,,'/

iJ "o/ /

T = 300°K • o experimenf.a~

--

calculated

~- - 6 0 0

,i -800 a

~

- 100~

,~

~-

~

'

~,avel.eng~.h X (~m)

i

i

O.04

i r.,~,

b

i •" i ; ',,. i ' "',,o~..~,,'-. ,

:d !

~

....":":: '~

i

i

\~ .~ / . , . / - E; L F "~.J ~.-- :,, y/:. ~:/~ ~' /

i

~;

"£

~'J

.

"

..

,. ...... ...... f"

•

..~ ,' /

C; Y / G ~ '

" ' iI

2

.

',.0....'!, \ :, : ,,'I ',, ,. "../'"..... \ "~" ,' / ' , ~'x ." -~;z_~_J;( ;.~- \ :'.-.Z.g '- .>q

-0.04

b

.

: "

i

y". .

-I'

r.

•-~

i

~-

"/ ,.

4

....

-

' Ie

~ phol;on energy (eV)

Fig. 64. Comparison of magnetooptical behaviour of Fe spinels and YIG. (a) Faraday rotation in near infrared (Zanmarchi and Bonders 1969). (b) Spectral dependence of the complex off-diagonal element for YIG and Li ferrite (Vi~fiovsk~) et al. 1979b).

S. KRUPI(~KA AND P. NOV/~d,~

284

~

~

T - - T - - T - - r - -

4

20

~

ReD (%)

Rco(o/o)

_ _ Co Rh, 5 Feo 50,; j ' .

12

2 ,,

,,

0

0 l

-4

-e ,,,,

\

ll~l

0.6

- 12

0.8

~

[0

1.2

~

1.4

~

¢.6

~

1.8

-20

Fig. 65. Reflectance circular dichroism of CoRhl.sFe0.sO4 and CoCr204 at 80 K (Ahrenkie] and Coburn

1975).

4.2. Mechanical and thermal properties 4.2.1. Infrared spectra The first important paper on the infrared spectra of spinels was published by Waldron (1955). To explain the experimental data obtained for seven ferrite spinels Waldron refers to a rhombohedral unit cell containing only 14 ions (for a normal spinel MFe204 it consists of two MO4 tetrahedra and one Fen tetrahedron). Four modes were found to be infrared active. Two of them, having the higher frequency, were supposed to arise from the motion of the oxygen ions, the remaining two were assigned to the motions of the cations only. Group theory, taking the full cubic crystallographic unit cell into account, was applied to the vibrational problem by White and De Angelis (1967) and by Lutz (1969). Waldron's conclusion that only four modes are infrared active in an ideal normal spinel was proved to be right, the origin of modes was, however, found to be more complex. Very thorough experimental investigation of infrared spectra of normal spinels, performed by Preudhomme and Tarte (1971a, b, 1972) confirmed the complexity of the problem. Typical infrared patterns for normal 2-3 spinels are shown in fig. 66, the observed frequencies are summarized in table 32. It is to be mentioned that Grimes (1972b) suggested an entirely different explanation of infrared spectra of spinels based on the two-phonon processes. The calculation of the force constants of thiospinels was performed by Brtiesch and D'Ambrogio (1972), Lutz and Haueuseler (1975) and Lauwers and Herman (1980). The last authors made corresponding analysis also for MgA1204 and ZnGa204 spinels. When the symmetry of the spinel structure is lower than cubic or/and supplementary ordering of cations exists, more infrared bands may appear (White and De Angelis 1967). A splitting of one infrared band is observed in some spinels containing octahedraUy coordinated Jahn-Teller ions Mn 3+ and Cu 2+ (table 33). It is to be noted that the bands may be split also due to the presence of two different kinds

OXIDE SP1NELS i

i

i

i

i

285 i

i

~

i

80 60 o~ 40 20 4° #_

_

i

__

8O 60 40 20

80 60 40

Zn Fe2 04

20 800

'

600

4bo

Cm-1

' 2bo

Fig. 66. Typical infrared patterns for three normal 2-3 spinels (Preudhomme and Tarte 1971b). of ions in the same sublattice. Such a splitting exists, e.g., in the system ZnAlxCr2-xO4 ( P r e u d h o m m e and Tarte 1971b). 4 . 2 . 2 . JUlastic c o n s t a n t s

There are only few spinels for which all the elastic constants are known. Corresponding values at room temperature together with the anisotropy factor A = 2 c 4 4 / ( c l l - cl2) are summarized in table 34 (for an isotropic material A = 1). It is seen that NiCr204 and to some extent TiFe204 differ markedly from other spinel systems as far as the elastic constants are concerned. This anomaly is connected with the cooperative Jahn-Teller effect (section 1 . 6 ) - f o r NiCr204 the corresponding critical t e m p e r a t u r e TjT is close to room temperature. In the vicinity of Trr the elastic response of the system is sensitive to the t e m p e r a t u r e - t h e crystal softens (at least to some extent) as TIT is approached. For the system NixZnl_xCr204 this softening is demonstrated in fig. 67. A similar situation exists also in TiFezO4 (see section 3.1.3) and FeCrzO4, the corresponding temperatures TjT are low, h o w e v e r , compared to NiCr204. For spinels which do not contain Jahn-Teller ~ions the elastic constants depend only weakly on the t e m p e r a t u r e (e.g. Kapitonov and Smokotin 1976).

S. KRUPIOKA AND P. NOV~6d~2

286

TABLE 32 Infrared absorption bands of several spinels.

System

Absorption bands (cm-1) /21 v2 /23 iv4

Fe304 NiFe204 CoFe204 MnFe204 ZnFe204 CdFe204 CoCr204 MgAI204 Fe2GeO4 NizGeO4

570 593 575 545 552 548 630 688 688 690

390 404 374 390 425 412 530 522 402 453

268 330 320 335 336 319 402 580 319 335

178 196 181

Ref. 1 1 2 3 4 4 4 4 5 5

166 197 309 178 199

1. Grimes, N.W. and A.J. Collet, 1971, Nature (Phys. Sci.) 230, 158. 2. Waldron, R.D., 1955, Phys. Rev. 99, 1727. Mitsuishi, A. et al., 1958, J. Phys. Soc. Jap. 13, 1236. 3. Brabers, V.A.M. and J. Klerk, 1974, Solid State Commun. 14, 613. 4. Preudhomme, J. and P. Tarte, 1971, Spectrochim. Acta 27A, 1817. 5. Preudhomme, J. and P. Tarte, 1972, Spectrochim. Acta 28A, 69.

TABLE 33 Splitting of the /24 band in three spinels exhibiting the cooperative Jahn-Teller effect (after Siratori 1967). Compound ZnMn204 Mn304 CuCr204

/2~ ,

/22 t

/24 $

c/a

265 cm-1 247 135

167 cm -1 165 194

232 cm -1 220 155

1.14 1.16 0.91

* Stronger line of the split v4. + Weaker line of the split /24' $ Weighted mean of the two lines.

I n t a b l e 35 t h e d a t a o n t h e e l a s t i c m o d u l i a n d t h e c o m p r e s s i b i l i t y m e a s u r e d o n polycrystalline ferrites at r o o m t e m p e r a t u r e are given. W e n o t e t h a t in a n a l o g y t o t h e m a g n e t i c r e l a x a t i o n , a n e l a s t i c r e l a x a t i o n w a s o b s e r v e d in s o m e s p i n e l f e r r i t e s ( G i b b o n s 1957, I i d a 1967) c o n n e c t e d w i t h d i f f u s i o n a n d r e a r r a n g e m e n t p r o c e s s e s in t h e l a t t i c e .

OXIDE SP1NELS

287

TABLE 34 Elastic constants of several spinels (in units of 10-11 dyn/cm) at room temperature. A is the anisotropy factor (see text). System

cx

MgA1204 Fe304 NiFe204 Lio.sFez504 ZnCr204 FeCr204 NiCr204 TiFe204

c~2

27.9 15.3 27.5 10.4 21.99 10.94 24.07 13.41 25.57 14.23 32.2 14.4 17.5 17.1 cu cm = 2.65

c44

A

Ref.

15.3 9.55 8.12 9.29 8.46 11.7 5.86 3.96

2.43 1.12 1.47 1.74 1.49 1.31 24.1 2.99

1 2 3 4 5 6 5 7

1. 2. 3. 4.

Lewis, M.F., 1966, J. Acoust. Soc. Am. 40, 728. Doraiswami, M.S., 1947, Proc. Indian Acad. Sci. A25, 413. Gibbons, D.F., 1957, J. Appl. Phys. 28, 810. Kapitonov, A . M . and E.M. Smokotin, 1976, Phys. Status Solidi a34, K47. 5. Kino, Y. et al., 1972, J. Phys. Soc. Jap. 33, 687. 6. Hearmon, R.F.S., 1956, Adv. Phys. 5, 323. 7. Ishikawa, Y. and Y. Syono, 1971, J. Phys. Soc. Jap. 31, 461.

vt3 f x=O

(krns")

2

?

o.~"

x : 0.37

TN oo• °

J

f

•

x = 0.73

."

e •

F

r.

(X) Fig. 67. Soft mode sound velocity Vt=[(Cll--Cl2)/2p] lj2 as a function of temperature in a NixZnl-xCr204 system. Ta, TN are the critical temperatures for cooperative Jahn-Teller transition and the N6el transition respectively (Kino et al. 1972).

4.2.3. H e a t capacity In f e r r i m a g n e t i c s p i n e l s t h e specific h e a t at l o w t e m p e r a t u r e s ( T < Tc, OD) is d o m i n a t e d by t h e m a g n e t i c c o n t r i b u t i o n . T h e t e m p e r a t u r e d e p e n d e n c e of Cp is t h e n w e l l d e s c r i b e d by t h e spin w a v e t h e o r y , w h i c h p r e d i c t s Cp ~ T a/2 ( s e c t i o n 2.4). A t h i g h e r t e m p e r a t u r e s t h e l a t t i c e c o n t r i b u t i o n ( p r o p o r t i o n a l t o T s f o r

S. KRUPI(~KA A N D P. NOV_,~d(

288

T A B L E 35 Elastic moduli of several polycrystalline ferrites; after Seshagiri Rao et al. (1971).

System

X-ray density (g/cm 3)

MgFe204 CoFe204 NiFe204 ZnFe204

Elastic moduli (1011 dyn/cm 2) E n k

4.52 5.29 5.38 5.33

19.73 17.34 15.59 18.64

7.34 6.54 5.89, 7.27

21.17 16.62 14.69 14.27

/3 × 1013 (cm2/dyn)

Poisson ratio

4.72 ,6.02 6.81 7.01

0.34 0.33 0.32 0.28

T < OD) prevails. An example of the temperature dependence of Cp is shown in fig. 68. In table 36 the values of C. at room temperature are summarized together with the values of Debye temperatures OD deduced from the low temperature measurements. Venero and Westrum (1975) noted that at elevated temperatures the lattice part of Cp for spinels may be well described by Kopp's rule based on the component oxides. For example for normal 2-3 spinels: Cp(AB204) = Cp(AO) + Cp(B203). T(K) 100

200

300

400

40

.-.

i....-- ............

,-"

"-'20

•

_~°~ /

//

/

t

~

,

,~

0

03

I

o"°

: / 0 L-'-'~°

600

mm.m.m"m "ww~m" mrm m m'm''m'm'am~

-~ 30

,o

500

~

10

/"

dO, "~

./ o/°/-Io,I ~o k

,

20

,

3'0

,

T(K)

I

40

Fig. 68. Heat capacity vs temperature for Li0.sFe2.504(O) and Lio.sAlzsO4 (O) (Venero and Westrum 1975).

4.2.4. Thermal conductivity Thermal conductivity is a composite e f f e c t - i n magnetic spinels besides phonons, both electrons and magnons may participate in the transfer of heat. It was shown,

OXIDE SPINELS

289

TABLE 36 Thermal properties of several spinels. Cp

K

ff x 10 6

(K-1)

(cal/K moo

Fe304 NiFe204

36.18 34.81

660 625(7)*

0.015 0.009

CoFe204 MnFe204 CuFe204 ZnFe204 MgFe204 Li0.sFe2.504

36.53

584 (10)*

0.015 0.017 0.015 0.015

MgAI204

Oo (K)

(cal/s cm K)

System

33.22 34.43 27.79

762 (15)* 512(5)

0.015 0.036

8

12 7.5 12 4.61t 5.905

Ref. 1, 5, 6 3, 4, 7, 12 3, 4, 9 8, 12 9 1, 6, 11 4 2, 4, 9, 14 3, 10, 13

* Nonstoichiometric samples. ~ Natural spinel. Synthetic spinel. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Bartel, J.J. and E.F. Westrum, Jr., 1975, J. Chem. Thermodyn. 7, 706. Venero, A.F. and E.F. Westrum, Jr., 1975, J. Chem. Thermodyn. 7, 693. King, E.G., 1956, J. Phys. Chem. 60, 410; 1955, Ibid 59, 218. Kouvel, J.S., 1956, Phys. Rev. 102, 1489. Polack, S.R. and K.R. Atkins, 1962, Phys. Rev. 125, 1248. Smit, J. and H.P. Wijn, 1959, in: Ferrites (Wiley, New York) p. 225. Kamilov, I.K., 1963, Sov. Phys-Solid State 4, 1693. Suemune, Y., 1966, Jap. J. Appl. Phys. 5, 455. Smit, J. and H.P. Wijn, 1954, Physical Properties of Ferrites, in: Advances in Electronic and Electron Physics (Acad. Press, New York) vol. 6, 83. Slack, G.A., 1964, Phys. Rev. 134A, 1268. Weil, L., 1950, Compt. Rend. 231, 122. Bekker, Y.M., 1967, Izv. Akad. Nauk SSSR Neorg. Mater. 3, 196. Singh, H.P. et al., 1975, Acta Crystallogr. A3I, 820. Brunel, M. and F. de Bergevin, 1964, Compt. Rend. 258, 5628.

however, that in spinels the role of m a g n o n s is n e g a t i v e ( D o u t h e t a n d F r i e d b e r g 1 9 6 1 ) - they cause a scattering of p h o n o n s thus r e d u c i n g the t h e r m a l conductivity. T h e c o n t r i b u t i o n of electrons to the heat transfer is b e l i e v e d to be small in spinels (Slack 1962). T h e c o n d u c t i v i t y is very sensitive to the i m p u r i t i e s particularly to the t r a n s i t i o n m e t a l ions with an orbitally d e g e n e r a t e g r o u n d level (fig. 69). I n table 36 the t h e r m a l c o n d u c t i v i t y at r o o m t e m p e r a t u r e for several spinels is given.

4.2.5. T h e r m a l expansion F o r most spinels the t e m p e r a t u r e d e p e n d e n c e of the lattice p a r a m e t e r a m a y b e well a p p r o x i m a t e d by a = ao+ b o T + b~T 2.

290

S. KRUPIOKA AND p. NOVzid
x i> 1 (Brabers et al. 1977); Am is small and negative ( - 5 x 10-6~ ' ~ - o - o _ ~ ; . . . . . .Q,,o-O ~ z ~ / ~ t k . ~~a'~:-.~.~'°--~o ~" o ~ o

-150

~

i

i

250

300

...o.o°

r/~/~ [~ .

i X = 02

l e t ~'-~

~... ~ /o

-I00

,

200

~/~o.~

_ o ~ . x:o.8 b~=o.o

~2~.~o~_o-/o

~= 0.2

~o o..o- ~-o.1 \'o~--o-°"°'...K~ *"~-a~,~ ~,~ I r ~ ' ~ - ¢ /(= 005 "

Fig. 78. Temperature dependence of K1 for MgxFe3 xO4 system (Brabers et al. 1980).

10

4t0.1

0.15

0.2 * 4.2K • 77K

-IO A

,o -20

~

~

~

~

A 300K

~-

" ; i

×

-30 L

t

Fig. 79. Dependence of magnetostrictions Am0, /~111 for MgFe204 on the degree of inversion 8 (after Arai 1973).

296

S. K R U P I C K A A N D P. N O V / k K

•

t"- q'3

r',- oo

oq

t"q t"q

d

),(

~5

z

oq. q3

t"q ,,.~

I

oo'~,

O e'~

I

o

o'3 ~,~

I

~D

I

I

I

I

I

I

X

/'q

u'3 t",,I ~-.a ee3

er~ eel

I

I

I

I

',,O P,-

I

X

q3

P'-

~,o

~

oq

eq I

I

,-.t

_=

o0

;>

I

e,,

.'= E O

?

,-...

¢e3

x~

I

t"'- t"q

~rq.

~5

"O

I

.,o e¢3 e-.

7

02

I

×~ (,.q

c5 I

t",- G', tt~

I

I

I

I

I

]

I

I

r~

o. t"q

I

I

I

I

,...-~ , ~

t'e3 e¢3

¢¢3 ee)

02

o (",,I

'~" 0 ~ e¢3 0'3

O 02 P-,- o o

~ ) tt3 q3 tr3 ~1~

1"-,-

17-,-

tt3 p--

oo

G'~ ©

E

q eq

o .¢)

eq

¢)

2

e~

r)

OXIDE

o

~

SPINELS

u

297

~

0

b

o

0

0

r~

©

u:

x

= -=

oo

r~

d 'E

©

.= :0 0 "O

~

M

~.,~ •

©

'.~

,

~~ ~ ~~ ~:~

~'~

~ ~=~

&

N

eg~e

~e~g

a

~

t---

~

...-k

0

© e.

~ ' - ~ ..~ . ~

..

~

~,o 0

a

~mN

,~

©


SrO-6Fe203 + (0.5 - x) × ½02. Bowman et al. (1969) investigated the formation mechanism of PbM in the PbO-Fe203 system and concluded that PbM is formed through the intermediate compounds of 2PbO-Fe203 or PbO'2Fe203, depending upon the mixing method, the time and temperature of heating. They used two kinds of co-precipitation methods for mixing, in which the aqueous solution of ammonium bicarbonate was added to the solutions containing lead nitrate and ferric nitrate, or lead nitrate and ferric oxide. The co-precipitation method was also used to obtain a high coercivity BaM or

316

H. KOJIMA

1.0 0.8

(b)

\\k\\\\\ M/

' ~

0.6 .o

\/,/,, \/-

0.4

\/

\

\

/

! !

0

! I

/ 'l

1.0

(0) •~ 0.8 (D

>, 0.6

P "

\

/

0.2

\

0.4

z

//. w

"~ 0.2 rr 0

0

400

800

1200

i./411600

Temperoture (°C) Fig. 10. Changes of BaO-5.5Fe203 compact during heating (Wullkopf 1972, 1975): (a) variation of reaction products, F: Fe203, Bc: BaCO3, B: BaO.Fe203, M: BaO.6Fe203, Y: 2FeO.2BaO.6FezO3, W: 2FeO-BaO-8Fe203, Z: 2FeO-3BaO.12Fe203; (b) variation of length L, weight G, grain size D and saturation magnetization M.

SrM by Mee and Jeschke (1963), Haneda et al. (1974a), Roos et al. (1977) and Oh et al. (1978). Furthermore, Shirk and Buessem (1970) obtained a high coercivity BaM from a glass with the composition 0.265BzO3-0.405BaO-0.33Fe203 in mole ratio. They reported that single domain particles can be crystallized in the fast-quenched glass with this composition by the heat treatment under the appropriate condition (see also table 10). A molten salt synthesis utilizing NaC1KC1 for BaM and "SrM submicron crystals with high magnetic quality was proposed by Arendt (1973). Moreover, Okamoto et al. (1975) applied hydrothermal synthesis with ol-Fe203 suspension in barium hydroxide aqueous solution and obtained BaO.2Fe203 crystals, whose space group was reported as P63/m with the lattice parameter of a = 5.160 A and c = 13.811 A. Kiyama (1976) obtained BaO.6Fe203, BaO.4.5Fe203 and BaO.2Fe203 with Fe(OH)3 or FeOOH and Ba(OH)2 under the similar conditions in an autoclave and studied magnetic properties. Single crystals of M compounds were obtained by cooling a nearly eutectic melt (Kooy 1958); under the high oxygen pressure (Van Hook 1964, Menashi et al. 1973); using various kinds of flux (Mones and Banks 1958, Brixner 1959, Linares

F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S

317

1962, Suemune 1972, Aidelberg et al. 1974); or discontinuous grain growth (Lacour and Paulus 1968, 1975). B a - Z n - Y , B a - Z n - W , B a - Z n - Z , B a - C o - Z n - W and B a - C o - Z n - Z etc. were also grown by the flux method (Tauber et al. 1962, 1964, Savage and Tauber 1964, AuCoin et al. 1966, Suemune 1972). BaC12, BaO-B203, BaO-B2Og-PbO, Na2CO3 and NaFeO2 were recommended as a flux for these compounds. Takada et al. (1971) found that topotactic reactions among a - F e O O H or ~-Fe203 and BaCO3 or SrCO3 are effective to obtain a grain oriented specimen. The crystallographic relationships of the materials are ( 100 )~-F~OOH//(0001)~,_F~203//(0001)S~O.6Fe203, [010],,-F~OOH//[11,201a -Fe203//[1010]SrO.6F~203 • Hot press or hot forging processes are also useful to prepare a dense oriented sintered body (St~iblein 1973, Haneda et al. 1974a).

2. M compound A Ba 2+ ion in the M compound, BaO-6Fe203 (BaM), can be replaced partly or completely by Sr 2+, Pb 2+ and a combination of, for instance, Agl++ La 3÷ or Nal++ La 3+, without changing its crystal structure. Substitutions of Fe 3÷ and 02ion in the compound are also possible. In all cases, substituted ions would be chosen to keep electrical neutrality and to have similar ionic radii with the original ions (see table 2; a more comprehensive table of ionic radii can be seen, for example, in the book of Galasso (1970)). BaM was at first the only main constituent of M-type oxide magnet, produced on an industrial scale but TABLE 2 Ionic radii of several related ions (Pauling 1960). Element

valence

r (A)

Element

valence

r (A)

Element

valence

r (4)

Ag AI As

+1 +3 +3 +5 +2 +3 +2 - 1 +2 +3 +2 - 1 +2 +3

1.26 0.50 0.58? 0.46t 1.35 0.96? 0.99 1.88 0.72? 0.63? 0.72? 1.36 0.74t 0.64t

Ga Ge In Ir La Li Mg Mn

+3 +4 +3 +4 +3 +1 +2 +2 +3 +4 +1 +5 +2 - 1

0.62 0.53? 0.81 0.68? 1.15 0.60 0.65 0.80? 0.66t 0.60? 0;95 0.70 0.69? 1.40

P

+3 +5 +2 +3 +5 +3 +4 +2 +5 +4 +3 +5 +2 +4

0.44t 0.35t 1.207 0.76? 0.62? 0.81 0.71 1.13 0.68t 0.68 0.95 0.59 0.74 0.80

Ba Bi Ca C1 Co Cr Cu F Fe

? Ahrens (1952).

Na Nb Ni O

Pb Sb Sc Sn Sr Ta Ti T1 V Zn Zr

318

H. K O J I M A

SrO-6Fe203 (SrM) has more recently taken over some part of BaM. PbO.6Fe203 (PbM) is used only as an additional material for oxide magnet purposes at present (see ch. 7 by Stfiblein for the applications). In the following section the fundamental properties of BaM, SrM and PbM are described. The properties of solid solutions among BaM, SrM and PbM, and substituted M compounds are treated separately in this chapter.

2.1. BaFele019, SrFe12019 and PbFea2019 2.1. i. Crystal struclure Adelsk61d (1938) determined the crystal structures of BaM, SrM and PbM, prepared by heating co-precipitated mixtures from the solutions of nitrates. Figure 11 is a perspective drawing of BaM. The 02 ions form a hexagonal close packed lattice, so that its layer sequence perpendicular to the [001] direction is A B A B . . . or A C A C . . . as is shown in the figure. Every five oxygen layers, one O 2 ion is replaced with Ba 2+, Sr 2+ or Pb 2+ in BaM, SrM or PbM respectively and this occurs due to the similarity of their ionic radii as given in table 2. Five oxygen layers

(15) (12)

(11)

A

(10)

C

(9)

A

(8)

C

(7) (6)

B

{5)

(4)

(3) (2)

Fig. 11. Perspective illustration of BaO.6Fe203.

FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES

319

make one molecule and two molecules make one unit cell. Each molecule shows 180° rotational symmetry around the hexagonal c-axis against the lower or upper molecule. The O z- layer containing Ba 2+ is a mirror plane, being perpendicular to the c-axis. Fe 3+ ions occupy the interstitial positions of the oxygen lattice. The space group of the compound is denoted as P63/mmc (D4h) using H e r m a n n Mauguin's (Sch6nflies') symbols. Figure 12 illustrates more clearly the layer structure of BaM, where z means the layer height along the [001] direction and the layer numbers are the same as in fig. 11. Explanation of the symbols used in the figures are also given here. Wyckoff's notations are adopted for every site in the crystal (Henry and Lonsdal 1952). The positions of each atom are tabulated in table 3 (Galasso 1970). Figure

~ (6) 0.45

C~) 0 -2 {12) 0,95

ion

(~) Be2+ ion

Fe3+(4f2)IOctahedral site (5) 0.35

(11) 0,85

(~ Fe3+(2o)J

T

141 0.25

clot 0.75

~

(~ Fe3+ under the layer Lt~ Fe3+ above the layer T relative orientation of magnetic moment

(5) 0.15

(9) 0.65

(2) 0.05

(8) 0.55

(I) Z=O

(7) 0.50

(13) 1.00

Fig. 12. The layer sequence of BaO.6Fe203.

320

H. KOJIMA TABLE 3 Atomic positions of BaFe120~9 (see fig. 12) (Galasso 1970).

Ion 2Ba 2+

24Fe 3+

3802-

Site

Coordinate

x

z

-

0.028 0.189 -0.108

2d 2a 2b 4fl 4f/ 12k

I, 2, 2; 2, ½, ¼ 0,0,0;0,0,1 0,0,¼;0,0, 3 )l I ±(½, 2, Z; 2, 5,Z ~q_ 1 ___(1, 2, z ; 2, 3,1 ~+z) +(x, 2x, z; 2x, x, Y.; x, 2, z; x, 2x, l - z; 2x, x, ½+ z; £, x, ½+ z)

0.167

4e

+(0, 0, z; 0, 0, 1+ z) 1 2 2 ±(3, 3, z; ~, ½, ½+ z) ±(x, 2x, ¼; 2x, x, 3; x, g, ¼) --+(x, 2x, z ; 2x, x, 2 ; x, 2, z; x, 2x, ~1- z; 2x, x, ~+z; £, x, 1+z) 1 1 1 ±(x, 2x, z ; 2 x , x, 2;x, 2, z ; x , 2 x , ~ - z ; 2 x , x , ~ + z ; x , x , ~ )

0.186 0.167 0.500

4f 6h 12k

-

--

0.150 -0.050 0.050 0.150

13, t h e (110) s e c t i o n of B a M , is a n o t h e r e x p r e s s i o n o f t h e c r y s t a l s t r u c t u r e , s h o w i n g a t o m s a n d s y m m e t r y e l e m e n t s in a m i r r o r p l a n e c o n t a i n i n g t h e c - a x i s ( B r a u n 1957). S a n d R a r e t h e b u i l d i n g b l o c k s of t h e crystal, a n d S* a n d R * i n d i c a t e t h e b l o c k s , o b t a i n e d by r o t a t i n g S a n d R t h r o u g h 180 ° a r o u n d t h e c-axis, as p r e v i o u s l y i l l u s t r a t e d . It can b e said, t h e r e f o r e , t h a t t h e u n i t cell of B a M is 21

63

6 C 6

63

++3++2,

R~

ooz

~'~hz ~U/~z iIz [JTo]

Fig. 13. The (110) cross section of BaO-6Fe203.

FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES

321

expressed as RSR*S*. Moreover, Townes et al. (1967) refined the crystal structure of BaM by X-ray investigation. They stated two points: o(i) The Fe 3÷ ion in the trigonal bipyramidal site, 2b, is split into half atoms 0.156 A away from the mirror plane, 4e. (ii) Some iron octahedra occur in pairs which share a common face to form Fe209 coordination groups. The former is supported by some M6ssbauer investigators (see ch. 2 section 4.2.1 M6ssbauer effect). Atomic coordinates, interatomic distances and structure factors are tabulated in their paper which gives more accurate results. Figure 14 shows perspective drawing of the R (BaFe6Oll), S (Fe6Os) and T (Ba2FesO14) blocks separately. The T block is related only with the Y, Z and U I-

0

(

Fig. 14. Perspective drawings of building blocks in the hexagonal compounds, T(Ba2Fe8014), S(Fe6Os) and R(BaFe6On).

322

H. KOJIMA j

Qlf

2

j ~ J

Fig. 15. Unit cell of BaO.6Fe20), showing the crystal structure composed of spinel blocks and Ba layers (Gorter I954). TABLE 4 Lattice constants, molecular weights and X-ray densities of M-type compounds. Lattice constant Compound

Molecular weight (g/mol)

a (,~)

c (,~)

c/a

X-ray density (g/cm ~)

Ref.

23.i94 23.20 23.182 23.17

3.936 3.94 3.936 3.943

5.29 5.29 5.30 5.33

(a) (b) (c) (d)

BaFe12019

1111.49

5.893 5.89 5.889 5.876

SrFe12019

1061.77

5.885 5.876 5.864

23.047 23.08 23.031

3.916 3.92s 3.928

5.10 5.11 5.14

(e) (c) (d)

PbFe12019

1181.35

5.877 5.889

23.02 23.07

3.917 3.917

5.70 5.66

(d) (c)

(a) Tauber et al. (1963) (b) Smit and Wijn (1959) (c) Bertaut et al. (1959) (d) Adelsk61d (1938) (e) Routil and Barham (1974)

FUNDAMENTAL PROPERTIES OF HEXAGONAL FERRITES

323

c o m p o u n d s but is shown here to illustrate the relationship a m o n g the blocks (see ch. 2 sections 4.l and 4.3). S has the cubic spinel structure with the [ l l l ] axis vertical. In other words, M is synthesized by piling up a Ba layer and a spinel block, whose layer sequence is A B C A . . . . alternatively (see fig. 11). G o r t e r (1954) showed this simply by fig. 15, where spinel block contains four oxygen layers. Molecular weight, X-ray density and lattice constants reported by various investigators are tabulated in table 4.

2. 1.2. Magnetic structure M-type c o m p o u n d s have a typical ferrimagnetic structure, that is, the orientation of the magnetic m o m e n t s of the ferric ions in the crystal are generally aligned along the c-axis in antiparallel with each other. Ndel (1948) and A n d e r s o n (1950) first considered from the theoretical view point that these alignments of magnetic ions can be realized by superexchange interaction through oxygen ions and such a structure has been proved from the experimental results of saturation magnetization, neutron diffraction, M6ssbauer effect and nuclear magnetic resonance etc. Grill and H a b e r e y (1974) calculated the exchange parameters of Fe > ions in BaM, as shown in table 5. H e r e it can be clearly seen that the closer the angle of the F e - O - F e b o n d approaches 18(t°, the larger the exchange p a r a m e t e r b e c o m e s

TABLE 5 Distances and angles of the Fe-O-Fe bonds and calculated exchange parameters in BaFe12Ot,~ (Grill and Haberey 1974). Distance (A)

Angle (degree)

Exchange parameter

Calculated value (K//z~)

'~ Fe(b')-OR2Fe(f2) { ]' Fe(b')-OR2-Fe(f:) ,~

1.886 + 2.060 1.886 + 2.060

142.41 132.95

Jbf2

35.96

{ Fe(f0-Os~-Fe(k) I" ,~Fe(f~)-Os2-Fe(k) ~"

1.897 + 2.092 1.907+ 2.107

126.55 121.00

Jkf~

19.63

]"Fe(a)-Osz-Fe(f~) +

1.997 + 1.907

124.93

Jaf~

18.15

{ Fe(f2)-OR3-Fe(k) ]"

1.975 + 1.928

127.88

Jf2k

4.08

]"Fe(b')-OR,-Fe(k) '[' '["Fe(b")-OR~-Fe(k) 1'

2.162+ 1.976 2.472 + 1.976

119.38 119.38

Jbk

3.69

]"Fe(k)-OR,-Fe(k) 1" ~"Fe(k)-Os,-Fe(k) ~" I"Fe(k)-Os2-Fe(k) ~ '["Fe(k)-OR~-Fe(k) ~"

1.976 + 1.976 2.092 + 2.092 2.107+ 2.107 1.928 + 1.928

97.99 88.17 90.08 98.05

J~k

52.0 22

BaM

* Spin wave line width (a) Smit and Beliers (1955) (b) W a n g et al. (1961) (c) Mita (1963) (d) D e Bitetto (1964) (e) Burlier (1962)

(f) (g) (h) (i)

Silber et al. (1967) Kurtin (1969) Dixon and Weiner (1970) Grosser (1970)

R.T. 21 200 300 35O 40O

F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S

349

T A B L E 12 (continued) Hr~ (kOe) [x 106/(4~-)A/ml hrr//'Hres 14.3 15.05 15.40 15.40 15.35

hrr-l-Hres -10 17.15 17.55 17.15 16.85 3.844 3.886 3.964 4.042 4.140 18.7-28.2

HA (kOe) [X 106/(47r)A/m]

A H (Oe) [x llY/(4~)A/m]

16.2 17.0 17.3 17.3 17.3 18.4

0-13

Ref.

47rMs = 6.67 (kG) 4.80 3.90 3.50 3.12

(a)

p = 5.13 (g/cm3) 3'4 = 2.62 (MHz/G)

(b)

17.55

10 Ixm on the domains of PbM. Rosenberg et al. (1966), moreover, obtained the relations for S r O - ( 6 - x)Fe2OyxA1203; D oc t 0.586 at x = 0, D oc t 0-616 at x = 1.0, D oct 0-665 at x = 1.5, D oct °.418 at x = 1.8, D oct 0.ass at x = 1.9 and D o c t 0.431 at x ~ 2.0. For thinner crystals observed by G o t 6 (1966), the results can be rewritten as D = [0.386(t- 1.460)] 1/2 for B a M and D = [0.432(t- 1.1260)] 1/2 for SrM respectively. H e n c e the one half Power law may be valid in this case, though the physical meanings of the constants are not clear. However, if we consider the existence of a surface layer where the Kittel model might b e c o m e unstable, giving a kind of lattice distorted layer, and also the resolution limit in m e a s u r e m e n t s with an optical microscope, the numerical values in these formulae seem to be reasonable. For thicker crystals, the two third power law related to spike domains seems to be valid. Some deviation from the law could be understood by the complicated domain structures and the resulting ambiguity in the measured values of domain widths.

358

H. KOJIMA

The temperature variation of the domain width D in BaM was studied by Kojima and Goff) (1962). They obtained the temperature coefficient of D as 8.9× 10-4/°C and that of O'w as - 2 . 3 × 10 3/°C. Gemperle et al. (1963) also performed similar experiment with PbM and found the thermal hysteresis of the domain width, as Shimada et al. (1973) observed with honeycomb domains. Kacz6r (1972) discussed these results from a theoretical point of view and showed the free energy decreases linearly to zero as T/Oc changes from 0.2 to 1.0, and the domain width almost doubles in the same temperature range. Furthermore, undulating Bloch walls, for which Goodenough (1956) first gave a theoretical explanation, can be seen on the surface of crystals with medium thickness, for instance, 10 fxm < t < 50 txm for BaM. Szymczak (1971) reported the temperature dependence of domain width, wave amplitude and wave length in these domains. The stability with temperature for honeycomb domains was investigated by Gemperle et al. (1963) with PbM and by Shimada et al. (1973) with BaM. The latter authors observed the increase of the nearest neighbour distance among the cylindrical domains during the temperature rise. The honeycomb domains reversibly change to a mixture of honeycomb and stripe domains by the heat treatment from 600 K to room temperature. It was pointed out that the equilibrium distance theoretically predicted by Kaczdr and Gemperie (1961) would be realized only in such a mixed domain structure. Regarding the same phenomenon, Kozlowski and Zietek (1965) showed from a theoretical consideration that the deviation from Kacz6r and Gemperle's equation in these experiments would rapidly increase for thinner specimens. Grundy (1965) observed Kittel type slab domains in PbM of 1000-2000 thickness by Lorentz microscopy and determined the Bloch wall thickness as 250 _+150 A. Grundy and Herd (1973) used the same technique and applied it in an investigation of the nucleation mode of bubble domains. They gave the material length l = Crw/(4~-M2) as 0.03-0.04 Ixm for BaM and PbM. Wall mobility constant ,1 of 0.7× 102cm/s/Oe for BaFe12019 and 1.6× 102cm/s/Oe for BaFeu.aA10.7019 were reported by Asti et al. (1968).

2.1.12. Optical properties The absorption coefficient a (=2~-K/nA) and Faraday rotation &F of BaM measured at 300 K as a function of wavelength from 1 ~m to 8 p~m by Zanmarchi and Bongers (1969) are shown in fig. 49. It is seen that &V changes sign between 2 ~m and 3 ~m. Drews and Jaumann (1969) measured the absorption coefficient K, refractive index n, Faraday rotation &F, Faraday ellipticity ~/v and Kerr rotation against air ~bw and against glass &KC for the same material in the shorter wavelength region of 0.4 ~m-1.7 ~m. The results are illustrated in fig. 50. Kahn et al. (1969) also added the data of the polar Kerr spectra for PbM, showing° a negative peak at 4.43eV (2799,~) and a positive peak at 5.5 eV (2254A). According to their conclusion, charge transfer transitions occurring at about 4 eV (3100 A) and 5 eV (2480 A), associated with Feoct and Fetet complexes, respectively, are responsible for the principal magnetooptical spectra. Blazey (1974) reported on the wavelength-modulated reflectivity spectra of BaM with the minima at 2.2eV (5636A) and 2.6eV (4769 A) corresponding to the internal

150

I00 'E

300

13

200

¢j

E rj

50 I00

0

"o

v

LL

-g. 0 0 2

0

4

6

X

8

'-I00 I0

(Fm)

Fig. 49. Absorption coefficient a(=2~'K/nA) and Faraday rotation ~bF of BaO.6Fe203 in infrared region at room temperature (Zanmarchi and Bongers 1969). xlO 2 I0.0

7.5

1~F

o o~

5.0

-

-

I--

xlO 2

"F]F

-2.0

LL 2.5

--I.0

o E

o

2

g,

~,,

o -

2.5

1.0

-8-

6

-5.0

2.0 I

3

m

r-

i o- 2

2

-

L

10.4

I

0

0.5

1.0

1.5

2.0

X (/~m) Fig. 50. Optical properties of BaO-6Fe~O3 as a function of wavelength. K: absorption coefficient, n: refractive index, OF: Faraday rotation, rTF: Faraday ellipticity, CbKL:Kerr rotation against air, ~bKo: Kerr rotation against glass, t: 4.5 p~m, / 4 : 1 5 kOe [1.19 x 106 A/m]. 359

360

H. K O J I M A

transition of Fetet and at 3.9 eV (3179 A), 4.3 eV (2883 A) and 4.8 eV (2583 A), these being assumed to be charge transfers to Feoct.

2.1.13. Magnetostriction The saturation magnetostriction in a hexagonal crystal is given by Mason (1954) in the form, a = /~A[(OZI~I q- a2~2) 2 -- (O/1]~ 1 q- O~2][~2)@3~3]q- ~.B[(I -- O~2)

x ( I - fl~) ~ - ( o ~ # , + o~=/?~)=] + a d o

- o d ) B 1 - (o~/3, + o~fl=),~,8~]

(18)

+ 4AD(alB1 + o12f12)a3B3,

where al, a2, O~3 and ill, fi2, r3 are the direction cosines of the magnetization vector and measuring direction. Here, the direction cosines are taken with respect to the Crystal axes, the z-axis coinciding the c-axis. Kuntsevich et al. (1968) determined the constants AA, As, Ac and AD in eq. (18) for BaM in measurements with the following geometry: •A:O/1 =/31: 1, AB:OZl= /3== 1, Ac:OZl = J~3= 1, h D : a l = / 3 1 = a 3 = / 3 3 = l/X/2. Thus, they found the constants at room temperature as AA = -- (15 --+0.5) X 10-6, AB = + (16 + 0.5) X 10-6, Ac = + (11 -+ 0.5) X 10-6 and AD = -- (13 --+0.5) X 10-6. For polycrystals, they also obtained the longitudinal and transverse magnetostrictions, hi! = -(9-+ 0.5)x 10 6 and h~ = + (4.5 -+ 0.5) x 10-6. However, these values do not coincide with the values derived by the simple averaging of the formula for a single crystal. The authors explained these results from the effects of the defects in the crystals and the interference of grains during deformation.

K

E

I

8.6

6

E

6.4

15.0

6.3

8.4

6.2 14.5 8.2

6.1

Z

6.0

/ 8.0

"14.0'

I00

200 T (K)

300

5.9

Fig. 51. Temperature dependence of Young's modulus E, rigidity modulus G and bulk modulus K (x 1011 dyn/cm 2) [× 101° N/m 2] (B.P.N. Reddy and P.J. Reddy 1974a).

F U N D A M E N T A L P R O P E R T I E S OF H E X A G O N A L F E R R I T E S

361

2.1.14. Mechanical properties Fundamental studies of the mechanical properties of hexagonal ferrites are quite few. Clark et al. (1976) referred to the following mechanical data for their BaM specimen at room temperature. Density: 5g/cm 3, porosity: 5%, Young's modulus: l a x 106kg/cm2 [1.38x 1011N/m2], Poisson's ratio: 0.28, compressive strength: 4.5 x 103kg/cm2 [4.41x 108N/m2], tensile strength: 5.6x 102kg/cm2 [5.52x 107 N/m2]. Reddy and Reddy (1974a) measured the elastic modulus of sintered BaM with a density of 4.8910 g/cm3. Figure 51 shows the relations of Young's modulus E, rigidity modulus G and bulk modulus K versus temperature. These moduli decrease with temperature, in contrast with those of Ni-Zn or Mn-Zn cubic ferrites. Hodge et al. (1973) investigated the compressive deformation of sintered BaM with 18% porosity in creep and press forging modes in the temperature range 1000° to 1200°C. Figure 52 is the true strain rate against l I T plot for an isotropic compact at 5% true strain. The activation energy for creep was estimated from the experiments as 123-+6kcal/mol [(5.15-+0.25)x 105 J/moll.

-2 (x 13

-- 0 . 5 , the compound changes to a mixture of M and W phases, then rapidly becomes single W phase with increasing x values, which was confirmed by X-ray and magnetic torque measurements in this paper. T A B L E 21

Magnetic properties of M 2+ and F 1- substituted M compounds (Robbins 1962). KI at R.T. (x 10 6 erg/cm 3) [x 105 J / m 3]

0% at 0 K (emu/g) [x 4~- x 10-7 Wbm/kg]

NB at 0 K (/xB)

0c (°C)

-

100

20

500

3.3

BaNixFe12-xOm-xFx

0.6

113

22.50

475

2.4

BaCuxFe~2-xO19-xFx

0.35 0.63 1.14

108.0 113.5 118.0

21.66 22.72 23.72

460 450 418

3.1 2.9 -

0.3 0.4

105 108.5

21.0 21.7

470 470-

-

Formula BaFez2019

BaCoxFel2-xOx9-xFx

x

FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES

387

References Adelsk61d, V., 1938, Arkiv Kemi. Mineral. Geol. 12A, 1. Aharoni, A., 1962, Rev. Mod. Phys. 34, 227. Aharoni, A. and M. Schieber, 1961, Phys. Rev. 123, 807. Ahrens, L.H., 1952, Geochim. et Cosmochim. Acta, 2, 155. Aidelberg, J., J. Flicstein and M. Schieber, 1974, J. Cryst. Growth, 21, 195. Albanese, G., M. Carbucicchio and A. Deriu, 1974, Phys. Status Solidi A23, 351. A16onard, R., D. Bloch and P. Boutron, 1966, Compt. rend. B263, 951. Aleshke-Ozhevskii, O.P., R.A. Sizev, V.P. Cheparin and I.I. Yamzin, 1968, Zh. ETF Pis'ma, 7, 202. Aleshke-Ozhevskii, O.P. and I.I. Yamzin, 1969, Zh. Eksp. Teor. Fiz. 59, 1490. Anderson, P.W., 1950, Phys. Rev. 79, 350. Appendino, P. and M. Montorsi, 1973, Ann. Chim. (Rome) 63, 449. Arendt, R.H., 1973, J. Solid State Chem. 8, 339. Asti, G., F. Conti and C.M. Maggi, 1968, J. Appl. Phys. 39, 2039. AuCoin, T.R., R.O. Savage and A. Tauber, 1966, J. Appl. Phys. 37, 2908. Banks, E., M. Robbins and A. Tauber, 1962, J. Phys. Soc. Japan, 17, Supplement B-I, 196. Bashkirov, Sh.Sh., A.B. Liberman and V.I. Sinyavskii, 1975, Zh. Eksp. Teor. Fiz. 59, 1490. Batti, P., 1960, Ann. Chim. (Rome) 50, 1461. Belov, K.P., L.I. Koroleva, R.Z. Levitin, Yu.V. Jergin and A.V. Pedko, 1965, Phys. Status Solidi, 12, 219. Beretka, J., and M.J. Ridge, 1958, J. Chem. Soc. A10, 2463. Berger, W. and F. Pawlek, 1957, Arch. Eisenhiittenwesen, 28, 101. Bertaut, E.F., A. Deschamps and R. Pauthenet, 1959, J. Phys. et Rad. 20, 404. Blazey, K.W., 1974, J. Appl. Phys. 45, 2273. Bonnenberg, D. and H.P.J. Wijn, 1968, Z. angew. Phys. 24, 125. Borovik, E.S. and Yu.A. Mamaluy, 1963, Fiz. Metal. Metalloved. 15, 300. Borovik, E.S. and N.G. Yakovleva, 1962a, Fiz. Metal. Metalloved. 13, 470. Borovik, E.S. and N.G. Yakovleva, 1962b, Fiz. Metal. Metalloved. 14, 927. Borovik, E.S. and N.G. Yakovleva, 1963, Fiz. Metal. Metalloved. 15, 511.

Bottoni, G., D. Candolfo, A. Cecchetti, L. Giarda and F. Masoli, 1972, Phys. Status Solidi A32, K47. Bowman, W.S., Saturno, F.H. Norman and J.H, Horwood, 1969, J. Can. Ceram. Soc. 38, 1. Bozorth, R.M. and V. Kramer, I959, J. Phys. et Rad. 20, 393. Brady, L.J., 1973, J. Material Sci. 8, 993. Braun, P.B., 1957, Philips Res. Rep. 12, 491. Brixner, L,H., 1959, J, Amer. Chem. Soc. 81, 3841. Buessem, W.R. and A. Doff, 1957, The Thermal expansion of ferrites at temperatures near the Curie point, Proc. 13 Ann. Meeting, Met. Powd. Ass., Chicago, Ill., USA, II, 196. Burlier, C.R., 1962, J. Appl. Phys. 33, 1360. Bye, G.C. and C.R. Howard, 1971, J. Appl. Chem. Biotechnol. 21, 319. Casimir, H.B.G., J. Smit, U. Enz, J.F. Fast, H.P.J. Wijn, E.W. Gorter, A.J.W. Duyvesteyn, J.D. Fast and J.J. deJong, 1959, J. Phys. et Rad. 20, 360. Clark, A.F., W.M. Haynes, V.A. Deason and R.J. Trapani, 1976, Cryogenics, May, 267. Cochardt, A., 1967, J. Appl. Phys. 38, 1904. Craik, D J . and E.H. Hill, 1977, J. Phys. Colloque, 38, C1-39. Davis, R.T., 1965, Thesis, Thermal expansion anisotropy in BaFe120~9, The Penn. State Univ. College of Mineral Ind. De Bitetto, D.J., 1964, J. Appl. Phys. 35, 3482. Dixon, S. Jr. and M. Weiner, 1970, J. Appl. Phys. 41, 1375. Dixon, S. Jr., T.R. AuCoin and R.O. Savage, 1971, J. Appl. Phys. 42, 1732. Drews, U. and J. Jaumann, 1969, Z. angew, Phys. 26, 48. Drofenik, M., D. Hanzel and A. Moljik, 1973, J. Mater. Sci. 8, 924. Dtilken, H., F. Haberey and H.P.J. Wijn, 1969, Z, angew. Phys. 26, 29. Dullenkopf, P. and H.P.J. Wijn, 1969, Z. angew. Phys. 26, 22. Du Pr6, F.K., D.J. De Bitetto and F.G. Brockman, 1958, J. Appl. Phys. 29, 1127. Eldridge, D.F., 1961, J. Appl. Phys. 32, 247 S. Erchak, M. Jr., I. Fankuchen and R. Ward, 1946, J. Amer. Chem. Soc. 68, 2085. Erchak, M. Jr. and R. Ward, 1946, J. Amer. Chem. Soc. 68, 2093. Esper, F.J. and G. Kaiser, 1972, Int. J. Magnetism, 3, 189.

388

H. KOJIMA

Esper, F.J. and G. Kaiser, 1975, Physica, 80B, 116. Fahlenbrach, H. and W. Heister, 1953, Arch. Eisenhtittenw. 29, 523. Florrescu, V., M. Popescu and C. Ghizdeanu, 1973, Int. J. Magnetism, 5, 257. Frei, E.H., M. Schieber and S. Strikman, 1960, Phys. Rev. 118, 657. Fuchikami, N., 1965, J. Phys. Soc. Japan, 20, 760. Galasso, F.S., 1970, Structure and Properties of Inorganic Solids (Pergamon Press, Oxford) p. 226-234. Gemperle, R., E.V. Shtoltz and M. Zeleny, 1963, Phys. Status Solidi, 3, 2015. Glasser, F.P., F.W.D. Woodhams, R.E. Meads and W.G. Parker, 1972, J. Solid State Chem. 5, 255. Goodenough, J.B., 1956, Phys. Rev. 102, 356. Gorter, E.W., 1954, Philips Res. Rep. 9, 295 and 403. Gorter, E.W., 1957, Proc. IEE, 104B, 255 S. Got& K., 1966, Japan. J. Appl. Phys. 5, 117. Goto, Y. and T. Takada, 1960, J. Amer. Ceram. Soc. 43, 150. Goto, Y. and K. Takahashi, 1971, J. Japan Soc. Powder and Powder Metallurgy, 17, 193 (in Japanese). Goto, Y. and K. Takahashi, 1973, Japan. J. Appl. Phys. 12, 948. Goto, Y., M. Higashimoto and K. Takahashi, 1974, J. Japan Soc. Powder and Powder Metallurgy, 21, 21 (in Japanese). Grill, A., 1974, Int. J. Magnetism, 6, 173. Grill, A. and F. Haberey, 1974, Appl. Phys. 3, 131. Grosser, P., 1970, Z. angew. Phys. 30, 133. Grundy, P. J., 1965, Brit. J. Appl. Phys. 16, 409. Grundy, P.J. and S. Herd, 1973, Phys. Status Solidi A20, 295. Haberey, F. and A. Kockel, 1976, IEEE Trans. Mag. MAG-12, 983. Haberey, F. and H.P.J. Wijn, 1968, Phys. Status Solidi, 26, 231. Haberey, F., M. Velicescu and A. Kockel, 1973, Int. J. Mag. 5, 161. Hagner, J. and U. Heinecke, 1974, Phys. Status Solidi A22, K187. Haneda, K. and H. Kojima, 1971, Phys. Status Solidi A6, 259. Haneda, K. and H. Kojima, 1973a, J. Appl. Phys. 44, 3760. Haneda, K. and H. Kojima, 1973b, Japan. J. Appl. Phys. 12, 355.

Haneda, K. and H. Kojima, 1974, J. Amer. Ceram. Soc. 57, 68. Haneda, K., C. Miyakawa and H. Kojima, 1974a, J. Amer. Ceram. Soc. 57, 354. Haneda, K., C. Miyakawa and H. Kojima, 1974b, Improvement of temperature dependence of remanence in ferrite permanent magnets, AIP Conf. Proc. 24, 770. Hareyama, K., K. Kohn and K. Uematsu, 1970, J. Phys. Soc. Japan, 29, 791. Heimke, G., 1960, J. Appl. Phys. 31, 271 S. Heimke, G., 1962, Bet. Deut. Keram. Ges. 39, 326. Heimke, G., 1963, Z. angew. Phys. 15, 217. Heinecke, U. and L. Jahn, 1972, Phys. Status Solidi hl0, K93. Hempel, K.A. and H. Kmitta, 1971, J. Phys. Colloque, 32, C1-159. Henry, N.F.M. and K. Lonsdal, 1952, International Tables for X-ray Crystallography (Kynoch Press, Birmingham) p. 304. Hodge, M.H., W.R. Bitler and R.C. Bradt, 1973, J. Amer. Ceram. Soc. 56, 497. Holz, A., 1970, J. Appl. Phys. 41, 1095. Hoselitz, K. and R.D. Nolan, 1969, J. Phys. D, Ser. 2, 2, 1625. Hunty, P., 1963, Fiz. Metal. Metalloved. 16, 132. Ichinose, N. and K. Kurihara, 1963, J. Phys. Soc. Japan, 18, 1700. Jahn, L. and H.G. Mfiller, 1969, Phys. Status Solidi, 35, 723. Jonker, G.W., H.P.J. Wijn and P.B. Braun, 1954, Philips Techn. Rev. 18, 145. Kacz6r, C., 1964, Zh. Eksperim, Teor. Fiz. 46, 1787. Kacz6r, J., 1972, Phys. Lett., 41A, '461. Kacz6r, J. and R. Gemperle, 1960, Czech. J. Phys. BIO, 505. Kacz6r, K. and R. Gemperle, 1961, Czech. J. Phys. Bll, 510. Kahn, F.J., P.S. Pershan and J.P. Remeika, 1969, J. Appl. Phys. 40, 1508. Kittel, C., 1946, Phys. Rev. 70, 965. Kiyama, M., 1976, Bull. Chem. Soc. Japan, 49, 1855. Kojima, H. and K. Got& 1962, J. Phys. Soc. Japan, 17, Supplement B-l, 201. Kojima, H. and K. Got& 1964, Determination of critical field for magnetoplumbite type oxides by domain observation, Proc. Int. Conf. Magn. Nottingham, p. 727. Kojima, H. and K. Got& 1965, J. Appl. Phys. 36, 538. Kojima, H. and K. Got& 1970, Bulletin. Res. Inst.

FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES Sci. Meas., Tohoku University, 19, 67 (in Japanese). Kojima, H. and C. Miyakawa, 1965, Bulletin, Res. Inst. Sci. Meas., Tohoku University, 13, 105 (in Japanese). K6moto, O. and H. Kojima, 1976, Hard Magnetic Materials, ed., S. Iida et al. (Maruzen, Tokyo) Voi. 3, p. 110 (in Japanese). Kooy, C., 1958, Philips Techn. Rev. 19, 286. Kooy, C. and U. Enz, 1960, Philips Res. Rep. 15, 7. Koroleva, L.I. and L.P. Mitina, 1971, Phys. Status Solidi AS, K55. Kozlowski, G. and W. Zietek, 1965, J. Appl. Phys. 36, 2162. Kreber, E. and U. Gonser, 1973, Appl. Phys. 1, 339. Kreber, E. and U. Gonser, 1976, Appl. Phys. 10, 175. Kreber, E., U. Gonser and A. Trautwen, 1975, J. Phys. Chem. Solids, 36, 263. Kuntsevich, S.P., Yu.A. Mamaluy and A.S. Miln6r, 1968, Fiz. Metal. Metalloved. 26, 610. Kurtin, S., S. Foner and B. Lax, 1969, J. Appl. Phys. 40, 818. Lacour, C. and M. Paulus, 1968, J. Cryst. Growth, 3, 814. Lacour, C. and M. Paulus, 1975, Phys. Status Solidi A27, 441. Laroria, K.K. and A.P.B. Shinha, 1963, J. Pure and Appl. Phys. 1, 215. Linares, R.C., 1962, J. Amer. Ceram. Soc. 45, 307. Lotgering, F.K., 1974, J. Phys. Chem. Solids, 35, 1633. Luborsky, F.E., 1966, J. Appl. Phys. 37, 1091. Ltitgemeier, M., A.V. Gonzales, W. Zietek and W. Zinn, 1977, Physica, 86--88B, 1363. MacChesney, J.B., R.C. Sherwood, E.T. Keve, P.B. O'Connor and L.D. Blitzer, 1971, New room temperature ferrimagnetic phases in the system CaO-AI203-Fe203, Ferrites, Proc. Int. Conf. Japan, p. 158. Mahoney, J.P., A. Tauber and R.O. Savage, 1972, Low temperature magnetic properties in BaFe12-x-y-zZnxTiyMnzO19, AIP Conf. Proc. no. 10, part 1, p. 159. Mason, W.P., 1954, Phys. Rev. 96, 302. Mee, C,D. and J.C. Jeschke, 1963, J. Appl. Phys. 34, 1271. Menashi, W.P., T.R. AuCoin, J.R. Shappirio and D.W. Eckart, 1973, J. Cryst. Growth, 20, 68. Mita, M., 1963, J. Phys. Soc. Japan, 18, 155.

389

Mones, A.H. and E. Banks, 1958, J. Phys. Chem. Solids, 4, 217. Mori, S., 1970, J. Phys. Soc. Japan, 28, 44. Moriya, T., 1960, Phys. Rev. 120, 91. Mountvala, A.J. and S.F. Ravitz, 1962, J. Amer. Ceram. Soc. 45, 285. N6el, L., 1947, Compt. rend. 224, 1488. N6el, L., 1948, Ann. Phys. (Paris) 3, 137. Neumann, H. and H.P.J. Wijn, 1968, J. Amer. Ceram. Soc. 51, 536. Oh, H.J., T. Nishikawa and M. Satou, 1978, J. Chem. Soc. Japan, 1, 42, (in Japanese). Okamoto, S., H. Sekizawa and S.I. Okamoto, 1975, J. Phys. Chem. Solids, 36, 591. Okazaki, C., B. Kubota and S. Mori, 1955, National Techn. Rep. 1, 23 (in Japanese). Okazaki, C., S. Mori and F. Kanamaru, 1961a, National Techn. Rep. 7, 21 (in Japanese). Okazaki, C., T. Kubota and S. Mori, 1961b, J. Phys. Soc. Japan, 16, 119. Palatnik, L.S., L.I. Lukashenko, L.Z. Lubyanyy, V.I. Lukashenko and Yu.A. Mamaluy, 1975, Fiz. Metal. Metalloved. 40, 61. Pauling, L., 1960, The Nature of the Chemical Bond, 3rd ed. (Cornell Univ. Press, Ithaca, N.Y.) p. 514. Paulus, M., 1960, Compt. rend. 250, 2332. Pauthenet, R. and G. Rimet, 1959a, Compt. rend. 249, 1875. Pauthenet, R. and G. Rimet, 1959b, Compt. rend. 249, 656. Perekalina, T.M. and V.P. Cheparin, 1967, Fiz. Tverd. Tela. 9, 217. Perekalina, T.M., M.A. Vinnik, R.I. Zevereva and A.P. Schurova, 1970, Zh. Eksp. Teor. Fiz. 59, 1490. Rathenau, G.W., 1953, Rev. Mod. Phys. 25, 297. Rathenau, G.W., J. Smit and A.L. Stuyts, 1952, Z. Phys. 133, 250. Ratnam, D.V. and W.R. Buessem, 1970, IEEE Trans. Magn. MAG-6, 610. Ratnam, D.V. and W.R. Buessem, 1972, J. Appl. Phys. 43, 1291. Reddy, B.P.N. and P.J. Reddy, 1973, Phys. Status Solidi A17, 589. Reddy, B.P.N. and P.J. Reddy, 1974a, Phil. Mag. 30, 557. Reddy, B.P.N. and P.J. Reddy, 1974b, Phys. Status Solidi A22, 219. Reed, J.S. and R.M. Fulrath, 1973, J. Amer. Ceram. Soc. 56, 207. Rensen, I.G. and I.S. van Wieringen, 1969, Solid State Commun. 1, 1139.

390

H. KOJIMA

Rensen, J.G., J.A. Schulkes and J.S. van Wieringen, 1971, J. Phys. Colloque, 32, C1-924. Richter, H.G. and H.E. Dietrich, 1968, IEEE Trans. Magn. MAG-4, 263. Robbins, M., 1962, Thesis, Fluoride-compensated cation substitution in oxides, Polytechnic Inst. Brooklyn, New York. Robbins, M. and E. Banks, 1963, J. Appl. Phys. 34, 1260. Rodrigue, G.P., 1963, IEEE Trans. Microwave Theory and Techniques, September, 351. Roos, W., H. Haak, C. Voigt and K.A. Hempel, 1977, J. Phys. Colloque, 38, C1-35. Rosenberg, M., C. Tfinfisoiu and V. Florescu, 1966, J. Appl. Phys. 37, 3826. Rosenberg, M., C. Tanasoiu and V. Florescu, 1967, Phys. Status Solidi, 21, 197. Routil, R.J. and D. Barham, 1974, Can. J. Chem. 52, 3235. Sadler, A.G., 1965, J. Can Ceram. Soc. 34, 155. Savage, R.O. and A. Tauber, 1964, J. Amer. Ceram. Soc. 47, 13. Schieber, M.M., 1967, Experimental Magnetochemistry in Series of Monographs on Selected Topics in Solid State Physics, ed. E.P. Wohlfarth (North-Holland, Amsterdam) v01. 8, p. 198-217. Shimada, Y., K. Got6 and H. Kojima, 1973, Phys. Status Solidi A18, K1. Shimizu, S. and K. Fukami, 1972, J. Japan Soc. Powder and Powder Metallurgy, 18, 259 (in Japanese). Shirk, B.T. and W.R. Buessem, 1969, J. Appl. Phys. 40, 1294. Shirk, B.T. and W.R. Buessem, 1970, J. Amer. Ceram. Soc. 53, 192. Shirk, B. and W.R. Buessem, 1971, IEEE Trans. Magn. MAG-7, 659. Sigal, M.A., 1977, Phys. Status Solidi A42, 775. Silber, L.M., E. Tsantes and P. Angelo, 1967, J. Appl. Phys. 38, 5315. Sixtus, K.J., K.J. Kronenberg and R.K. Tenzer, 1956, J. Appl. Phys. 27, 1051. Sloccari, G., 1973, J. Amer. Ceram. Soc. 56, 489. Slokar, G. and E. Lucchini, 1978a, J. Mag. and Mag. Mat. 8, 232. Slokar, G. and E. Lucchini, 1978b, J. Mag. and Mag. Mat. 8, 237. Smit, J., 1959, J. Phys. et Rad. 20, 370 (see Casimir et al. 1959).

Smit, J. and H.G. Beljers, 1955, Philips Res. Rep. 10, 113. Smit, J. and H.P.J. Wijn, 1959, Ferrites (Philips Technical Library, Eindhoven) p. 177-210. Smit, J., F.K. Lotgering and U. Enz, 1960, J. Appl. Phys. Supplement, 31, 137 S. St~iblein, H., 1973, Z. Werkstofftechnik, 4, 133. St~iblein, H. and W. May, 1969, Ber. Deut. Keram. Geselschaft, 46, 69. Standley, K.J., 1972, Oxide Magnetic Materials (Clarendon Press, Oxford) p. 149-160. Stoner, E.C. and E.P. Wohlfarth, 1948, Phil. Trans. A240, 599. Streever, R.S., 1969, Phys. Rev. 186, 285. Suchet, J.P., 1971, Compt. rend. S6ri C, 271, 895. Suemune, Y., 1972, J. Phys. Soc. Japan, 33, 279. Summergrad, R.N. and E. Banks, 1957, J. Phys. Chem. Solids 2, 312. Szymczak, R., 1971, J. Phys, Colloque, 32, C1-263. Takada, T., Y. Ikeda and Y. Bando, 1971, A new preparation method of the oriented ferrite magnets, Ferrites, Proc. Int. Conf. (Univ. Tokyo Press, Tokyo) p. 275. Tfinfisoiu, C., 1972, IEEE Trans. Magn. MAG8, 348. Tfinfisoiu, C., P. Nicolau and C. Micea, 1976, IEEE Trans. Magn. MAG-12, 980. Tauber, A., R.O. Savage, R.J. Gambino and C.G. Whinfrey, 1962, J. Appl. Phys. 33, 1381. Tauber, A., J.A. Kohn and I. Bandy, 1963, J. Appl. Phys. 34, 1265. Tauber, A., S. Dixon, Jr. and R.O. Savage, Jr., 1964, J. Appl. Phys. 35, 1008. Tebble, R.S. and D.J. Craik, 1969, Magnetic Materials (Wiley-Interscience, London) p. 359-368. Townes, W.D., J.H. Fang and A.J. Perrotta, 1967, Z. Kristallogr. 125, 437. Trautwein, A., E. Kreber, U. Gonser and F.E. Harris, 1975, J. Phys. Chem. Solids, 36, 325. Van Diepen, A.M. and F.K. Lotgering, 1974, J. Phys. Chem. Solids, 35, 1641. Van Hook, H.J., 1964, J. Amer. Ceram. Soc. 47, 579. Van Loef, J.J. and P.J.M. Franssen, 1963, Phys. Lett. 7, 225. Van Loef, J.J. and A.B. van Groenou, 1964, On the sub-lattice magnetization of BaFe12019, Proc. Int. Conf. Magn. Nottingham, p. 646. Van Uitert, L.G., 1957, J. Appl. Phys. 28, 317.

FUNDAMENTAL PROPERTIES OF H E X A G O N A L FERRITES Van Uitert, L.G. and F.W. Swanekamp, 1957, J. Appl. Phys. 28, 482. Van Wieringen, J.S., 1967, Philips Tech. Rev. 28, 33. Van Wieringen, J.S. and J.G. Rensen, 1966, Z. angew. Phys. 21, 69. Verstegen, J.M.P.J., 1973, J. Solid State Chemistry, 7, 468. Villers, G., 1959a, Compt. rend. 248, 2973. Villers, G., 1959b, Compt. rend. 249, 1337. Vinnik, M.A. and R.I. Zvereva, 1969, Kristallografiya, 14, 697. Wang, F.F.Y., K. Ishii and B.Y. Tsui, 1961, J. Appl. Phys. 32, 1621. Wells, R.G. and D.V. Ratnum, 1971, IEEE Trans. Magn. MAG-7, 651. Went, J.J., G.W. Rathenau, E.W. Gorter and G.W. van Oosterhout, 1951/1952, Philips Techn. Rev. 13, 194.

391

Wijn, H.P.J., 1952, Nature, 170, 707. Wijn, H.P.J., 1970, Landolt-B6rnstein Numerical Data and Functional Relationships in Science and Technology. New Series, III/4b. ed. K.-H. Hellwege (Springer, Berlin) p. 552681. Williams, H.J. and R.C. Sherwood, 1958, J. Appl. Phys. 29, 296. Wisnyi, L.G., 1967, Powder Diffraction File, 7-85. Wullkopf, H., 1972, International J. Magnetism, 3, 179. Wullkopf, H., 1975, Physica, 80B, 129. Zanmarchi, G. and P.F. Bongers, 1969, J. Appl. Phys. 40, 1230. Zfiveta, K., 1963, Phys. Status Solidi, 3, 2111. Zinn, W., S. Hfifner, M. Kalvius, P. Kienle and W. Wiedemann, 1964, Z. angew. Phys. 17, 147.

chapter 6 PROPERTIES OF FERROXPLANA-TYPE HEXAGONAL FERRITES

M. SUGIMOTO Saitama University, Faculty of Engineering 225 Shimo-ohkubo, Urawa 338 Japan

Ferromagnetic Materials, Vol. 3 Edited by E.P. Wohlfarth © North-HollandPublishing Company, 1982 393

CONTENTS

1. C h e m i c a l c o m p o s i t i o n s , crystal s t r u c t u r e a n d spin o r i e n t a t i o n 1.1. BaMezFe16Oz7 ( W - t y p e ) . . . . . . . . . . . . 1.2. BaeMeeFel~Oz2 ( Y - t y p e ) 1.3. Ba3MeeFe24041 ( Z - t y p e )

. .

. .

. .

. .

. .

. .

. .

. .

. .

1.4. BazMe2Fe28046 ( X - t y p e ) . . . . . . . . . 1.5. Ba4MezFe36060 ( U - t y p e ) . . . . . . . . . 1.6. O t h e r c o m p o u n d s . . . . . . . . . . . 2. P r e p a r a t i o n ~nd f o r m a t i o n kinetics . . . . . . 3. SatuJ atic n r~ a g n e | i z a t i o n . . . . . : . . . . 4. M a g n e t o c r ~ stalline a n i s o t r o p y a n d r e l a l e d p h e n c m e n a

.

. . . . . . . . . . . . . . .

395 395 397 399 400 401 401 402 4O4 412 421 425

. .

. .

. .

. .

. .

. .

. . . . .

. . . . . .

. . . . .

. . . . .

. . . . .

. . . . .

.

.

.

. .

. .

. .

. . . . . .

. . . . . .

. . . . . .

. . .

. . .

. . .

. .

. . . . . . . . . . .

. . .

. . . .

. . . .

. . . . . .

.

. .

. . . . . . . . . . . . .

5. M6ssb~ u e r effect . . . . . . . . . . . . . . . . . . 6. M a g n e l ostriction a n d N M R . . . . . . . . . . . . . . 6.1. M a g n e t o s l r i c t i o n . . . . . . . . . . . . . . . .

. . .

. . .

6.2. N M R . . . . . . . . . 7. H i g h f r e q u e n c y m a g n e t i c lzrol:crties 8. E l e c t r i c p r o r erties a n d o l h e r effects

.

.

8.1. Cc n d u c l i v i l y . . . . 8.2. E ieleclric c c n s t a n t . 8.3. J a h r - T e l l e r effect . . 8.4. M a g n e t o - o p t k al effect 8.5. E ' o m a ! n c bse r v a l i o n a n d References . . . . . . .

.

. . .

. . .

. . .

. . .

.

. . .

. . .

. . .

. . .

. . .

. . .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c h e m ; c a l analysis . . . . . . . . . . . . . . . . . . . . .

394

. .

. . .

. . . .

. . . . . . . . . . . .

. . . . . .

425 427 428 434 434 435 435 436 436 439

1. Chemical compositions, crystal structures and spin orientation A group of compounds consisting of isotropic materials with spinel structure and higher anisotropic materials with hexagonal structure has been developed by Jonker et al. (1956/57). They are generically referred to as the ferroxplana-type compounds. The general chemical formula of these compounds is denoted by m(Ba2++ Me2+)-nFe203, where Me 2+ represents the divalent metal ions Mn, Fe, Co, Ni, Cu, Mg and Zn. In the triangle of fig. 1 in ch. 5 the symbols W, Y, Z, X and U represent the compounds with chemical composition BaMezFe16027, Ba2MezFe12022, Ba3Me2Fe24041, BazMezFe28046 and Ba4Me2Fe36060, respectively. If Me 2+ ions in the W-structure, as an example, are substituted by Zn 2+ ions, the composition may be conveniently indicated by the short notation of Zn2W. In the case of substitution of both Zn 2+ and Fe 2+ ions for Me 2+ ions it may be represented by ZnFeW.

1.1. BaMe2Fe16027 (W-type) The unit cell of the W-type compound is built up by superposition of four spinel blocks (S-block) and two blocks containing Ba ions (R-block) as shown in table 1 of ch. 5. Figure 1 shows a cross section of the W-structure having a hexagonal packing, which is closely related to the M-structure (Albanes e et al. 1976b). The only difference is that the successive R-blocks are interspaced by two S-blocks instead of one, as is the case in the M-structure. The crystal structure of R-blocks with chemical composition BaFe6Oll as well as that of S-blocks with chemical composition Me2Fe408 are represented in fig. 14 of ch. 5. In table 1 the number of ions and the coordination of the different cation sublattices in the W-structure are shown (Albanese et al. 1976b). The cations occupy seven different sublattices of 12K, 4e, 4fw, 4fw, 6g, 4f and 2d, in the nomenclature used by Braun (1957). The spin orientation according to the generally accepted collinear model is also indicated. This magnetic classification has been justified by the assumption that the magnetic behaviour of the nearest neighbour cations is determined by superexchange interaction.

395

396

M. S U G I M O T O

W- type Structure 4fly ® 4e © 4f e6g e 12K 4fv I • 2d

R

©o 20

I S*

Ba 2+

I S* R*

Fig. 1. Unit cell of the BaMe2Fe16027, Me2W, compound. T h e anions of O 2 , the divalent barium cation Ba 2÷, the metallic ions in the sublattices 4fw, 4e, 4f, 6g, 12K, 4fvi and 2d are indicated. T h e coordination figures of the metallic ions in the different lattice sites are shown (Albanese et al. 1976b).

TABLE 1 N u m b e r of ions, coordination and spin orientation for the various cations of a W-type c o m p o u n d (Albanese et al. 1976b).

Magnetic sublattice K fw

fvI a b

Sublattice

Coordination

N u m b e r of ions per formula unit

12K 4e 4fry 4fvi 6g 4f 2d

octahedral tetrahedral tetrahedral octahedral octahedral octahedral hexahedral

6 2 2 2 3 2 1

Block

Spin

R-S S S R S-S S R

up down down down up up up

PROPERTIES OF FERROXPLANA-TYPE HEXAGONAL FERRITES

397

1.2. Ba=Me2Fe12022(Y-type) T h e u n i t cell of t h e Y - t y p e c o m p o u n d is b u i l t u p b y t h e s u p e r p o s i t i o n of t h r e e S - b l o c k s a n d t h e so c a l l e d t h r e e T - b l o c k s as s h o w n in fig. 2, in w h i c h t h e d i f f e r e n t

Y - type Structure S

T

3 oVl (I) 6cvl 3 bvi o 1Bhvt o 6Civ

® 6clv O 0 2-

•

BCl 2+

S

T

S

T

Fig. 2. Unit cell of the Ba2Me2Fe12Oz~, Me2Y, compound. The anions of O 2-, the divalent barium cation Ba 2÷, the metallic ions in the sublattices 3avi, 6cvl, 3bvl, 18hw, 6cw and 6c~v are indicated. The coordination figures of the metallic ions in the different lattice sites, together with their spin orientation, are shown (Albanese et al. 1975b).

398

M. S U G I M O T O

lattice sites are distinguished by different symbols (Albanese et al. 1975). The Y-structure has the crystal symmetry characterized by the space group R3m. As shown in fig. 14 of ch. 5, the T-block with Ba2Fe8014 composition is formed by four oxygen layers having hexagonal packing and plays an unique role in the , TABLE 2 Number of ions, coordination and spin orientation for the various metallic sublattices of Y-structure? (Albanese et al. 1975b).

Sublattice

Coordination

Block

Number of ions per unit cell

tetrahedral octahedral octahedral octahedral tetrahedral octahedral

S S S-T T T T

6 3 18 6 6 3

6cw 3aw 18hvi 6cw 6c•v 3by1

Spin down up up down down up

t Sublattices having the same crystalline symmetry but belonging to different blocks are marked by an asterisk. TABLE 3 Strength of the superexchange interactions between Fe 3+ ions in the Y-structure (Albanese et al. 1975b). Interacts with n Fe 3+ ions Each Fe 3+ ion in lattice position 3avi 6Civ

18hvl

0Cvi

6C}'v

3bvl

n 6 6 3 3 9 1 3 2 1 4 6 3 1 3 3 3 6 2

lattice position 6cw 18hvl 6cIv 3avi 18hw 3avr 6clv 6Cvi 6C~v 18hvi 18hvl 6CTv 3bvi 6cw 18hvl 3bvI 6c•v 6Cvi

Strength of the superexchange interaction1 25 0(+) 0(+) 25 26 0(+) 26 30 25 0(+) 30 9(+) 1.7 9(+) 25 77 77 1.7

t The cross indicates interactions between sublattices with parallel spins.

PROPERTIES OF FERROXPLANA-TYPE HEXAGONAL FERRITES

399

Y - s t r u c t u r e . In fig. 2, t h e c o m m o n faces of t h e o c t a h e d r a inside t h e T - b l o c k a r e h a t c h e d . T h e p r e s e n c e of a n i o n o c t a h e d r a with c o m m o n faces is g e n e r a l l y r e s p o n s i b l e for t h e l o w e r stability of t h e s t r u c t u r e , d u e to t h e h i g h e r p o t e n t i a l e n e r g y of t h e s y s t e m as c o m p a r e d with s i t u a t i o n s w h e r e o n l y c o r n e r s a r e s h a r e d a n d t h e c a t i o n s a r e thus f u r t h e r a p a r t . This fact f a v o u r s t h e M e 2+ ions having a m a r k e d p r e f e r e n c e for t h e o c t a h e d r a l c o o r d i n a t i o n of t h e 6Cvi a n d 3bw lattice sites. T a b l e 2 shows t h e spin o r i e n t a t i o n for v a r i o u s s u b l a t t i c e s t o g e t h e r with t h e i r c o o r d i n a t i o n in t h e Y - s t r u c t u r e . A l b a n e s e et al. (1975b) c a l c u l a t e d t h e s t r e n g t h of t h e v a r i o u s s u p e r e x c h a n g e i n t e r a c t i o n s b e t w e e n F e 3+ ions in t h e Y - s t r u c t u r e . T a b l e 3 shows t h e results o b t a i n e d on t h e basis of t h e a s s u m p t i o n t h a t t h e i n t e r a c t i o n e n e r g y follows an e x p o n e n t i a l d e p e n d e n c e on t h e a n i o n - c a t i o n dist a n c e s a n d a c o s 2 0 law for t h e a n g u l a r d e p e n d e n c e . F r o m this t a b l e it a p p e a r s t h a t t h e s t r o n g e s t s u p e r e x c h a n g e i n t e r a c t i o n is t h e o n e b e t w e e n t h e t e t r a h e d r a l ions 6Cfv a n d t h e o c t a h e d r a l ions 3bvi inside t h e T - b l o c k , a n d t h e o n l y a p p r e c i a b l e p e r t u r b i n g i n t e r a c t i o n a p p e a r s to b e t h e o n e b e t w e e n t h e 6C?v a n d 6Cvr ions, b o t h b e l o n g i n g to t h e T - b l o c k .

1..3. Ba3Me2Fe24041 (Z-type) T h e c r y s t a l l i n e s t r u c t u r e of t h e Z - t y p e c o m p o u n d s is s h o w n in fig. 3 ( A l b a n e s e et al. 1976a). T h e unit cell is f o r m e d by the s u p e r p o s i t i o n of f o u r S-blocks, two T-blocks and one R-block, and the divalent and trivalent cations are distributed a m o n g ten different lattice sites. T a b l e 4 shows t h e n u m b e r of ions r e l a t i v e to t h e v a r i o u s c a t i o n sublattices t o g e t h e r with t h e i r spin o r i e n t a t i o n . TABLE 4 Number of ions, coordination and spin orientation of the various metallic sublattices of Z-structuret (Albanese et al. 1976a).

Sublattice 12kv~ 2dv 4fw 4f-}i 4etv 4fiv 12k~}i 2avl 4evl 4f]~v

Coordination octahedral five-fold octahedral octahedral tetrahedral tetrahedral octahedral octahedral octahedral tetrahedral

Block R-S R R S S S T-S T T T

Number of ions per unit cell

Spin

12 2 4 4 4 4 12 2 4 4

up up down up down down up up down down

t Sublattices having the same crystalline symmetry but belonging to different blocks are marked by an asterisk.

400

M. SUGIMOTO

Z - type S t r u c t u r e

R

S

© 12Kvx ® 2dv 4f-Vl ® 4f~ 1 @ 4elv ~ 4fly 12K~,I I) 2clvl • 4evl

T

© 4fly

© 0 zBCI 2÷

R.

T* I S* Fig. 3. Unit cell of Ba3Co2Fe24041, Co2Z, compound. The coordination figures of the metallic ions in the main lattice sites are shown (Albanese et al. 1976a).

1.4. Ba2Me2Fez8046 (X-type) T h e u n i t cell of the X-type c o m p o u n d s consists of f o u r a l t e r n a t e layers of the M - s t r u c t u r e a n d W - s t r u c t u r e , b e l o n g i n g to the space s y m m e t r y g r o u p R3m. F i g u r e 4 shows a cross section of the Zn2X structure, in which the spin o r i e n t a t i o n

PROPERTIES OF FERROXPLANA-TYPE HE XAGONAL FERRITES

401

X - type S t r u c t u r e f~

W

Y3~_

(

A

Q O

-- 0 2 -

Oct.

@ •

/X

A

ZX

-- BQ2÷ -

Tet.

[]

-

Tri.

Fig. 4. A collinear spin model for Zn~X (Tauber et al. 1970).

as well as the coordination figures of all cations are represented (Tauber et al. 1970).

1.5. Ba4Me2Fe3606o (U-type) The unit--cell of the U-type c o m p o u n d is a rhombohedral structure belonging to space group R3m, and is formed by three molecules. The structure is built up by the superposition of two M-blocks and one Y-block along the c-axis. Figure 5 shows a cross section of the Zn2U structure and the spin orientation of all cations (Kerecman etoal. 1968). Referring to hexagonal structure, its lattice p a r a m e t e r s are c = 113.2 A, a = 5.88 A and the X-ray density is 5.36.

1.6. Other compounds Kohn et al. (1964a,b) reported a new hexagonal ferrite with Ba4Zn2Fes2Os4 composition. T h e new structure is made up by the sequence of composite TS- and RS-block. Interleaving the TS- and RS-block at various ratios leads to a structure with unit cells ranging from 18 to 138 oxygen layers; these give rise to hexagonal unit cells with c parameters ranging up to about 1600 A. The expected empirical formulae for this group of compounds are listed in table 5. Kohn and Eckart (1971) discovered a new c o m p o u n d w~th composition, BasZn2Ti3Fe12031, which is a hexagonal structure with a = 5.844 A and c =-43.020 A and contains 18 oxygen layers, indicated by the symbol Zn2-18H.

402

M. SUGIMOTO

U type Structure -

(

)

i

A

0

_

0 2-

-

Oct.

•

M

A

_

Be2*

-

Tet.

[]-

Tri.

Fig. 5. A collinear spin model for Zn2U (Kerecman et al. 1968).

TABLE 5 Chemical compositions and crystallographic properties for new ferroxplana-type compounds (Robert et al. 1964).

Chemical composition

Structural unit (blocks)

Bal0ZnaFes60102 Ba12ZnmFe680124 Ba14Zni2Fes00146

[(TS)4T]3 [(TS)sT]3 (TS)6T

Ba16Zn14Fe920168 Ba4Zn2Fe52084

[(TS)TT]3 [RS2(RS)3]3

2. Preparation

and formation

Number of oxygen layers

Lattice parameter c (A)

Primitive symmetry

Space group

28 x 3 34 x 3 40 46 x 3 22 × 3

203 247 97 334 154

Rhombohedral Rhombohedral Hexagonal Rhombohedral Rhombohedral

P63/mmc P63/mmc R3m

kinetics

The processes for producing the ferroxplana-type compounds are very similar to those for M-type compounds. However, more accurate procedures based on the phase equilibrium are necessary to obtain the ferroxplana-type compounds,

PROPERTIES

OF FERROXPLANA-TYPE

HEXAGONAL

FERRITES

403

.. because their chemical compositions are"very complex. In particular, it is very difficult to produce a crystallographicall'y pure compound containing various amounts of ferrous iron. Neuman and Wijn (1968) shed light on the chemical equilibrium between the oxygen partial pressure o f gas atmosphere and the formation of Fe2W phase. In order to obtain a homogeneous W-compound, the samples must be sintered at 1250° to 1400°C in an atmosphere with a partial oxygen pressure between 2 x 10 .4 and 2 x 10-1 atm. Figure 6 shows the formation temperature and stability range of the phases for the W, Y and Z compounds. The spinel phase appeared as the first major reaction product of the raw oxides at about 555°C. The M phase was detected next by X-ray analysis and followed by the formation of a Y, Z, W phase in turn. Castelliz et al. (1969) also studied the kinetics of phase formation as well as the stability of the phases. Lotgering (1959) evolved a new method for making a sintered crystal-oriented ferroxplana compound. The advantage of crystal orientation is evident from the fact that the permeability of its compounds can be about 3 times larger than that of non-oriented compounds. This method differs essentially in the formation mechanism from that for the M-type compound. A paste or thick suspension consisting of BaFe12019 powder and raw oxides such as ZnO or CoO is poured into a die and then introduced into a static magnetic field. The crystal orientation is made topotactically by compressing the suspension into a pellet. The orientation preserved through the firing at 1100° to 1300°C. Licci and Asti (1979) tried to produce topotactically the crystal-oriented CoZnY compound. The hot-pressing method was performed to obtain a crystal-oriented Co2W compound by Okazaki and Igarashi (1970). A large and nearly perfect single crystal of the ferroxplana-type compounds, t

i

[

I

F

i

[

i

r

0.8

.=-

J

Z

o.z,

\/

/

\

0.2

Co

rr

4

~;oo

600

Boo

~ooo

~2oo

~oo

T('C) Fig. 6. F o r m a t i o n

temperature

a n d s t a b i l i t y r a n g e o f W - , Y-, Z - a n d M - p h a s e s 1964).

(Neckenbiirger

et al.

404

M. SUGIMOTO

which is useful for microwave devices, can be grown relatively easily by the flux method. Tauber et al. (1962, 1964) investigated many kinds of flux materials useful for growing single crystals of ferroxplana compounds. It was found that BaOB203 flUX must be less volatile and less viscous than the NaFeO2 flux to obtain a single crystal with lower ferromagnetic resonance linewidth. In general, the Wand Y-type compounds are easily melted at a lower temperature. The difficulty in growing the crystals of Z-, X-, and U-type compounds may be attributable to the high-melting composition necessitated by the large concentration of Fe203. Stearns et al. (1975) and Glass et al. (1980) have grown single crystal films of ZnzY or Zn2W by the isothermal dipping method of liquid phase epitaxy using a PbO-BaO-B203 flux. Many investigations on microstructures of sintered samples have been presented: Huijser-Gerits and Rieck (1970, 1974, 1976) studied thoroughly the influence of sintering conditions on microstructure; Drobek et al. (1961) observed the microstructures by the Use of electron microscope; both Cook (1967) as well as Landuyt and Amelinckx (1974) observed the stacking sequence by electron microscope.

3. Saturation magnetization Many attempts have been made to improve the saturation magnetization by the substitutions of various kinds of metal ions for cations occupying the octahedral and tetrahedral sites in the oxygen framework structure of the ferroxplana-type compounds. This may be attributed to their unique crystallographical structure as well as their importance as promising materials for technological application in the field of permanent magnets and microwave devices. Smit and Wijn (1959) proposed a formula on the basis of the over-simplification that the number of Bohr magnetons at saturation for the W-type compound is simply equal to the sum of the corresponding number for M- and S-structures, i.e.: (ns)w = (nB)M+ 2(nn)s.

(1)

This concept implies that we treat as different the two S-blocks which are perfectly equivalent. This drastic consequence frequently leads to a discrepancy with the experimental values. For example, the formula gives the value of (ns)w = 20/XB for the ZnzW compound, while Albanese et al. (1976a) and Savage and Tauber (1965) determined it experimentally as 35/x8 and 38.2/XB at 0 K (= 123 G cm3/g and 134 G cm3/g, respectively). The assumption of Smit and Wijn is applicable to the Y-type and Z-type compounds, but problems slightly analogous to that for the W-type compound still remain. The W-structure is characterized by the presence of two additional spinel blocks instead of one, as in the M-structure. Such a structure creates the possibility of changing the magnetic properties by a suitable substitution of the cation. Uitert and Swanekamp (1957) attempted to improve the saturation magnetization of W-type compounds by the substitution of non-magnetic ions for cations in

PROPERTIES OF FERROXPLANA-TYPE H E X A G O N A L FERRITES

405

tetrahedral and octahedral sites, and showed that the saturation magnetization is generally apt to decrease with increasing amount of substitution. In fig. 7, zinc ions seem likely to occupy the tetrahedral sites in BaMe2Fe16027 and a much greater fraction of A1, G a and In ions appears to occupy the octahedral sites. An anomalous behaviour of curve (1) at around zero saturation can be attributed to a lack of homogeneity in the samples. Albanese et al. (1977) reported that the saturation magnetization of BaZn2AlxFe16_xO27 is reduced when the amount of substitution of AP + for Fe 3+ in a-sites is increased, and a compensation point of superexchange interaction results at x = 4. In fig. 8 the saturation magnetization, o-s, for a number of simple and mixed W-type compounds is plotted as a function of temperature. It appears from the figure that almost straight lines are found over a large temperature range, and that zinc ions give higher saturation magnetization at low temperatures. In Zn2W compounds, the Z n 2+ ions may occupy two tetrahedral sublattices 4e and 4f~v (Albanese et al. 1976b), and in Mg2W compounds 90% of the Mg 2+ ions may

4000

E 3000 -x

7 \ ,~ \ \

g "~

2000

w

\ i1

I/1

3" .~

I000

I I

-

E

1000 2

6

B

Fig. 7. Effect of various substitutions on room-temperature saturation magnetization for BaNi2Fe16OzT. X denotes the number of metal ions replaced per formula unit. (1) AI for Fe, (2) Ga for Fe, (3) In or Cr for Fe, (4) Zn for Ni, (5) BaZn2GaFelsOz7, (6) BaZn2Ga3Fe13027 and (7) BaZn2AI3Fe13027 (Van Uitert and Swanekamp 1957).

406

M. S U G I M O T O 120

I

i

I

I

t

I

'

100 ~ ' ~ "

,

~'

ao

"'-Lx,. ~

Me2= ZnFe~

Me 2 W

0Yg

.

N o "k I.-~ 60 '4"

F

LO

Ni

F'

"""'/-c~'~'-.XX~D"'~IL~_

2o

0

l

J

1

-273 -200

I

r

0

,

,a,~

200

~a,z

400

600

T(°C) Fig. 8. Saturation magnetization as a function of temperature for a n u m b e r of c o m p o u n d s with W-structure, m e a s u r e d on polycrystalline specimens at a field of 6600 Oe (Smit and Wijn 1959).

,Zn

60

E

I

i

I

MeY

40 x

/Mg

E 20

0

-273

.d

Ni

I

-200

I

I

I

0

200

400

T [°0)

Fig. 9. Saturation magnetization as a function of temperature for a n u m b e r of c o m p o u n d s with Y-structure measured on polycrystalline specimens at a field of 11000 Oe (Smit and Wijn 1959).

PROPERTIES OF FERROXPLANA-TYPE H E X A G O N A L FERRITES

407

occupy the octahedral sites, and 10% of Mg the tetrahedral sites (Smit and Wijn 1959). Many other reports on the saturation magnetization of W-type compounds have been presented. A study on Fe2W substituted by Ni 2+ and F- (Banks et al. 1962), Fe2W substituted by Co 2+ and F- (Robbins et al. 1963), (NiZn)W and (Nil.6Co0.4)W (Hodges et al. 1964) and (Co165Fe0.35)W (Yamzin et al. 1966). An expected improvement in magnetic moment in the Y-type compounds was proposed by Albanese et al. (1975b). If all cations occupying 3by1 sites in a T-block can be substituted by non-magnetic ions, the magnetic moment might be markedly improved. This is due to the fact that 3bvi sites alone link the upper and lower parts of the unit cell through the strong interaction with six ions 6cw. Furthermore, the inversion symmetry around 3bvi sites might be broken by the partial substitution of iron ions in 6Cvi sites. However, such a drastic change in the magnetic order, has so far not been reported. Figure 9 shows the saturation magnetization of a number of simple Y-type compounds as a function of temperature. In the case of Y-type compounds, zinc ions also give the highest saturation magnetization. Albanese et al. (1975b) reported that in Ba2Mg2Fe~2022(Mg2Y), Mg2+ ions mainly occupy 3bvi and 6Cw sublattices of the tetragonal sites inside the T-block, and this occupation leads to the weakening effect of the superexchange interaction caused by a critical competition of the two exchange interaction 3bvr-6CTv and 6Cvr-6C•v. The temperature dependence of the saturation magnetization parallel and perpendicular to the c-axis of (Ba0.05Sr0.95Zn)Y single crystals is shown in fig. 10 (Enz 1961). We can see from these curves that this compound has a preferential plane. According to Albanese et al. (1975b), since the Co 2+ ions in Ba2Co2Fe12022(Co2Y) have a marked preference for octahedral coordination, 0.9 Co 2+ ions may occupy only the spin-down octahedral sublattice 6Cw, while the residual 1.1 Co 2+ ions probably distribute themselves among the 3avl, 18hvb 3by1 sublattices. In Ba2Zn2-2xCu2xF12022,(Zn2-2xCU2x)Y, the substitution of Zn by Cu resulted in a linear decrease of the saturation magnetization, o-~, as well as a flattening of the o-~ vs. T curve (Albanese et al. 1978). This suggests that for all the compositions nearly 28% of Cu ions enter the spin-down sublattices and the residual 72% occupy the spin-up sites. Among the spin-up sublattices, the 3bvi sites at the centre of the T-block play an important role for the equilibrium of the superexchange interactions in this compound, as already described. In addition, other experiments on Zn2Y by Savage and Tauber (1964), Mn2Y and (MnZn)Y by both Tauber et al. (1964) and Dixon et al. (1965) have been performed. In fig. 11 the saturation magnetization is plotted as a function of temperature for polycrystalline specimens of Z-type compounds. Zn2Z shows the highest saturation magnetization. The distribution of Co 2+ ions in Co2Z was deduced by Albanese et al. (1976a) such that 1.08 Co 2+ ions per unit formula occupy the spin-up sublattice, while the residual 0.92 enter the 4fvi and 4ev~ sublattices which are the only spin-down octahedral lattice sites. The Curie temperatures as seen in fig. 11 are in agreement with their values obtained from M6ssbauer measurements. Petrova (1967) measured the saturation magnetization and Curie temperature of (Co2-xZnx)Z.

408

M. SUGIMOTO BO

( Boo.05 Sr o.g5 Zn)Y 40 H.Lc

~

c

-

(a)

o - - - ' _ ~ T~290 ~K

0

80

I

I

i

F:

% -4"

(b)

40 0

BO

40 t

~

(c)

E

0~

-

80

0

Hllc i

0

5

-r

T=I2OO°K r

10

15

20

H ( k Oe ) [ x 106/(z./T) A / rn ] Fig. 10. Magnetization curves of single crystal of (Ba0.0sSr0.95Zn)Y(Enz 1961).

80 \

E

C o " ~

i

Me=Zn

Me2Z

60

x

/.0

~

2o

0

-273

-200

-100

0

100

200

300

/+00

500

T(*C)

Fig. 11. Saturation magnetization as a function of temperature for compounds with Z-structure, measured on polycrystalline specimens at a field of 11000 Oe for Co2Z and Zn2Z and 18000 Oe for Cu2Z (Smit and Wijn 1959).

PROPERTIES OF FERROXPLANA-TYPE

HEXAGONAL

FERRITES

409

Figure 12 shows the temperature dependence of the saturation magnetization for Ba2Zn2Fe~O46(Zn2X), Ba2Co2Fe2sO46(Co2X) and BaeZn2Fe36060(Zn2U) single crystals (Tauber et al. 1970 and Kerecman et al. 1968). If we assume that the Zn 2+ ions in Zn2X are equally distributed over the sublattices (spin-up and spin-down), the magnetic moment can be calculated as n u = 50.0/XB ( H = % T = 0 ) by reference to the collinear Gorter-type spin model of fig. 4. This calculated value is in excellent agreement with the experimental value 50.4/xB ( H = w, T = 0). However, crystal chemistry would require most of the Zn 2+ ions to be on tetrahedral site, leading to: 20 x 5 - 8 x 5

= 60/x B .

Tauber et al. (1970) explained that this roughly 18% difference between experimental and calculated result in ZnzX may arise because of the spin system is not colinear or because of non-stoichiometry of the crystals. In the case of Co2X, the calculated value 47#B ( H = ~, T = 0) is in good agreement with the experimental value 46/XB. As pointed out by Tauber et al. (1970), the agreement may be fortuitously given by the stoichiometry. The Curie temperatures of 705-+ 3 K for Zn2X and 740_+ 4 K for CozX are the highest values among the ferroxplana-type compounds containing Zn 2+ ions. The magnetic moment of Zn2U was calculated as 60.5/xB from O-s ( H = o0, T = 0 K). The value of the magnetic moment obtained from the sum of those for M- and Y-blocks, 58.4 (Gorter 1957) and 59.2 (Vinnik 1966), is in good agreement with the experimental value. However, a simple Gorter-type model (where all

100

_•

I

l

I

'

r

'

500

4OO 13r}

.x

80 .a

300

~

(:3

~:

6O C)

×

=

x

200

d~ (Co~X)

40

-.t x c9

v

E 100

2O

:~

0 0

200

/-.00

600

T (K) Fig. 12. Saturation magnetization as a function of temperature for Zn2X, Co2X and Zn2U (Tauber et al. 1970, K e r e c m a n et al. 1968).

410

M. S U G I M O T O

Z n 2+ ions are tetrahedral in the layers of Y and M but not all in spinel blocks) gives 60tXa, seemingly in better agreement. The magnetic m o m e n t s in spinels containing large amounts of Zn are lowered by the formation of angles between the m o m e n t s of octahedral ions. T a u b e r et al. described that since this effect is more pronounced in Zn2W than in Zn2Y, the experimental m o m e n t for Zn2U is still less than the value predicted from theory. The Curie t e m p e r a t u r e of Zn2U was given as 673 + 2 K. Figure 13 shows the saturation magnetization of BasZn2Ti3Fe12031(Zn2-18H) and BasMg2Ti3FeI2031(Mg2-18H) as a function of temperature. Zn2-18H could be saturated in 7 k O e fields below 15 K in the easy plane and followed a o's = o-0 + x H law. A magnetic m o m e n t nB ( H = ~, T = 0) = 14.1 ¥ 0.6/XB and Curie t e m p e r a t u r e Tc = 310~-5 K were extracted from the magnetization data. Mg2-18H crystals could not be saturated in 15.5 k O e field applied parallel to either the (0001) plane or [0001] axis below 120 K. A b o v e 120 K the magnetization followed a o%= cro+ x H law. At 300 K, Tc was measured as 391-7-3 K and nB ( H = ~, T = 0 ) = 7 . 8 * 5tXa was obtained by extrapolation from 120 K. Tauber et al. (1971) discussed the magnetic m o m e n t of these compounds as follows: A ferrimagnetic resultant according to the following site arrangement per formula unit, 9°~--~--4tet~--4 °~t was predicted. When this alignment was used to compute the

40

~30 E

B

% ×

~ 20 X

I O0

200

300

~00

T(K) Fig. 13. Saturation magnetization as a function of temperature for Znz-18H and Mg2-18H (Tauber et al. 1971).

P R O P E R T I E S OF F E R R O X P L A N A - T Y P E H E X A G O N A L F E R R I T E S

411

moment for Zn2-18H assuming the following cation distribution, ( 7 . 4 1 F e 3+, l T i 4+, 0 . 5 9 Z n 2+) ~



0

t~

.r.

0 e'~ ,,..,

'=~

C,

A

A

.=Z

6

©

Z

0 e~ 0 t'~ 0

< 455

456

. H. ST~d3LEIN

I00~

9O

tool % BaO Fig. 13. Quasi-ternary system FezO3-BaO.Fe203 (BF)-MeI10-Fe203 (S). Symbols explained in table 2.

TABLE 2 Compounds of the quasi-ternary system BaO-Fe203-MeO, Me--Divalent cation, e.g., Fe z+, Zn 2+. Stoichiometric composition (mol %)

Compound Symbol

Formula

BaO

MeO

Fe203

S BF T (hypothetical)

2(MeO.Fe203) BaO-Fe203 BaO.2Fe203

50 33.3

50 -

50 50 66.7

M M6S M4S X (M2S) W (MS)

BaO.6FezO3 2(3BaO-MeO. 19F~O3) 2(2BaO.MeO. 13Fe203) 2(BaO.MeO.7Fe203) BaO.2MeO.8Fe~O3

14.3 13.04 12.50 11.1 9.1

4.35 6.25 11.1 18.2

85.7 82.61 81.25 77.8 72.7

U (M2Y) Z (MY) Y

2(2BaO.MeO.9Fe~O3) 3BaO.2MeO. 12Fe203 2(BaO.MeO.3Fe203)

16.7 17.6 20.0

8.3 11.8 20.0

75.0 70.6 60.0

HARD FERRITESAND PLASTOFERRITES

457

(Lucchini et al. 1980a) and established that the primary magnetic properties were not changed substantially by the Ca substitution (Asti et al. 1980). According to Kojima et al. (1980) (CaO)l_x(BaO)x'n(Fe203) has a solubility range of x = 1.0 to 0.6 and n = 5.0 to 5.6. Isotropic magnets with Br = 222mT, (BH)ma~= 10.2 kJ/m 3 (1.28MGOe), BHc = 121 kA/m (1.52 kOe) and 1He = 168 kA/m (2.12 kOe) were prepared. The subject is also dealt with in section 1.3.7. The BaO-Fe203-SiO2 system is of particular interest owing to the usual addition of SiO2 in the commercial manufacture of permanent magnets. Haberey (1978) and Haberey et al. (1980a) furnished a tentative diagram for air atmosphere. At 1250°C, up to 0.55% by weight of SiO2 dissolves in BaFe120~9. Any surplus forms a second glassy phase which is rich in SiO2, has a melting point of about 1050°C and promotes sintering while impeding grain growth, cf. section 2.1.6. St/iblein (1978) too, found a glassy phase of very similar composition. 1.3.3. SrO-Fe203 system This system was examined by Batti (1962a) in I bar 02 and by Goto et al. (1971) in air. Their findings are shown in figs. 14 and 15, respectively. Both diagrams agree very well. The homogeneity range is very narrow and in the eutectic range somewhat enlarged, at most towards the side rich in SrO (Routil et al. 1974). Towards higher temperatures incongruent melting occurs at 1448°C (1 bar 02) and 1390°C (air), with the W-phase SrFe18027 (=SrO.2FeO.8Fe203) being formed. Haberey et al. (1976) likewise observed the formation of the W-phase in annealing in air above 1300°C, while in vacuum annealing above ll00°C Fe304 and 87F5 (or $4F3)formed with the release of 02. In contrast to the behaviour of BaFe12019 (figs. 7, 8, 10), in 8rFe12019 the corresponding X-phase was only found as an intermediate product (Goto 1972). Towards lower temperatures SrFe12019 is stable according to experience hitherto gained.

1600 oC

L'+SF., ~~ 1600°t100 lSO0o

~ ~ > ,

Liquid 1520°'10° 1

J

1400

, s;

÷

1210o+_10° S F+M 75

1200 ,

M Fe203

L÷M

I

f

1448°?_10°

"55 :L i

0

20

60

80

I00

Fe203

rnol ~ = Fig. 14. Phase diagramof SrO-Fe203 (Batti 1962a). Atmosphere: 02.

458

H. STJ~d3LEIN

1600 oC

i

l~O0

SrFe(}-x'L---1225+-~ 1200

•

L÷M

55.L M 6"0203

I000

8O0

0 SrO

20 ZO SrFe03x 5 5 -

i

60 rnol %

'l

80

DO

M

Fe25

Fig. 15, Phase diagram of SrO-Fe203 (Goto et al. 1971). Atmosphere: air.

Towards the Fe203-richer side the two-phase region (SrFe12019+ o~-Fe203) follows analogous to the BaO-Fe203 system. On the SrO-richer side the phases S7F5 and $3F2 are given in figs. 14 and 15 as neighbouring phases, both of them being very close to the composition $4F3 mentioned by Kanamaru et al. (1972). The eutectic temperatures of 1210°C (1 bar 02) or 1195°C (air) as well as the eutectic contents of 53.8 or 55 mole % Fe203 are close to one another. An SF phase analogous to BF does not Seem to exist (Routil et al. 1974, Haberey et al. 1976, Vogel et al. 1979a).

1.3.4. SrO-Fe2OB-based systems Very little has become known on investigations into the SrO-Fe203-MeO system. As mentioned above, the occurrence of the X- or W-phase was observed especially for Me = Fe 2+. In the S r O - F e 2 0 3 - Z n O system Slokar et al. (1978b) found the corresponding X- and W-phases at ll00°C in air. In the Sr-Fe oxide compounds containing proportions of F e 4+ a r e found more frequently than in the B a - F e oxides (Brisi et al. 1969, Goto 1972). In fig. 16 the compounds known from literature are compiled (Haberey et al. 1976). A review was also given by Sch6ps (1979). Investigations into the SrO-FeaO3-A1203 system at 1 bar 0 2 and 1200°C were carried out by Batti et al. (1967); a complete solid solution between SrFe12019 and SrAl12019 was found. The SrO-FeRO3-CaO system was investigated by Lucchini et al. (1976). It was found that at 1100°C in air there is a solid solution with M-structure between

HARD FERRITES AND PLASTOFERRITES

459

SrO

sue°g x Sr. Fe 0

20

-

Sr Fe 0

SrFe03-~"/~'-"""~- / ,

t S.Ze. o~

'°2

h

J~

(SF)

Z/\/\ 2(FeO2 )

80

60

/\

/\

gO

20

Fe203

mol % 2(FeO2) Fig. 16. Compositionsof the Sr-Fem-FeTM oxides mentioned in literature (Haberey et al. 1976). SrFe120 m and a hypothetical CaFesO13 up to a molar ratio of about 2: 1. On re-examination the result was not confirmed completely (Lucchini et al. 1980b). The primary magnetic properties were not changed substantially by the Ca substitution (Asti et al. 1980). According to Kojima et al. (1980) (CaO)l-~(SrO)x.n(Fe203) has a solubility range of x = 1.0 to 0.6 and n = 5.0 to 5.6. Isotropic magnets with Br = 220 mT, (BH)max = 10.7 kJ/m 3 (1.34 MGOe), ~Hc = 153 kA/m (1.92 kOe) and jHc = 218 kA/m (2.74 kOe) were prepared. The subject is also dealt with in section 1.3.7. Investigations into the SrO-FeaO3-SiO2 system were carried out by Kools (1978a), Kools et al. (1980), Haberey (1978) and Haberey et al. (1980a). At 1250°C they found the maximum solubility of SiO2 in SrFe12Om to be 0.6 and 0.4% by weight. Any additional SiO2 leads to the occurrence of phases which at usual sintering temperatures are liquid and, similarly to barium hexaferrite (section 1.3.2), promote sintering and impede grain growth, cf. section 2.1.6. The occurring phases were also reviewed by Broese van G r o e n o u et al. (1979b). 1.3.5. P b O - F e 2 0 3 system

The phase diagrams in air given by Berger et al. (1957) and by Mountvala et al. (1962) are shown in figs. 17 and 18, respectively. Concerning the homogeneity range of the hexaferrite phase, there is only moderate agreement. While Berger et al. (1957) give no appreciable homogeneity range, Mountvala et al. (1962) have found such a range from PbO-5Fe203 to

H. ST,g~BLEIN

460

...:-"..J /I

/J .,'

1400 oc

/

r / ,, /

•/

,PJ

! ! ! !

t

/ ,"

~

I

/

/

, /

I

/

' --- ~ pl

I I A~ "--

/7 \ \\

Viscous or / Granular ,,,

/

\ \

,

\ \

- \\

f

x "

1/

\

~%03

I

solid

"P F+PF

/LL%~I..... z: z/" '°2 F÷ Fe203

20

P~o

/

/L÷MI

%F+W

¢../

i

PbO÷P2F

6000

/

/

/ ~

t

// / L"r?;÷%%

, ,~._

1200 Gelantineous

[

,'

iI

Liquid

/I

#

I P~°:%5

5~

~o

,

60

8ol

~%

mol %

lw

M

~-~o~

=

Fig. 17. Phase diagram of PbO-Fe203 (Berger et al. 1957). Atmosphere: air.

1~00 °C

! /.. - _,

L+Fe203

1

/ 1200

1315°

//

L +.NI'"

]1

/I

looo

-

"\\

i

o~,

/L÷%~-

,oo~I PbO+L ,,~ \ I[

o I

%~-.e% ,

I"C% .M'"

II1 " 7 6 0 °

750°

i ..... ,,j..;~_o__j] -;~÷~%% Pbo

;'o--:,%

'

%F tool %

I I

' "%"~~%%~oo

,o ,' P~

,'

M

~o£~

=

Fig. 18. Phase diagram of PbO-Fe203 (Mountvala et aI. 1962). A t m o s p h e r e : air.

HARD FERRITES AND PLASTOFERRITES

461

PbO.6Fe203. The results obtained by Cocco (1955) who found a solid solution between the boundaries PbO-2.5Fe203 and PbO-5Fe203 show an even greater variance. It should be taken into account, however, that according to Adelsk61d (1938) only the composition PbO.6Fe203 explains the measured radiographic data and density values, not, however, the composition PbO@Fe203, for instance. The existence of the PbO-rich side of the PbO.6Fe203 phase therefore cannot be regarded as being proven beyond doubt, especially since equilibrium adjustment proceeds very slowly and the structures of PbO.6Fe203 and of the neighbouring phase richer in PbO are very similar and so it is difficult to distinguish between them radiographically. The thermal stability of lead hexaferrite is rather small in comparison with that of the Ba or Sr compound, namely 1250°C (Berger et al. 1957) and 1315°C (Mountvala et al. 1962); one of the decomposition products is o~-Fe203. Nothing is known about the presence of FeO-bearing compounds such as X, W, Y etc. in the PbO-Fe203 system. The differences mentioned are probably attributable to the high vapour pressure of PbO (Berger et al. 1957, Bowman et al. 1969). Towards lower temperatures the phase diagrams shown give rise to confusion as they seem to indicate the decomposition of the compound PbO-6Fe203 below 820° and 760°C, respectively. However, even after prolonged anneals of up to 1000 h in the range from 650 to 850°C this could not be determined (Berger et al. 1957). The diagrams should therefore be interpreted to the effect that no formation of PbO.6Fe203 was observed from the starting materials at these low temperatures. All workers unanimously mention o~-Fe203 as neighbouring phase for the side poorer in PbO, but PzF and PF2 for the side richer in PbO, each forming low-melting peritectics with PbO-6Fe203 at about 900 and 950°C, respectively. This is of importance for the industrial manufacture of the Ba or Sr hard ferrites when small additions of PbO are added to the raw mix as a flux.

1.3.6. BaO-SrO-PbO-Fe203-mixed systems In view of the identical structure and the only slight difference between the lattice constants of the compounds MO.6Fe203 (M = Ba, St, Pb) (maximum deviation Ac/c = 6.5%~ after Adelsk61d (1938); see also table 31) it is obvious that complete miscibility exists in the entire region of stoichiometric composition, cf. Goto (1972). Special conditions may, however, occur on the side poorer in Fe203 when the composition is not stoichiometric because the structure and molar ratio FezO3/MO of the neighbouring phases differ depending on the type of oxide MO. Batti (1962b) examined the compounds of the BaO-SrO-Fe203 system produced at 1100°C and found that depending on the BaO/SrO ratio the phases BF (Ba can in part be substituted by Sr), BSF2 (a small portion of SrO can be substituted by additional BaO) and $7F5 o c c u r . Later on isothermal sections up to 1235°C were investigated by Batti et al. (1976). Batti et al. (1968) synthesized specimens of the BaO-SrO-FezO3-AI203 system at 1400°C in i bar O2 and found that iron can be largely substituted by aluminium in the entire Bal-xSrxFe12019 region. Equal solubility of CaO was found in the entire range of BaxSrl-xFe12019 (Sloccari et al. 1977b).

462

H. STJ~BLEIN

1.3. 7. CaO-Fe203-based system In spite of the close chemical affinity of calcium, strontium and barium no hexaferrite phase exists in the system CaO-Fe203 (Adelsk61d 1938), probably because of the smaller ionic radius of Ca. However, a magnetic Ca hexaferrite phase can be stabilized by the presence of at least 2 mol % La203 (Ichinose et al. 1963, Lotgering et al. 1980). From this material isotropic and anisotropic grades exhibiting useful magnetic properties can be prepared (Yamamoto et al. 1978a, 1979a) even if La203 containing some Nd203 is used (Yamamoto et al. 1980). The magnetic properties can be improved by substitution of Ca by Ba (Yamamoto et al. 1979b) or by Sr (Yamamoto et al. 1978b).

2. Manufacturing technologies of hard ferrites

2.1. Usual technology The principle underlying the usual manufacturing process is shown diagrammatically in fig. 19. The raw materials used are generally the barium and strontium carbonates as well as natural and synthetic iron oxide o~-Fe203 (rarely magnetite Fe304). In addition to these main constituents so-called additives such as SiO2, A1203 etc. are used individually or combined in amounts of about 0.5 to 2.5% by weight. They serve to control the reaction kinetics, shrinkage and grain growth (see section 2.1.6) but sometimes they also affect the primary magnetic properties of the hexaferrite phase (saturation polarization, crystal anisotropy energy). The raw materials are intimately mixed and, if required, granulated or briquetted, and annealed at temperatures of between about 1000 and 1300°C in air ('reaction sintering', 'calcination'). Hexaferrite is thus produced more or less completely as a reaction product. The reacted mass is crushed and ground to a powder of sufficient fineness. There are several possibilities for further treatment depending on which magnet grades are to be manufactured. (a) Being anisotropic, the highest grades are obtained by wet compression moulding in a magnetic field. For this purpose the aqueous suspension, whose ferrite particles are, in the ideal case, single crystals and consist of a magnetic domain, is poured into the mould cavity. A magnetic field is applied to align the ferrite particles, thus producing a 'preferred direction' in the suspension. Compression takes place in this state, removing most of the water. (b) Not quite such high anisotropic grades are obtained by dry compression moulding of ferrite powder in a magnetic field because with this process the particles cannot be as easily aligned. The ferrite powder is obtained by removing the water and drying the ground suspension. The resultant caking of the ferrite particles impairs the directional effect of the magnetic field, which is the reason why the dried mass has to be loosened. (c) For the lowest (i.e. isotropic) grade the powder does of course not have to be alignable in compression moulding. The dried powder is therefore turned into an easier-to-process granulate which is compacted in dry condition.

HARD FERRITES AND PLASTOFERRITES

463

Section

J (4 milling)

dry [ wet

2,1.2

Granulation or of ready-to-

hard powderferrite fromraw press

materials

_ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I Reaction sintering I 4 .......

.............

I 2.1.3. ~ ............

',

I ,,r ,orushio

I

Wetm""ng

O-con'ent I' I

__/

Ioeogglomerotionl Gronu,ot,on with binder

/

PressureFiltrati°n] I magnetic Drypressingin I ~ Orypressing .......... field 4 in magnetic field ~ ................ I~

I

Production of shaped from powderParts

onisotropic magnets

. . . . . . .

-

-~

I~

l

anisotropic

I

I ~

mag,',ets I I

~-q2

- ~ - -

-..7--- ~

2.1.5.

isotropic | magnets I

--~J- -

I Final sintering I

. . . . . . . . . . .

2.1.6. ...........

.........

[

Gri!ding - i

Assemblage,

Magnetization

)-21~7.--

~ 2.1,8.

Fig. 19. Usual production technology of bulk isotropic and anisotropic hard ferrites.

Compression moulding provides a porous compact with a relative density of about 60% of the radiographic density and only little strength. Indirect shaping by machining the compact is therefore only possible to a very limited extent. In subsequent finish-sintering the relative density increases to about 90 to 98%. The attendant shrinkage (contraction) of the linear dimensions occurs parallel to the preferred direction 1.5 to 2 times as great as in the direction perpendicular to it. The compact is then much stronger but also brittle and can only be machined by grinding, cutting, etc. If necessary, the bulk magnet is completed to form a magnet system and magnetized. Under certain circumstances the sequence of these two latter operations can be reversed. This outline shows that the method usually employed in manufacturing hard ferrites consists of steps well known in powder metallurgy. Compaction under the

464

H. STJ~d3LEIN

action of a magnetic field is the only technological suitable and useful variant for magnetic powder which up to recently has frequently been improved process-wise. The manufacturing operation must be seen as the sum of a number of interdependent separate steps. Any change at one point affects the subsequent steps. The following provides details of the individual steps in manufacture and their interdependence.

2.I.1. Raw materials; main components and additives According to the molar formula MO.6Fe203 the main constituents are the oxides of iron, barium and strontium. It was found at an early stage that extreme purity is not required in production and is even undesirable if optimum magnetic values are to be achieved. This is one of the reasons why iron oxide, for instance, made in different ways and from different sources can, in principle, be used. However, undefined variations in the starting materials must be avoided owing to the interdependence of the individual steps (fig. 19). In production it is therefore of major importance that the physical and chemical parameters of the starting materials remain constant. Other important factors are a minimum price, storage capability and ease of handling. For these reasons synthetic and natural iron oxides of the a-Fe203 type (hematite) have mainly proved successful for production in long runs. Some pertinent data are compiled in table 3. With these data it must be borne in mind that purity, grain size, size distribution and shape, apparent powder and tap density of the iron oxide etc. are very much dependent on the manufacturing conditions (Gallagher et al. 1973, Stephens 1959, Balek 1970, Gadalla et al. 1973) and are controlled as much as possible by the manufacturers so that reactivity, apparent density and the content of impurities, for instance, are matched to production requirements (Erzberger 1975). Natural iron oxides have long been used in the manufacture of hard ferrites. Depending on source, the ores contain varying amounts of impurities ("gangue"), especially SiO2, which must be reduced to admissible values of less than 1% by weight. Further attendant oxides may be A1203, TiO2 etc. The particles of these iron oxides are generally angular with smooth cleavage surfaces, cf. fig. 20, and only become rounder after a long period of milling, cf. fig. 21. In this way the reactivity increases as a result of the, at first relatively large, oxide particles being reduced in size. Some of the iron oxides used are obtained by spray roasting HC1 pickling solutions from steel plants according to the formula (Eisenhuth 1968): 4FeCI2 + 4H20 + 02 ~ 2Fe203 + 8HC1. If the reaction is not fully completed some tenths percent by weight of chlorine usually remain in the iron oxide which can affect storage and processing owing to corrosion and its impact on the environment and must therefore be allowed for. The chlorine content can generally be reduced to below 0.1% by washing with water. The other impurities obviously depend on the type of steel pickled. Typical

HARD FERRITES AND PLASTOFERRITES

465

© ,.,d

'K

:Z

(2

e.

6

O

e'~

H"~

I

v..a

©

oq.

%

q3 oo

oq. cq..

c5 t-z.

cq..

06

,7

oo ¢¢)

e..,

.! ©

"7

I

tt3

e-,

oq.

c'q e-,

I

cA G~

o0 G~

i©

O o9

,o e~ ©

L) "~.=: Z

r,,t3

O

'0


"

0.6

¢11

~ 200 .~ 160 E

iI

80

~-~..~_

i

0

2.6

3.0

4.0

........

g/cm 3

~--

0.2

i--

0.1

5.0

5.3

A p p a r e n t density

Fig. 46. Remanence Br and intrinsic coercivity ~Hc vs. apparent density of Ba-hexaferrite specimens pressed with (a) and without (i) orienting magnetic field (St~iblein 1968a).

sintering relatively coarse powders shrink according to a power law whereas very fine powders shrink according to a logarithmic law (Bungardt et al. 1968). The influence of the pressure decreases with increasing compaction (Sutarno et al. 1970c, St~iblein 1973). Considering the values as a function of density provides a more quantitative view of the phenomena during sintering. The remanence values, measured parallel and perpendicular to the preferred direction, and coercivity jHo, measured parallel to the preferred direction, are shown in this way in fig. 46. The values marked (a) relate to the same specimens as in figs. 44 and 45, whereas those marked (i) refer to specimens which were manufactured from the same powder as (a) but without the application of a magnetic orienting field. The degree of alignment is shown as a dotted line. ~: = 1.0 corresponds to the saturation polarization, numbers ~ < 1.0 to fractions of it. With the isotropic specimen the degree of alignment is sc = 0.5. There are three density ranges, I, II and III, which correspond roughly to temperature ranges up to 1000, 1000 to 1200

HARD FERRITES AND PLASTOFERRITES

505

and above 1200°C, respectively, and in each of which characteristic phenomena occur. The remanence values only increase in temperature range II almost linearly but not quite proportional to the density. There are two reasons for this: the shearing effect caused by porosity (Denes 1962) and the change in the crystal texture caused by crystal growth (Rathenau et al. 1952). If the shearing effect is considered mathematically the dot-dash curves obtains in fig. 46. For the (almost) isotropic specimen this gives degrees of alignment of sc = 0.55 and 0.464 measured parallel and perpendicular to the direction of pressing respectively, regardless of specimen density, as is reasonably expected. Conversely, the degree of alignment of the anisotropic specimen only rises slightly at first in range II and then considerably in range III (Reed et al. 1973). This sharpening can also be quantitatively verified radiographicaUy, as fig. 47 shows, and also with the angular dependence of the remanence (Stiiblein et al. 1966a). c~

8

50-

40.

"s 30-

20. J 10-

g. o

11100

I

12100

I

I

1300 oIc

t~O0

Sintering temperature

Fig. 47. Pole densities of the basal plane of barium ferrite parallel to the preferred direction (St~iblein et al. 1966a).

Figures 48--50 show the structure of the specimens sintered at 1000, 1225 and 1385-1395°C. It is easy to see the transition from the initial, very porous, state (fig. 48) to a rather dense microstructure with at first relatively slight, continuous crystal growth and intercrystalline pores (fig. 49). This is followed by the appearance of a discontinuous, pronounced laminar crystal growth with intracrystalline pores (fig. 50). The phenomena in ranges I to III (fig. 46) can therefore be summarized as follows: Range ! is characterized by the curing of lattice defects, which can be best seen in the substantial rise in coercivity and a smaller rise in remanence. Compaction of the specimens and a relatively slight grain growth take place in range II. Coercivity gradually drops and the crystal texture of anisotropic specimens becomes somewhat sharper. In range III exaggerated crystal growth is the cause of the sharp drop in coercivity and the noticeable sharpening in the texture of the

506

H. STABLEIN

Fig. 48. Micrographs of Ba-hexaferrite specimens sintered at 1000°C, not etched (Stfiblein 1968a): (a) anisotropic specimen cut parallel to preferred direction, (b) as (a) but cut perpendicular to preferred direction, (c) isotropic specimen.

Fig. 49. Micrographs of Ba-hexaferrite specimens sintered at 1225°C, etched with 50% HCI at 80°C (Sti~blein 1968a): (a) anisotropic specimen cut parallel to preferred direction, (b) as (a) but cut perpendicular to preferred direction, (c) isotropic specimen.

Fig. 50. Micrographs of Ba-hexaferrite specimens, etched with 50% HC1 at 80°C (Sti~blein 1968a): (a) anisotropic specimen, sintered at 1395°C, cut parallel to preferred direction, (b) as (a) but cut perpendicular to preferred direction, (c) isotropic specimen, sintered at 1385°C.

HARD FERRITESAND PLASTOFERRITES

507

anisotropic specimen. That this sharpening is linked with an increase in remanence in spite of a sharp jHo drop, shows that the nucleation for remagnetization is made more difficult, i.e., it only begins with a negative field. On the other hand the local stray fields of the crystallites in the isotropic specimen promote the formation of remagnetization nuclei in positive fields (Rathenau et al. 1952) so that remanence becomes less than half of the saturation polarization. Further tests showed that the same magnetic values can be achieved in range II by using various temperature/time combinations, provided that sintering was adjusted to produce equal density values. It is therefore unimportant for the magnetic values whether a shorter annealing time is used at higher sintering temperature or vice versa and how high the heating and cooling rates are. Shrinkage and grain growth cannot therefore be influenced independently by varying the sintering temperature. This can be most simply interpreted by assuming a common elementary process for both phenomena (Stfiblein 1968a). Reference has already been made above to the anisotropic shrinkage of oriented specimens which is caused by the anisotropic growth rate of the hexaferrite crystals and which results in their platelet-like shape, cf. section 2.1.3 and figs. 49 and 50. Other properties, too, are more or less anisotropic, cf. sections 3.3 and 3.4, in particular thermal expansion, which amounts to about 14 or 10 x 10-6/K parallel or perpendicular to the c-axis. This results in particular difficulties in manufacturing toroidal magnets with a radial preferred direction (Kools 1973). Pieces which have been die pressed in the normal way break when heated owing to inhomogeneity of density and alignment. The inhomogeneities can be reduced by isostatic compaction and the compact strength increased so that the pieces can be heated without breaking. The stresses in the toroid which then occur with anisotropic shrinkage during sintering can balance each other out by creep; thus producing an unbroken piece at the end of the sintering cycle. During cooling, however, stresses occur as a result of the different coefficients of expansion. These stresses can result in radial cracks at the hole (maximum tangential stress) and in tangential cracks with an average diameter (maximum radial stress). They can be avoided if the ID/OD ratio of the toroid exceeds 0.80 to 0.85 because then the maximum stresses during cooling are below the ultimate strength. In large-scale commercial production sintering is usually carried out in electrically- or gas-heated continuous kilns (Petzi 1974a, 1975, 1980) where the compacts are stacked on plates and pushed through, see fig. 51. Because air is needed as sintering atmosphere these kilns are simpler than those for sintering soft magnetic ferrites which require a protective atmosphere. Barium and strontium hexaferrites are predominantly sintered at 1200 to 1250°C for several hours and the heating and cooling steps both require another 5 to 10 hours, with larger pieces even longer. Recently, however, also faster and more economic sintering techniques have been considered. Lead hexaferrites can and must be sintered at a temperature several hundred degrees lower even if only to minimize evaporation losses of PbO. Batch kilns are used for smaller quantities and in the laboratory. Fairly large batch kilns can also be used if special burners (jet burners) and rapid air circulation are employed (Remmey 1970, Bohning 1978).

508

H. ST~d3LEIN

Fig. 51. Electrically heated pusher type kiln for sintering of hard ferrites. Ceramic conveyor trays are automatically returned. Length of furnace 11 m, useful width and height 280 × 100 mm 2 (courtesy of Fa. Riedhammer, D-8500 N~rnberg).

2.1.7. Machining (grinding etc.) After sintering the magnet parts have dimensions which correspond only to a varying degree to the required dimensions. With good manufacturing methods they lie within a range below the limits listed in table 5. According to the German magnet standard D I N 17410 (May 1977) these limits are admissible for the supply of unground magnets unless manufacturer and purchaser agreed otherwise. Dimensional variations are the result of variations in the raw materials supplied and individual production steps, inhomogeneities in the material and processing conditions. This needs to be explained in more detail. With isotropic homogeneous shrinkage sintered pieces and compacts are exactly similar in the mathematical sense and dimensional variations from piece to piece only occur as a result of different degrees of shrinkage, e.g., owing to different green and/or sinter densities. The situation is similar with anisotropic, homogeneous shrinkage where there are merely different degrees of shrinkage for different spatial directions as is the case with oriented magnets. Additional dimensional variations occur with inhomogeneous shrinkage. A more or less deformed line stems from a straight edge, a more or less concave or convex surface from a plane, two parallel edges or surfaces are inclined towards one another or warped, concentric circles become

HARD FERRITES AND PLASTOFERRITES

509

TABLE 5

Permissible deviations in size of hard ferrite magnets (in mm) to D I N 17 410 (May 1977).

Isotropic hard ferrites

Rated size from to

4 6 8 10 13 16 20 25 30 35 40 45 50 55 60 70 80 90

4 6 8 10 13 16 20 25 30 35 40 45 50 55 60 70 80 90 100

perpendicular to pressing direction

in pressing direction

Anisotropic hard ferrites perpendict/lar in to pressing pressing direction direction*

___

±

-4-

0.25 0.25 0.25 0.30 0.30 0.30 0.30 0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.75 0.90 1.10 1.25 1.40

0.30 0.30 0.30 0.40 0.40 0.40 0.40 0.40 0.45 0.50 0.55 0.60 0.80 0,90 1.00 1.10 1.35 1.55 1.70

0.25 0.25 0.25 0.30 0.30 0.35 0.45 0.55 0.70 0.80 0.95 1.10 1.20 1.30 1.45 1.65 1.90 2.15 2.40

0.30 0.30 0.30 0.40 0.40 0.45 0.55 0.70 0.90 1.00 1.20 1.35 -

* Wet pressed hard ferrites are machined on the pole faces.

non-concentric and deformed etc. The causes for this are inhomogeneities in the material and varying processing conditions. Further configurational deficiencies are burrs on the edges, undesired sintered-on loose particles etc. In all these cases where these geometric defects are intolerable the piece must be machined. This is especially advisable for the pole faces of the magnet when otherwise unnecessary air gaps occur in the magnetic path which absorb too much magnetic energy. Owing to the brittleness of the material only such machining methods can be considered which produce very fine chips, e.g., grinding, tumbling, lapping or polishing. Diamonds are predominantly used as grinding medium, owing to their hardness even compared with ceramics, and sometimes silicon carbide. Good cooling is always necessary. In recent years highly advanced processes for grinding segment magnets have been used where, for example, the magnets, lying behind one another on guideways, are pushed through a gap formed by 2 grinding wheels. Both inside and outside radii can be ground in one operation. A number of fundamental investigations were carried out on the very complicated mechanism of grinding ferrites (Broese van Groenou 1975, Veldkamp et al. 1976, Broese van Groenou et al. 1977). Zones of tensile and compressive stress

510

H. STJ~3LEIN

with plastic deformation, brittle fracture and crumbling occur. Scratching on the basal plane results in more crumbling than on the prism face; other factors such as power requirement, and specific grinding energy are anisotropic, too. One particular result was that the specific grinding energy does not depend very much on the circumferential speed of the grinding wheel. During high-speed grinding with speeds of up to roughly 100 m/s a faster removal rate is possible at constant shear force, i.e., grinding time saved, or less energy can be applied with the same rate of removal, thus producing less deformation in the piece. Reference should be made at this point to the manufacture of magnets by indirect shaping. Normally the sintered piece already has its final shape and size ("direct" shaping), apart from corrective grinding. It may, however, be advisable or necessary to produce smaller parts from larger, pressed or sintered stock, i.e., as semi-finished parts, e.g., because they have better magnetic properties or because a cylinder with diametral preferred direction is easier to manufacture in this way. Assuming the pieces are sintered, precision machining methods are used in this process, too, e.g., parting off by cut-off wheels of pieces less than 1 mm thick. With pressed pieces actual machining is relatively easy to carry out but owing to their low strength they require careful handling.

2.1.8. Magnetizing and demagnetizing In as-manufactured condition a permanent magnet is either totally non-magnetic or only incompletely magnetized. It is usually magnetized after being incorporated into the magnet system. The required amount of field strength effective in the permanent magnet is 2 to 3 times as great as its coercivity jHc (St/iblein 1963, Dietrich 1969). The direction and spatial directional distribution of the magnetizing field are brought into line with the desired polarized state of the permanent magnet. How well this must be done depends, among other things, on the material. With isotropic magnets the remanence accurately reflects the directional distribution and any inhomogeneities of the magnetizing field after it has been switched off. With anisotropic magnets, however, the preferred direction largely determines the remanent state. Figure 52 shows that remanence is independent of /3 where deviations/3 of the magnetizing field from the preferred direction are not too great. This is due to the fact that the polarization direction in every crystallite in the remanent state runs parallel to the local c-axis. With complete alignment of all crystallites remanence would be independent of angle/3 (apart from a certain small range around/3 ~ ~-/2). With actual specimens it depends on the degree of alignment. With the well-aligned 1350°C specimen in fig. 52 remanence only drops from/3 ~ 50 to 60 ° upwards, whereas with the less well-aligned 1100°C specimen it starts falling from/3 ~ 30 to 40 ° upwards. In many cases a permanent magnet is not used in the fully magnetized state. One reason for this may be that a certain magnetic flux is required of the magnet. However, in large production runs geometrical and magnetic variations occur from piece to piece. These are eliminated by defined, individual weakening ('calibration'). Another reason is the higher stability of the weakened condition (Gould 1962,

HARD FERRITES AND PLASTOFERRITES

511

Preferred axis Remanence~

kfagnetizing field

~

Remanence r2

Perfect alignment ~" 1.0

_

~ ~ 5 0 o c

/ _

1250°C~\ ,

E ~

si, feting mp t e\

\\

O~

Q~

IlO0°C -1250oC 1350°C i

i

i

i

i

30 ° 60° Deviation from preferred axis

~0 o

Fig. 52. Relative remanence values rl and r2 of oriented barium hexaferrite, measured parallel and perpendicular, respectively, to the preferred direction, after magnetizing at /3° from preferred axis (St~iblein et al. 1966a).

Dietrich 1968). This condition is achieved by partial demagnetization, generally using an alternating field of sufficient amplitude which diminishes slowly enough, and less frequently by means of an opposing field, rotating field or by thermal treatment. Defined weakening is not simple, particularly with anisotropic grades owing to their rectangular hysteresis loop, if the alternating field is applied parallel to the preferred direction as the dependence of the field amplitude is relatively large, cf. fig. 53. This disadvantage can be avoided when the position is perpendicular to the demagnetizing field and preferred direction. However, higher field strengths are required for the same degree of weakening. The abovementioned methods can, of course, be used for complete demagnetization ('neutralization') too. The various weakening or demagnetizing methods result in different domain structures (Tanasoiu 1972) even if the overall macroscopic condition is the same. This can be seen, for instance, in the shape of the magnetization curve, cf. fig. 54 (St/iblein 1970). Specimens demagnetized thermally or with an a.c. or d.c. field react completely differently to any applied field. Moreover, with a.c. demagnetizing field weakening the temperature and field direction with respect to the preferred direction are important. Magnetization and demagnetization techniques have been described in numerous papers and text books (Rademakers et al. 1957, Dambier et al. 1960, Underhill 1957, Parker et al. 1962, Knight 1962, Schiller et al. 1970).

~00 rn7

300

¢ 200

~ 2

I00

00

200

400 No

600 kA/rn

--

Fig. 53. Remanence Br of an anisotropic hexaferrite magnet with intrinsic coercivity 1He = 143 k A / m after full magnetization and subsequent demagnetization in a gradual diminishing a.c. field of initial amplitude H0. Curve (1): field parallel to preferred axis, curve (2): field perpendicular to preferred axis.

400mf

300L200.7

100.

s

O

kA/

Fig. 54. Magnetization curves and parts of the outer hysteresis loop (first quadrant) of an anisotropic barium hexaferrite specimen having Br = 364 mT (3.64 kG) and jHc = 240 k A / m (3.02 kOe), measured parallel to preferred axis, after different methods and conditions of demagnetization (St/iblein 1970). Curve (1): thermal; curve (2): a.c. at -196°C, ± preferred axis; curve (3): a.c. at -196°C, [[ preferred axis; curve (4): a.c. at 20°C,.A- preferred axis; curve (5): a.c. at 20°C, I] preferred axis; curve (6): a.c. at 300°C, ± preferred axis; curve (7): a.c. at 300°C, II preferred axis; curve (8): d.c., starting from outer loop, third quadrant. 512

HARD FERRITES AND PLASTOFERRITES

513

2.2. Special technologies In terms of the magnetic values attainable, the manufacturing process described in section 2.1 has proved to be highly economic but it is not the only one that can be employed. In the following further possibilities for the manufacture of hard ferrites are described. In table 6 they are compared diagrammatically with the TABLE 6 Technologies available for manufacturing magnets.

D~ hnique

0 "i"~ Manufacturing step

to

Mechanical m i x i n g P r e c i p i t a t i o n of the raw materials Reaction in furnace Reaction in fluidized bed Reaction in salt bath

Crushing,

grinding

Die p r e s s i n g at room temperature S h a p i n g by rblling,

extruding

i

Hot p r e s s i n g

Sintering

Further p r o c e s s i n g

514

H. ST]kBLEIN

conventional process. Some of these processes require fewer main operations, e.g., the sing!e-sintering technique where reaction and final sintering take place simultaneously, or hot pressing of the powder where shaping and sintering are carried out at the same time. In other processes one operation is replaced by another. This includes the precipitation techniques where mechanical mixing is at least partly replaced by a precipitation reaction, the fluidized bed processes where the reacting mass is suspended in the form of fine particles in a stream of gas, or plastic working (rolling, extruding) which, compared with the pressing of a powder or a suspension of powder particles, offers different possibilities. In the salt bath processes both mixing and reaction takes place together in a molten bath. Naturally, the processes can be combined, for instance, co-precipitation with hot pressing or single sintering with rolling. A review on non-conventional powder preparation techniques of ceramic powders was given by Johnson (1981). While offering some advantages, these special technologies generally entail major drawbacks. With further advances in technology, it may be that one or the other process will be employed to a greater extent than at present.

2.2.1. Single sintering technique The characteristic feature of this technique is that only one single sintering operation takes place, cf. table 6. This means that during sintering the raw materials must react to form hexaferrite (cf. section 2.1.3) and, at the same time, a dense, true-to-shape body must be produced (cf. section 2.1.6). Good mixing and high reactivity of the raw materials are, of course, particularly important in this process. This is facilitated or ensured by intensive mixing and milling of the mix and by the addition of substances (e.g. SiO2, PbO, B203) which promote sintering. Shrinkage on sintering is about 1.5 times that in double sintering as the raw mix which is shaped generally has a density on pressing of between 2.0 and 2.6 g/era~ at the usual pressures of around 0.5 kbar compared with a typical density of pressed ferrite powder of 2.7-3.3 g/cm3. This has to be taken into account in the sizing of the press-working tools. The sintering temperature is roughly equal to that applied in double sintering. Milling time and sintering temperature have to be adapted to one another, as is shown in fig. 55 (Stfiblein 1971), to ensure that a dense and, at the same time, high-coercivity body is produced. Single-sintered parts show a greater tendency to inhomogeneous shrinkage (distortion) than doubled-sintered parts. The extent, however, largely depends on the raw material used and the processing conditions. Isotropic or at the most weakly anisotopic magnets are normally obtained by means of single sintering. More detailed investigations have, however, shown that appreciably anisotropic parts can also be manufactured owing to the fact that the platelet-shaped hexaferrite crystals grow on plane Fe203 surfaces (section 2.1.3). It was found that sintering always produces an isotropic magnet if the raw mix contains iron oxides of isometric shape (spherical, cubical) regardless of other conditions under which manufacture takes place. Anisotropic magnets, however, are obtained when mixes are reacted where the iron oxide particles are anisometric (acicular, platelet-shaped) and if these were oriented during shaping

H A R D FERRITES AND PLASTOFERRITES

515

oc 1300

1250

2.2

0.8

0.2

0

0

0

0.8

7.~

7.5

Z6

Z9

3.6

0.8

1.2

7.3

Z5

Z6 ', 8.3

"8.'~

6.0

f

E " 1200

•

~\

.....

•

.

.

8.5 •

jJ

\

•

/

89

L..

1150

1100

6.5

6.9

72

7"6. 01 ./?6

6o

2/

2.8

4.8

~.5

56

i

t

i

i

1

2

4

6.6 i

8 16 Milling time

go i

I

32 h 6~

Fig. 55. (BH)m.x value in kJ/m 3 vs. milling time (vibration mill, wet) and sintering temperature. Material: mixture of synthetic a-Fe2Oa (Bayer 1660) and BaCO3.

and retained their configuration up to the hexaferrite reaction. Acicular iron oxides occur, for instance, when moisture is carefully withdrawn from the acicular a-FeOOH (goethite). However, the particle shape of the natural iron oxides (hematite) is as a rule isometric. Nevertheless, there are noteworthy exceptions probably connected with the formation of the iron ore deposits where the particles show a propensity for cleavage along the basal plane. Processing is basically the same as with the isotropic magnets. Owing to the shape of the particles only a few special requirements have to be met. Milling is not only important for increasing the activity during sintering but also because it permits the shape of the particles to be influenced. Depending on the oxide used, particulate aggregates, for instance, not capable of being aligned can be separated into single alignable particles or an existing anisometry of the particles can be destroyed so that these lose their alignability. In shaping the anisometric particles have to be aligned. In dry or wet pressing this occurs when the punch moves into the die; this is also the case with the platelet-shaped hexaferrite particles (press working anisotropy, cf. section 2.1.5). The particles can also be aligned by rolling or extruding a plasticized raw mix. Suitable plasticizing agents are soft waxes, for instance, with fusion points of around 45°C, which are easy to shape at room temperature and can be easily evaporated or drained after shaping. Figure 56 shows the influence of the sintering temperature on the demagnetization curve of a specimen which originally consisted of a mixture of SrCO3 and acicular a-Fe203. Within a narrow temperature range (a few multiples of 10 degrees) the transition takes place from the high coercivity to the low coercivity condition,_ the duration of annealing also making itself felt. This transition is due to abnormal grain growth. In the case described the growing crystallites were fairly well aligned so that growth at the expense of the small, poorly aligned crystallites led to an improvement in texture and thus to an increase in remanence. The remanence

516

H. STJifl3LEIN 400

rnT 300 200 tO0 1 6 l~J

-400

_._

~

b

o.~

kA/rn -300 Field strength H -

tO0 ~-

- 200 -300 -

400

-500 Fig. 56. Demagnetization curves of differently sintered specimens. Starting material: mixture of synthetic, needle-like c~-FeaO3 (Bayer) and SrCO3, wet pressed.

~00 mT

(BH)max=15.9 k J

j

300 200 100

Field strength H /

-30'9

kA/m

~00

~,I

/.J~'-~'O0

,~,"

b

"~-lb

/ k

too 200 300

-400

Fig. 57. Demagnetization curves of differently prepared specimens after sintering at 1230°C. Starting material: mixture of natural hematite with pronounced cleavability along basal plane and BaCO3, Curves (la) and (lb): anisotropic magnet due to wet milling and wet pressing of the mixture, measured parallel and perpendicular to pressing direction. Curve (2): isotropic magnet due to dry milling and dry pressing.

HARD FERRITES AND PLASTOFERRITES

517

values attainable correspond to those of double-sintered, anisotropic magnets. As, however, this high anisotropy occurs owing to crystal growth and thus at the expense of coercivity, the magnetic values of single-sintered anisotropic specimens are, as a rule, not as good as those of the double-sintered specimens. It should be pointed out that with poorly oriented specimens abnormal crystal growth does not lead to an improvement in remanence. This behaviour is analogous to that of double-sintered magnets (section 2.1.6). Figure 57 shows the demagnetization curves of a mix subjected to a different treatment. Natural iron oxides and barium carbonate were used. After 16 hours of wet milling in a vibration mill, wet die pressing and sintering at 1230°C an anisotropic magnet was obtained with a (BH)max value of 15.9 kJ/cm 3 (2.0 MGOe) in the preferred direction. After 22 hours of dry milling, dry die pressing and sintering at 1250°C, however, an isotropic body with a (BH)max value of 7.2 kJ/m 3 (0.9 MGOe) was obtained. Even better values can be achieved with synthetic iron oxides or hydroxides (Takada et al. 1970b, Esper et al. 1974). Brief mention may also be made of another manufacturing method which is similar to both single and double sintering. However, in this process anisometric iron oxide particles are also used and the mix die pressed. After reaction, pressing is repeated in the same die without prior milling, which is analogous to calibration, and sintering repeated. This process enables oriented magnets to be produced without using any magnetic field (DE-OS 2 110 489).

2.2.2. Precipitation techniques With these techniques at least one of the metal ions derives from a feed substance obtained by precipitation or hydrolysis from an aqueous solution. The term co-precipitation is used when all cations are derived from a common solution. The aim of these techniques is to obtain as intimate mixing of the feed materials as possible from the very start. This facilitates the formation of the compound in the subsequent reaction step owing to the short diffusion paths. The reaction can take place at relatively low temperatures and under optimum conditions a powder can be obtained containing single domain particles of correspondingly high coercivity. The next logical step would be to obtain the hexaferrite rather than the mix of feed substances from the aqueous phase. This appears to be possible but its practicability cannot yet be assessed for hexaferrites. The advantages offered by these techniques are the following: they can be used even with contaminated raw materials (self-cleaning effect), there is no carry-over of impurities by abrasion in milling and a narrow particle-size range is obtained. The large water requirements must be regarded as a disadvantage for commercial applications. In actual operating practice, an aqueous solution of one or several salts is used. As metal salts, especially chlorides (not with lead) nitrates, oxalates, and acetates can be considered. The hydroxides or carbonates of these metals, which are practically insoluble in water (exception: Ba(OH)2), can be recovered from the solution. This takes place either by precipitation by means of an alkaline solution (e.g. NaOH, NH4OH) and/or water-soluble carbonate (e.g. Na2CO3, ammonia

518

H. ST~kBLEIN

carbonate) or passing NH3 and C O 2 gas through the solution or by means of the thermal hydrolysis of the salts. Another technique is called freeze drying, because a thin stream of aqueous solution is squirted into a cold, immiscible liquid forming freezed granules there. The granules are separated from the liquid and the ice is sublimated, while the raw mixture is retained (Schnettler et al. 1968). The particle size of the precipitated product depends not only on the type of product but particularly on the conditions under which precipitation takes place and can range from about 0.01 to 10 txm. The temperature necessary in the subsequent hexaferrite reaction depends on the particle size. Hexaferrite single-domain particles of very high coercivity can only be obtained from very fine feed substances which react at temperatures of 800 to 900°C. Table 7 shows some of the results published in literature. The precipitation techniques can be subdivided into chemical co-precipitation, chemical partial precipitation, thermal hydrolysis, electrolytic co-precipitation and hydrothermal treatment. Most of the tests were carried out using chemical precipitation. In the tests carried out by Sutarno et al. (1967) the metal salts separated in very different particle sizes (table 7). While the iron hydroxide was amorphous, the carbonates of barium, strontium and lead were present in particle sizes of around 5 ~xm. As a result, segregation occurred with larger mixes and the formation of hexaferrites took place in the same temperature range as with mechanically mixed feeds. Obviously it is of no advantage if only one raw material is highly reactive. All raw materials must exhibit a sufficient degree of reactivity and steps must be taken to ensure that they are intimately mixed. The tests carried out by Haneda et al. (1973b, 1974b) led to amorphous pre~ cipitation products and the main quantity reacted to form hexaferrite after annealing at 800 to 850°C. After two hours of annealing at 925°C, a particle size of 0.15 ixm (BET-method), a specific saturation polarization of Js/p = 85.16 mT cm3/g (o-s = 67.8emu) and a c0ercivity jHc of 480 kA/m (6 kOe) were obtained with non-oriented specimens. The hysteresis loops measured and calculated according to Stoner-Wohlfarth (1948) compared favourably from which the conclusion can be drawn that there was coherent reversal of magnetization in these obviously almost ideal crystals. Further processing by pressing and sintering or by hot pressing (cf. section 2.2:5) produced partly oriented, high-coercivity specimens. Similar results were attained by Gordes (1973) and Roos et al. (1977) who, in addition, succeeded in increasing the coercivity of the particles to 1He = 510 kA/m (6.4 kOe) and the specific saturation polarization to JJp--88.8mTcm3/g (O's= 70.7 emu) by strong etching in hydrochloric acid with an attendant loss of material of about 70%. The hexaferrite formation of the co-precipitated mixture took place between 700 and 800°C possibly without BaFe204 as an intermediate phase and yielded a small grain size distribution (Roos 1979, 1980), see also section 2.1.3. Mee et al. (1963) used a chemical precipitation technique (not described in detail) for making platelet-shaped Ba- and Sr-hexaferrite particles with diameters from 80 to 150nm and coercivities of 425 and 456kA/m (5.35 and 5.75 kOe) respectively. Goldman et al. (1977) investigated the influence of different manufacturing parameters in chemical co-precipitation for magnetically soft ferrites. Qian et al. (1981) prepared Sr-hexaferrite by annealing a co-precipitated

HARD FERRITES AND PLASTOFERRITES

519

mixture of ferric hydroxide and strontium laurate for 70 days at 550°C. The mixture was prepared from iron nitrate, strontium nitrate, lauric acid and ammonium hydroxide. Intermediates are y-Fe203 and solid solutions of SrO in y-Fe203. No magnetic or grain size data were reported. While the above-mentioned co-precipitation method mainly served to produce magnetically ideal hexaferrite particles, tests for chemical partial precipitation were conducted with a view to establishing possible advantages in the industrial manufacture of hard ferrites. The iron oxide is not precipitated but exists from the very start as a solid phase. The alkaline earth component is either introduced in the form of a solution, e.g., St(NO3)2 (Sutarno et al. 1969) or Ba(OH)2 (Erickson 1962) or initially as a solid phase SrSO4 which is re-precipitated into SrCO3 by ion exchange (Cochardt 1966). In the latter process, the fact that SrCO3 is even more insoluble in water than SrSO4 is utilized so that the ion exchange takes place in the presence of Na2CO3 or (NH3)2CO3. The process has long been known for making SrCO3 from SrSO4 (Gallo 1936, Ullmanns Encyclopfidie 1965, Sutarno et al. 1970b) but was used by Cochardt (1969) for making strontium hexaferrite. In this H - C process (H for hematite, C for celestite = natural strontium sulphate) the raw materials iron oxide and celestite are ground as an aqueous suspension together with Na2CO3 in a mill, with size reduction, blending and chemical reaction taking place simultaneously (Steinort 1974). An analogous approach cannot be used for barium hexaferrite because BaSO4 is more insoluble in water than BaCO3. By thermal hydrolysis of a Ba- and Fe-acetate solution in contact with paraffin oil at a temperature of 300°C Metzer et al. (1974, 1975) produced amorphous precipitates with a specific surface area of more than 100 m2/g and particle sizes from 10 to 20 nm from which hexaferrite powder with a specific surface area of 5.7 m2/g, a particle size of 0.2 Ixm and a coercivity jHo of 420 kA/m (5.3 kOe) could be obtained by annealing. Beer et al. (1958) described a continuous electrolytic co-precipitation process for making powders for isotropic barium hexaferrites. This process uses metallic cathodes and an alkaline electrolyte; no detailed information, however, is given. By means of freeze drying Miller (1970) produced barium hexaferrites starting with a solution of iron oxalate and barium acetate. Other substance combinations turned out to be more disadvantageous. Specimens with different Fe203/BaO ratios having different additives of SiO2, A1203, PbO, Bi203, CaO or TiO2 were dry or hot pressed without application of a magnetic field. While all the processes described above furnish a raw mix which needs to be heat treated for the formation of hexaferrites, the hydrothermal process (Takada et al. 1970a, Van der Giessen 1970) furnishes barium hexaferrite particles directly as precipitate. No magnetic data, however, were given. With the DS process the techniques of co-precipitation and spray calcining are carried out simultaneously, see section 2.2.4.

2.2..3. Melting techniques As explained in section 1.3, it is not possible to directly separate Ba(Sr)Fe~:O19 crystals from a melt of alkaline earth and iron oxide with a cation ratio,

520

H. STABLEIN

¢

(#)

L

=

"d

o .=

II

~=~

a3

0

t'-

~o~ 0

0

n =

0

i

to~ ~

h

#,=

0 =

!D.

,.-1

= 0

H A R D FERRITES A N D PLASTOFERRITES

521

tt3

0

>

~o~

•. ~ ~.s •~.~ ~o ..~

so ~

o~ -

~., ..~ '7:J

>

o

i

0 ~.~ 0

0

~o

.~

0

.'=

< cO

p~ o

[]

o.. = 0

0

,~

t'¢3

522

H. ST~A3LEIN

Ba(Sr):Fe = 1:12, at least not in air. This was confirmed in tests carried out by Bergmann (1958) who attempted to make BaFe12019 and found a lack of oxygen in the reaction product. With BaFea2019 and, presumably, also SrFelzO19, higher oxygen pressures are needed to avoid the formation of primary phases containing Fe 2+. From melts richer in B a O or SrO, however, hexaferrite can be separated as a primary phase (Kooy 1958, Goto et al. 1971). This process supplies monocrystals in sizes of up to several millimeters. Whether high-coercivity crystals in sizes from 0.1 to 1 ~ m can also be made is not known. Non-crystalline solid specimens of the systems BaO-Fe203 and PbO-Fe203 can be made in a larger range of compositions by splat-cooling the melt (Kantor et al. 1973). On heating a eutectic specimen (40mol % BaO, 60tool % Fe203) BaO.Fe203 crystallizes at 610°C and at 770°C BaO-6Fe203 also (Monteil et al. 1977). No detailed information was given on their magnetic properties, however. In an analogous way amorphous specimens of the system SrO-Fe203 can be prepared, too, in which SrO.6Fe203 crystals are formed at temperatures of at least 720°C (Monteil et al. 1978). Relatively large crystals can be crystallized out of molten fluxes, e.g., from melts containing NaFeO2 or PbO, Bi203, B203 or alkali halide/earth alkali halide (composition, for instance, as with Arendt 1973b). These processes are used to make crystals for scientific purposes, e.g., for studying domain configurations and wall movements. In the past few years a number of melting processes has become known in which technically interesting aspects play a role. They are compiled in table 8. According to Routil et al. (1969, 1971, 1974), Ba- and Sr-hexaferrites can be made directly using their sulphates, i.e., from the most important minerals of barium and strontium without it being first necessary to convert them into carbonates. In addition to the raw materials sulphate and iron oxide only NaCO3 or other suitable additives are required. Stoichiometric hexaferrite crystals crystallize from a large range of compositions; two possibilities are shown in table 8. Typical reaction conditions are 1 hour at 1200°C in air. The formation of strontium hexaferrite was investigated in detail and NazFe204 and 7SrO.5Fe203 were found as intermediate products. Depending on the composition of the raw mix and temperature, the process can be operated as a straight-forward solid state reaction or as a reaction in which a molten component is present. The iron oxide used need not be particularly fine and an excess of A1203 and SiO2 impurities is converted into water-soluble Na-compounds (self-cleaning). Phase separation of the reaction product is carried out by leaching and magnetic separation. Depending on reaction conditions, the hexaferrite particles can be in millimeter-sizes. Magnetic properties are not mentioned. The process of Wickham (1970) is based on the normal raw material mix of iron oxide and Ba- or Sr-carbonate which can react in a melt composed of 80 mol % Na2SO4 and 20 mol % K2S04 at 940°C. In this composition, the sulphate mixture has the lowest melting point of 845°C. Fine crystalline reaction products BaFe12019 or SrFe~20~9 can therefore presumably be made although no information is furnished on this.

H A R D FERRITES A N D PLASTOFERRITES

523

S" ,-£

.~ ....,


1 bar) and temperature (~ 800°C). In this way the microstructure can be influenced as desired to a much greater extent than is possible in a two-stage process of pressing at room temperature (section 2.1.5) followed by sintering (section 2.1.6). Owing to the effect of the pressure, the temperature can be 100 or even several 100°C lower than in normal sintering so that crystal growth is reduced. In many cases the process produces particles of very low porosity and/or particularly small crystallite size. Such a structure is also desired in hard ferrites in order to obtain at the same time higher remanence and high coercivity (Stuijts 1970, 1973, Jonker et al. 1971). Compaction is usually effected in a die with punches, similar to die pressing at room temperature (section 2.1.5). The hot isostatic method could, in principle, also be used but nothing is as yet known about its use in the manufacture of hexaferrites. Contrary to hot pressing, hot working ideally uses a dense body, the shape of which is changed in the plastic stage. Press forging (upsetting) is such a possibility in which the width is enlarged at the expense of the height of the part. An inverse change of shape is obtained in extruding which produces a thinner and longer part. While such forming is impossible with hexaferrites at room temperature, it can be carried out to a limited extent at elevated temperature. Table 10 and 11 give data from literature on hot pressing and hot forming. It should be taken into account that in some cases both operations took place more or less simultaneously. As the outlines show, very differently prepared starting specimens were used, namely from raw mixes, from reacted hexaferrite powder or from pre-oriented and pre-sintered specimens. The composition of the specimens also varies greatly and has not been defined in all cases. The following processing parameters are mentioned: pressing 5 seconds to 1 hour; temperature preferably 1000 to 1200°C; pressure 35 bar to 12 kbar; tool material A1203, graphite, ZrO2, SiC, Fe. It can be seen that the magnetic values attained vary within wide limits. This is attributable, on the one hand, to the different conditions of the specimens used and, on the other, to the different conditions in hot forming. For a given specimen density, the type and extent of crystal orientation is, of course, of decisive importance for the remanence. With the specimens previously subjected to orientation in a magnetic field a higher remanence is generally obtained than with non-pre-oriented specimens. Flow of the material and crystal growth during compaction play a considerable role in the formation of the texture. According to Von Basel (1981) oriented grain growth is the main reason for the increase of the degree of texture with increasing pressing time. Even die pressing of a raw mix gives anisotropic sintered bodies with a c-axes fibre texture. Such a fibre texture seems to be even more pronounced in press forging because the specimen is then not only shortened axially, but also widened radially. The opposite occurs in extrusion where the specimen is elongated axially and made smaller radially. The c-axes therefore orient themselves preferably perpendicularly to the direction of extrusion and a c-axes ring fibre texture is

HARD FERRITES AND PLASTOFERRITES

527

formed. With such a texture the remanence perpendicular to the direction of extrusion can at best only reach the 2/7r part (approximately 64%) of the saturation polarization, see fig. 70(b). The highest jHc values after hot forming are attained if high-coercivity ferrite powder is used which was obtained by co-precipitation (section 2.2.2). Haneda et al. (1974b) produced in this way dense specimens with iHc = 400 kA/m (5 kOe) which corresponds to about 83% of the initial value of jHc = 480 kA/m (6 kOe) of the powder used. The possible reaction between the hexaferrite and the die wall is a difficulty which these hot techniques entail. The presence of magnetite and other not identified phases impairs the saturation polarization and the permanent magnet characteristics and causes, particularly towards the abscissa, a buckled, e.g. concave, course of the demagnetization curve in the second quadrant so that the (BH)max value and the coercivities fl-/~ and jHc are adversely affected to a fairly great extent. In such cases, these characteristics can be substantially improved by an oxidizing annealing treatment in air, e.g. for two hours at 950°C (St~iblein 1974).

2.2.6. Rolling and extrusion techniques Ferrite powder is usually shaped by pressing using a die and punch as described in section 2.1.5. This technique enables practically all shapes of magnets required in various applications to be manufactured. The typical feature of this technique is that well defined components can thus be made. In contrast, rolling (calendering) or extrusion produces semi-finished products of any length or width which then has to be cut or stemmed to the desired dimensions in a further operation. While these techniques are frequently used for plastic-bonded hard ferrites (section 4.1) they are of a more limited importance for the compact ferrites. Ferrite powder alone is not amenable to rolling or extruding. A binding agent has therefore to be added to make the powder cohesive, to impart movability to the particles and plasticity to the mix and which can be removed on sintering without leaving any or few residuals. For this purpose, the same substances can be used as in granulation (cf. section 2.1.2), but in a much higher concentration, e.g. 50% by volume. Some possible combinations of binding and plasticising agents were mentioned by Schat et al. ~(1970). Strijbos (1973) investigated the mechanism of removing carbonaceous residuals of burnt binding agents. Table 12 gives some data from literature. A particularly important feature of these techniques is that they enable anisometrically-shaped powder particles (acicular or platelet shape) to be oriented by the shearing forces set up between the rolls or in the die and in this way to make the product anisotropic. Using this method, Carlow et al. (1968) oriented Si3N4 whiskers by extrusion with the whisker axes being arranged parallel to the direction of extrusion. With hexaferrites the platelet shape of the particles is utilized (cf. section 2.1.5). The hexaferrite powder used must consist of alignable crystallites. In the "Ferriroll" process (BH)m,x values of up to 28kJ/m 3 (3.5MGOe) are said to have been attained by rolling or calendering, with 0.25 mm thick foils having been stacked until the desired thickness of the part was reached (anonymous, 1967). For this purpose, lead hexaferrite powder with

528

H. STJid3LEIN

P ,...i

-4

o~ ~

£ o

0

p

~z

~E

~E e~

"0

&

..~ ~..~ "~ ~ 0 0

•~ -'~

~ .=

"~~

~ ~

~

o

o

©

~ o

~~§o

e-

~a

o

HARD FERRITES AND PLASTOFERRITES

.-Z

D~

v

0

cr~

+

~'"

~z

t---

,.j

r,

.i ~

1

1

¢'4

0

~ ~ ~ -~ ~ , ~ . ~ ~ . ~

r~

ii i.! o

='~~

529

530

H. ST)i~BLEIN

t~

8

~ z

C)

~z

~~

~z

C)

e..

©

~'~

&

~'~

-..~

;:h

•- . ~ .o ~ ~

-:

~=~

Z

0

,.~ ,-

,.9o r~ ~ c ~ o "~

'~

~.~.~,~ 0

0

©

0

r~

HARD FERRITES AND PLASTOFERRITES

,.A t~ ,-.A

Z

e., O

tt3

O

e-, e-,

0

i

,'

O

,"'

,9

e.,

?

O

"L"

'~

O

~5

"~

,A ©

~

e-, ," 09 e'., r/)

;~

e'~ t.N

~::~ .,-., © O

O

531

532

H. ST~d3LEIN

t'--

,...i

O

O

,;4

..= o

m

,m

t"q

o

~

~oq.

O

..= E

E e©

+ o

..= ,= ~ '~ ~ ~ o

#

e~

"6 •,.

~

~

~

g ~ o'z=-

i o E

7

O

25

O oe,,~ e-.

-.=

~, :.m

"

O

e~

H A R D FERRITES A N D PLASTOFERRITES

oo

0 O0

0

~

~0

~

~0~

~.~

i

"~ °~

0

o~

533

534

H. ST~d3LEIN Z {-q

'6

©

©

z.. o

~=

~

O

¢'5

o

0

O

c-

'6 o

~oo ~

-o ~NI

o

.~

~a 0.


686

Reference Kools (1973) IHamamura (1973) Clark et al. (1976) TDK (1978) Gershov (1963) Kools (1973) Hamamura (1973) TDK (1978) Cavallotti et al. (1979) Kools (1973) Clark et al. (1976) TDK (1978)

On the other hand, the compressive strength determined by various authors exhibits comparatively small variations. As expected, the values are considerably higher than the tensile and flexural strength values. For the impact strength (notched-bar impact test) Hamamura (1973) found values between 2.4 and 9.8 kgm/cm 2 without any distinct effect of anisotropy but proportional to the density. The critical stress-intensity factor K~c was determined in connection with studies on crack formation and the grindability of hexaferrites, cf. section 2.1.7. The values in table 29 clearly show an influence of anisotropy. Cleavage along the TABLE 29 Critical stress-intensity factor Krc in MN/m 3/2 of commercial hard ferrites at room temperature. Specimen Anisotropic SrM, fracture surface ]]preferred axis Anisotropic SrM, fracture surface ± preferred axis Anisotropic SrM, fracture surface II preferred axis Anisotropic SrM, fracture surface 2 preferred axis Anisotropic BaM, fracture surface II preferred axis Anis0tropic BaM, fracture surface ± preferred axis Isotropic BaM Isotropic BaM * Maximum values are obtained for molar ratio FeaO3/SrO ~ 5.5.

Value

Reference

2.12"8[)

Veldkamp et al. (1976)

2.1-2.5" 1.5-2.1"

Veldkamp et al. (1979)

2.83-+0.101 0.96±0.05~ Iwasa et al. (1981) 1.57 ± 0.04J 1.3-3.2 Cavallotti et al. (1979)

574

H. S T ~ 3 L E I N

basal plane is easier than perpendicular to it. According to Veldkamp et al. (1976) K~c depends on the molar ratio Fe2OjSrO = n with anisotropic SrM. It slowly increases from n = 4.4 to a maximum at n ~ 5.5 and drops even more quickly when n is higher. The figures in table 29 are averages; the related variations reached a maximum of about _ 1 g N / m 3/2. A dependence on the molar ratio was also found with isotropic BaM specimens, but the K,c maximum occurred at n ~ 4 . 5 or lower (Cavallotti et al. 1979). The same authors also observed an influence of the pressing process: with dry-pressed specimens K~c= 2.73 _+0.24 MN/m 3/2, with wet-pressed specimens K~ = 2.05 MN/m 3/2. According to Iwasa et al. (1981) KI~ of BaM specimens decreased between room temperature and 1000°C linearly and rather slightly and between 1000 and 1200°C drastically. In the first mentioned region the temperature dependence is 6.23--_ 0.03 (isotropic), 0.42 -- 0.03 ([]c) and (8.38 -+ 0.06) x 10 .4 MN/m 312K (±c), and for the second region in the order of 10 -a MN/m 3/2 K. No anomaly was found around the Curie temperature. Fracture surface energies of 6.35 + 0 . 3 2 (isotropic), 2.82-+0.30 (][c) and 11.92-+ 0.84 J/m 2 ( ± c ) w e r e deduced.

T A B L E 30 Hardness of commercial hard ferrites at room temperature. Hardness Vickers

Specimen Anisotropic SrM, II preferred axis Anisotropic SrM, L preferred axis SrM Anisotropic B a M SrM, single cryst, no. 33,

Value

Reference

8.6 k N / m m ; 5.6 k N / m m 2 6.5 k N / m m 2 ca. 6 k N / m m 2 10.3 ± 1.0 k N / m m 2

Veldkamp et al. (1976) Broese van Groenou et al. (1979a) see fig. 44

IIc-axis SrM, single cryst, no. 33, ± c-axis SrM, single cryst, no. 57,

7.5 ±0.5 k N / m m 2

Jahn (1968)

9.6 ± 1.0 k N / m m 2

II c-axis SrM, single cryst, no. 57, L c-axis PbM, single crystal Ritz

SrM

Rockwell, Scale A Rockwell, Scale N load 147 N

Isotropic B a M Anisotropic B a M Isotropic B a M

Mohs

M

8.3 ± 0.5 k N / m m 2 11.0 k N / m m 2

Courtel et al. (1962)

24 k N / m m z

Broese van Groenou et al. (1979a)

73-76 } 72-80, 80-90

6-7

Gershov (1963) Cavallotti et al. (1979)

Schiller et al. (1970)

HARD FERRITES AND PLASTOFERR1TES

575

Hardness Table 30 shows hardness values determined by various tests. Like most of the mechanical properties hardness is thus anisotropic. Figure 44 shows the hardness as a function of the sintering temperature and thus of the density.

Lattice constants, X-ray density Lattice constants of M-ferrites are compiled in table 31. There is only a slight difference for the Ba, Sr and Pb compounds so that the volumes of the unit cells only differ by a maximum of 1%, giving values for the theoretical densities of 5.3, 5.1 and 5.6 to 5.7g/cm 3 respectively. A density of 5.59g/cm 3 obtains for the mineral magnetoplumbite with the lattice constants given by Berry (1951) and the (idealized) composition given by Blix (1937) as PbFev.sMn3.sA10.sTi0.sO19. TABLE 31 Lattice constants of M-ferrites in nm (at room temperature). Specimen

a

c

c/ a

Reference

BaM BaM BaM Ba0.sSr0.2M Ba0.6Sr0.4M Ba0.4Sr0.6M Bao.zSr0.sM SrM SrM SrM SrM PbM PbM

0.5876 0.5893 0.5894 0.5887 0.5890 0.5882 0.5884 0.5884 0.5885 0.5887 0.5864 0.5877 0.5893

2.317 2.3194 2.321 2.318 2.316 2.311 2.308 2.308 2.303 2.305 2.303 2.302 2.308

3.943 3.936 3.938 3.937 3.932 3.929 3.923 3.923 3.914 3.915 3.927 3.917 3.916

Adelsk61d (1938) Townes et al. (1967) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Haberey et al. (1977b) Adelsk61d (1938) Adelsk61d (1938) Klingenberg et al. (1979)

Magnetoplumbite Magnetoplumbite

0.606 0.588

2.369 2.302

3.91 3.915

Aminoff (1925) Berry (1951)

Chemical stability Being oxides, hard ferrites are, by nature, particularly unstable in strong acids, but are subject to more or less rapid chemical attack even in weak acids, alkalis and in other chemicals. Qualitative information on this is contained in table 32 (Schiller et al. 1970, Valvo 1978/79). Quantitative data on corrosion behaviour in different media will be found in table 33 (Hirschfeld et al. 1963) in which the specific loss of weight after 14 days of treatment is given. These and other data point to a number of remarkable aspects: (1) Fluoric acid and hydrochloric acid are by far the most aggressive media. (2) An increase in the temperature of the medium of only 30°C can mean a dramatic increase in corrosion. (3) The rise in the corrosion rate with increasing temperature is not uniform for

576

H. ST~ilBLEIN TABLE 32 Chemical stability of BaM-ferrites. Rather stable in: Ammonia Acetic acid Benzol-trichloroethylene (50 : 50) Citric acid (5%) Citric acid (10%) Cresol Developer Fixing bath Hydrogen peroxide (15%) Hydrogen peroxide (30%) Petrol Phenol solution Potassium hydroxid solution Sodium chloride solution (30%) Sodium hydroxide solution Sodium sulphate solution

More or less unstable in: Hydrochloric acid Hydrofluoric acid Nitric acid Oxalic acid Phosphoric acid Sulfuric acid

various media, so that the consecutive order, in terms of aggressiveness, depends on temperature. (4) A comparison between periods of treatment of 1, 4 and 8 days shows that the specific loss of weight is not constant. For this reason the loss of material cannot be extrapolated quantitatively to other reaction periods. (5) The above comparison further indicates that in some media the specimen TABLE 33 Specific weight loss of non-oriented Ba-hexaferrite specimens after being treated for 14 days in different aqueous media (Hirschfeld et al. 1963). Concentration: 15 wt %.

Medium

Hydrofluoric acid Hydrochloric acid Sulfuric acid Phosphoric acid Potassium hydroxid solution Nitric acid Tartaric acid Acetic acid Ammonia Aqua destillata

Specific weight loss in g/m 2 at 20-25°C 50-55°C (a) (a) 57 25 11 8 4 4 1 2(c)

(a) (a) 300 650 9 610 60 4 (b) - 15(c)

(a) Specimen completely dissolved (b) not determined (c) means weight increase

HARD FERRITES AND PLASTOFERRITES

577

weight increases first and then decreases, Firmly adherent reaction products obviously form in the initial stage. These dissolve as the attack progresses. All in all the corrosion behaviour is very c o m p l e x and it depends to a considerable extent upon the test parameters. Quantitative predictions therefore require exactly defined test conditions.

3.5, Comparison with other permanent magnet materials; applications Since their discovery around 1950 hard ferrites have enjoyed a bigger upswing in sales than any other p e r m a n e n t magnet material. Figure 77 shows the rate of increase in output of various hard magnet grades as estimated by various authors. In spite of considerable fluctuations, a hard ferrite output in the order of 108 kg/a can be assumed for the beginning of the eighties in the western countries. Since the average price of hard ferrites is estimated at 10 DM/kg, this represents a value today of approximately 109DM/a. The value of the other p e r m a n e n t magnet materials can be expected to be in roughly the same order of magnitude because the comparably smaller tonnage output is set against a correspondingly higher average price. T h e main reason for this large proportion of hard ferrites in the total output of p e r m a n e n t magnets is their economy (see also section 1.2). The price per unit of magnetic energy ((BH)m~ value) is much lower for hard ferrites than for the other magnet materials (Steinort 1973, Rathenau 1974). A m a j o r advantage offered by hard ferrites is the low-cost and almost inexhaustible supply of raw materials which opens up excellent prospects for the use of this material in f u t u r e - in spite of the fact that the energy density values of hard ferrite grades are inferior to those of other materials as can be seen from figs. 78 and 79.

108 +/A/

5

f

2-

//.-

10z 5

/

/

/

/

.

.---"

t /' • t

2.

106

I

I

I

I

I

1930 1940 1950 1950 19F0 1980year

Fig. 77. Annual mass production of permanent magnets between 1940 and 1980 in the western world: ( ) hard ferrites (upper curve, Cartoceti et al. 1971, Steinort 1973, Andreotti 1973; lower curve, Van den Broek et al. 1977/78, Rathenau 1974); (0) hard ferrites (Schiller 1973); (---) all permanent magnets, (..... ) alloys only (Van den Broek et al. 1977/78, Rathenau 1974); (+) all permanent magnets (Schiller 1973).

578

H. ST~BLEIN /.5 T

2O II

/,

\

/.0

~,1~'°'~ 2 N

a5 ~

0,5

-750

kA/m

- 500

0

-250

Field s t r e n g t h

H

Fig. 78. Typical demagnetization curves of various permanent magnet materials: (1) hard ferrite; (2) AlNiCo, high B~ grade; (3) AlNiCo, high H~ grade; (4) Mn-AI-C alloy; (5) RECo5 alloy; (6) RE(Co, Cu, Fe)7 alloy.

QI I~

1 ~

I

I I !!II

tO

I,

~

I

I I III!I

kOe I

!

I I

: kh 25

'MGOe

kJ/m3 l

I00. /

J

xt6\ 14 ,~x~

24 xU/"

,,*_L3 _ 9 - "

×23 - - -7--" % :~o ×191"72"', .... , ", /

x I

," 3/ [× /

10.

x22

, 9 × ,17. 'L*×~2#21

q8

: ~ -x',

"--"

/x 6 ,'J~7,"

x 20

ix ', ',~ 10

',

', ', ', 1:',II lO0

',

', ', ' , ; I I ' , I 1000

', ', kA/m

jH c

Fig. 79. Permanent magnet materials compared by (BH)max (static energy) and intrinsic coercivity aHc (stability) (St~iblein 1972): (1) Co steel; (2) Cu-Ni-Fe, anisotropic; (3) Co-Fe-V-Cr, anisotropic, wire; (4) Co-Fe-V-Cr, anisotropic, strip; (5)-(7) AlNiCo, isotropic; (8)-(12) AlNiCo, anisotropie; (13)-(16) AlNiCo, columnar; (17) ESD (elongated single domain), anisotropic; (18) and (19) Cr-Fe-Co, anisotropic; (20) Hard ferrite, isotropic; (21) Hard ferrite, anisotropie, see table 18; (22) Mn-Bi, anisotropic; (23) Mn-AI-C, anisotropic; (24) Pt-Co, isotropic; (25) RE-Cos-type alloys, anisotropic; (26) RE-(Co, Cu, Fe, Mn)7-type alloys, anisotropic.

HARD FERRITES AND PLASTOFERRITES

579

Figure 78 shows the demagnetization curves of typical modern permanent magnet grades with their (BH)max points. Owing to their relatively low (B/-/')max values hard ferrites are not particularly suitable for those applications in which the most important requirement is to keep the volume of the (static) magnet system as small as possible. As soon as minimum possible mass is required conditions change, however, as can be seen from the comparison of the columns "volume efficiency" and "mass efficiency" in table 34. Owing to its low density hard ferrite is appreciably better in this case. The same applies to those cases where importance is attached to stability or reversible magnetic behaviour under alternating magnetic fields, i.e. to coercivity jHc. For a qualitative comparison of the materials in terms of their static as well as dynamic characteristics, it is advisable to use the (BI-I)max-jHcdiagram, cf. fig. 79. This brief description is also used in more recent standardization, cf. section 3.1. The hard ferrites are thus found to range in stability between the Alnico, C r - F e - C o and ESD magnets, on the one hand, and the intermetallic compounds MnBi, PtCo and R E (Co, Cu, Fe, Mn)y, on the other. The (BpH)max value* is a quantitative measure for the energy conversion capability with dynamic operation of the permanent magnet, cf. table 34. In these applications hard ferrites are at least equal to the AlNiCo alloys. In fig. 78 the ( B H ) m a x points are marked on the demagnetization curves. If flux density and field strength in the permanent magnet assume the values corresponding to the (BH)m~ point, a minimum volume of permanent magnet is required (with static applications). This can be achieved by an appropriate design of the magnet system. In this case B/txoH has to assume the values listed in table 34. The smaller this value is the more compact the permanent magnet has to be designed. Like the R E - C o alloys, hard ferrites therefore as a rule have compact shapes (small ratio between magnet length and magnet cross-sectional area) in contrast to AlNiCo alloys. Another important criterion for actual use is the temperature response of the magnetic properties, cf. section 3.2. Table 34 shows the temperature coefficients of the remanence a(Br) and of the intrinsic coercivity a(jHc) of some materials, as applying for a certain range around room temperature. Hard ferrites can be seen to exhibit the greatest temperature response of remanence, and this applies, of course, to the temperature response of the magnetic flux in the permanent magnet system. Hard ferrites are thus less suitable for applications where functioning must remain unaffected by temperature. Special mention has already been made in section 3.2 of the consequences of the large positive temperature coefficient of jHc of hard ferrites and in particular of the risk of irreversible losses on cooling below room temperature. Certain AlNiCo grades show a similar although less pronounced behaviour. Amenability to shaping and machining is an important criterion in actual * For the definition see section 3.1, footnote on p. 536. Some authors use half or one quarter of this value. References: D e s m o n d (1945), Schwabe (1958, 1959), Schiller (1967), St~iblein (1968b), Gould (1969), Zijlstra (1974).

580

H. S T ~ 3 3 L E I N

¢,q

g~

?

x

~s A

× tt%

x

,4

©

.d

,?

I

?

? e.-,

,..-i ,.a

E

tel

,,'5

$
am for ionic compounds, and this is indeed observed for oxyspinels (the smallest value a =-7.94 A occurs for LiomAls/204 (Blasse 1964). I n sulphides with spinel structure, a runs from 10.24A for CdCr2S4 to 9 . 3 9 A for NiCo2S4 (table 1). a < 9.84,~ means that the mean S-S distance is smaller than the shortest $2--S 2distance, i.e., the normal ionic S 2- state does not occur. We will see later that this is reflected in the electric and magnetic properties, which are essentially different from those of oxyspinels (and other oxides) for a < 9.84 A, but not for a > 9.84,~. For example (see table 1 and section 5.2) Zner204 and ZnCr2S4 (a = 9.99 A) are semiconductors and exhibit Curie constants corresponding to the metal ions (Zn 2+, Cr3+). This holds also for C o 3 0 4 (Wagner 1935, Cossee 1958) but C o 3 S 4 is metallic and the Curie constant does not agree at all with ionic C02+Co~+X2-, in contrast to CosO4. Since ions are not rigid spheres, the ionic S 2- radius and thus am are not determined exactly, so that the rule does not hold for a near oto am (e.g. CoRh2S4 with a = 9.80 has normal ionic properties). CuTi2S4 (a = 9.99 A), which is Pauli paramagnetic and metallic, is the only clear exception. Consequently the metallic conduction has another origin than in the o t h e r sulphospinels (section 4.2). A comparison of the A - X distances in the compounds CuM2S4 of table o 2 demonstrates that this distance is almost constant with an average value of 2.25 A, close to the value 2.26 A obtained from a more extensive analysis by Riedel and o H o r v a t h (1973a). In the selenospinets CuM2Se4 the average value is 2.38 A and in o the tellurospinel the C u - T e distance is 2.53 A. These distances compare well with the C u - X distances in other chalcogenides (Lotgering and Van Stapele 1968b). T h e A - X distances in MCr2X4 with M = Zn, Cd and Hg and X = S and Se compare well with the tetrahedral covalent radii as derived by Pauling (1960) from the sphalerite and wurtzite structures of the compounds M X (table 3).

TABLE 2 Cation-anion distances

Compound CoCr2S4

FeCr2S4 ZnCr2S4

MnCrzS4 CdCr2S4 HgCrzS4 CoRh2S 4

CuCr2S4 CuTizS4 CuVzS4 CuCo2S4 CuRh2S4 CuCr2Se4 ZnCr2Se4

CdCrzSe4

HgCr2Se4 CuRhzSe4 CuCr2Te4

A-X (~)

B-X (~)

References

2.27 2.32 2.34 2.34 2.32 2.34 2.39 2.41 2.48 2.48 2.48 2.26 2.26 2.28 2.27 2.26 2.24 2.16 2.26 2.27 2.23 2.38 2.40 2.43 2.44 2.46 2.61 2.59 2.61 2.61 2.38 2.34 2.53

2A1 2.41 2.40 2.40 2.41 2.40 2.42 2.41 2.42 2.42 2.42 2.38 2.38 2.37 2.44 2.44 2.38 2.30 2.25 2.36 2.39 2.50 2.49 2.52 2.51 2.52 2.54 2.54 2.53 2.54 2.48 2.50 2.72

Raccah et al. (1966) Shirane et al. (1964) Raccah et al. (1966) Baltzer et al. (1965) Raccah et al. (1966) Riedel and Horvath (1973a, 1969) Raccah et al. (1966) Menyuk et al. (1965) Baltzer et al. (1965) Riedel and Horvath (1973a, 1969) Baltzer et al. (1%5) Kondo (1976) Riedel and Horvath (1973a) Raccah et al. (1966) Riedel and Horvath (1973a) Le Nagard et al. (1975) Riedel and Horvath (1973a) Riedel and Horvath (1973a) Williamson and Grimes (1974) Dawes and Grimes (1975) Riedel et al. (1976) Riedel and Horvath (1973b) Robbins et al. (1967b) Plumier (1965) Raccah et al. (1966) Riedel and Horvath (1969) Baltzer et al. (1965) Raccah et al. (1966) Riedel and Horvath (1969) Baltzer et al. (1965) Dawes and Grimes (1975) Riedel et al. (1976) Riedel and Horvath (1973b)

TABLE 3 Cation-anion distance on tetrahedral sites in the compounds MCr2X4, compared with the distance in the compounds M X

Compound

A-X (A)

ZnCr2S4 CdCrzS4 HgCr2S4 ZnCr2Se4 CdCr2Se4 HgCr2Se4

2.33 2.48 2.48 2.44 2.60 2.61

compound M X ZnS CdS HgS ZnSe CdSe HgSe

615

M-X (A) 2.35 2.53 2.52 2.45 2.63 2.63

616

R.P. V A N S T A P E L E

3. Localized and delocalized states in sulphospinels

Many metallic conducting chalcogenides of transition metals are known. In most of them the magnetic moments do not agree with the spin-only value of magnetic ions. For example, CrTe and MnSb, which might be compounds of Cr z+ and Mn 3+, are metallic ferromagnets. The experimental ferromagnetic moments of 2.4 and 3.5 txB and the paramagnetic moments of 4.0 and 4.1 #B, respectively (Lotgering and G o r t e r 1957) deviate strongly however from the spin-only values 4/xB and 4.9/XB of the ferromagnetic and paramagnetic moment of the 3@ ions Cr z+ and Mn 3+. Metallic conduction and a non-integer number of d electrons per metal atom point to delocalized electrons in energy bands. In our opinion, an unambiguous interpretation of such properties has never been given (see, e.g., Bouwma and Haas 1973). A few metallic conducting chalcogenides exhibit magnetic moments that are in reasonable agreement with the presence of transition metal ions having the expected valency. This has been found clearly in Mel_~LaxMnO3 with Me = Ca, Sr or Ba (Jonker and Van Santen 1950), and in CoS2 (Benoit 1955, Ohsawa et al. 1976). Such "ionic" moments are also found in the non-oxidic spinels CuCr2X4, which makes an interpretation easier than in the case of the MnSb compounds. The metallic conduction of these spinels is to be attributed to delocalized electrons, their magnetic behaviour to electrons in localized 3d states of the Cr ions (section 4.8). We will now give a short review of the electronic structure of transition-metal chalcogenides*. This structure is characterized by two broad bands (with a width of 5 to 10 eV) separated by an energy gap, and narrow d bands or ionic levels of cations M n+ with a d m configuration. The broad bands arise from the strong overlap of the occupied outermost s and p states of the anions (e.g. 2s and 2p of 02-) with the first empty s states of the cations (e.g. 4s of Mn 2+) which gives rise to a "bonding" valence band and an "anti-bonding" conduction band. For a cation d orbital the overlap with the anion orbitals is much smaller. This overlap tends to break the highly correlated state of the d electrons in the cations Mn+(d m) and to delocalize the d electrons in a narrow d band. This delocalization is counteracted by the energy required for the excitation 2Mn+(dm)--->M~"+l)+(dm-l) + M("-l)+(dm+l). Delocalization or localization occurs if the effect of the overlap or the excitation energy dominates (Mott 1949). With an increasing ratio of the two factors, a sharp transition from a localized to a delocalized state is expected (Mott transition). The electrical and magnetic properties will be discussed with the help of schemes (fig. 4) which represent the relative energies of electrons in the broad valence and conduction bands and in d states, localized or otherwise. On the right-hand side of such a scheme the one-electron energy versus the density of states of the bands is sketched. The bands are occupied below and empty above a Fermi level EF. On the left-hand side of each scheme we place the ionic levels of cations M n+ with a d m electron configuration. Such an ionic level denotes the relative energy (with respect to the broad bands) of the localized mth electron. * See notes added in proof (a) on p. 737.

SULPHOSPINELS

E MIo-~

617

J --E

F

M~*__ ~ density of states

b

(3

Mn*~

F d

Mn*

c

F e

f

Fig. 4. Schematic band structure of chalcogenide spinels. O n the right-hand side the schemes show the conduction band and at a lower energy the valence band. T h e left-hand side shows the valency states of a transition metal ion. UF denotes the Fermi energy.

Each level can accommodate one electron only. If occupied (situated below Ev) it represents an ion with valency n, if empty (situated above UF) an ion with valency (n + 1). For a given metal M, the M (n-l)÷ level lies above the M n÷ level. The energy difference is the energy needed to excite an electron from Mn+(d m) to M(n-1)+(dm+l)), i.e., the transition 2 M " + ~ Mtn+~)+ + M (n ~)+. E F coinciding with M "+ levels indicates a mixed valency state (a mixture of M "+ and M (n+l)+) that gives an electrical conduction with a high concentration of charge carriers with a low mobility (~1 cm2/Vs). In oxides the valence and conduction bands are separated by a wide gap in which successive valency states are situated (fig. 4(a)). It has been proposed (Albers and Haas 1964, Albers et al. 1965) that the properties of chalcogenides and pnictides may be explained by cation levels that fall in one of the broad bands. The various possibilities are drawn in figs. 4(b), (c) and (d), Which represent semiconductors with conduction of electrons in a narrow band or holes in a broad band (b), of electrons in a broad band or holes in a narrow band (c) and of electrons or holes in a broad band (d). In figs. 4(e) and (f) there is metallic conduction of either holes in the valence band (e) or electrons in the conduction band (f). A narrow d band is expected to consist of two separated or overlapping branches arising from the cubic crystal field splitting (Goodenough 1969). In our energy schemes narrow bands are drawn schematically without such details, because experimental information is lacking.

618

R.P. VAN STAPELE

4. Sulphospinels containing copper

4.1. Valency of the copper ions The Cu oxides CuCr204 and CuFe204 with spinel structure are semiconductors and exhibit ferrimagnetic and paramagnetic properties that are consistent with the valencies c,, '~2. . . .2+g-~3+g-~22 ,-,4 and t~ u 2+12" , e 23 + g,-,4. In contrast with this, all non-oxidic TM

spinels CuM2X4 show metallic conduction and essentially different magnetic properties. For M = Cr they are ferromagnets with Curie temperatures above room temperature, and the others ( M # Cr) show a temperature independent paramagnetism. CuV2S4, CuRh2S4 and CuRh2Se4 become superconducting at low temperature. A survey of the electrical and magnetic properties of the compounds CuM2X4 is given in table 4. Detailed data will be given later, when each of the compounds is discussed separately. The striking difference in properties between the non-oxidic spinels CuM2X4 and the corresponding oxyspinels CuM204 points to an essential difference in electronic structure. Two explanations have been proposed. The first is based on the assumption that copper ions in the sulphospinels are monovalent, i.e., in the 3d 1° state, in contrast to their divalent state in the oxyspinels (Lotgering 1964a, b, Lotgering and Van Stapele 1968a). The second is based on the assumption that the copper ions are formally divalent, but that their 3d electrons are delocalized in a band formed by the copper 3d states (Goodenough 1965, 1967 and 1969). The crucial question in these matters is the valency of the tetrahedrally coordinated copper ions in non-oxidic chalcogenides. The following arguments and experimental results lead us to adopt the monovalent state: (a) Divalent Cu ions are known to have a great instability in a sulphur lattice (Akerstrom 1959), in agreement with the fact that no sulphides, selenides or tellurides are known with tetrahedrally coordinated Cu ions, exhibiting the properties of Cu e+, as CuCr204 does, for example. (b) The C u - X distances in the copper sulpho-, seleno- and tellurospinels do not differ significantly from the C u - X distances in other chalcogenides containing monovalent Cu (Lotgering and Van Stapele 1968b) (see section 2 and Sleight 1967). (c) A zero moment is observed at the A'sites in CuCr2Se4 and CuCr2We4 at temperatures down to 4 K by means of neutron diffraction (Colominas 1967, Robbins et al. 1967b) in contrast with 1/xB expected for a spin-ordered state at T = 0 with Cu 2+ on the tetrahedral sites (see also section 4.8). (d) The X-ray photo-electron spectrum of the copper 2p energy levels in CuCr2Se4 closely resembles the spectra of CuCrSe2, CuCrS2 and CuA1S2, in which compounds Cu is monovalent. All the spectra have the narrow peaks typical of Cu + at the same energy, while satellites due to the simultaneous excitation of an electron into empty states of the 3d shell are absent (Hollander et al. 1974). (e) The chemical Shift of the K absorption edge of copper in CuCr2S4, Cufr2Se4 and CuCrzTe4 with respect to Cu metal is small and indicative of Cu + (Ballal and Mande 1976) (table 5).

SULPHOSPINELS

619

...-t O~

E = .=

II ,,,..¢ vh +-

I

"~

~x x ',R.

,

x

x ~ " oo,~

i

,.- I "T'

Q

I

b,-

~.~. d~

e~

,

~,,

~,

+ +

÷

x××

×~

,~

3~ .,,-

8 ii

~...' E

x~

d

620

R.P. VAN STAPELE TABLE 5 Wavelengths of the K discontinuity of copper in various compounds, according to Ballal and Mande (1976).

A (x.u.) Compound

Valency

(-+0.09X.U.)

AA

Cu metal CuO CuSO4.SH20 CuC12.2H20 CuCO3

2 2 2 2

1377.67 1376.76 1376.42 1376.44 1376.65

0.91 1.25 1.23 1.02

CuC1 Cu20 Cu2Se

1 1 1

1377.10 1377.54 1377.41

0.57 0.13 0.26

1376.80 1377.36 1377.46 1377.56

0.87 0.31 0.21 0.11

CuCr204 CuCr2S4 CuCr2Se4 CuCraTe4

Especially the last three experiments provide a direct establishment of the monovalent state of copper in non-oxidic CuCrzX4. We adopt Cu ÷ in all sulphospinels, which is represented by a completely occupied Cu + level sufficiently far below the top of the valence band. The experimental data do not give information about the precise position of the Cu + state, so that this level will not be drawn in the energy level schemes.

4.2. CuTi2S4 CuTi2S4 is a normal spinel (Hahn and Harder 1956) with lattice parameters as given in table 1. Le Nagard et al. (1975) reported the existence of strongly Cu-deficient CUl-xTi2S4 compositions with 0 ~< x ~ ions in the low spin t 6 state and hole conduction in the valence band the susceptibility can be explained as the sum of the diamagnetic susceptibility (-2.1 x 10 .4 cm3/mol), the Van Vleck susceptibility of the Rh 3+ ions (3 x 10-4 cm3/mol) and a Pauli susceptibility of 0.7 x 10 .4 cm3/mol (Lotgering and Van Stapele 1968a). As in CuCo2S4 (section 4.4) and in CuRh2Se4 (section 4.6), such a small Pauli susceptibility does not agree with the large linear temperature coefficient of the specific heat (y = 30 mJmol-lK -2) (Schaetter and Van Maaren 1968), which corresponds to a Pauli susceptibility of 4 x 10 .4 cm3/mol. The Knight shift of the Cu nmr lines measured on CuRh2S4 (Locher 1968) is negative and has nearly the same value as in CuRh2Se4 (fig. 8). A complete solubility has been observed in the series CuRh2(Sl_xSex)4 (Riedel et al. 1976). The lattice constant varies linearly with x. The anion sublattice shows a random distribution of chalcogen atoms with a mean value for the anion parameter u of 0.381.

SULPHOSPINELS

627

4.6. CuRh2Se4 and CuRh2-xSnxSe4 CuRh2Se4 is a normal spinel with lattice parameters as given in table 1. The c o m p o u n d has a p-type metallic conduction (Lotgering and Van Stapele 1968a) with at r o o m t e m p e r a t u r e a Seebeck coefficient of +7.3 p.V/deg and a resistivity of 1.3 × 10 -3 ~ c m . The magnetic susceptibility depends weakly on the temperature. At r o o m t e m p e r a t u r e the value is 1.1 × 10 -4 cm3/mol. Based on the assumption of monovalent copper ions, the properties of CuRh2Se4 have been attributed to Rh 3+ ions and hole conduction in the valence band, as sketched in fig. 4e, with the Rh 3+ states below the Fermi level (Lotgering and Van Stapele 1968a). At low temperatures the c o m p o u n d becomes superconducting. Van Maaren et al. (1967) found a transition at 3.47 K with a width of 0.04 K, which agrees with the findings of Robbins et al. (1967a) who observed the transition at 3.46 K with a width of 0.09 K, and those of Dawes and Grimes (1975), who obtained 3.50_+ 0.05 K. Shelton et al. (1976) measured the influence of a hydrostatic pressure up to 22 kbar on To. On samples with Tc -- 3.49 K and 3.38 K the pressure derivative has a value of 1.53 and 1.44 × 10 -5 K / b a r respectively. These m e a s u r e m e n t s were done to confirm the suggestion that in spinel compounds the transition to superconductivity occurs at a t e m p e r a t u r e determined by the D e b y e temperature, the strength of the electron-phonon interaction being roughly constant within the class of superconductive spinel compounds. However, a study of the properties of the system CuRh2_xSnxSe4 with 0~<x ~ 1 (Van Maaren and Harland 1969, Van Maaren et al. 1970a, b) has shown that the occurrence of superconductivity in CuRh2Se4 is determined critically by the details of the band structure. In this investigation use has been made of the possibility to change the n u m b e r of charge carriers drastically by substitution of Sn for Rh 3+. The Sn ions are expected to be tetravalent and to decrease the n u m b e r of holes in the band, which is responsible for the p-type metallic conduction. This turns out to be the case. T h e lattice p a r a m e t e r changes linearly with the composition from 10.26 ,~ at x = 0 to 10.62 at x = 1. T h e conduction changes from metallic for 0 ~< x ~< 1 to semiconductive at x = 1, at which composition the valencies are given by Cu+Rh3+Sn4+Se]-. The Seebeck voltage is positive in the complete range o f compositions, whereas the Hall coefficient RH is positive for 0.15 ~< x ~ 1 and negative for x ~< 0.15 (fig. 11). For 0.5 < x ~< 1, R~I1 at r o o m t e m p e r a t u r e is about proportional to the n u m b e r ( 1 - x) of charge carriers per molecule C u +Rh2_xSn 3+ 4+ x Se4 (fig. 11). For x < 0.5, however, R n behaves anomalously. The value of R ~ 1 increases strongly with decreasing x and R u changes sign at x -~ 0.15. The dependence of the transition to superconductivity on the Sn concentration is strongly correlated to that of RH. To decreases with x and no superconductivity above 0.05 K has been observed for x > 0.5 (fig. 11). Van Maaren and Harland (1969) conclude from these m e a s u r e ments that conduction takes place in at least two bands, one of which shows n-type behaviour for x < 0 . 5 . This can be reconciled with conduction i n the valence band, which at the top is split into a single narrow upper branch and a

628

R.P. VAN STAPELE

T

× 300 K o

i

77 K

A 4.2K

D u

_¢ O

E

I I I I

J lh-

4-1

.1

p-type

.3 /

.6

.8 X

,92 I

Fig. 11. Superconducting critical temperature To and reciprocal Hall constant R h 1 vs x of CuRh2-xSnxSe4 according to Van Maaren and Harland (1969).

broader two-fold degenerate lower branch (Rehwald 1967). The additional assumption which had to be made is that in the rigid band model the upper branch will show p-type conduction for 0 ~<x < 1, whereas the lower branch changes sign of conduction near x = 0.5. For x < 0.5 holes occur in the upper branch and electrons in the lower branch. The simultaneous presence of holes and electrons is apparently responsible for the appearance of superconductivity. At this point it should be noted that the transport properties have also been measured by Robbins et al. (1967b) and that they obtained a positive Hall coefficient at room temperature. However, the sample used in the measurements did not show superconductivity (Van Maaren and Harland 1969). Schaeffer and Van Maaren (1968) have measured the heat capacity of CuRh2Se 4 and Van Maaren et al. (1970a, b) extended the measurements to the series CuRh2-xSnxSe4 with 0 ~ x ~< 1. The Debye temperature, as calculated from the lattice contribution, increases linearly with x from 200 K at x = 0 to 267 K at x = 1. For x ) 0 . 6 the constant T in the linear term of the heat capacity is proportional to ( 1 - x) 1/3, the electronic density of states expected for a parabolic band with (1 - x) charge carriers per molecule. At smaller values of x, for which compositions the compounds are superconductive, y vs ( 1 - x ) 1/3 is again linear, but with a steeper slope. However, after correction of T for the enhancement of T by the electron-phonon interaction, y vs ( 1 - x) ~/3 is linear in the full interval 0 1. The substitution of Sn for Cr in CuCr2S 4 has the same effect as the substitution of Ti. The strongly ferromagnetic interactions between the Cr ions have disappeared in CuCrSnS4, which is paramagnetic down to 4 K with an asymptotic Curie t e m p e r a t u r e of - 2 0 K (Sekizawa et al. 1973). The ion distribution has been determined by Strick et al. (1968). Cu occupies the tetrahedral sites; the Cr and Sn ions occupy the octahedral sites. As shown in fig. 19, the lattice p a r a m e t e r increases and the Curie t e m p e r a t u r e decreases linearly with x in the series CuCr2_xSnxS4 in the interval 0~<x in CuCrzSe4 by Rh 3+ will ultimately give a material that contains exclusively Cr 4+. This has been investigated in the system CuCrz_xRhxSe4 (Lotgering and Van Stapele 1968a)*. It turned out that there is p-type metallic conduction throughout the series, the Seebeck coefficient being small and positive for all values of x (fig. 22). The asymptotic Curie t e m p e r a t u r e decreases gradually with increasing x (fig. 23), while ferromagnetic ordering remains down at x = 1.7. As fig. 23 shows, the magnetic m o m e n t in the ferromagnetic saturation is close to 2/xB per Cr ion for x > 1, while the paramagnetic Curie constant per g r a m a t o m Cr is close to 1.0, the spin-only value of Cr 4÷ (fig. 24). This confirms remarkably well the tetravalent state of the Cr ions in CuCr2_xRhxSe4 with x > 1. T h e behaviour of the system CuCr2_xRhxSe4 can qualitatively be understood on * See notes added in proof (c) on p. 737.

SULPHOSPINELS

639

seebeckcoeff.(jJV/deg)

2C 10 I

0

1

2 ~X Fig. 22. Seebeck coefficient of CuCrz_xRhxSe4, according to Lotgering and Van Stapele (1968a).

e(K)

%\ T/*00 '~ 300

N% xx~'~

20C

-Mf(JJB} l ~\

5

100

3 1 r

0

1

2

Fig. 23. Asymptotic Curie temperature ( 0 ) and ferromagnetic moment /x~ (O) of CuCr2_xRhxSe4 (Lotgering and Van Stapele 1968a, Van Stapele and Lotgering 1970). The solid lines represent/xf vs x for Cr 4+ (a) and Cr 3+ (b).

Cm

I

1

~X

Fig. 24. Molar Curie constant of CuCr2_xRhxSe4 (Lotgering and Van Stapele 1968a, Van Stapele and Lotgering 1970). The solid lines represent Cm vs x for Cr 3+ (a) and Cr 4+ (b).

640

R.P. V A N S T A P E L E

the basis of the energy level diagram for CuCr2Se4 (fig. 21(a)). Substitution of Rh replaces Cr 3+ levels by deeper Rh 3+ levels. This lowers the Cr 3+ concentration, leaving the number of holes in the valence band unchanged as long as the Fermi energy falls in the Cr 3+ levels. Figure 21(b) illustrates the situation in CuCrRhSe4 with 6Cr 3+ ions, (1 - 6)Cr 4+ ions and ~ holes in the valence band. If the resonance width of the Cr 3+ levels is sufficiently small, a further increase of the Rh concentration will finally increase the number of holes in the valence band, leaving the remaining Cr ions in the tetravalent state. This is sketched in fig. 21(c) for CuCr0.3Rhl.7Se4 with 0.3 Cr 4+ and 0.7 holes in the valence band. The consequence is that if the Fermi level is shifted to higher energies at a constant Cr concentration, the valency of the Cr ions should also change from C r 4+ to Cr 3+, This has been accomplished in CuCr0.3Rhl.ySe4 by substituting Sn 4+ for Rh 3+ (Van Stapele and Lotgering 1970). As we have discussed in section 4.6, this substitution reduces the number of holes in the band of CuRhzSe4 to zero in the semiconductor CuRhSnSe4. In the series of compounds CuRhl.7_xSnxCr0.3Se4 the properties change in the same way. As shown in fig. 25, the Seebeck coefficient is positive and increases strongly if x approaches 1, indicating that CuRh0.7SnCr0.3Se4 is a semiconductor. The asymptotic Curie temperature decreases strongly and, most important, the Curie constant per gramatom Cr changes gradually from the spin-only value 1.0 of Cr 4+ to the spin-only value 1.87 of Cr 3+. The change of valency cannot be detected from the magnetic moment in the ferromagnetic state, since for x >~0.3 the magnetization of CuRhl.y_xSnxCr0.3Se4 is difficult to saturate. It is difficult to account for the paramagnetic moment observed in CuCrzSe4 in terms of paramagnetic moments of Cr 3+ and Cr 4+ (Lotgering and Van Stapele 1968a, Yamashita et al. 1979b). The observed value of the molar Curie constant (Cm = 2.50) is lower than the spin-only values 2.97 and 3.06, which are expected

Cm/0.3

cdJaV,/deg)

e (K)

t 2.0

60'-

Cr 3+

a(A)

A

10.8

i6oo

40

10.6

20

IOL

1.5

1.0~ n

o o

o CFt~+

0 0

I

05 --I.-

O5

0

05

10.2

X

Fig. 25. Curie constant per gram atom chromium Cm/0.3, paramagnetic Curie temperature 0, Seebeck coefficient a and cell edge a of CuCr0.3Rhl.7 ,SnxSe4 as a function of the composition (Van Stapele and Lotgering 1970).

SULPHOSPINELS

641

for (1.1 C r 3+ + 0.9 Cr 4+) and (1.2 Cr 3+ + 0.8 Cr 4+) respectively. This means that in the paramagnetic state, too, the negative interaction between the Cr spins and the spins of the conducting electrons cannot be left out of account. Hyperfine fields in CuCrzSe4 have been measured on the nuclear spins of Cu, Cr and Se ions. Locher (1967) found the Knight shift K of the Cu nmr to be proportional to the magnetic susceptibility: K = c~X with c~ = 1.17x 103gcm -3. Extrapolation to the magnetic moment in the ferromagnetic saturation gave a hyperfine field of +68 kOe on the Cu nuclear spin. This agrees well with the hyperfine field actually measured by Yokoyama et al. (1967a, b) and Locher (1967) in the ferromagnetic state (table8). TABLE 8 Hyperfinefieldsin CuCr2Se4;(a) accordingto Locher (1967);(b) according to Yokoyama et al. (1967a, b).

63'65Cu 53Cr 77Se

77 K

Extrapol. to 0 K

+70.4 kOe +70.6 kOe - 159 kOe 71.4 kOe

+72.6 kOe - 161 kOe 73 kOe

4.2 K

Ref.

+72.1 kOe

(a) (b) (b) (b)

The positive hyperfine field on the Cu nuclear spin is larger than the positive field measured in semiconducting selenides: +72 kOe as compared to +32 kOe in CUl/2Inl/zCr2Se4. This means that the negative polarization of the band in CuCr2Se4 gives a hyperfine field of the opposite sign on the Cu nuclear spin. This sign agrees with the observations in the Pauli paramagnetic CuRhzS4 and CuRhzSe4, where a negative Knight shift of the Cu nmr has been observed (fig. 8). The hyperfine field on the 53Cr nuclear spin ( - 1 6 1 k O e of table 7) differs by 22 kOe from the - 183 kOe measured in the semiconducting CdCr2Se4 (see section 5.6). With Cr 3+ in both compounds this hyperfine field must be attributable to the (negative) polarization of the polarized band. The hyperfine field due to the Cr neighbours has been measured on the 119Sn nuclear spin in CuCrl.9Sn0.1Se4 (Lyubutin and Dmitrieva 1975) where it has the value of +490_+ 10 kOe. This compares well with the values found in CuCr2S4 (section 4.7).

4.9. CuCr2Te4 and Cul+xCrzTe4 CuCr2Te4, which was first prepared by Hahn et al. (1956), resembles CuCr2S4 and CuCrzSe4. It is a normal spinel (Colominas 1967), which can be prepared in a pure state like CuCrzSe4. The lattice parameters are given in table 1. CuCr2Te4 is a ferromagnet (Lotgering 1964b) with a Curie temperature Tc = 365 K and a saturation m o m e n t / ~ = 4.93/~B/molecule (fig. 14 and table 6). Above the Curie temperature the paramagnetic susceptibility follows a Curie-Weiss law with Cm = 2.90 and 0 = 400 K (fig. 15). The Curie temperature is not affected by hydrostatic pressure (Kanomata et al. 1970, Kamigaki et al. 1970).

642

R.P. V A N S T A P E L E

The small shift of the K absorption edge of the Cu ions, as measured by Ballal and Mande (1976), indicates these ions to be monovalent (table 5). Hyperfine fields have been measured on the nuclear spins of 63Cu, 65Cu, 53Cr and tZ~Te (see table 9). Locher (1967) measured the nmr of 63'65Cu in the paramagnetic state and found the Knight shift K to be proportional to the gram susceptibility gg: K = t~Xg with o~ = 0.80 x 103 gcm -3. Extrapolation to the ferromagnetic saturation moment gives a field of 32.5 kOe, in good agreement with the values actually measured. TABLE 9 Hyperfine fields in CuCr2Te4: (a) according to Yokoyama et al. (1967a, b); (b) according to Berger et al. (1968b); (c) according to Ullrich and Vincent (1967); (d) according to Frankel et al. (1968).

63'65Cu

77 K

Extrapol. to 0 K

+38.0 kOe

+39.9 kOe

1.4 K

Ref.

39.9 kOe 53Cr

-145 kOe

lZSTe

-181 kOe _+148 kOe _+160 kOe

-151 kOe 151.1 kOe -187.5 kOe

(a) (b) (a) (b) (b) (c) (d)

The Cu content can be strongly enlarged and single-phase CUl+xCr2Te4 with 0 ~< x ~< 1 has been obtained (Lotgering and Van der Steen 1971c). These materials are metallic and ferromagnetic. Figure 26 gives a, Tc and/xf (4.2 K) as a function of x. The crystallographic and magnetic properties can be attributed to a spinel lattice with the excess Cu occupying a part of the tetrahedral sites normally not occupied. QtA) _

,mc(k) ~f

11.30 " ' ~ ~ ~ ~ -

u f

o

-

400

4

200

2

0

0

11.2C

I

11.10 0

0.5

1.0

Y

Fig. 26. Cell edge a, ferromagnetic Curie temperature T~ and ferromagnetic moment /zf of CUl+yCrzTe4, according to Lotgering and Van der Steen (1971c).

SULPHOSPINELS

643

4.10. CuCr2(X ~St)4 with X, X ' = S, Se and Te O h b a y a s h i et al. (1968) o b s e r v e d c o m p l e t e solubility in the series CuCraS4_xSex. Their data agree well with the results of later investigations. T h e cell edge varies linearly with x, but the f e r r o m a g n e t i c Curie t e m p e r a t u r e does not, having a m i n i m u m value at x ~ 1 (fig. 27). T h e magnetic m o m e n t also has an a n o m a l o u s l y low value at x--~ 1 (fig. 28) (Belov et al. 1973, O b a y a s h i et al. 1968), the actual magnetic b e h a v i o u r d e p e n d i n g to a great extent on the firing conditions (Obayashi

!

I oIAI ,0L

..~o

10.2

O ~o ~' Sg ~

Tc(K)

. ..,.~.-"

T

10.0

"~

9.8

LLO

af' 400

Tc

: i ""

360 320 I

I

I

1

2

3

~X

Fig. 27. Lattice parameter and ferromagnetic Curie temperature of CuCr2S4-xSex. (n) Data of Ohbayashi et al. (1968); (×) Data of Riedel and Horvath (1973b); (O) Data of Belov et al. (1973).

5

~3 :a,

2 1 0 0

1

2

I 3 =X

Fig. 28. Ferromagnetic moment at 77 K and 12 kG of CufreS4-xSex, according to Below et al. (1973).

644

R.P. VAN STAPELE

et al. 1968). The anomalies in the X-ray intensities of CuCr2S3Se, observed by Obayashi et al. (1968), were not seen by Riedel and Horvath (1973b), who concluded that no deviations from a statistical distribution of the anions occur. Data on the electrical behaviour have not been published, except by Belov et al. (1973) who reported that the sample with x ~ 1 had a resistivity with a negative temperature coefficient, while the samples with a different composition had a resistivity with a positive temperature coefficient. A satisfactory explanation of the properties of CuCr2S4_xSex has not been given. However, the electronegativity of Se is smaller than that of the S ions. It is possible that the Se ions, substituted for S in CuCr2S4, start to act as traps for the holes in the valence band that are responsible for the metallic conduction and the strong ferromagnetic interaction. It at least suggests that in the case of an extremely strong binding of the holes to the Se ions, one can expect the compound Cu+Cr3+S~-Se - to be a semiconductor with a much lower Curie temperature than CuCr2S4 and CuCr2Se4. A broad miscibility gap has been observed in the series CuCr2Se4_xTe~ (Riedel and Horvath 1973b). Solid solutions are found only in the Te-rich samples with x > 2.8, where the cell edge increases approximately linearly with x.

4.11. CuCr2X4-xYx w i t h X = S, S e or T e a n d Y = Cl, B r or I The anions of sulphospinels can be replaced by halogen ions (Robbins et al. 1968, Miyatani et al. 1968). Starting from the electronic structure of CuCr2X4 discussed in section 4.8, one expects that the electrons produced by a replacement of X 2- by Y- occupy the holes in the valence band and the C r 3+ levels (fig. 21(a)). A semiconductor Cu+Cr~+X3Z-Y- is then expected to be the end of the series of mixed crystals. The Curie temperature of CuCr2X4-xYx is expected to decrease with increasing x, because the strength of the ferromagnetic interaction via the conducting electrons will decrease with the decreasing number of holes in the valence band. Although this behaviour has actually been observed, complications have arisen. A difficulty encountered in the study of these materials is the preparation of chemically pure and stable samples. The following experimental results have been reported. The series CuCr2S¢_xClx shows an increase of the cell edge and the saturation magnetization with x, and a decrease of the ferromagnetic Curie temperature (Sleight and Jarrett 1968). A sample with x ~ 1 and T c ~ 2 1 0 K exhibits an electrical behaviour typical of an impure semiconductor. Miyatani e t al. (1971a) prepared CuCr2Se4-~Clx with 0~<x ~ 1 are not possible. However, more recent work has shown that materials with x > 1 can still be obtained. A single crystal with a = 10.444 A, corresponding to x = 1.06 (fig. 31), was found to be a semiconductor with Tc = 110 K and a band gap of 0.9 eV, as deduced from optical properties (Lee et al. 1973). A series of polycrystalline samples and single crystals from x = 0 to x - 2 could be prepared (Pinko et al. 1974). Figures 30 and 31 give a and Tc. In this series the largest a (10.444 A) and

61jdf

~'1 / ///+'1

(.uB)~ b

0

02

0.Z+

0.6

+

I

08 1 ~X Fig. 29. ]Ferromagnetic moment of CuCr2Se4 ~Br~; (a) in 10 kOe at 4 K, Robbins et al. (1968); (b) for 0.1 ~< x ~< 0.5, /xs = (5.0 + x) ~B, Sleight and Jarrett (1968); (c) Miyatani et al. (1971a).

646

R.P. VAN STAPELE i

o

&O0

Tc(K)

~.+ O ~+~"

3O0

\ x~ I

I I

4-

200

100

x 0

,

,

,

,

,

,

,

02_

0.4

0.6

08.

10

1.2

1.4

,

,

x

16 1.8 =X

2.0

Fig. 30. Ferromagnetic Curie temperature of CuCr2Se4-xBrx (symbols as in fig. 31).

10.46 10.44

x

10.42

[]

o

x x

x x

"E 10.40

t-I

x

,,F

x

+ +e

G~ 410

[3

10.38

+

O £.3

1036t 10.34]_~

o

uu~ u

,

o12

,

,

d4'o:6'o18'

~

1'.2

,

114 1'.6 P-X

, ,

,

118

2

Fig. 31. Cell edge of CuCr2Se4_xBrx according to: (0) Robbins et al. (1968); (C)) White and Robbins (1968); ([~) Sleight and Jarrett (1968); (+) Miyatani et al. (1971a) and (x) Pink et al. (1974).

SULPHOSPINELS

647

lowest Tc (84 K) of the halogen-substituted sulphospinels have been measured on a chemically analyzed sample with the composition Cu0.99CrzSe2.mBr2.02. Deviations from the stoichiometry according to CuyCr2Se4_zBr, with 0.8 ~< y ~< 1.2, 0 ~< x ~ 1 are not. The unstable spinels could be stabilized by means of a treatment with NH4OH, which mainly extracts the excess Cu. The Cu content of stable spinels depends on the Br content. It is always less than 1, with a minimum of y = 0.78 at x ~ 1 (fig. 32). The origin of this behaviour is not known. Since electridal and magnetic measurements have not been carried out, it is not possible to discuss the valencies in these complicated materials. Magnetostriction (Unger et al. 1974) and hysteresis loops (Unger 1975) have been measured on some CuCr2Se4_xBr~ single crystals.

0

1

~× Fig. 32. Composition of stable compounds CuyCr2Se4-zBrx,according to Pink et al. (1974).

5. Ferromagnetic and antiferromagnetic semiconductors 5.1. General aspects In this section we will treat the normal spinels ACr2X4 (X = S or Se) with

diamagnetic Zn 2+, Cd 2+ or Hg 2+ on A sites and magnetic Cr 3+ on B sites. The existence of this kind of compounds was discovered by Hahn (1951). The spinels CdCrzS4 and CdCrzSe4 exhibit the rare combination of quite strong ferromagnetism and semiconductivity (Baltzer et al. 1965, Menuyk et al. 1966). For this reason they have been investigated more than any other of the sulphospinels. In particular the influence of the magnetic ordering on the electrical and optical properties is the subject of many papers. Before treating the compounds separately we will discuss some general aspects. The first spinels of this type to be investigated were ZnCrzS4 and ZnCrzSe4. They are antiferromagnets and are anomalous in that they have a positive asymptotic Curie temperature 0. The corresponding oxyspinels ZnCr204 or

648

R.P. VAN STAPELE

MgCrzO4 exhibit a normal antiferromagnetism and have a strongly negative 0. The anomalous behaviour of the non-oxidic compounds has been attributed to the combination of a ferromagnetic nearest-neighbour interaction between the Cr 3+ ions and antiferromagnetic superexchange CrXXCr interactions at larger distances (Lotgering 1964b). The difference in sign of 0 for X = O and X = S or Se has been attributed (Lotgering 1964b) to a superposition of a ferromagnetic 90 ° Cr3+X2-Cr3+ superexchange interaction via the X 2- ion (Kanamori 1959) and an antiferromagnetic exchange interaction caused by the direct overlap of the d orbitals of the two Cr 3+ ions. The possibility of the latter interaction mechanism was anticipated (Kanamori 1959, Goodenough 1960, Wollan 1960) before a clear-cut example of it was known. In the oxyspinels the CrZ+-Cr3+ distance is small (2.94A in ZnCr204) so that a strong d - d overlap gives a dominating negative interaction. As a consequence of the much larger distance in the sulphospinels (3.53 A for X = S and 3.71 A for X = Se) the negative interaction is weakened so that the positive superexchange dominates. This is demonstrated in a plot of 0 versus a (fig. 33). The increase of 0 with increasing lattice parameter or Cr-Cr distance fits with the behaviour of a much wider class of Cr compounds with a dominating 90 ° C r - C r superexchange interaction (Rtidorf and Stegemann 1943, Bongers 1957, Lotgering 1964b, Baltzer et al. 1966, Menyuk et al. 1966, Bongers and V a n Meurs 1967, Motida and Miyahara 1970). The strength of the various terms that contribute to the 90 ° Cr3+-Cr3+ interaction has been determined in a detailed analysis of the optical spectrum of Cr 3+ pairs in Cr-doped ZnGa204 spinel (Van G o r k o m et al. 1973). The interaction - J S a " Su between the spins $ of two nearest-neighbour Cr ions a and b is the result of nine interactions -J~jsi • sj between the spins si of the three electrons in

M:Cd,Hg 200 100

--

o

0

,/ *--0~ x~

,t'×--s / 10 of-A) 11

100

200

300

Z,00

/ x=0

Fig. 33. Asymptotic Curie temperature versus lattice parameter of the compounds MCr2X4.

SULPHOSPINELS

649

the d states day, d~z and dax of ion a and the spins sj of the three electrons in the d states dby, dbyz and d~x of ion b. Due to the symmetry of a pair of nearestneighbour Cr ions there are four independent interactions among the nine £j: J~, the direct interaction between spins of electrons in the dxy orbits; J,~, the superexchange interaction between electrons in d states overlapping with the same ligand p state; J', the superexchange interaction between electrons in d states overlapping with two orthogonal p states of the same anion and Jc, the interaction between electrons in d states overlapping with p states on different anions (fig. 34). The direct interaction was indeed found to be by far the strongest (Jd = -561 cm-1), while J= = - 1 0 5 c m -1, J'c = +117 cm -1 and Jc = +39 cm -1. The existence of antiferromagnetic interactions MXXM via two anions X appears from the antiferromagnetic ordering in many layer structures, in which layers of magnetic ions M are separated by double anion layers. The sulphospinels under considerations are ferromagnetic or antiferromagnetic and the kind of ordering is determined by the relative strength of the positive MXM and negative M X X M interactions. The occurrence of both ferromagnets and antiferromagnets shows that the positive and negative interactions in sulphospinels are in equilibrium. From this it can be concluded that the M X X M interactions are about ten times weaker than the MXM interactions (Lotgering 1964b). It is difficult to derive the strength of the exchange interactions from the observed magnetic properties. The attempts that have been made, all except one, have been based on simplifying assumptions with regard to the more distant interactions. Lotgering (1965) analyzed the data of ZnCr2Se4, calculating the

dby

° ~ l

~~'-y o

b

Jo:dxy-dxy

~

~

,-y

dyz Jc

P~ dbz dyz -Pz ond dyz-Pz o

b

Z

- c / I d;x

x L.-"I

J.~ : dzx-Pz- y~

J~

d~×-p=± Px-dby

Fig. 34. (a) The negative interactions in the 90 ° Cr3+-Cr3+ superexchange. (b) The positive interactions in the 90 ° Cr3+-Cr3+ superexchange.

650

R.P. VAN STAPELE

interactions J1, J2, J3 and J4 from the asymptotic Curie temperature, the pitch of the observed helix a n d the magnetic susceptibility on the assumption that J3 = J4. (We use the notation of table 10 and fig. 35.) Plumier (1966a, b) used the same data to calculate J1, J2 and J3. Baltzer et al. (1966) used the interactions J1, J2, J4 and J5 and neglected J3 in a high temperature expansion of the magnetic susceptibility to calculate the Curie temperature. Assuming all the more distant interactions to be equally strong (e.g. K =-/2 = J4 = Js) they calculated J1 and K from the Curie temperature and the asymptotic Curie temperature for the ferromagnets CdCr2S4, CdCr2Se4 and HgCr2Se4 and the metamagnet HgCr2S4. A similar approximation has been made in a multi-sublattice molecular field analysis of these compounds (Holland and Brown 1972). However, the impressive analysis given by Dwight and Menyuk (1967) showed that the magnetic properties are very sensitive to the strength of J2 . . . . ./6 and that the validity of results obtained using simplifying assumptions is doubtful. They analyzed the stability of the various classical spin ground states, minimizing the Heisenberg exchange energy, and found that in the specific case of ZnCr2Se4 a spiral ground state with the observed properties can exist if the values of the interactions J~ . . . J6 fall inside a limited

TABLE 10 Notation of pairs of octahedral ions in the spinel lattice (fig. 35) and of exchange constants. Notation

According to

BoB1 BoB2 BoB3 BoBa Wo W1 W2 W3 J WJ UJ U'J.

BoB5 W4 VJ

BoB6 U2J

J1

J5

J6

J2

J3

J4

Baltzeret al. (1966) Lotgering (1965) Dwightand Menyuk (1967) this work

133

i

/

,

,

A

I

© [30 Fig. 35. Octahedral sites and anions in the spinel lattice.

e. 136

SULPHOSPINELS

651

region. In a similar analysis the stability at T = 0 of various possible spin configurations has been systematically investigated by Akino and Motizuki (1971) with the restriction that J3 = J4 and J6 = 0. Applying the Goodenough-Kanamori rules to the more distant exchange interactions Dwight and Menyuk (1968) expected a negative sign for J3, J4 and J6, a positive sign for Js, whereas the sign of J2 remained uncertain. However, a direct determination of the strength of the more distant exchange interactions between Cr 3+ ions in Cr-doped ZnGa204 by means of electron spin resonance revealed all interactions to be negative. The constants J~ of the exchange interactions -J~so" si were found to be: J 2 = - 0 . 9 4 c m -1, J 3 = - l . 2 2 c m -1, Y4=-0.80cm -I, Js = -0.45 cm -1 and J6 = -0.55 cm -1 (Henning 1980). The compounds under discussion are semiconductors, the behaviour of which is usually not intrinsic but determined by small deviations of the stoichiometry or the presence of impurities in small concentrations. The most striking property is a strong influence of the magnetic ordering on the resistivity and magnetoresistance in certain n-type compounds, e.g., in suitably doped CdCr2S4 and CdCr2Se4. Measured as a function of temperature these quantities show a maximum close to the ferromagnetic Curie temperature. These phenomena are due to the interaction between the spins of the charge carriers and the spins of the Cr 3+ ions. A generally accepted mechanism has not been found, and which of the proposed models applies depends on the type of conduction and the strength of the interaction between the spin of the Cr 3+ ions and that of the charge carriers. If the conduction is in a broad band and if the interaction between the spin of the charge carriers and the Cr 3+ spins is relatively weak, so that the influence of the charge carriers on the magnetic behaviour of the Cr 3+ spin system can be neglected, the theory of Haas (1968) applies. It describes the dependence of the number of charge carriers on the temperature and the strength of an applied magnetic field as it is due to the splitting of the conduction band and donor or acceptor levels in the exchange field from the Cr magnetization (Bongers et al. 1969). The scattering of the charge carriers at the spin disorder in the Cr spin system gives the carriers a mobility that can also be strongly dependent on the temperature and the magnetic field strength (Haas 1968, Patil and Krishnamurthy 1978, Aers et al. 1975). Both effects can give rise to a peak in the resistivity at the Curie temperature and to a negative magnetoresistance with a maximum at the Curie temperature. The critical behaviour of the resistivity has been studied theoretically by Alexander et al. (1976) and Balberg and Helman (1978). If the interaction between the spin of the charge carriers in a broad band and the Cr spins is sufficiently strong, the magnetic state of the Cr spin system changes and a magnetic polaron can exist. In this state the charge carrier is surrounded by a cloud of magnetic polarization of the Cr spins. Yanase et al. (1970) and Yanase (1972) have discussed the conditions for the stability of the magnetic polaron state. They find the magnetic polaron to be stable in a region around the Curie temperature, where it has a much smaller mobility than the original charge carrier would have had. Qualitatively, this can explain the observed anomalies in the electrical resistivity. The entropy of the polarized Cr spins gives rise to an

652

R.P. V A N S T A P E L E

anomalous thermoelectric power and, as Yanase (1971) has pointed out, this can explain the observation by Amith and Gunsalus (1969) that a maximum in the resistivity of Cdl-xInxCr2Se4 coincides with a minimum in the thermoelectric power. In the case of an impurity conduction influenced by the magnetic ordering, Yanase and Kasuya (1968a, b) and Kasuya and Yanase (1968) proposed the model of the magnetic impurity state. In this model the spins of the Cr ions, which are neighbours of an occupied impurity state, are polarized by the exchange interaction between the spin of the impurity electron and the Cr spins. This stabilizes the occupied impurity state and the stabilization energy will increase towards the Curie temperature, where the Cr spin system is highly susceptible. This leads to an activation energy that is maximum at the Curie temperature. Application of a magnetic field will decrease the activation energy. The model of the magnetic impurity state explains in this way a maximum in the resistivity and a maximum negative magnetoresistance at the Curie temperature.

T A B L E 11 Magnetic data of the semiconductors MCr2X4: the asymptotic Curie temperature 0, the ferromagnetic Curie temperature Tc or the antiferromagnetic N6el temperature TN, the molar Curie constant Cm and the ferromagnetic moment /zr. References: (1) Menyuk et al. (1966), (2) Lotgering (1956), (3) Plumier et al. (1975), (4) Lotgering (1964b), (5) Von Neida and Shick (1969), (6) Baltzer et al. (1966), (7) Srivastava (1969), (8) Hastings and Corliss (1968), (9) Le Craw et al. (1967), (10) Eastman and Shafer (1967).

Compound ZnCr2S4

0 (K)

Tc (K)

TN (K)

18 _+8

Cm

m (/xB/molecule)

3.34 18

CdCr2S4

152 156

HgCr2S4

142

84.5 86

3.70 3.8

5.15/./ 5.55 (,/ 6.02 co)

3.62

5.35 (a~

84

ZnCr2Se4

115

CdCr2Se4

204 210 172

HgCr2Se4

200

36.0 - 6 0 (c~ 36.1 -20 20 105 (dl 129.5 130 140 127.7 129_+2 106 105.5

Ref. (2) (1) (6) (1) (5) (7) (6)

(8) (7) (4) (1) (3)

3.54

3.82 3.66 4.48

5.62 (a) 5.6 (,/ 5.98 _+0.4 ~e~

3.79

5.94 -+ 0.04 5.64 (a)

(6) (1) (9)

(7) (10) (6)

(7)

(a) At 4.2 K in 10 kOe. co)At 1.5 K. (c)A spiral spin configuration in zero field. (d) A spiral spin configuration at T < 21 K, antiferromagnetic microdomains at T > 21 K. (e)At 1.5 K in 15 kOe.

SULPHOSPINELS

653

Effects of the magnetic ordering have also been seen in optical properties. The generally observed p h e n o m e n o n is an anomalous shift of the optical absorption edge (Busch et al. 1966, Harbeke and Pinch 1966) to a higher energy, as in CdCrzS4, or to a lower energy, as in CdCrzSe4. The interpretation of these observations depends heavily on the nature of the absorption at the edge. If a broad conduction band plays a role in the transition, a red shift of the absorption edge can be explained by the spin splitting of the band due to the exchange interaction between the Cr spins and the spin of the excited electron. Rys et al. (1967), Haas (1968) and Kambara and Tanabe (1970) have discussed this mechanism in detail. The critical behaviour of the band gap in this case has been treated by Helman et al. (1975) and Alexander et al. (1976). Helman et al. (1975) included the influence of an applied magnetic field. Callen (1968) has suggested another mechanism in which the shift of the absorption edge arises from a change of the band energy due to exchange striction, which distorts the lattice. The shift of the edge can have either sign, but it is estimated to be too small in all cases of interest, as we will discuss later on. White (1969) has pointed out that the absorption edge due to an indirect transition between the valence band and the conduction band can show a shift to the blue below the Curie temperature. Nagaev (1977) argued that a blue shift can arise from interband s-d exchange. Since the magnetic, the electrical and the optical properties and their mutual relation depend strongly on the detailed composition of the compounds, we will review in the following each of the compounds separately. The magnetic data are summarized in table 11".

5.2. ZnCr2S4 ZnCr2S4 is a normal (Hahn 1951) spinel (Natta and Passerini 1931) with lattice parameters, as given in table 1. In the paramagnetic region Lotgering (1956) observed above 100 K a CurieWeiss behaviour with 0 = 18 _+8 K and a molar Curie constant Cm = 3 . 3 4 - 0.06. According to Menyuk et al. (1966) the Cr spins order antiferromagnetically below TN = 18K. A b o v e TN Stickler and Zeiger (1968) observed a paramagnetic resonance with g ~ 2 and an antiferromagnetic resonance at lower magnetic fields below Ty. The zero-field antiferromagnetic resonance frequency follows an S = 3 Brillouin function fairly well. The antiferromagnetic spin structure is not known. A flat spiral, as observed in ZnCrzSe4, does not seem to fit the neutron diffraction spectrum of ZnCr2S4 (Stickler and Zeiger 1968). Bouchard et al. (1965) found the compound to be a semiconductor with p (300 K) = 5 x 10 l° f~cm and an activation energy q = 0.59_+ 0.03 eV at higher temperatures. The samples measured by Albers et al. (1965) had a much smaller resistivity and a small positive Seebeck coefficient. The cold-pressed samples studied by Lutz and Grendel (1965) had a p-type conduction with acceptor states 0.5 to 0.8 eV above the valence band. Doping with W for Cr or with In for Zn can compensate the p-type conduction. Above 200°C the activation energy in undoped samples is 1.5 eV, which is considered to be the band gap energy. * S e e n o t e s a d d e d in p r o o f (d) o n p. 737.

654

R.P. V A N S T A P E L E

5.3. CdCr2S4 is a normal (quoted by Hahn 1951) spinel (Passerini and Baccaredda 1931). Crystallographic data are given in table 1. As shown in fig. 36, the lattice constant a decreases in a normal way down to 100 K, but increases slightly below that temperature (Martin et al. 1969, Bindloss 1971 and G6bel 1976). More striking is the anomalous increase of the width of the X-ray diffraction lines (to A a / a ~ 10-3) observed by G6bel (1976) in CdCr2S4 and other sulphospinels below 200 K. This broadening is not correlated with the magnetic behaviour of the substances, and G6bel (1976) concludes that the spinel structure becomes rather soft at lower temperatures so that weak random stresses can give rise to remarkable random strains. The ferromagnetism of CdCr2S4 was discovered by Baltzer et al. (1965) and Menyuk et al. (1966). In the paramagnetic state the Curie constants are close to the value 3.75 for trivalent Cr ions (table 11). However, the moment in the saturated ferromagnetic state is often found to be less than the expected 6 txs per molecule (table 11). The observed moments depend strongly on the stoichiometry and the purity of the samples. For example at 1.5 K the single crystals grown by Von Neida and Shick (1969) have 3.01/xB per Cr ion in the ferromagnetic saturation. The asymptotic Curie temperature 0 is appreciably higher than the ferromagnetic Curie temperature (table 11). Baltzer et al. (1966) have analyzed this on the basis of a simplified model for the interactions between the Cr 3+ moments (see CdCr2S4

10.28

10.27

*d 10.26 113

g 10.2s u

.~ 10.24 O J

10.23

I I iiii i i

10.22 / I

I

I

I

200

300

400

I

I

I

500 600 700 T (K) Fig. 36. Lattice constant of CdCr2S4 versus temperature, according to Martin et al. (1969) (I), Bindloss (1971) (--) and G6bel (1976) (O). 0

100

SULPHOSPINELS

655

section 5.1). They find J/k = 11.8K for the nearest-neighbour interaction - 2 J S i ' N and K / k = - O . 3 3 K for the next-nearest-neighbour interactions - 2 K 8 i . ~. These values should be regarded with some caution since the results are expected to be very sensitive to the suppositions about the more-distantneighbour interactions (Dwight and Menyuk 1967). Under hydrostatic pressure the Curie temperature decreases at a rate dTJdP = -0.58 K/kbar, which corresponds to the value dTJda = +46 K / A for the rate of increase of T~ with the lattice parameter a (Srivastava 1969). The dependence of the magnetic moment on the details of the composition has been investigated by Pinch and Berger (1968). Annealing a polycrystalline sample with a magnetic moment of 5.79/xB (at 4.2 K and 10 kOe) for 46 h between 800 and 900°C in a sulphur pressure between 30 and 60 atm, they observed a small increase to a magnetic moment of 5.84/XB, while a reduction treatment in hydrogen at 800°C for 72h resulted in a smaller decrease to 5.73#B. They attribute these variations to Cr 2+ ions that charge-compensate the sulphur deficiency and that couple their magnetic moments of 4~B antiparallel to the moments of the Cr 3+ ions. They obtained larger variations by replacing Cd z+ with In 3+. At 4.2 K and 10 kOe polycrystalline samples of Cdl-xInxCr2S4 with x up to 0.15 showed a magnetic moment per molecule that decreased at a rate close to --7XtXB, corresponding to the replacement of 3 tXB of Cr 3+ parallel to the magnetization by 4 txB of C1a+ antiparallel to the magnetization (fig. 37). Pinch and Berger (1968) observed that the rate of approach to saturation was smaller the larger the In concentration, which they attributed to an increasing magnetic

6

-'X.

-5 o

-6 E ~5

\\'~

^Cdl_ x InxCr 2 $4

\

\

\

Z

o\ \

E 0 ~E

\ \ \ CdCr2-xInxS~ \

\

\ 3

\ \

=F 0

i

I 0.1

I

[

0.2 X

Fig. 37. Magnetic moment of Cdl xInxCr2S4 (Pinch and Berger 1968) and of CdCr2-xInxS4 (I.otgering and Van der Steen 1971a) at 4.2 K and 10 kOe.

656

R.P. VAN STAPELE

anisotropy, expected for Cr 2+. These results were in keeping with the existence of Cr 2+ in the inverse spinels CrIn2S4 and CrAlaS4 (Flahaut et al. 1961). However, Lotgering and Van der Steen (1969, 1971a, b) in a study of the paramagnetic properties of the latter compounds, found that the Curie constant corresponded to Cr 3+ instead of Cr 2+ and showed that the single phase compounds were the metal-deficient spinels Crs/9M16/9[[]l/3S4 3+ 3+ (M = A1 or In). Moreover, they discovered that the magnetization of CdCrzS4 decreased surprisingly fast if they replaced magnetic Cr 3+ ions by diamagnetic In 3+ ions in CdCr2_xInx 3+ 3+$4 (fig. 37). It is seen that the magnetic behaviour is comparable to that in Cdl_xInxCr2S4, though no Cr 2+ is present. The decrease of the ferromagnetic moment with x has been attributed by Lotgering and Van der Steen (1971a, b) to spin canting around the In ions due to negative exchange interactions between next-nearest Cr neighbours (see section 5.1)*. Two conclusions can be drawn from these experiments. The first is that the divalent state of chromium is not stable in CdCrz84. The second is that the ferromagnetic ordering in CdCr2S4 is easily disturbed. This last property makes it dangerous to use the magnetization of substituted CdCr2S4 as a measure of the magnetic moment of the substituted ions, as Robbins et al. (1969) had done. These authors prepared the spinels Cd0.sIn0.zCrl.80M0.2S4 with M = Co or Ni and CdCrl.sM0.2S4 with M = Ti and V. From the change in magnetization they concluded that the coupling between the spins of Ni 2+ and Co 2+ and the Cr 3+ spins is negative, while Ti 3+ and V 3+ appear to have no magnetic moment. Not only the magnetic moment, but also the ferromagnetic resonance spectra have been found to depend on the sample (Berger and Pinch 1967). Pinch and Berger (1968) studied the 9.49 G H z ferromagnetic resonance spectra of vapourgrown single crystals at 4.4 K. In the "as-grown" state the angular dependence o f the field for resonance was anomalous with sharp peaks in the [111] directions, while the line width was also anisotropic with a sharp maximum in the same direction. The angular variation could not be described by the usual cubic anisotropy constants K1 and /(2. Heating of the crystals in a sulphur p r e s s u r e reduced the anisotropy and produced samples with a small K~ = 3.8 x 103 erg/cm 3 and K2 = 1.3 x 10 3 erg/cm 3 and an isotropic line width. On a single crystal, exposed to air for 1½ years, Arai et al. (1972) measured at 9.5 G H z and 4.2 K an angular variation of the resonance field, corresponding to K1 = 1.6 x 10 4 erg/cm 3, and from the shift of the resonance fields while applying a uniaxial stress along the [110] direction they measured magnetostriction constants Am = - 2 . 9 x 10 -5 and h~oo= - 4 . 7 x 10-5. The observed variations in the magnetic anisotropy were attributed to the action of Cr 2+ ions, which could be present in non-stoichiometric crystals. However, Hoekstra and Van Stapele (1973) recognized the similarity between the angular variation of the anomalous resonance spectra and their spectra of Fe 2+ doped CdCr2S4 (Hoekstra et al. 1972, Hoekstra 1973). They showed that a small amount of 7 x 10 .4 tetrahedrally coordinated Fe 2+ per formula unit can explain the resonance spectra of the "as-grown" crystals of Pinch and Berger (1968). Hoekstra and Van Stapele (1973) also showed that Cr a+ ions on octahedral sites in the spinel lattice are * See notes added in proof (e) on p. 737.

SULPHOSPINELS

657

expected to give rise to peaks in the resonance field and the line width in the [110] and [112] directions, unless a static or a dynamic Jahn-Teller effect quenches most of the orbital moment. Anomalies in the [110] and [112] directions are not, however, specific to Cr2+; they can also be due to ions, such as Fe z+ on octahedral sites. In the ferromagnetic resonance spectrum at 9.5 G H z and helium temperatures of an "as-grown" single crystal of CdCr2S4 Hoekstra and Van Stapele (1973) actually observed small peaks in the [110] and [112] directions, additional to strong anomalies in the [111] directions, due to 7 x 10-5 tetrahedral Fe 2+ ions per formula unit. If the small peaks are due to Cr 2+ ions, their concentration is low: 2 x 10 -5 ions per formula unit. Single crystals of CdCr2S4, prepared from very pure starting materials, such that the Fe concentration was too small to be detected spectrochemically ( 106

y

J

to 0) Or"

10 ~

102

100

C

Z, 6

8 10 12 1/-, 16 103/T (K-1)

Fig. 38. Resistivity of CdCr2S4 (a) annealed in a low sulphur pressure and of Cd0.98Ga0.02Cr2S4 (b) a highly compensated sample after annealing in a low sulphur pressure and (c) another sample without annealing, according to Larsen and Voermans (1973).

SULPHOSPINELS

659

1.0 0.8 ~- 06

e

0.1., 0.2 I

0

60

80

I

100 120 T(K)

t

I

1L0

I

I

160

Fig. 39. Magnetoresistanceof Cd0.98Ga0.02Cr2S4, accordingto Larsen and Voermans (1973)((b) and (c) see caption fig. 38). the conduction mechanism shifts from impurity conduction to band conduction. Although no definite explanation of the phenomena has yet been given, it is clear that the electrical transport properties show signs of an exchange coupling between the spin of the charge carriers and the Cr spins. Such effects have also been observed in optical properties, such as absorption and reflection spectra, photoconduction, magneto-optic spectra and Raman scattering, to which we will now turn our attention. A b o v e 2 eV the optical absorption of CdCr2S4 rises steeply. Towards longer wavelengths the absorption edge has a long tail with a complicated temperaturedependent structure (Busch et al. 1966), which also depends on the doping and the stoichiometry (Miyatani et al. 1971b). The absorption coefficient in the tail is so large that the optical density of the 4 x 10_3 cm thick single crystal studied by Harbeke and Pinch (1966) increased at room temperature to log(Io/I)= 3 at 1.57 eV. The position of the " e d g e " shifts to higher energies at lower temperatures, while a structure between 1.6 and 1.7eV develops most strongly between say 120 and 50 K. In the literature this behaviour has been known as the "blue shift of the band edge", but it was soon recognized that part of the absorption at energies below 2 eV is due to crystal field transitions of Cr 3+ and that the transitions between the valence band and the conduction band occur at higher energies (Berger and Ekstrom 1969, Wittekoek and Bongers 1969, 1970). All the lower energy crystal field transitions 4A2g~ 2Tlg + 2Eg' 4A2g i.) 4T2g' 4A2g__+2T2g' 4A2g~ 4Tlg have been observed. Their energies are listed in table 12 and we have indicated them at the left hand side of fig. 40. The transition 4A2g---~4Tlg has only been observed in the polar magneto-optic Kerr effect spectrum (Wittekoek and Rinzema 1971), where it occurs at the same energy (2.29eV) as in the absorption spectrum of Cr-doped CdIn2S4 (table 12). The other crystal field transition observed in the magneto-optic Kerr effect is 4A2g---~2T2g , but this transition,

R.P. V A N S T A P E L E

660

T A B L E 12 Crystal field transitions of Cr 3+, observed in CdCr2S4 and CdIn2S4: Cr 3+. Energy (eV) Transition

CdCr2S4

4A2g --> 2Tlg , 2Eg

1.64 1.62 1.61

4A2g -~ 4T2g

1.82

CdIn2S4: Cr 3+

Reference

1.85

Harbeke and Pinch (1966) Berger and Ekstrom (1969) Larsen and Wittekoek (1972) Berger and Ekstrom (1969) Koshizuka et al. (1978a) Larsen and Wittekoek (1972) Wittekoek and Bongers (1969, 1970) Berger and Ekstrom (1969) Koshizuka et al. (1978a) Wittekoek and Rinzema (1971) Larsen and Wittekoek (1972) Wittekoek and Rinzema (1971) Wittekoek and Bongers (1969, 1970)

1.76

4A2g -~ 2T2g

2.14

4A2g ~ 4Tig

2.12 2.1 2.29 2.29

- 2.60

••,otoconduction edge

2.50 2.LO

Z'A2 ~,,STlg ~-.-.-.

2,30 220

Z'A2-~2T2g

~

2.10 [~

g 2.o0 c~,

C,C"

LU

1.90 .

.

.

.

1.80

1.70 4A2-~Tlg ,2Eg~--~

Tc '~i

100

1.60 I

200

I

300 T IK)

i

LO0 5OO

Fig. 40. Energy of the transitions observed in CdCr2S4 as a function of temperature ( A, B and C, Berger and Ekstrom 1969, - - - - Wittekoek and Bongers 1969 and 1970, - . . . . . Wittekoek and Rinzema 1971, ,,~ Larsen and Wittekoek 1972, ~ A', A~ and C', Koshizuka et al. (1978a).

SULPHOSPINELS

661

together with the transitions from 4A2g t o *Tzg, 2Tlg and 2Eg, has also been observed in the absorption spectrum of thin films (less than llxm) (fig. 41, Berger and Ekstrom 1969, Koshizuka et al. 1978a) and in the photoconduction of poly: crystalline undoped n-type samples (fig. 42, Larsen and Wittekoek 1972). At 6 K the latter authors also observed a weak luminescence at 1.6eV due to the transition 2Tlg , 2Eg-->4A2g (fig. 43). A progression of 330+30cm 1 phonons, possibly associated with this transition, had been observed in absorption by Moser et al. (1971). The lower part of the absorption edge, as observed by Harbeke and Pinch (1966), consists of the crystal field transition 4A2g--">2ylg , 2Eg and the wing of the crystal field transition 4Azg~ 4T2e (Wittekoek and Bongers 1969, 1970). The blue shift of the edge is attributed by Wittekoek and Bongers (1969, 1970) to sharpening of the 4A2g--> 4T2g transition at lower temperatures. Berger and Ekstrom (1969) are of the opinion that another transition (A) is also present. It shows a small blue shift (fig. 43) and has a moderate oscillator strength of f ~ 10-3. Because no other crystal field transitions are expected in this region, Berger and Ekstrom (1969) conclude that A may be due to an indirect band-to-band transition or to a weak charge transfer transition. Below the Curie temperature the spectrum in the region around 2 eV shows even more structure. A peak C appears that shifts to lower energies with decreasing temperature (Berger and Ekstrom 1969, Wittekoek and Bongers 1969, 1970). The oscillator strength is small ( f ~ 10-4) and the absorption is strongly circularly polarized (fig. 41, Berger and Ekstrom 1969). In spite of the small oscillator strength, the transition has a considerable Kerr rotation (Wittekoek and

1.5

Z,A2 ~¢- 1.3

.2 1.1 O

I

A2

C

/.i/

0.9

Y...

0.7

_.// ,,,'"-

.~'

/ "~..~J" Am ----- + I

/ 0.5

-1

¢

---

0

I

1.7

,"'I

j

I

1.8

I

.r

I

I

19 2.0 Energy (eV)

I

21.1

I

2.2

Fig. 41. Circularly polarized absorption spectra of CdCr2S4 at 2 K in a magnetic field of several kOe, according to Berger and Ekstrom (1969). The m = +1 spectra are displaced by 0.12 to higher optical density.

662

R.P. V A N S T A P E L E

2.5

Energy (eV)

2.0

I

I

E

1.5

I

i

z' A2-.-~2 T2

T12E

cD 2 r~

& LL D o O

1

~5 ro_

~A2-~4T2

I

L

0.5

0.6

L

I

I

0.7

0.8

Wavelength (microns) Fig. 42. Photoconductivity of a polycrystalline undoped n-type sample of CdCr2S4 as a function of the wavelength in zero magnetic field and in a transverse magnetic field of 6 kOe, according to Larsen and Wittekoek (1972).

3.0 2.5 i

2.0

i

Energy (eV) 1.5

i

I

1.2 i

1.0 i

E

0.8 i

i

4A2--~4T2 2.0 / / ' 4 A 2 - ~ 2 T 2 ~ 4^

"41.0:/o / /

2T

2 E-

V i ~IR line of Cr3+ i. 200 x enhanced

A /

g E i

0.4

i

I

0.6

0.8 1.0 1.2 Wavelength {microns)

1.4

1.6

Fig. 43. Luminescence at 6 K (--) and excitation spectrum at 80 K (- . . . . . ) of undoped CdCr2S4 powders, according to Larsen and Wittekoek (1972).

SULPHOSPINELS

663

Rinzema 1971). These authors also found the position of the structure in the Kerr effect spectrum to depend on heat treatment and doping. This indicates that peak C is not due to an intrinsic excitation. A possible explanation is a transition from the valence band to an F-centre-like state of an electron bound to a sulphur vacancy (Harbeke and Lehmann 1970, Lehmann et al. 1971, Natsume and Kamimura 1972). In a repetition of the absorption measurements reported by Berger and Ekstrom (1969), Koshizuka et al. (1978a) found essentially the same structure in the region around 2 e V (see fig. 40). Apart from the peak C, however, these authors found a second red shifting peak A2, which was also observed by Berger and Ekstrom (1969) (fig. 41) at 2 K and which has the opposite circular polarization of peak C. Koshizuka et al. (1978a) interpret A2 and C as components of a transition to an exchange split state, separated at 4.2 K by 0.07 eV. The onset to strong absorption occurs at B (figs. 40 and 41). Berger and Ekstrom (i969) attribute this edge to transitions between the valence band and the conduction band. Its position 2.3 eV at low temperatures agrees well with the band gap of CdS (2.58eV) and of CdIn2S4 (2.2 eV). The direct edge in the photoconduction has been observed by Larsen and Wittekoek (1972) to occur at the slightly higher energy of 2.5 eV (fig. 40). The edge shifts weakly to higher energies at lower temperatures and shows no trace of a shift to the red in the ferromagnetic state. At still higher energies a transition at 3.4 eV has been found by Wittekoek and Rinzema (1971) as a strong resonance in the polar Kerr effect spectrum. This transition, which is responsible for the dispersive part of the Faraday rotation between 0.8 and 10 ~m (Wittekoek and Rinzema 1971, Moser et al. 1971) has been attributed by Wittekoek and Rinzema to a charge transfer transition of an electron from sulphur p orbitals to an empty Cr orbital. Reflection spectra (Wittekoek and Rinzema 1971, Fujita et al. 1971, Ahrenkiel et al. 1971), thermoreflectance spectra (Iliev and Pink 1979) and measurements of the reflectance d i c h r o i s m - o n e measures in a magnetic field 2 [ ( R + - R _ ) / ( R + + R )], where R+ and R_ are the specular reflectivities for right-handed and left-handed circularly polarized l i g h t - (Ahrenkiel et al. 1971, Pidgeon et al. 1973) have provided data that generally agree with the results reviewed above. This is also the case with the Faraday rotation of thin films of CdCr2S4, measured by Golik et al. (1976) in the visible region. Values of the refractive index have been derived by Wittekoek and Rinzema (1971) from the reflectivity and from interference patterns in thin hot-pressed polycrystalline samples by Moser et al. (1971) and Lee (1971), who measured n = 2.8 in the wavelength range of 2-10 Ixm. The data, which agree roughly, are given in fig. 44. Additional data were reported by Pearlman et al. (1973). T o conclude this review of the spectral properties of CdCr2S4, we return to the study of the photoconductivity reported by Larsen and Wittekoek (1972). The fact that they observe the crystal field transitions in the photoconductivity (fig. 42) reveals that excited C r 3+ ions are not stable with respect to either an indirect minimum of the conduction band or a direct minimum, to which optical tran-

664

R.P. V A N S T A P E L E

L

1

c o E~

"53

~ X ~ x ~ . x ~ x _ _

x c

'2 I

100

[

,

I

500 1000 W o v e l e n g t h (nm)

I

I

5000

Fig. 44. Refraction index of CdCr2S4; ( 0 ) data of Wittekoek and Rinzema (1971) at 80 K; (x) data of Moser et al. (1971) at 300 K.

sitions from the valence band are forbidden, at 1.6 eV or less above the valence band. The destabilized Cr ions give rise to holes in the valence band, which accounts for the observed photoconductivity. Larsen and Wittekoek (1972) observed that the photoconductivity depended strongly on the strength of an applied magnetic field (fig. 42), which they attribute to a hole mobility influenced by spin disorder scattering (Haas 1968). A strong fluorescence line observed at 0.9eV (fig. 43), which has an excitation spectrum showing the crystal field transitions, indicates that the holes can recombine with electrons from an acceptor state at 0.9 eV above the valence band (Larsen and Wittekoek 1972). Finally we mention that the photoconduction experiments have been extended to Ga-doped CdCr2S4 samples (Larsen 1973) and that the results corroborate the conclusion that the photoconduction is mainly due to photo-excited holes, which are responsible for the observed dependence on magnetic field and temperature. We now turn to the phonon structure of C d C r 2 S 4 . White and DeAngelis (1967) have shown that in normal spinels four vibrations (Tlu) are infrared and five (Alg + Eg + 3T2g) Raman-active. The four Tlu vibrations have been observed in infrared absorption and reflection studies and the observed frequencies at room temperature are given in table 13". Below the ferromagnetic Curie temperature at 79 K, the phonon frequencies are increased by only about 1%, while the oscillator strength of the highest two vibrations have not changed markedly (Lee 1971). This is at variance with the Raman-active modes, some of which show a strongly temperature-dependent intensity. Harbeke and Steigmeier (1968) were the first to observe this and by scattering light quanta of 1.96 eV they observed the Raman lines listed in table 14 (Steigmeier and Harbeke 1970). All lines were found to have an intensity that varies with temperature. This has to do with the temperature-dependent absorption at 1.96 eV, which is the only cause of the variation of the intensity of the light scattered by the Eg vibration (Raman line C), whereas * See notes added in proof (f) on p. 737.

SULPHOSPINELS

665

TABLE 13 Frequencies of the four infrared-active phonon modes of CdCrzS4. Frequencies (cm-1) at room temperature 381 385 376.9-+0.2 385

332 240 337 321.6-+0.3 347 234

Reference 97.0

Lutz (1%6), Lutz and Feh6r (1971) Riedel and Horvath (1969) Lee (1971) Moser et al. (1971)

TABLE 14 Raman lines of CdCr2S4, quoted from Steigmeier and Harbeke (1970). Line A C D E F G H I

Assignment 300 K 40 K mixed Eg T2g mixed Alg

mixed Eg T2g mixed mixed

Raman shift (cm-1) 300 K 40 K 101 -+2 256 -+2 280 -+ 1.5 351 _+2 394 -4-2 -460 -506 -600

105 _+2 257 + 2 281 -+ 1.5 353 -4-2 396 -+2

Rel. intensity 40 K 12 44 49 74 112 6 5 6

it is only partly the origin of the variation of the intensities of the other R a m a n lines. W h a t has strongly attracted attention was the observation of Steigmeier and H a r b e k e (1970) that the t e m p e r a t u r e variation of the ratio of the intensity of the lines A, D, E and F to the intensity of line C resembles that of the correlation function (Si • S j ) / S 2 of n e a r e s t - n e i g h b o u r Cr spins Si and S/. H o w e v e r , K o s h i z u k a et al. (1976, 1977a) subsequently s h o w e d that the way in which the R a m a n intensity varies with t e m p e r a t u r e d e p e n d s on the wavelength of the scattered light. A b o v e the ferromagnetic Curie t e m p e r a t u r e m a r k e d resonances are not observed, whereas at 15 K especially the R a m a n lines E and F show a strong r e s o n a n c e at 650 rim, which m e a n s that light q u a n t a are maximally scattered if their energy is a b o u t 1.9eV. A s can be seen in fig. 40, this is the wavelength region w h e r e the red-shifting absorption has been observed. T h e absorption in this region is strongly circularly polarized and Koshizuka et al. (1978a, b) o b s e r v e d that the R a m a n scattering of circularly polarized light d e p e n d e d systematically on the sense of the polarization of the incoming and the scattered light if the sample was placed in a magnetic field. These experiments were d o n e at 40 K with a Kr laser at 1.92 e V and with an A r laser at 2.01 e V in an a t t e m p t to observe the influence of the right-handed circularly polarized absorption C and the lefth a n d e d circularly polarized absorption A2 (figs. 40 and 41). A t 1.92 e V the effects of the polarization were m u c h m o r e p r o n o u n c e d than at 2.01 e V but neither spectra s h o w e d a c o m p l e t e right-left s y m m e t r y (see also Koshizuka et al. (1980)).

666

R.P. VAN STAPELE

An analysis of the phonon frequencies in terms of a simple force model has been given by Briiesch and D'Ambrogio (1972). These authors as well as Baltensperger (1970) and Steigmeier and Harbeke (1970) discussed the influence of magnetic ordering on the Raman and infrared-active phonons on the basis of the ion position dependence of the superexchange interaction. Suzuki and Kamimura (1972, 1973) formulated a phenomenological theory of spin-dependent Raman scattering, starting from the general form for a polarizability tensor that depends on the Cr spins. They obtained an integrated intensity I ( T ) IR + M ( S o . S~)/$212 with a temperature dependence that is determined by the signs of R and M and their relative magnitude. The values of R and M can be calculated for specific microscopic Raman scattering mechanisms. Suzuki and Kamimura (1973) did this for phonon-modulated transfer integrals and oildiagonal exchange and were able to explain the temperature dependence observed by Steigmeier and Harbeke (1970), mentioned above. However, the experimental situation turned out to be much more complex and a more definite theoretical picture will have to await more complete experiment data. Nuclear magnetic resonance studies of CdCrzS4 have been made by Berger et al. (1968a, 1969a) and Stauss (1969a, b). The spectrum of 53Cr is complex and has been analyzed by Berger et al. (1968). They described the spectrum by v = (y]2rr)Hi~o + [(y]2rr)Ha, is + vo(rn - ½)](3 cos 2 0 - 1), where u is the frequency, 3' the gyromagnetic ratio of 53Cr, m = 3, ½, _ ½for the three m = +1 transitions between the I = 3 nuclear spin states of 53Cr and 0 is the angle between the local trigonal axis of the octahedral site and the magnetization in the randomly oriented Weiss domains. At 4.2 K the isotropic hyperfine field Hiso = - 1 9 1 . 0 k O e , the anisotropic hyperfine field Hanis= +2.07kOe and the quadrupole interaction vQ = eZqQ/4h = 0.95 MHz. Berger et al. (1969a) discussed the strength of /-/~so in connection with the strength of the nearest-neighbour superexchange interaction, while Stauss (1969b) stressed the importance of transferred spin density in the Cr 4s states in the process that lowers Hiso from its purely ionic value. The hyperfine field on the 111Cd and H3Cd nuclei of the diamagnetic Cd ions is large, namely +167.0kOe at 4.2K (Stauss 1969b) and +168.10kOe at 1.4K (Berger et al. 1969a). This field is mainly due to transfer of spins from the filled Cr 3d states to the unfilled Cd 5s state. A density of 2.0% of an electron spin in the Cd 5s state can explain the observed strength of the hyperfine field (Berger et al. 1969a, Stauss 1969a, b).

5.4. HgCr2S4 HgCr2S4 is a normal spinel (Hahn 1951). Crystallographic data are given in table 1. In the paramagnetic region the magnetic susceptibility follows a Curie-Weiss law with a molar Curie constant close to the spin-only value 3.75 of Cre (table 11).

SULPHOSPINELS

667

As observed by magnetic measurements (Baltzer et al. 1966) and by neutron diffraction (Hastings and Corliss 1968a, b) the compound behaves as a metamagnet with an ordering temperature of 36.0 K or 60 K respectively. At 4 K the magnetic structure is a simple spiral, with a propagation vector parallel to the symmetry axis of the spiral and directed along a particular cube edge in a given domain. The spiral wavelength is 42 A at 4 K. It increases with temperature (fig. 45), reaching a value of about 90 A at 30 K, and shows little further variation up to the N6el point (Hastings and Corliss 1968a, b). Application of a magnetic field up to 4 kOe along a cube edge produces a growth of the domains in which the propagation vector is parallel to the magnetic field. In higher fields the spiral collapses in the field direction, saturating at about 10 kOe (Hastings and Corliss 1968a, b). These observations are consistent with the magnetization curves (fig. 46) measured by Baltzer 100

c-

8O c o [D

60 -8 t_ 5. O3

4O

10

20

30

40

T(K)

Fig. 45. Temperature dependence of the spiral wavelength of HgCr2S4 (Hasting and Croliss 1968b).

°1 ~5

o

0

0

2

4 6 8 Applied field H (kOe)

10

Fig. 46. Magnetizationof HgCr2S4 as a function of applied field and temperature (Baltzer et al. 1966).

668

R.P. V A N S T A P E L E

et al. (1966). The saturation magnetization measured by these authors at 4.2 K and 10 kOe corresponds to 5.35 p~B/molecule. This is lower than the theoretical 6/~B, probably for reasons of stoichiometry. Srivastava (1969) estimated the shift of the transition temperature with pressure by measuring the relative shift of the mutual inductance as a function of temperature and pressure. He did not observe anomalies around 60K, but reported the ordering temperature to be 36.1 K, in agreement with the value of 36.0 K given by Baltzer et al. (1966). This temperature increases with pressure at a o rate dTJdP = +0.14K/kbar, which means that dTJda = - 1 0 K/A. The pressure dependence, however, differs in sign from that of the Curie temperatures of CdCrzX4 and HgCrSe2 (Srivastava 1969). There have been hardly any measurements of the electrical properties. Baltzer et al. (1965) have reported that HgCrzS4 is a semiconductor. The behaviour of the absorption edge of HgCr2S4 has been studied by Harbeke et al. (1968) and Lehmann and Harbeke (1970). Using relatively thick samples (33 and 20 p~m) they did not observe any structure nor any change in the shape of the edge between 4 K and 600 K. The position of the edge, defined by the energy at which the absorption coefficient had risen to 1500 cm -1, showed a large red shift and a further shift to longer wavelength if a magnetic field was applied (fig. 47). Lehmann and Harbeke (1970) explain the temperature dependence and the magnetic field dependence in terms of the properties of the spiral spin structure and the nearest-neighbour spin correlation function. They also note that the magnetic field-induced shift at 8 kOe has a maximum at (60.0-+ 1) K, which they take to be the true N6el temperature. The infrared absorption spectrum of HgCrzS4 has been measured by Lutz (1966) and Lutz and Feh6r (1971). At room temperature four infrared-active vibrations were observed at 376, 336, 227 and 71.4 cm-L

1.5

1.L @ ,m

u

1233

H =0/.f'" . . . . . ~"-- .... . /" /

1.3

~ ~.2 c

1.1 i ! :

8kOe

1.0 0

[

I

100

200

I

I

~

300 400 500 Temperature (K)

I

600

Fig. 47. Energ y gap of HgCr2S4 as a function of t e m p e r a t u r e for H = 0 and H = 8 kOe, according to L e h m a n n and H a r b e k e (1970).

SULPHOSPINELS

669

Hyperfine fields on various nuclei have been measured by Berger etal. (1969a, b). At 1.4 K the isotropic hyperfine field on the nuclear spin of 53Cr w a s found to be -189.9 kOe (Berger e t a l . 1969a). The nmr lines of mgHg and 2°1rig were found to be very anisotropic, which is due to a reduction of symmetry by the spiral spin structure of HgCr2S4. The isotropic hyperfine field at the Hg nuclear spins, which corresponds to the high frequency peak, amounted to +524.3 kOe at 1.4 K (Berger et al. 1969a), while the centre of the Hg spectra was found at 507 kOe (Berger et al. 1969b). This means a spin density of 2.0% for an electron spin in the Hg 2+ 6 s state (Berger et al. 1969a). The same spin density was found in the 5s state of Cd 2+ in CdCr2S4 (see section 5.3). The much larger hyperfine field on the Hg nuclear spins is due to the larger amplitude of the 6s function on the site of the Hg nucleus.

.5.5. ZnCr2Se4 ZnCr2Se4 is a cubic spinel (Hahn and Schr6der 1952). Values of the lattice parameters are given in table 1. Using neutron diffraction, Plumier (1965) found the compound to be less than 1% inverse. The cell edge has been measured as a function of temperature down to 4 K by Kleinberger and De Kouchkovsky (1966). The compoufid is cubic down to 20.4 K. Below that temperature it shows a small tetragonal distortion (fig. 48), which is connected with the magnetic ordering. Magnetic data are summarized in table 11. Above 300 K, in the paramagnetic state, the magnetic susceptibility follows a Curie-Weiss law with a molar Curie constant Cm = 3.54 and an asymptotic Curie temperature 0 = +115 K (Lotgering 1964b). Ce(l edge (~,1

acubic

io.L8~ If

0

I

20

I

I

AO

I

I

60

I

/ 810 L

i

100

l

i

120

Temperature {K} Fig. 48. Cell edge of ZnCr2Se4 as a function of temperature, according to Kleinberger and De Kouchkovsky (1966).

In spite of the positive 0, the Cr spins order antiferromagnetically at 20 K as indicated by the minimum in the reciprocal susceptibility, shown in fig. 49. Subsequent neutron diffraction experiments by Plumier (1965) showed that the magnetic structure is a simple spiral with a propagation vector along the symmetry axis of the spiral and directed along a [001] axis. The turning angle between the magnetic moments in adjacent (001) Cr planes varies from 42_+ 1 degrees at 4.2 K (Plumier 1965) to 38 degrees at 2 1 K (Plumier et al. 1975b). Plumier (1966a, b) studied the influence of magnetic felds up to 15 kOe on the neutron diffraction

670

R.P.

300

VAN

STAPELE

6

I L~O~

2OO O0

20

100 l

S

/

If

O0

f

J I

200

I

I

z,o0

I

I

I

600 Temperature (K)

I

800

Fig. 49. Molar magnetic susceptibility of ZnCr2Se4, according to Lotgering (1964b). spectrum. His study shows that in zero magnetic field domains occur in which the helical axis is oriented along one of the cube edges. In magnetic fields up to 3 kOe the domains with a preferred orientation of the spiral axis grow. In higher fields a conical spin structure exists with an increasing net magnetization. The magnetization has been measured at 4.2 K in magnetic fields up to 30 kOe and 69 kOe by Lotgering (1965) and Siratori (1971) respectively and in pulsed magnetic fields up to 108 kOe by Allain et al. (1965). The magnetization, shown in fig. 50, saturates at 6.! #B/molecule in fields larger than 64kOe. Hydrostatic pressure shifts the N6el temperature to higher values at the rate dTN/dp = 0.90 x 10-3 K/bar (Fujii et al. 1973). As Lotgering (1964b) has stressed, the combination of a positive asymptotic Curie temperature and an antiferromagnetic behaviour is a clear indication of the important role of the more distant exchange interactions in ZnCr2Se4. Attempts have been made to extract quantitative information about the strength of the various exchange interactions from the paramagnetic data, the low temperature spin structure and its initial magnetic susceptibility. Lotgering (1965) and Plumier (1966a, b) have made such an analysis, assuming J5 = 3"6= 0 (see table 10, and fig. 35) and -/3 = J4. Lotgering (1965) used the experimental values of the turning angle and the asymptotic Curie temperature and calculated J1, J3 and the initial susceptibility Xi as a function of an antiferromagnetic J2 in the range - 7 < Jz/k < 0 K. Under these circumstances J1/k < 3 0 K , -5<J3/k < O K and Xi has a value close to the experimental one. Plumier (1966a, b) used the same experimental data, but calculated the al-

SULPHOSPINELS

671

:D (3 d~ O

E 3

3 E 2 E O ~E

1

I

I

I

I

I

I

I

20 40 60 80 Magnetic field (k0e)

100

Fig. 50. Magnetization versus magnetic field of powder samples of ZnCrzSe4. Curve (a) magnetization at 4.2K, according to Lotgering (1965); curve (b) according to Allain et al. (1%5) and curve (c) magnetization at 4.2 K, according to Siratori (1971). gebraic solution with a ferromagnetic -/2: J1/k = 24.9 K, J2/k = 7.8 K and J3/k = -10.65 K. Dwight and Menyuk (1967) analyzed the stability of the spiral spin configuration, taking into account all the interactions J 1 . . . J6. They showed that neither of these interactions can be neglected. Lotgering's set of interactions lies outside the region where the spiral spin configuration is stable. The values of Plumier are within this region, but Dwight and Menyuk (1967) judge them to be physically unreasonable from the point of view of the mechanism of the superexchange interactions. They do not give a better solution, but mention as an illustrative "zeroth approximation" the following set of interactions: J~/k = +25.4 K, J2/k = +2 K, J3/k = - 7 K, J4/k = - 7 K, Js/k = +1 K and J d k = - 1 K. In a similar analysis A k i n o and Motizuki (1971), who used the restriction -/3 = J4 and J6 = 0, came to the conclusion that the stability of the spiral spin configuration requires a negative J3 and that this stability is increased by a positive .15. Paramagnetic resonance with g = 2 had been observed in powder samples above TN = 21 K by Stickler and Zeiger (1968). Below TN, an antiferromagnetic resonance appeared abruptly in fields stronger than 4 k G , as the paramagnetic resonance line disappeared. The antiferromagnetic resonance faded out at lower fields. T h e antiferromagnetic resonance frequency, extrapolated to zero magnetic field, was found to follow an S = ~ Brillouin function. At the Ndel t e m p e r a t u r e the zero field frequency drops to zero abruptly. The magnetic resonance of single crystals has been studied by Siratori (1971) in the frequency range 38-83 GHz. His theoretical explanation of the frequency and angular dependence of the resonance field at 5.5 K gives the values of the Fourier c o m p o n e n t of the exchange and the magnetic anisotropy energy at three points 0,

672

R.P. VAN

STAPELE

k0 and 2ko in the reciprocal space (k0 is the spiral wave vector). Transformation to local exchange interactions via one and two Se ions gives values for J1 • • • J5 that do not stabilize the spiral spin configuration, from which Siratori concluded that superexchange interactions through more than two Se ions (like J6) cannot be neglected. With the temperature increasing from 5.5 K to 20 K Siratori (1971) observed a shift of the resonance field and a decrease of the angular dependence and the line width. Above 20 K, the resonance field is independent of the direction of the magnetic field, but the shift of the resonance field persists up to about 70 K. Specific heat measurements done by Plumier et al. (1975a, b) indicate that, in addition to a fairly large peak from 17 to 23 K with a mazimum at 20.5 K, two narrower peaks exist at 45.5 K and 105 K. The nature of these extra peaks is not yet clear. Plumier et al. (1975b), studying carefully the neutron diffraction spectrum of a powder sample, observed above 20.5 K broad satellites with angular positions corresponding to a pitch angle ~-/5, indicating that ZnCr2Se4 at such temperatures is a metamagnet with a centred tetragonal cell (a/V'-i, a/~/-i, 5a). The large line width is ascribed to the small size of the reflecting magnetic domains, 53 A ( - 5 a ) between 21 and 45 K and 32 A ( - 5 a / 2 ) between 45 and 105 K. When a magnetic field was applied below 20.5 K, Plumier et al. (1975b) observed that the sharp satellites of the helical spin configuration disappeared at a critical field strength and that broad peaks appeared at higher field strengths. The width and the position of these peaks corresponded to those observed in zero field above 20.5 K. The findings of Plumier et al. (1975a, b) prompted Akimitsu et al. (1978) to study the neutron diffraction of a single crystal and to reinvestigate the differaction on powder samples. They concluded that the broad peaks observed by Plumier can be ascribed to critical scattering, observed in their single crystal experiment in the wide temperature range from 20 to 40 K, and found that there is no reason to place the N6el temperature higher than 21.2K. However, the peaks at 45.5 and 105 K in the specific heat then remain unexplained. Another result of their work that is difficult to explain is the enormous deviation of the magnetic moment of the C13+ ions (1.71/xB) from the 3#B observed in the magnetic measurements. The weak temperature dependence of the turning angle (Akimitsu et al. 1978) and the susceptibility in the propagation direction (Kawanishi et al. 1978) have been correlated with the tetragonal deformation (Kleinberger and De Kouchkovsky 1966) mentioned above and shown in fig. 48. The reciprocal of both quantities was found to depend linearly on ~5= [1 - (c/a)] (Akimitsu et al. 1978, Kawanishi et al. 1978), which was interpreted as being due to exchange interactions with a strength depending on ~5 and the wave vector near the propagation vector of the spiral spin configuration*. The influence of stoichiometry and impurities on the magnetic properties has scarcely been investigated. The single crystals studied by Kawanishi et al. (1978) had a small residual ferromagnetic moment, varying from crystal to crystal. Small amounts of Cu (up to 0.04 per formula unit), substituted for Zn, had been * S e e n o t e s a d d e d in p r o o f (g) o n p. 737.

SULPHOSPINELS

673

reported to lower the N6el temperature from 20 to 11 K, while they decreased the high temperature magnetic susceptibility (Menth et al. 1972). Replacement of Zn by Mn had been reported to increase at 4.2 K the magnetization in magnetic fields up to 80kOe (Siratori et al. 1973). Neutron diffraction experiments on Znl-xMnxCr2Se4 with x = 0.1 showed that the spiral spin structure is not seriously changed by the presence of the Mn ions (Siratori and Sakurai 1975). It was concluded that the Mn-Cr exchange interaction is weakly ferromagnetic. Single crystals of Mn-doped ZnCr2Se4 have recently been reported to have a strong cubic paramagnetic anisotropy (Kawanishi et al. 1979). ZnCr2Se4 is a semiconductor (Lotgering 1964b, Albers et al. 1965). Replacement of 0.02 Zn per formula unit by Cu lowers the resistivity strongly (Lotgering 1968b). This result has been used as an argument for the monovalent state of copper because the replacement of Zn 2+ by Cu + gives rise to holes in the valence band. The miscibility in the series of mixed crystals Znx-xCuxCr2Se4 between the spinels ZnCr2Se4 and CuCr2Se4, which have about equal cell edges, has been reported to be limited to x ~ 0.2 with a ferromagnetic Curie temperature that varies slowly from 380 K at x = 0.2 to 415 K at x = 1. This behaviour is reminiscent of that of the series CuCrzSe4_yBry (fig. 30). In this system high Curie temperatures occur for 0 ~"

5

> 10 :,,.% u3

103

10~

I

2

z,

I

6

1

I

I

8

20 12 1/. 16 IOS/T (K -1 ) Fig. 56. Resistivity of hot-pressed polycrystalline undoped samples of CdCr2Se4: (a) with p-type conduction, according to Lehmann (1967); (b) with n-type conduction, according to Larsen and Voermans (1973); (c) sample b after 60 h at 600°C with Pse = 10-4 mm Hg and quenching to room temperature, according to Larsen and Voermans (1973).

T__ lOq {3

10-2 >,

:z. 10-3 *d D

-~ ~0-~ o O

10-s

@/rc 10-6 2

I

I

L

6

~'l

I

I

10 12 1L 103/T (K q ) Fig. 57. Electrical conductivity of p-type Ag-doped and n-type In-doped CdCr2Se4, according to Lehmann (1967). 680

8

SULPHOSPINELS

681

600

3

_••/•

400

oJ

200 o

0

i

]

300

250

Ag Tc ~

i

i /c

"~

200 150 100" T e m p e r a t u r e (K)

r

/

Fig. 58. Seebeck coefficientof p-type Ag-doped and n-type In-doped CdCr2Se4,accordingto Lehmann (1967).

2.0

0,8

0.6

?o_ 0.4

0,2

0100

~

, 120

I

I 140

l

i 160

i ....

T (K)

Fig. 59. Magnetoresistance of n-type Ga-doped CdCr2Se4 (2% Ga) in a magnetic field of 12 kOe, according to Haas et al. (1967).

anomalous magnetic field dependence at lower temperature (Lehmann 1967). Changes in the sign of the longitudinal magnetoresistance as a function of applied magnetic and electric fields were observed in Ag-doped single crystals (Balberg and Pinch 1972), Strong electric fields influence the properties of Ag-doped CdCr2Se4. The microwave absorption (Solin et al. 1976), the electrical conductivity (Samokhalov et al. 1978) and the magnetization (Samokhalov et al. 1979) decrease, which is attributed to the excitation of spin waves by electron-magnon interaction.

682

R.P. VAN STAPELE

The substitution of In and Ga for Cd gives rise to a strong n-type conduction. Unlike that of the p-type samples, the resistivity of the n-type samples shows a pronounced maximum around the ferromagnetic Curie temperature (fig. 57), while a large and negative magnetoresistance is maximum in that temperature region (fig. 59) (Haas et al. 1967, Lehmann and Harbeke 1967, Lehmann 1967, Amith and Gunsalus 1969, Feldtkeller and Treitinger 1973, Merkulov et al. 1978, Coutinho-Filho and Balberg 1979). The maximum in the resistivity has also been observed in the high-frequency conductivity of n-type Ga-doped hot-pressed samples, where it decreases with increasing frequency (Kamata et al. 1972). Lehmann (1967) and Amith and Gunsalus (1969) also studied the thermoelectric effect (fig. 58) and the Hall effect, and found that the Hall mobility of the electrons was of the order of i cm2/Vs, which is much smaller than that of the holes in p-type samples. The study reported by Amith and Gunsalus (1969) revealed a crucial anomaly, namely the coincidence at 150 K of a secondary minimum of the absolute value of the Seebeck coefficient with the maxima of the resistivity and the absolute value of the Hall coefficient. Amith and Friedmann (1970) concluded that this finding cannot be explained in terms of electrons in a single spin split conduction band which are scattered by the spin-disorder in the ferromagnetic Cr spin system (Haas 1968, Bongers et al. 1969) and these authors proposed a two-band model in which one band is an n-type conduction band and the other a p-type hole band in the band gap. As already discussed at some length in section 5.1, other models have been proposed. In particular the model of the magnetic impurity states seems to be applicable in the case of n-type Ga-doped or In-doped CdCr2Se4 (Larsen and Voermans 1973, Treitinger et al. 1978a). Treitinger et al. (1978a) varied the concentration of Se vacancies of In-doped single crystals of CdCrzSe4 and observed that the height of the maximum of the resistivity and of the magnetoresistance, as well as the temperature at which this maximum occurs, depended on the concentration of the Se vacancies (fig. 60), whereas the ferromagnetic Curie temperature was not affected. They ascribed these properties to conduction in magnetic impurity states at lower temperatures, the conduction at higher temperatures being dominated by electrons in the conduction band. In their study of In-doped CdCr2Se4 Treitinger et al. (1978a) also observed that the line width of the X-ray diffraction lines increases from the value in the as-grown state after annealing in Se vapour and also after annealing in hydrogen. Subsequent annealing in hydrogen after a heat treatment in Se vapour restores the as-grown value, indicating, as Treitinger et al. conclude, that the crystals in their as-grown state have a Se deficit that corresponds to a state of minimal internal stress. The optical absorption spectrum of stoichiometric pure CdCr2Se4 shows no structure between the bands near 17 txm, which are due to overtones of lattice vibrations, and the absorption edge near 1 Ixm (Bongers and Zanmarchi 1968), whereas doped or non-stoichiometric crystals have some characteristic absorption lines in that region (Miyatani et al. 1971b) (fig. 61). Hl/dek et al. (1977) have discovered that a similar absorption spectrum can be induced by illumination with

SULPHOSPINELS

683

T 200 160

107 300

J

i

120

100

i

i

105 3000

~103 400 C

(3-

10 L50C 10-1

10-3

I

I

5

7

103/T {K-1)

9

11

Fig. 60. Resistivity of n-type In-doped CdCr2Se4 with an increasing number of Se-vacancies, obtained by a heating in hydrogen at the temperatures indicated in the figure, after Treitinger et al. (1978a).

0.15

Photon energy (eV) 0.2 0.3 O.Z 0.6 1.0 2.0

i

i

i

i

i

i

JEll

.d c o) 1.3

o

In-doped

c 0 0-

undoped .13


,,

"

1.40 1.30

~

/,,

-.

/ /

1.20

./..~..

t I

1.10

/Tc 0

Fig. 62.

¢"~

t

100

200

f

i

300 T(K)

400

500

Energy of transitions observed in CdCr2Se4 as a function of temperature: Pinch 1966; (---) Sato and Teranishi 1970), (-.-.-.) Stoyanovet al.

( ) Harbeke (1976).

and

on the sample and that only the lowest energy absorption edge is shifted to the red with decreasing temperature, whereas the higher energy edge is weakly shifted to shorter wavelengths (fig. 63). The intensity at the lower energy edge could also appreciably be changed by a heat treatment (Prosser et al. 1974). Harbeke and Lehmann (1970) concluded that the red-shifting absorption is not due to an intrinsic excitation but most probably to vacancy states. Eagles (1978) explained the absorption profiles observed by Harbeke and Lehmann (1970) at photon energies below 1.6eV in terms of a combination of transitions between the valence band and hydrogen-like local 13 103

c 103 .£ .~
0.8 and x < 0.4. The Mn-rich compounds are metastable, heating at 300°C effects a decomposition into two spinel phases. In the single-phase regions the variation of the cell edge is smaller than would correspond to a linear variation between the lattice parameters of MnCr2S4 and CuCr2S4. From the magnetic moments measured for x = 0, 0.05, 0.2 and 0.8 between 1.6 and 50 K in magnetic fields up to 150 kOe, it was concluded that the Mn ions remain in the divalent state in the mixed compounds (Nogues et al. 1979, Mejai and Nogues 1980). A different situation is encountered in the series Fel-xCuxCr2S4. The electrical and magnetic properties of these compounds clearly indicate that the Cu ions ionize the ferrous ions to ferric ions (Lotgering et al. 1969)*. The series does not show a miscibility gap. Throughout the series, single-phase samples were prepared and the cell edge varies approximately linearly with x (Haacke and Beegle 1967). The electrical transport properties vary in a remarkable way (fig. 87) (Haacke and Beegle 1968, Lotgering et al. 1969). The occurrence of n-type conduction is observed at composition with x between 0.2 and 0.5, whereas samples with a smaller or larger Cu concentration have a p-type conduction (Haacke and Beegle 1968, Lotgering et al. 1969), and the observation that Fel/2Cut/2Cr2S4 is a semiconductor (Lotgering et al. 1969) led Lotgering et al. (1969) to the conclusion that the Fe z+ levels fall in the energy gap between the valence and the conduction band, as sketched in fig. 88. A replacement of 2Fe 2+ in FeCrzS4 by Fe3++ Cu + is represented by a hole in the Fe z+ level (section 3) and a filled Cu + level below the top of the valence band. The Fe 2+ levels are empty at x = ½. When x increases * See notes added in proof (1) on p. 737.

SULPHOSPINELS

719

500, 400t

T

3OO 2OO 100

:3, ml

o -100

.£3 -200 PA

-300 -4ooi

0

I 0

0.5 1 X----~

0.5 X

~-

Fig. 87. Seebeck coefficient c~ and resistivity p at room temperature of Fel-xCuxCr2S4, according to Haacke and Beegle (1%8) (©), Bouchard et al. (1%5) (0) and Lotgering et al. (1969) (11). Sample A has been quenched from 700°C, sample B has been slowly cooled with annealing at 500 ° and 100°C.

further, Fe 3+ is replaced by Cu ÷ with charge compensation by two holes in the valence band. The formal valence distribution is consequently written as 2+ 3+ + 3+ 2 3+ + Fel-2xFex CuxCr2 $4 in the range 0 ~< x < ½ and as Fel_xCuxCr2S4 with ( 2 x - 1) holes in the valence band and the Cr 3+ states for ½ < x ~< 1". This explains the observed p-type conduction for x >½ and for small x as well as the n-type conduction in the intermediate region, where the conduction is due to the simultaneous presence of ferro and ferric ions with less than half of the iron ions

nduction bGnd Fe3. (X) 2~ --g Fe *(1-2X

Fe3+{1/2)~

EF

Cr3*E;~NTZ,{~)~Volence

~r.'//,/~

Cr3÷

Fe3+(I_X)r(2X-1)holes C r ~ F

hood

g(E)~,,-

0~XxNixCr2S4 with M = Mn, Fe, Co, Cu or Zn. References: (a) Lisnyak and Lichter (1969), (b) Lutz et al. (1973), (c) R o b b i n s and Becker (1974) and (d) Itoh et al. (1977). o

Lattice constant (A)

System Mnt-xNixCr2S4 Fel-xNix Cr2S4 Col-xNixCr2S4

Cul-xNixCrzS4 Znl-.NixCr2S4

Curie t e m p e r a t u r e (K)

Stability range

x = 0

at maximal x

x = 0

x = 0.3

Ref.

x x x x x x x

10.11 9.995 9.918 9.923 9.936 9.820 9.986

10.068 9.953 9.898 9.909 9.898 9.801 9.945

74 185

110 214

235

250

TN = 16

-- 170 at x = 0.4

(c) (c) (a) (b) (c) (b) (d)

~0.3 ~ 0.3 ~. The magnetization versus temperature curves measured in 16 k O e (fig. 91) show a m a x i m u m at low temperatures. The magnetization cannot be saturated except for the composition x = 0.4, where it reaches at 4 . 2 K a value of 3.0/xB/molecule. This is much smaller than the 5.2/xB/molecule expected for a simple Nrel configuration with 2/xB on the Ni 2+ ions (Itoh et al. 1977). 6.8. The mixed crystals MCrz-xlnxS4 with M = Mn, Fe, Co and Ni In this section we review briefly the properties of mixed crystals between the ferrimagnets MCr2S4 with M = Mn, Fe and Co and the corresponding indium sulphospinels MIn2S4. A m o n g the latter c o m p o u n d s MnIn2S4 is a partially inverse spinel, the other c o m p o u n d s MIn2S4 (M = Fe, Co and Ni) being inverse spinels

SULPHOSPINELS

60

I

i

i

,

723

i

•',•.

50 • X=O./.

l

•',;,

4O

c~ 30

X= 0.3 '

E

(11

2C

X=0.2

,....

10

x:ol ........ "'.... '

'

'

"...:.... '

temperature (K)

'

'2oo

~-

Fig. 91. Magnetization o- per gram of Znl xNixCr2S4 measured as a function of temperature in 16 kOe (Itoh et al. 1977).

(Hahn and Klingler 1950)• The indium sulphospinels are all paramagnetic down to 4.2 K (Schlein and Wold 1972)• The magnetic susceptibilities follow a Curie-Weiss law with a negative asymptotic Curie temperature. The molar Curie constant agrees with the spin-only value in the case of Fe and Ni, but deviates from it in the other cases (table 22). Electrical resistivity measurements at room temperature indicate that the c o m p o u n d s are semiconductors (Schlein and Wold 1972). The large negative asymptotic Curie temperature of NiIn2S4 is anomalous, since the 90 ° Niz+-S-Ni 2+ exchange interaction is expected to be positive• This anomaly and the lack of antiferromagnetic ordering have been discussed by G o o d e n o u g h (1972)• In the system MnCrz_xInxS4 single-phase spinels were prepared between x = 0 and x = i o(Darcy et al. 1968)• Theo lattice parameter changes linearly from a = 1 0 . 1 0 8 A at x = 0 to a = 1 0 . 4 1 8 A at x = 1. It was concluded from X-ray diffraction data that the In 3+ ions replace Cr 3+ ions on the octahedral sites, so that T A B L E 22 Cell edge (a), asymptotic Curie temperature (0) and molar Curie constant (Cm) of the compounds MIn2S4, according to (1) Schlein and Wold (1972) and (2) Eibschfitz et al. (1967a).

Cm

Cm

Compound

a (A)

0 (K)

(exp.)

(spin-only)

Ref.

Mnln2S4 FelnzS4

10.72 10.61 10.630 10.58 10.50

-78 -76 - 122 - 134 -144

4.00 3.10 2.94 2.84 1.16

4.38 3.00

(1) (1) (2) (1) (1)

Coln2S4 Niln2S4

1.87 1.00

724

R.P. VAN STAPELE

the tetrahedral sites are always occupied solely by Mn 2+ ions. MnCr2S4 is a canted ferrimagnet in which a strongly positive Cr3+-Cr3+ superexchange interaction combines with weaker negative Mn2+-Cr 3+ and MnZ+-Mn 2+ superexchange interactions (section 6.2). Substitution of In for Cr reduces the magnetic m o m e n t (at 4.2 K and 10 k O e from 1.27/xB/molecule at x = 0 to 0.85/zB/molecule at x = 0.3) as well as the Curie t e m p e r a t u r e (fig. 92), effecting a r e m a r k a b l e change from ferrimagnetism to antiferromagnetism at x = 0.4. The measured paramagnetic m o m e n t s are low c o m p a r e d to the theoretically expected values (Darcy et al. 1968). 100

I

50

'\% \

\ o

~J c~.

E

0

I~L

I

×~"

I

o

~

I

~ x ~ 0 ~°

~

o

I

I

I

X - - ~

I

1.'0

x~,~

-50

Fig. 92. Curie temperature Tc, Ndel temperature TN and asymptotic Curie temperature 0 of MnCrz-xInxS4, according to Darcy et al. (1968). MnCrInS4 was also prepared by Mimura et al. (1974). These authors confirm the cation distribution determined by Darcy et al. (1968), but their samples are paramagnetic down to 4.2 K. In the system FeCrz_xInxS4 a complete series of mixed crystals can be prepared. The lattice p a r a m e t e r increases linearly from 9.998 A at x = 0 to 10.610 A at x = 2 (Brossard et al. 1976). From the intensity of X-ray diffraction lines and from paramagnetic 57Fe M6ssbauer spectra the cation distribution was determined (Brossard et al. 1976). The fraction y of In ions on tetrahedral sites in Fel yIny[Cr2 xInx_yFey]S4 increases gradually with x (fig. 93). Magnetic m e a s u r e m e n t s (Goldstein et al. 1977a) show that the compositions 0 0 . 5 and the observed variation of the asymptotic Curie temperature and the ferrimagnetic Curie temperature cannot be explained within a molecular field approximation, the behaviour of the saturation magnetization as a function of x is typical of an anomalously strong C o - C o interaction in the whole range of x. This shows that the strong C o - C o interaction is not due to the presence of Rh 3+ ions (Lotgering 1968b). In the system NiRh2_xCrxS4 single-phase spinels were prepared in the range 0.3 ~< x ~ 1 (section 4.6), the anomalous values of the magnetic moments cannot be reconciled with a specific valency of the Cr ions. This points to delocalized Ni 3

I

2

D O

o o

•

/

I

1

/

1.65

2

~x Fig. 97. Saturation moment Ms at 4.2 K of CoRh2-xCrxS4.The straight lines have been calculated with a Co moment of 3.6/zB and a Cr moment of 3/x~ for: (a) a triangular spin configuration with a = J A A / J A B = 1.37 (Ms=3(1-a-1)x) and (b) a simple N6el configuration (Ms = 3x-3.6). After Lotgering (1968b).

732

R.P. VAN STAPELE

100

8O

o

o

B 60

o o

(9

E

40 o o

I 20 ' o'2 ' o'.~ ' o's ' o18 X

'110

Fig. 98. Asymptotic ((2)) and ferromagnetic (O) Curie temperature of NiRh2_xCrxS4(Itoh 1979).

1.0/,

:z,

081 Q

.~_ 0.E .N_ "$ 0.4 cE 0.2

l

o

I

I

I

I

o12 o.~ o;

I

0'.8

I

1'.o

-----.,. X

Fig. 99. Magnetization at 4.2 K and 14.5 kOe of NiRhz-xCrxS4 (ltoh 1979). electrons that are partially spin-polarized in a direction opposite to that of the ferromagnetically coupled Cr spins (Itoh 1979).

7.4. The mixed crystals Fel_xCuxRh2S4 and C01-xCuxRh2S4 Inspired by the 1:1 ionic ordering on the tetrahedral sites in Fet/2Cul/2Cr2S4, Plumier and Lotgering (1970) investigated the properties of the c o m p o u n d FemCUl/2Rh2S4. The c o m p o u n d has the spinel structure with a = 9 . 8 5 A and u = 0.3815. X-ray diffraction clearly showed a 1 : 1 ordering of Fe 3+ and Cu 1÷ ions on the tetrahedral sites. The material is semiconducting with a large Seebeck coefficient, the sign depending on the details of the preparation. The most remarkable observed property of FemCUl/2Rh2S4 is its strong antiferromagnetism. A b o v e 170 K, the magnetic susceptibility follows a Curie-Weiss law with an asymptotic Curie t e m p e r a t u r e 0 = - 4 2 0 K and a molar Curie constant Cm = 2.32. T h e magnetic susceptibility contains a rather large temperature-in-

SULPHOSPINELS

733

dependent part, due to the diamagnetic susceptibility and the Van Vleck susceptibility of the Rh 3+ ions. Correction for these terms gives 0 = - 3 6 7 K and Cm = 2.09 (Boumford and Morrish 1978). The value of Cm agrees fairly well with the value 2.19 for trivalent iron ions. The susceptibility shows a maximum at 145 K below which the iron spins order antiferromagnetically. Neutron diffraction experiments revealed that the antiferromagnetic ordering is of the second kind, as in MnO. In this type of ordering the second-neighbour interaction dominates the nearest-neighbour interaction, which leads in the case of Feu2CuuzRh2S 4 to the conclusion that a surprisinglYoStrong superexchange interaction exists between Fe 3+ ions at a distance of 9.85 A. A study of the 63'65Cu nuclear magnetic resonance as a function of temperature in the paramagnetic state indicates a N6el temperature of 135 K, slightly below the value of 145 K mentioned above (fig. 100). The Fe 3+ ions were observed to give a negative transferred hyperfine field at the Cu nucleus, which would amount to -12.5 kOe for a saturated Fe 3+ magnetization (Locher and Van Stapele 1970). The semiconduction and the valencies Fel/zCul/zRh2S4 3+ ~+ clearly indicate that the Fe 2+ levels fall in the energy gap between the valence and the conduction band as in Fel-xCuxCrzS4 (section 6.6 and fig. 91 with Rh 3+ instead of Cr3+). This was recently confirmed by a study of the properties of Fel_xCuxRh2S4 with X/>0.06 (Boumford and Morrish 1978). Using X-ray diffraction these authors observed an undistorted spinel structure with a linearly varying lattice parameter throughout the series. Ordering of copper and iron ions was detected in the range 0.3 ~< x ~< 0.54. Magnetic measurements indicate antiferromagnetic behaviour for all compositions. The N6el temperature, as determined from M6ssbauer spectra, and the

200

l

100

o!2 ' o',~ ' o:~

-200

o:a

I

1.0

X

G)

× X

-300 × •

x

X

-4.00

X

8 Fig. 100. Fel-xCuxRh2S4. N6el temperature (T~) (from M6ssbauer spectra) and asymptotic Curie temperature (0) before (O) and after correction for the Rh 3+ Van Vleck susceptibility (x), according to Boumford and Moorish (1978); ([~) data of Plumier and Lotgering (1970), (O) data of M.R. Spender, Ph.D. thesis (University of Manitoba, 1973, unpublished).

734

R.P. VAN STAPELE

asymptotic Curie temperatures are given in fig. 100. Iron-rich compounds with 0.06 ~< x ~< 0.5 exhibit remanence and displaced hysteresis loops after cooling to 4 K in an external magnetic field of 18kOe. Both the isomer-shift in the M6ssbauer spectrum and the paramagnetic m o m e n t s indicate the presence of solely Fe 3+ for x/> 0.5 and a gradual change from Fe 3+ to Fe 2+ for x decreasing from 0.4 to 0.06. The observed behaviour agrees with the valencies 2+ 3+ + + Fel-2xFex CuxRh2S4 in the range 0 ~ x ~< 0.5 and Fel3 + xCuxRh2S4 for x I> 0.5. In contrast to the behaviour of Fel_xCuxRh2S4 the properties of Col_xCuxRh2S4 do not indicate Co 2+ levels in the energy gap. As has been mentioned in section 6.6, this is not the case either in Col_xCuxCr2S4, in which system indications were found for Co 2+ levels below the top of the valence band. However, particularly in the system COl-xCuxRh2S4, this position gives rise to remarkable properties, i.e. antiferromagnetism for 0 < x ~< 0.4, spontaneous magnetization for 0.4 ~< x ~< 0.7 and paramagnetism for 0.7 ~< x ~< 1. Single-phase preparations of Col_~CuxRhaS4 were prepared for 0.1~<x ~< 1 (Lotgering 1969). X-ray diffraction, which shows the presence of a spinel phase with a lattice p a r a m e t e r of 9.78 A, cannot establish the formation of mixed crystals, because of the equal values of the lattice parameters of CoRh2S4 and CuRh2S4. However, the change in physical properties proves the existence of solid solutions. The samples have a nearly temperature-independent, low resistivity and a positive Seebeck coefficient, decreasing from 125 ixV/deg for x = 0.1 to 25 txV/deg for the Cu-rich compositions with x t>0.5. Measurements of the magnetic susceptibility show that the Co-rich compositions with x ~ 1. At very low temperatures the variation of pi(T) in T 2 can be attributed to electron-electron scattering, as it has been concluded in section 2.2.2. Above 10K the electron-phonon collisions become progressively more important. When approaching room temperature the electron-magnon collisions should begin to make a substantial contribution to pi~(T). Theoretical estimates of the electron-phonon contributions to Pit and pi+ at 300 K are 4.25 ~ c m and 19.2 ~l"~cm respectively (Yamashita and Hayakawa 1976); we can reasonably infer that additional contributions of a few ~ c m from electron-magnon scattering account for the experimental pi~(300). Without magnon contributions to pi~(300) and without p~ ~ term the resistivity of pure nickel at 3 0 0 K would be predicted to amount to roughly 4.25x 19.2/(4.25+ 1 9 . 2 ) 3.5 ~ c m , instead of 7 p ~ c m experimentally. We conclude that: (i) at low temperature the main contributions to p~(T) arise from electronelectron and electron-phonon scatterings; electron-magnon collisions come into play through p~ ~(T) and are important in alloys with ~ very different from unity; (ii) at near room temperature the electron-magnon collisions contribute to both pi~ and p~ +; they will become increasingly important as temperature increases. The analysis of the experimental data on Ni alloys by Yamashita and Hayakawa (1976), although based on a different treatment of the two current conduction, arrives at similar conclusions.

2.3.2. Cobalt host The o~ values of a large number of impurities have been obtained in Co metal (Durand and Gautier 1970, Loegel and Gautier 1971, Durand 1973, Ross et al. 1978), table 2. They are again consistent with the magnetic structures of the impurities. The parameters Pit (T), pi+ (T) and p, +(T) of Co have been evaluated by Loegel and Gautier (1971); the behaviour of p~ ~(T) is similar to that of Ni.

2.3.3. Iron host Extensive work has been done on Fe based alloys (Campbell et al. 1967, Fert and Campbell 1976, Dorleijn 1976, Dorleijn and Miedema 1977, Ross et al. 1979), table 3. The resulting ~ values from different authors, both from ternary alloy data or from temperature dependence, are in reasonable agreement with each other. The range of c~ values is very great, po ~/po ~ varies from 0.13 for F__eeVto 9 for FeIr (table 3). There is a good correlation between the resistivity p0 in each band and the charge screening in that band for each impurity (Dorleijn 1976).

772

I.A. C A M P B E L L A N D A. F E R T

,_NC

12

T C) v k-4P

J

I

I

I

I

I

10

20

30

40

50

Temp6rature (K) Fig. 9. Experimental (dashed line) and calculated (solid line) curves for p$ ,~/T 2 in nickel. The experimental curve is after Fert and Campbell (1976); the calculated curve is obtained from the model calculation of Fert (1969) with 01 = 38 K.

The behaviour of p, +(T) in Fe is similar to that in Ni and the value of pi+/pi, seems to be near 1 (Fert and Campbell 1976). More complete low temperature measurements would be necessary to decide this. As in Ni, the low temperature p(T) data cannot be understood without including the p, ~ term.

2.3.4. Alloys containing interstitial impurities Ni, Co or Fe based alloys containing small concentrations of interstitial impurities of B or C can be prepared by rapid quenching. Swartz (1971), Schwerer (1972) and Cadeville and Lerner (1976) have investigated the resistivity of NiC, C__o_oC, Nil_xF_eexC alloys. The residual resistivity of these alloys is equal to about 3.4 ~flcm/at.% for C in Ni and 6.6 txOcm/at.% for C in Co. From the deviations from Matthiessens' rule in N__iiCrCand CoCuC alloys, Cadeville and Lerner (1976) have estimated that the resistivity P0+ was about twice as large as Pot. This result, together with magnetization and thermo-electric data by the same authors, are consistent with a predominant screening by the electrons of the d + band. In Ni~-xFexC alloys the resistivities Pot and p0+ of the C impurities are found to become nearly equal for x >0.4, which has been ascribed to the change from strong to weak ferromagnetism (Cadeville and Lerner 1976). The resistivity of B impurities in Ni and Co have been found to be fairly small ( - 1 ixl)cm/at.%). This has been ascribed to a predominant screening by the d ~, electrons resulting in a small resistivity for the spin 1' electrons (Cadeville and Lerner 1976).

TRANSPORT PROPERTIES OF FERROMAGNETS

773

2.4. High temperature and critical point behaviour It was observed a long time ago that the resistivities of ferromagnetic metals changed slope as a function of temperature at the Curie temperature. For Ni this was originally interpreted by Mott (1936) as indicating a reduction of the spin T resistivity on ordering. Later work (Kasuya 1956, Yoshida 1957, Coles 1958, Weiss and Marotta 1959) showed that spin disorder scattering provided a more general explanation. When the resistivities of the 3d ferromagnetic metals are compared with those of their non-magnetic 4d and 5d counterparts it can be seen clearly that there is an extra magnetic scattering contribution which is approximately constant above T~ and which decreases gradually below T~ (fig. 10). The simplest disorder model shows that the paramagnetic term above T~ is equal to kv(mF)2 t t r Pm = 4~e2zfi3 ~ + 1),

(26)

where J is the effective local spin and f ' the local spin conduction electron spin coupling parameter. De Gennes and Friedel (1958) suggested that the critical magnetic scattering near Tc was similar in type to the critical scattering of neutrons and that it should lead to a peak in p(T) at To. Later work by Fisher and

I0[

[3

Tc

Qcm

~/

80

6C

Tc

Pd 20

~ I r 0 0

I 1

T//80 L 2

I 3

I /~

Fig. 10. Resistivity of several transition metals as a function of T/OD. OD is the D e b y e t e m p e r a t u r e .

774

I.A. CAMPBELL AND A. FERT

Langer (1968), using a better approximation for the spin-spin correlation function near To, modified this prediction to that of a peak in dp/dT at To. They also made the important remark that just above To the same leading term in the spin-spin correlation should dominate dp/dT and the magnetic specific heat, so that these two parameters should have the same critical behaviour as T tends to Tc from above. Both magnetic entropy S and magnetic scattering rate should be proportional to

fo2kvF(k, T)k 3dk,

(27)

where F(k, T) is the spin-spin correlation function. Later theoretical work showed that the same correspondence should hold equally in the region just below Tc (Richard and Geldart 1973). Renormalization theory can predict the critical coefficients for dp/dT (Fisher and Aharony, 1973) but it is difficult to decide over what range of temperature each side of To the strictly "critical behaviour" should be observed; Geldart and Richard (1975) discussed the cross-over from a regime near To where the shortrange correlations dominate to a long-range correlation regime. The theory of resistivity behaviour at To in weak ferromagnets has been developed by Ueda and Moriya (1975), Der Ruenn Su and Wu (1975). Experimentally, the critical behaviour of dp/dT has been studied very carefully for Ni, Fe, Gd and the compound GdNi2 (Craig et al. 1967, Zumsteg and Parks 1970, Shaklette 1974, Kawatra et al. 1970, Zumsteg and Parks 1971, Parks 1972, Zumsteg et al. 1970). For Ni (Zumsteg and Parks 1970) and Fe (Shaklette 1974) it is found that dp/dT and the specific heat do indeed show the same A point type of behaviour around To (fig. 11). The data are parameterized using I

J

i

i

i

l

l

, ooo

o°

oo

.0.05 o o

oo

o

1.04

o

1.03

oo

oO o o

.OOl o o

o

o

1.02

o

1.01 -~ .005

1,00 n,-

.002

099

o°°2 o

,001

n*"

0.98

o

o

0.97

o o

.000 348

096 ~

,

352

,

,

356

I

i

I

360 T(oC)36&

I

I

368

I

I

372

I

I

376

Fig. 11. Resistivity R(T) of nickel and dR/dT versus temperature in the region of the Curie point (after Zumsteg and Parks 1970).

TRANSPORT PROPERTIES OF FERROMAGNETS 1 dp A pcdT-h (e-*-l)+B,

T > To,

775 (28)

and 1 dp

A'

p o d T - -h (lel-~'- 1 ) + B "

T < To,

(29)

where

e = ( T - Tc)lTc.

(30)

Renormalization theory predicts h = h ' ~ 0 . 1 0 and A/A'~-1.3 (Zumsteg et al. 1970) for a 3 dimensional exchange ferromagnet. The accurate determination of A and h' is extremely delicate especially as Tc must be fitted self-consistently from the data and it appears essential to have the theoretical predictions as a guide. In pure Fe, Kraftmakher and Pinegina (1974) find h, h ' = 0-+ 0.1 while Shaklette (1974) observes A, A'=-0.12--_0.01 by imposing h----h'. Agreement with the magnetic specific heat data in Fe is very good (Shaklette 1974, Connel!y et al. 1971). For Ni, the values obtained were h = 0.1 _+0.1, h' = 0.3_+0.1 (Zumsteg and Parks 1970) but within the fitting accuracy this is presumably also consistent with theoretical values. In G d which is hexagonal the critical behaviour looks very different when measured along the c- and the a-axes. Zumsteg et al. (1970) suggest that the resistivity changes are complicated by the critical behaviour of the lattice parameters, but this has been questioned (Geldart and Richard 1975). GdNi2 was investigated in the hope that it would correspond to a simple local moment system, dp/dT shows similar critical behaviour to Fe and Ni but has more complicated temperature dependence a few degrees above Tc (Kawatra et al. 1970, Zumsteg and Parks 1971). The significance of this has been discussed (Geldart and Richard 1975). The resistivity variation has also been measured at the structural and ferromagnetic transition in T b Z n (Sousa et al. 1979). The critical behavi0ur of dp/dH has been studied for Ni (Schwerer 1974) and for Gd with the current in the basal plane (Simons and Salomon 1974). The behaviour of transport properties near Tc can also be studied in alloys, but local inhomogeneity leads to a spread in the local values of Tc at different parts of the sample and so the critical behaviour is smeared out. This has been observed in NiCu alloys (Sousa et al. 1975) and in PdFe (Kawatra et al. 1970, Kawatra et al. 1969). Finally, behaviour at the critical concentration for ferromagnetism (the concentration at which To-> 0) can be studied. Very varied behaviour has been found in different alloy systems. In N iCu alloys there is a peak in dp/dT at T~ as long as Tc exists and there is a maximum in p(T) some degrees higher, while for c > cent a minimum in p(T) is observed (Houghton and Sarachik 1970). In NiAu (splat cooled to avoid segregation) p(T) shows a maximum at T0 for c < cent (Tyler et al.

776

I.A. CAMPBELL AND A. FERT

1973). For NiCr, Yao et al. (1975) find weak minima in p ( T ) for c > Ccrit while Smith et al. find giant minima in the region c - cent (Smith et al. 1975). In NiPd alloys, Tari and Coles (1971) express the low temperature resistivity behaviour as p = po = A T n and find A is sharply peaked at cc~t while n has a minimum with n - 1. The Curie point "is not easy to detect on the p ( T ) curves". A m a m o u et al. (1975) using the same way of expressing the resistivity behaviour found n --> 1 and strong peaks in A at the critical concentrations of a large number of alloys systems. The transition from low temperature two current behaviour to high temperature spin disorder behaviour has been studied in Fe based alloys (Schwerer and Cuddy 1970). The high temperature resistivity behaviour of the alloy seems to depend essentially on the local impurity moment.

3. Other transport properties of Ni, Co, Fe and their alloys Here we will summarize results on different transport properties in these metals and alloys and outline the interpretations which have been given. We will generally find that Ni has been studied in most detail while rather less is known about Fe and Co. In the interpretation of the results, we will refer to what has been learnt about the different systems from the resistivity measurements which we have already discussed. 3.1. Ordinary magnetoresistance We have outlined the situation for pure metals in section 2.2. For non-magnetic alloys the low temperature magnetoresistance behaviour generally follows Kohler's rule ( p ( B ) - p ( O ) ) / p ( O ) = f(B/p(O)), where f is a function which varies from metal to metal but which is rather insensitive to the type of impurity present for a given host. In a ferromagnet above technical saturation the same effect, due to the Lorentz force on the electrons, can be observed but as B includes the magnetization term 47rM, p(0) cannot be attained except by extrapolation. Schwerer and Silcox (1970) showed by a careful study of dilute Ni alloy samples that for a given series of alloys (e.g. NiFe samples) the ordinary magnetoresistance follows a Kohler's rule, but that the Kohler function f varied considerably with the type of scatterer (fig. 12). Other work (Fert et al. 1970, Dorleijn 1976) is consistent with these data. It can be seen in fig. 12 that the strongest magnetoresistances are associated with impurities having large values of p0+/P0t (i.e. N__iiFe, __NiCo...). The longitudinal magnetoresistance of these alloys is also high [Apll/P(O ) saturates at about 10 in NiFe (Schwerer and Silcox 1970)] considerably greater than that observed for Cu based alloys for instance, where ApJp(O) saturates at about 0.7 (Clark and Powell 1968). Attempts have been made to understand this behaviour in the two current model. In its simplest form the two types of electron (spin 1' and spin $ ) can be represented by electron-like spheres in k space with different relaxation

TRANSPORT PROPERTIES OF FERROMAGNETS

,.,o

777

oo////

1.05

IDO ~ ~ R u 0 10

~ 20

, 30

, &O

, 50

B/~O (k G/,u.~.cm)

Fig. 12. Kohler plots for the transverse magnetoresistance at 4.2 K of nickel containing Co, Fe, Mn, Ti, A1, Cr, Pt, V or Ru impurities (after Dorleijn 1976). times. In this approximation (Fert et al. 1970) the transverse magnetoresistance is indeed an increasing function of p~ (O)/pt (0), but the model is not satisfactory as it predicts a zero longitudinal magnetoresistance in disagreement with experiment. As a next step, it is possible to invoke relaxation time anisotropy within each spin band. Dorleijn (1976) suggests that the intrinsic magnetoresistivity of the spin 1' band of Ni is much greater than that of the spin band so that the longitudinal and transverse magnetoresistances are much greater when the current is carried mainly by the spin 1' electrons. Jaoul (1974) proposes that there is a mixing between spin 1' and spin ~ currents which is an increasing function of B/p(O). This is because spin-orbit effects mean that an electron on a given orbit on the Fermi surface passes continuously between spin 1' and spin +, progressively mixing currents as B/p(O) increases. This model predicts the saturation magnetoresistances of the different alloy series reasonably well. The ordinary magnetoresistance in Fe based alloys is m o r e difficult to express in the form of Kohler curves, because the much higher value of 4 ~ M in Fe means that extrapolations to B = 0 are always very extended. D a t a given by Dorleijn (1976) again indicate different Kohler curves for Fe samples containing different impurities, but the correlation with the value of p+ (O)/p, (0) is much less clear than in the case of Ni based alloys. There is an additional effect that appears under similar experimental conditions as the Lorentz force ordinary magnetoresistance, but which is due to the high field susceptibility of the ferromagnetic metal. This high field susceptibility can have two origins. First, there is an increasing magnetic order in an applied field which can also be thought of as a reduction in the n u m b e r of magnons with increasing field. This term is m a x i m u m around Tc and goes to zero as T goes to zero. Secondly, for a band ferromagnet, the local magnetic m o m e n t s can be altered by an applied field at any temperature, even T = 0 (Van Elst 1959).

778

I.A. CAMPBELL AND A. FERT

Insofar, as an increasing field produces increasing magnetic order and hence lower spin disorder scattering, dp/dH due to the first term will be negative. The second type of effect can in principle give either positive or negative magnetoresistance depending on the electronic structure of the system. Van Elst (1959) measured at 300 K (1/p)(dp/dH)l I~- (1/p)(dp/dH)l with effects of the order of 10-4/kG and with significant variations from one alloy to another. This behaviour is due to the first effect. At low temperatures the Lorentz-force magnetoresistance dominated except for NiMn alloys which showed negative dp/dH even at low temperature; this is probably due to an unusual band susceptibility in these alloys.

3.2. Ordinary Hall coefficient In non-magnetic metals it is known that the ordinary Hall coefficient R0 behaves to a rough approximation as Ro oc 1/en* where n* is the effective density of current carriers and e is their charge (e is negative for electron-like carriers and positive for hole-like carriers). The actual values of R0 can be considerably modified by Fermi surface and scattering anisotropy effects (Hurd 1972); for the high field condition wc >> 1, R0 depends only on the Fermi surface geometry and can be highly anisotropic in single crystals. In ferromagnetic metals the ordinary Hall effect can be separated from the extraordinary Hall effect by measurements above technical saturation, as long as the susceptibility of the sample in high fields is negligible so that there is no paramagnetic extraordinary Hall effect correction (see section 3.4). The ordinary Hall coefficient in Ni at room temperature is R0-~ - 6 x 10 1312cm/G (Lavine 1961), which corresponds to conduction by electronlike carriers with an effective electron density n* of about 1 electron per atom. R0 varies by about 20% between room temperature and 50 K; at lower temperatures the low field condition ~0c~-'~ 1 no longer holds for high purity Ni samples so R0 tends towards the high field value (Reed and Fawcett 1964). Pugh and coworkers (Pugh et al. 1955, Sandford et al. 1961, Ehrlich et al. 1964) and Smit (1955) showed that for a number of Ni based alloys, in particular NiFe and NiCu, the low temperature Hall coefficients in concentrated samples correspond to much lower effective carrier concentrations, n * - 0 . 3 electrons per atom. They pointed out that this low number of carriers was probably, associated with a regime where only the conduction band for one direction of spin was carrying the current. Later work on Ni and NiCu alloys (Dutta Roy and Subrahmanyam 1969) showed that R0 is very temperature dependent in the alloys, and that above the Curie point n* returns to a value of about 1 electron-atom, i.e., to a situation where both spin directions carry current. This would seem to fit in well with other data on the two current model. However, careful measurements by Huguenin and Rivier (1965) and by Miedema and Dorleijn (1977) on a wide range of Ni based alloys have shown that the situation is more complicated. The data can be summarized as follows: the low temperature R0 is very close to zero in dilute alloys (concentration - 0 . 5 % ) for

TRANSPORT PROPERTIES OF FERROMAGNETS

779

which Po+/Pot > 1 (i.e. NiFe, N__iiCu, N i C o . . . ) but then increases rapidly with impurity concentration to a value corresponding to n* - 0.3 in samples where the impurity resistivity is greater than about 5 txf~cm. For alloys for which po ~/po t < 1, R0 is essentially independent of impurity concentration at about - 6 x 10-13 l~cm/G (note that only samples of this type having p > 2 ix~cm were studied). Now in a two current model R0 is given by

Ro= p2 Rot/p2 + Ro+/p~ ,

(31)

where Rot, R0+ are the ordinary Hall coefficients for the two spin directions taken separately. From the experimental data it can be concluded that R0+ is reasonably constant, while Rot varies strongly with p~. Dorleijn and Miedema suggested that the effect is due to a "smudging out" of the details of the spin 1' Fermi surface of Ni with increasing Pt and they associated this with the observed changes of the magnetocrystalline anisotropy with alloy concentration (Miedema and Dorleijn 1977). As we will see in section 3.3, the resistivity anisotropy of the same alloys changes similarly with impurity concentration until a certain residual resistivity value is reached. The R0 data suggest that the "smudged out" Fermi surface situation corresponds more closely to the extreme s-d model with conduction entirely by an s t like band containing about 0.3 electrons per atom. The results on R0 in Fe based alloys are less clear, partly because the separation into ordinary and extraordinary Hall components is more difficult because of the large value of 4~-M. Fe has a positive ordinary Hall coefficient, as have the dilute Fe based alloys except for FeCo (Beitel and Pugh 1958) although R0 for __FeNi alloys changes sign with temperature and with concentration (Softer et al. 1965). There appears to be evidence (Carter and Pugh 1966) that alloys for which pt(O)/p+(O)> 1 such as FeCr, behave similarly to Ni in that R0 is high at low temperatures and drops considerably at higher temperatures as both spin directions begin to participate in the conduction.

3.3. Spontaneous resistivity anisotropy This was defined in section 1 and is a spin orbit effect. The mechanism can vary from system to system. The simplest case to understand, at least in principle, is that of dilute rare earth impurities (Fert et al. 1977). Because of the unclosed f shell, the magnetic rare earths can be regarded as ion-like with a non-spherical distribution of charge (apart from the spherical ion Gd3+). A conduction electron plane wave encounters an object with a different cross section depending on whether it arrives with its k vector parallel or perpendicular to the rare earth moment, which provides an axis for the non-spherical charge distribution. The anisotropy of the resistivity is proportional to the electronic quadrupole moment of the particular rare earth. The theory of this effect has been worked out in detail (Fert et al. 1977). In transition metals, the spin orbit coupling is usually a weak perturbation on the spin magnetization. The lowest order terms leading to a resistivity anisotropy

780

I.A. CAMPBELLAND A. FERT

will be either mixing terms of the type ( L + S - ) 2 o r polarization terms of the type (LzSz)2. Smit (1951) calculated the resistivity anisotropy to be expected on an s-d model from the mixing terms acting between spin 1' and spin ,~ d bands. When data became available for both the anisotropy and the p ~/p t ratios in various Ni alloys, it was found that there was good agreement between the results and predictions which could be made using the Smit approach (Campbell et al. 1970). Agreement is however less good for impurities having a virtual bound d state near the Fermi surface, and an additional (LzS~) 2 mechanism was suggested for these cases (Jaoul et al. 1977). The relative anisotropy of the resistivity (Pll- P±)/P defined in section 1 has been measured for Ni and a large number of Ni alloys as a function of concentration and temperature (Smit 1951, Van Elst 1959, Berger and Friedberg 1968, Campbell et al. 1970, Vasilyev 1970, Campbell 1974, Dedi6 1975, Dorleijn 1976, Dorleijn and Miedema 1976, Kaul 1977, Jaoul et al. 1977) and for many dilute Fe based alloys, mainly at He temperature (Dorleijn and Miedema 1976). We will first discuss the Ni data. The anisotropy ratio for pure Ni is near +2% from nitrogen temperature up to room temperature, and then gradually drops as the temperature is increased up to the Curie point (Smit 1951, Van Elst 1959, Kaul 1977). Below nitrogen temperature the anisotropy is difficult to estimate for pure samples because of the rapidly increasing ordinary magnetoresistance, but it appears t o remain fairly constant. For most dilute N__iiXalloy series the limiting low temperature anisotropy ratio is relatively concentration independent for a given type of impurity X over a fairly wide concentration range but the value depends strongly on the type of impurity, table 4. For NiCo, NiFe and N__iiCu (fig. 13) the anisotropy ratio increases continuously with concentration up to concentrations corresponding to residual resistivities of about 2 p~cm. It is a disputed point as to whether the appropriate characteristic value of the anisotropy ratio for these alloys is the plateau value (Jaoul et al. 1977) or a value at some lower concentration (Dorleijn and Miedema 1975b, 1976). When the temperature is increased, the anisotropy ratio of a given sample tends towards the pure Ni value and finally becomes zero at the Curie point of the alloy (Vasilyev 1970, Kaul 1977). There is a clear correlation between the value of a and the low temperature a n i s o t r o p y ratio (Campbell et al. 1970). Alloys having high values of a N(~Co, NiFe, N i M n . . . ) have high positive resistivity anisotropies while alloys with c~ ~ 1 have small positive or negative anisotropies. A spin-orbit mixing model originally suggested by Smit (1951) gives a convincing explanation of the overall variation of the anisotropy ratio with the value of a. As Ni metal has a fully polarized d band, there are no d 1' states at the Fermi surface for the conduction electrons to be scattered to. However because of the spin-orbit mixing by the matrix element AL+S- some d 1' character is mixed into the d $ band. The resulting weak s ]' to d $ scattering can be shown to depend strongly on the relative orientation of the k vector of the s conduction electron and the sample magnetization. This leads to a resistivity anisotropy of the form

T R A N S P O R T P R O P E R T I E S OF F E R R O M A G N E T S

781

TABLE 4 Anisotropy of the residual resistivity of dilute nickel based alloys*. Impurity PJ - P± x 102 t~

Impurity P_JI- P± x 102

Co

Fe

Mn

Cr

V

Pd

20 Ca)

13.6 o')

9.9 °)

--0.3500)

0.6 C")

14.8 Cb)

14 Cd)

7.8 Cb)

--0.28 (a)

O. 15 c°)

28 (c)

19.5 Cc)

9.5 Co)

-0.23 Cd)

Ru

Mo

0.05 C°)

-0.600')

0.1 Ca)

0.05 C~)

- 0 . 8 2 C~)

0.05 (0)

W

Cu

Au

Rh

Nb

Impurity

Re

pp!- Pa x 102

- 0 . 5 0 C°)

0.4 Ca)

6.8 C°)

- 0 . 4 5 Cc)

0.8 ¢ )

7.8 Co)

0.15 (~)

2 C~)

Pt

Ir

0.4 C°)

- 1 . 5 2 C~)

0.4 C~)

A1

Si

Zn

Sn

7.5 C°)

4.7 (a)

2.5 (")

5.7 Ca)

3.4 Ca)

7.9 Co)

3.9 Co)

2.1 co)

4..7 (b)

2.9 Co)

4.6 Co)

2.8 (c)

6.5 ¢)

3.5 Co)

*After: ca)Van Elst 1959, C°)Dorleijn and Miedema 1974, Dorleijn 1976, e)Jaoul et al. 1977, ca)Schwerer and Silcox 1970. We indicate - when this is possible - the resistivity anisotropy of alloys in the concentration range where the concentration dependence is weak (see fig. 13). The experimental data on (P/I- P±)/Pll has been re-expressed in terms of (PH- P±)/P.

aOtf (%) 3C

25

I

20 oo

ooo i

15

\

10

x

5

~\ ""x

x

%,

x

0

io

i

40

"x

60

Impur i ty concentrat

L

on, at °/o

Fig. 13. Concentration dependence of the resistivity anisotropy at 4.2 K for several nickel based alloys. AA: NiCo, OC): N iFe, ×: N_iiCu (after Jaoul et al. 1977).

782

I.A. CAMPBELL AND A. FERT (32)

P l l - P . / P = ~(o~ - 1 ) ,

where y is a spin-orbit constant which can be estimated to be about 0.01 from the Ni g factor. This model explains the sign, the magnitude and the general variation of the anisotropy with a (fig. 14). In addition, it has been shown (Ehrlich et al. 1964, Dorleijn and Miedema 1976, Jaoul et al. 1977) that an analysis of the anisotropy ratio of ternary alloys can lead to estimates of the individual anisotropies for the spin 1' and spin $ currents and that for alloys with a > 1 the results are in agreement with the predictions of the Smit mechanism. However, for a number of alloys of Ni for which c~ < 1, although the resistivity anisotropies remain small as would be expected from the Smit mechanism, eq. (32) is not accurately obeyed and the anisotropies of the two spin currents do not obey the Smit rules (Ehrlich et at. 1955, Jaoul et al. 1977). A further mechanism needs to be invoked for these systems, which are characterized by virtual bound states at the spin I' Fermi level. A mechanism has been proposed involving the )tLzSz spin-orbit interaction on the impurity site, particularly for impurities which have strong spin-orbit interactions (Jaoul et al. 1977). Dorleijn and Miedema (1976) pointed out that for most impurities, whatever the value of c~, (Ap/p)t > 1 and (Ap/p)$ < 1 but they did not explain this regularity. The temperature variation of the anisotropy ratio can also be understood using the Smit model (Campbell et al. 1970). As phonon and magnon scattering increases with increasing temperature, the effective value of a for an alloy tends to approach the pure metal value. Data on NiCu alloys have been analyzed in this

30

l

//

20

I0

I

1o

20

3'0

Fig. 14. Resistivity anisotropy of Ni based alloys at 4.2 K as a function of a = P0J,/P0t- The straight line is Ap/~ = 0.01 (a - 1) (after Jaoul et al. 1977).

TRANSPORT PROPERTIES OF FERROMAGNETS

783

way over a wide temperature and concentration range (Kaul 1977) so as to estimate

pit(T), pi~(T) and p~ ~(T). High concentration effects in certain alloy series have been interpreted as due to characteristic changes in the electronic structure with concentration (Campbell 1974). The resistivity anisotropy of a large number of Fe based alloys has also been studied (Dorleijn and Miedema 1976). Here, the alloys having p,(O)/p+(O),> 1 have strong positive resistivity anisotropies while those with Pl (O)/p+(0) < 1 have small anisotropy ratios (table 4). Again, an analysis in terms of the anisotropies of the spin ]' and spin $ currents has been carried out and the predictions of the Smit approach seem well borne out (Dorleijn 1976). As we have seen in section 1 the resistivity anisotropy in cubic ferromagnetic monocrystals can be expanded in a series of D6ring coefficients k l . . . ks. Once again, Ni and Ni alloys have been the most studied [pure Ni (Bozorth 1951), Ni 15% Fe (Berger and Friedberg 1968), Ni 1.6% Cr and N_j 3% Fe (Jaoul 1974), N__ii 0.5% Fe, Ni 0.55% Pt and Ni 4% Pd (Dedi6 1975)]. Very roughly the individual ki coefficients are simply proportional to the average polycrystal anisotropy with the exception of k3 (table 5). This coefficient may behave differently from the others because it does not strictly represent an a n i s o t r o p y - i t corresponds to an average change of the sample resistivity with the moment direction which is independent of the current direction. TABLE 5 Magnetoresistance anisotropy in Ni and Ni alloy single crystals. D6ring coefficients ki are givenin percent. References: (a~D6ring 1938,Co)Berger and Friedberg 1968, (c~Jaoul 1974, cd~Dedi6 1975. kl Ni, 300 K (a)'(d) NiFe 15% 4.2 K(b~ NiCr 1% 4,2K(c~ NiPd 4% 4.2 K(d~

55.0 -3.0 4.0

ke 14.5 -0.3 1.0

k3

k4

k5

-3.4 -26.3 -1.2 -5.5

-5.2 -37.8 +2.3 -4.0

+ 1.7 +24.7 0_+0.7 -3.0

There are also measurements of the D6ring coefficients for Fe at room temperature (Bozorth 1951). No convincing model has been proposed to explain the monocrystal anisotropy coefficients which presumably depend on the detailed band structure of the metal. The fact that the terms which are fourth order in the direction cosines of the magnetization (k3, k4, k5) are as large as the second order terms (kl, k2) is remarkable.

3.4. Extraordinary Hall effect Apart from the resistivity, the property of ferromagnetic metals which has attracted the greatest theoretical attention is the extraordinary Hall effect, Rs; the extraordinary Hall voltage is remarkable in being both strong and rapidly varying

784

I.A. CAMPBELL AND A. FERT

with temperature and impurity concentration. The fundamental mechanisms which are believed to produce this effect were proposed some years ago by Smit (1955) and Luttinger (1958) but the physical understanding of these effects has been considerably improved quite recently (Berger 1970, Lyo and Holstein 1972, Nozibres and Lewiner 1973). We will outline the discussion given byNozibres and Lewiner (1973); although this theory was developed specifically for semiconductors the same physics can broadly be used for ferromagnetic metals. An electron in a band submitted to the spin-orbit interaction acquires an effective electric dipole moment p= -Akxs,

where A is a spin-orbit parameter, k is the k vector and s the spin of the electron. If there were no scattering centres, the effective Hamiltonian would he Ygen = k 2 / 2 m - e E . (r + p )

(where r is the centre of the electron wave packet) for a metal in a uniform electric field E. Local scattering potentials give local terms in the Hamiltonian

V ( r ) - A(k × s). v v . Here, the second term arises from spin-orbit coupling in the lattice. An additional contribution to A can also arise from a local spin-orbit interaction. There are two distinct effects: (a) the scattering matrix elements between plane wave states are expressed as (k'] V - A(k x s ) . V V I k ) : Vu,[1 - iA(k x k')- s] (by applying the general commutator rule If(x), kx] ~ i 0 f ( x ) / 0 x to V(r)). This means that the probability of scattering k ~ k' is not the same as the probability k'~k because of interference between the spin-orbit term and the potential scattering. For a weak 3 function potential, Wkk' = V2[1 + 2A V r r n ( k x k ' ) . s] , where n is the density of states at the Fermi level. This "skew scattering" leads to a Hall current such that the Hall angle ~bn oc A V, which is independent of scattering centre concentration, but which can be of either sign, depending on the sign of V. (b) Now we come to the "side jump" term. The total Hamiltonian is = k2/2m + V(r)-

eE. r+p

• [VV- eE],

TRANSPORT PROPERTIES OF FERROMAGNETS

785

and the total velocity is: v : / ~ - i[r, gel = k/m + A [ V V - eE] x s + p . Without scattering, p changes as k increases under the influence of E, and secondly, the energies of the different k states are altered by the second term in v. However, when scattering is introduced, both of these currents are exactly cancelled out in static conditions; the first because ( p ) = - A ( t ~ ) × s --- o ,

and the second because the electron distribution readjusts itself to minimize energy, and this new distribution automatically has an average velocity perpendicular to E equal to zero. It would thus appear that the spin orbit terms do not lead to any extra current. But, during each scattering event there is also a "side j u m p " or shift of the centre of gravity of a scattered wave packet

8r = f 6v d t = - A A k × s (as 6v --- A V V × s = -A/¢ x s during the scattering event). Now, there are two side j u m p contributions: (i) electrons travelling with a c o m p o n e n t of k parallel to E jump sideways on being scattered; the resultant of these jumps is a current. (ii) electrons with a c o m p o n e n t of k perpendicular to E gain or lose an energy - e , 3 r . E on scattering. This shifts the total electron distribution to provide a second current. These terms are not cancelled out by any compensating terms. They lead to a total Hall current of 2ANe2E x (s), which is proportional to the electric field E but independent of the scattering rate. The definition of R, is Vy/IxMz, where y is the Hall p r o b e direction, x the current direction and z the m o m e n t direction. Putting Vy = ply and E = pIx, with the Hall current just given we clearly obtain R, ~ Ap2. Note that the p a r a m e t e r h represents the rate of change of the spin-orbit dipole - A k x s with k. This is a band property. However, local spin-orbit interactions on scattering centres can give an additional contribution to A and complicate the picture. We can now turn to the experimental data. The skew scattering term can be expected to dominate in dilute alloys at low temperatures, and indeed in Ni based alloys for which p(0) ~< 1 tzf~cm at helium temperatures (fig. 15) it has been shown that the Hall angle ~bH is independent of impurity concentration, but depends strongly on the type of impurity (Jaoul 1974, Fert and Jaoul 1972, Dorleijn 1976). It is possible to define Hall angles for each direction of spin, ~bHt and 4~H~ and experiments on ternary alloys (Dorleijn 1976) or on the t e m p e r a t u r e dependence

786

I.A. CAMPBELL AND A. FERT - ? H ('1"1.~. cm) "XTRAORDINARY 10

HALL RESISTIVITY AT /-,.2°K

Cu

Mn~Fe

5

Co 2

0

1

-5

c tat*l,)

Cr lr

Os

Fig. 15. Extraordinary Hall resistivity of several types of Ni based alloys as a function of their impurity concentration. The data are limited to alloys having a resistivity smaller than about 1 Ixf~cm; in more concentrated alloys, a side-jump contribution progressively appears and becomes predominant for p = 10 ixf~cm (see fig. 16) (Jaoul 1974). of t h e H a l l angle (Jaoul 1974) allow o n e to e s t i m a t e t h e s e two H a l l angles for each i m p u r i t y . R e s u l t s a r e given in t a b l e 6. T h e v a l u e s of t h e s k e w s c a t t e r i n g H a l l angles can b e discussed in t e r m s of t h e e l e c t r o n i c s t r u c t u r e of t h e v a r i o u s i m p u r i t i e s (Fert a n d J a o u l 1972, J a o u l 1974). F o r s a m p l e s with h i g h e r resistivities (either b e c a u s e of h i g h e r i m p u r i t y c o n c e n t r a t i o n o r b e c a u s e t h e y are m e a s u r e d at h i g h e r t e m p e r a t u r e s ) t h e side j u m p t e r m b e c o m e s i m p o r t a n t . C o n s i d e r i n g only d a t a t a k e n at low t e m p e r a t u r e s , results for a given alloy series can g e n e r a l l y b e fitted (Jaoul 1974, D o r l e i j n 1976) b y t h e

TABLE 6 Skew scattering Hall effect in dilute Ni based alloys. For each impurity, qSH is the dilute limit Hall angle in millirad, and ~bHt, ~bH~ are the corresponding spin 1" and spin $ Hall angles. References: * Dorleijn 1976, *Jaoul 1974. Impurity 42H ~bH1' qSH~

Impurity ~bH ~bat ~bH;

Ti +1.5", -4.5 -3.4* +5.5*

Fe --6.2, --10t -7", -10 t +6", +10 t

V -3", -2.5* -4*, -79 +6", -3*

Co --6.2*, --10.5' -6", -10 t +2.5", +7 t

Cr

Mn

+2.8", +2 t - 3*, - f +4", 3t

Cu --10", --23t -14", -24* +3.5", +10'

-6.5", -9.5 t - 10* +1.5 t

Ru +2.5*, +3 t -4.7", +3 t +3", +3 t

Rh 0", --4t -1.4", - 3 t +1.3", -5*

TRANSPORT PROPERTIES OF FERROMAGNETS

787

expression (33)

Rs = ap + bp :2,

or alternatively (fig. 16)

(34)

c/:,H = ~b° + B p ,

if the variation of the magnetization with impurity concentration is neglected. It is usually assumed that this represents a separation into the skew scattering term and the side jump term. For most Ni based alloy series, as we have seen the values of 4~° vary considerably, but the values of B hardly vary from one impurity to another, with B -~ - i m i l l i r a d / ~ c m . However, for those Ni based alloys with p+ (O)/pt (0)>> 1, the data as a function of concentration cannot be represented by eq. (33) unless only a very restricted range of concentration is considered. It is interesting to note that these particular alloys are those which also show anomalous R0 and resistivity anisotropy behaviour as a function of concentration. At room temperature, p in Ni and Ni alloys is always "high" so that the side jump mechanism can be assumed to dominate. The experimental value of the ratio R d p 2 increases from the pure Ni value, R s / p 2 ~ 0.1 (~cmG) -1, as a function of impurity concentration and rapidly saturates at a plateau value of about 0.15 (f~cmG) -~ for a wide range of Ni alloys (K6ster and Gm6hling 1961, K6ster and R o m e r 1964), (fig. 17). The room temperature R s / p 2 values for the alloys are close to the values at low temperatures for the same alloys (Dorleijn 1976). However, for certain alloy systems R s / p 2 measured at room temperature changes steadily with impurity concentration. Thus for NiFe, R~ changes sign at about 15% Fe (Smit 1955, Kondorskii 1964). Alloys with this concentration of Fe show low values of R~/p: even if a second high resistivity impurity is introduced (Levine 1961). In pure Fe and FeSi alloys, R s / p 2 is remarkably constant over a wide range of concentrations and temperatures (Kooi 1954, Okamoto et al. 1962, where this ratio remains constant although R~ varies over three decades) (fig. 18). For other Fe based alloys the ratio generally approaches the pure Fe value at moderate or

20

EL°

-r-

t

10

-r 1C

./"

//

to

/ 1'0 2~0 . ~ (p~cm)

¢0 20 9±(#.O_cm)

Fig. 16. The extraordinary Hall. angle at 4.2 K as a function of the residual resistivity of FeA1 and NiRu alloys (Dorleijn 1976).

788

I.A. C A M P B E L L A N D A. F E R T

Rs/ )2 (~.cm9)._i o

~

-0.15 o

i /~

.0

/t

-0.1 o CF Ru Mo

oNb • Ti

-0.05

x V

Concentration, %

0

I

I

I

I

I

/

1

2

3

4

5

6

•

Fig. 17. The ratio Rs/p 2 in Ni and Ni alloys at room temperature (after K6ster et al. 1961 and 1964).

l

Fe

o

#

A 2.04% Si-Fe * 3.83% Si-Fe

/

xO,

109 g b. E o

-

E

fc~0

o

? 1611

,

156

,

,,I

lO-5

,

,,

I

lo-~ Resistiv'lty ~o (D.cm)

Fig. 18. Log-log plot of R5 against p for Fe and some Fe alloys above nitrogen temperature (after Okamoto et al. 1962).

TRANSPORT PROPERTIES OF FERROMAGNETS I

I

I

[

789

A I

A12.7% Cr IN Fe o 5.1% CF IN Fe

50

/ / /~/~ / /

• 0.75 °/o CFIN Fe

// /

x 2.3 % CFIN Fe

20

t

#j/,y'

~" 10 o.~~ , t o

N

s

! 0.5

I

2

I

5

I

10

I

20

50

~ (10-8OHMM) Fig. 19. Log-log plot of Rs against p for FeCr alloys, with temperature as an implicit variable (after Carter and Pugh 1966).

high temperatures (Softer et al. 1965, Carter and Pugh 1966). However, at low temperatures where skew scattering can be important, the behaviour can be completely different (fig. 19) (Carter and Pugh 1966). It seems that in the F__~eCr case, there is a strong skew scattering effect at low temperatures which has disappeared by room temperature (but see Majumdar and Berger 1973). Dorleijn (1976) has made an analysis in terms of skew scattering, side jump and ordinary Hall effect in Fe alloys at helium temperatures, but the interpretation is tricky, particularly because samples frequently show a field dependent Hall coefficient. The extraordinary Hall coefficient has been measured as a function of temperature in pure Co (Cheremushkina and Vasileva 1966). Kondorskii (1969) suggested that the sign of the side jump effect was related to the charge and polarization of the dominant carriers, which can be compared with the model outlined above. No satisfactory quantitative estimates of the size of the effect seem to have been made for ferromagnetic metals, and other basic questions concerning this mechanism remain open. The anisotropy of the Hall effect in single crystals is technically difficult to study, and, as a result, the existence of an anisotropy in the extraordinary Hall coefficient of cubic metals has been uncertain. Now evidence has been provided for the anisotropy in Rs for Fe (Hirsch and Weissmann 1973) and for Ni (Hiraoka 1968) at room temperature. In hexagonal Co both R0 and Rs are highly anisotro-

790

I.A. C A M P B E L L A N D A. F E R T

pic (Volkenshtein et al. 1961) which means that measurements on hcp Co polycrystals are subject to severe texture problems.

3.5. Thermoelectric power In non-magnetic metals under elastic scattering conditions, the thermoelectric power (TEP) coefficient depends on the differential of the resistivity at the Fermi surface through the Mott formula: dp s=

3 lel

p

In ferromagnets the situation is complicated by the existence of the two spin currents at low temperatures and by magnetic scattering at higher temperatures. The TEP curves as a function of temperatures for Fe, Co and Ni metals show effects which are clearly due to ferromagnetic ordering (fig. 20). For Co and Ni, the curve of S(T) shows a bulge towards negative values of S in the ferromagnetic temperature range, and a distinct charge of slope at To. For Fe, the behaviour is similar but complicated by a positive hump in S(T) just below room temperature. The critical behaviour of S(T) has attracted considerable attention. In Ni, the curve for dS/dT near Tc resembles the specific heat curve in the same way as does dp/dT (Tang et al. 1971). Although it has been argued that the TEP anomaly represents strictly the specific heat of the itinerant electrons (Tang et al. 1972) a more reasonable interpretation is in terms of the critical behaviour of the elastic scattering (Thomas et al. 1972). Combining the Mott formula and the expression 20

10

0 _10 ¸ iI

"T

x,¢

> -20 (13

-31 -41

Tc -50

400 Tc(Ni) 8 00

1200

T (K)

Fig. 20. T h e absolute thermoelectric power of Ni, Fe, Pd and Co (Laubitz et al. 1976).

TRANSPORT PROPERTIES OF FERROMAGNETS

791

for the resistivity as a function of k near Tc leads to

Pn/P),

S = Sp - 1 A o T ( 1 +

where AQ = 27r2k~/3[elEv, and Sp is the background non-magnetic TEP. Results on GdNi2 were discussed in terms of this approach (Zoric et al. 1973). The systematics of S(T) were studied at room temperature and above in a number of Ni based alloys (Vedernikov and Kolmets 1961, Kolmets and Vedernikov 1962, K6ster and Gm6hling 1961, K6ster and R o m e r 1964). S at room temperature becomes rapidly more positive with impurity concentration for those alloys for which p;(O)/p~(O)~ 1 (fig. 21). The negative bulge in S(T) remains very strong for a wide range of NiFe alloys measured up to Tc (Basargin and Zakharov 1974), but tends to disappear in NiV alloys (Vedemikov and Kolmets 1961). The low temperature T E P of Ni based alloys has been analyzed using the two current model (Farrell and Greig 1969, 1970, Cadeville and Roussel 1971). If the intrinsic T E P coefficients for the two spin directions are S t and S+ then the observed value of S should be S = (p; S t + Pt S;)/(p~ + p+) at low temperatures; at high temperatures where the two currents are mixed, the impurity diffusion thermopower becomes S = ½(St + S+). Using these two expressions, Farrell and Greig (1969) extracted S t , S , for a number of impurities in Ni and similar analyses have been done in Ni and Co based alloys (Cadeville et al. 1968, Cadeville 1970, Cadeville and Roussel 1971). A detailed discussion has been given

26

T (K)

8.8%Cr

(a)

2O

24

'

22

11.

20

5.2

18

.8

40

60

80

100

i

-2 -4

16

-6

14 -Q

12

::k ~'4C 8 -1;

6 Ni Cr

4

--ld

2 r

i

,

i

,

i

,

i

,

i

.

i

.

i

40 80 120 160 200 2z,0 280

J (K) Fig. 21. The absolute thermoelectric power of some nickel based alloys as a function of temperature (after Beilin et al. 1974 and Farrell and Greig 1970). (a) NiCr; (b) Ni alloys.

792

I.A. CAMPBELL AND A. FERT

of the relationship between the electronic structure of the impurity and the T E P coefficients (Cadeville and Roussel 1971). Another aspect of the two current situation is the influence of magnon-electron scattering (Korenblit and Lazarenko 1971). Scattering of a spin $ electron to a spin I' state involves the creation of a magnon, which needs positive energy, while spin 1' to spin + scattering is through the destruction of a magnon. The electron-magnon scattering will then lead to a positive term in S at moderate temperatures in alloys where the spin $ current dominates, and a negative term in alloys where the spin 1' current dominates. The T E P due to this effect will be superimposed on the elastic electron-impurity term except at very low temperatures, and will complicate the analysis of the diffusion terms. Results on Ni alloys have been interpreted with this mechanism (Beilin et al. 1974). A magnon drag effect has been suggested (Bailyn 1962, Gurevich and Korenblit 1964, Blatt et al. 1967). Measurements on the T E P in a NiCu and a NiFe alloy in applied fields appear to be consistent with this mechanism (Granneman and Berger 1976). However, the strong positive T E P hump in pure Fe does not have this origin (Blatt 1972). The value of S is anisotropic with respect to the magnetization direction in a ferromagnet. Measurements on Fe and Ni single crystals at room temperature (Miyata and Funatogawa 1954) gave AS100 = + 0.70 IxV/K,

ASm -- - 0.13 txV/K

in F e ,

AS~00 = +0.57 ~xV/K,

ASm = +0.69 txV/K

in Ni.

and

The Fe result was confirmed by Blatt (1972). 3.6. Nernst-Ettingshausen effect

This is the thermoelectric analogue of the Hall effect. It has been studied in the pure ferromagnetic metals and in a number of alloys (Ivanova 1959, Kondorskii and Vasileva 1964, Cheremushkina and Vasileva 1966, Kondorskii et al. 1972, Vasileva and Kadyrov 1975). Like Rs, this coefficient varies strongly with temperature in ferromagnets. Kondorskii (1964) proposed the phenomenological relationship Q = - (a + jgp)T,

and the origin of the effect was discussed in terms of the side jump mechanism by Berger (1972) and Campbell (1979). 3. 7. Thermal conductivity

This is not a purely electron transport effect, as heat can be carried also by phonons and even magnons, and separating out the different contributions is difficult. Farrell and Greig (1969) in careful measurements on Ni and Ni alloys have shown that a coherent analysis of the alloy data needs to take into account

TRANSPORT PROPERTIES OF FERROMAGNETS

793

the two current character of the conduction. They found that it was not possible to decide for or against the presence of any electron-electron term in pure Ni at low temperatures (White and Tainsh 1967). At higher temperatures, Tursky and Koch (1970) have shown that it is possible to use the spontaneous resistivity anisotropy to separate out phonon and electron thermal conductivity. By measurements in strong fields, Yelon and Berger (1972) identified a magnon contribution to the low temperature thermal conductivity in N_iiFe. The thermal conductivity of Ni shows an abrupt change of slope at Tc (Laubitz et al. 1976). This property is very difficult to measure with high precision.

4. Dilute ferromagnetic alloys 4.1. Palladium based alloys

It has been known for some time that P dFe, PdCo, PdMn and P__ddNialloys are "giant moment" ferromagnets at low concentrations; the transport properties of these systems have been well studied. 4.1.1. Resistivity and isotropic m agnetoresistance PdFe alloys are soft ferromagnets down to at least 0.15% Fe. The Fe magnetization at T ~ Tc saturates completely in small applied fields (Chouteau and Tournier 1972, Howarth 1979). The magnetic disorder at relatively low temperatures is in the form of magnons; for the dilute alloys (C < 2% Fe), it appears that the magnon-electron scattering is essentially incoherent so the magnetic resistivity is proportional to the number of magnons present, leading to a temperature dependent resistivity proportional to T 3/2 for T ~ Tc and a characteristic temperature dependent negative magnetoresistance (Long and Turner 1970, Williams and Loram 1969, Williams et al. 1971, Hamzi6 and Campbell 1978). At higher concentrations a T 2 resistivity variation replaces the T 3/2 behaviour (Skalski et al. 1970). At the Curie temperature there is a change in slope of the p ( T ) curve but it is difficult to analyze the results in terms of critical scattering behaviour because of smearing due to the spread of Tc values in the samples (Kawatra et al. 1969). PdMn alloys are "ferromagnets" below 4% Mn concentration in that they show a high initial susceptibility below a well defined ordering temperature (Rault and Burger 1969, Coles et al. 1975). In fact, high field magnetization measurements (Star et al. 1975) show that the Mn magnetization only becomes truely saturated when very strong magnetic fields are applied. The temperature dependence of the resistivity of these alloys is qualitatively similar to that observed in PdFe, with a change of slope in p ( T ) at Tc and a T 3/2 variation of the resistivity at low temperatures (Williams and Loram 1969). In contrast to the PdFe alloys the magnetoresistance remains strongly negative even when T tends to zero (Williams et al. 1973).

794

I.A. C A M P B E L L A N D A. F E R T

PdCo alloys have very similar ordering temperatures and total magnetic moments per atom as the PdFe alloys (Nieuwenhuys 1975), and the temperature dependence of the resistivity is again of the same type (Williams 1970). However the paramagnetic resistivity at T > Tc is proportional to the Co concentration (Colp and Williams 1972) whereas in P__ddFealloys it increases as the square of the Fe concentration (Skalski et al. 1970). The PdCo alloys below 5% Co show a negative magnetoresistance at T ~ Tc which indicates that they are not true ferromagnets (Hamzi6 et al. 1978a)*. PdNi alloys are ferromagnets above a critical concentration of 2.3% Ni (Tari and Coles 1971). Near this concentration the low temperature variation of the resistivity of the alloys becomes particularly strong (Tari and Coles 1971). Both the paramagnetic and ferromagnetic alloys show a large positive magnetoresistance due to an increase in the local moments at the Ni sites with the applied field (Genicon et al. 1974, Hamzi6 et al. 1978a).

4.1.2. Magnetoresistance anisotropy PdFe, P__d_dCoand PdNi alloys all show positive anisotropies Pll > P± at moderate magnetic impurity concentrations. At low concentrations P_ddFe samples show vanishingly small anisotropies (Hamzi6 et al. 1978a). From this and other evidence it has been concluded that the Co and Ni impurities carry local orbital moments. 4.1.3. Extraordinary Hall effect Over a broad concentration range the Hall coefficient in PdFe alloys behaves similarly to that in concentrated NiFe alloys, changing sign near 20% Fe (Matveev et al. 1977, Dreesen and Pugh 1960). At low concentrations the Hall angle tends to zero for PdFe and P__d_dMnbut takes on a concentration independent value for P dNi and PdCo (Hamzi6 et al. 1978b, Abramova et al. 1974). This should be related to the local orbital moments of Co and Ni impurities. 4.1.4. Thermoelectric power In the concentrated ferromagnets, features clearly associated with the ferromagnetic ordering are visible in the temperature dependence of the TEP. For the Pd based alloys this does not seem to be the case except perhaps when the magnetic impurity concentration is greater than 5% (Gainon and Sierro 1970). At 1%, or lower, concentrations PdFe and PdMn show weak negative or positive TEP below 20 K varying in a rather co'--mplex way with concentration and temperature (Gainon and Sierro 1970, Macdonald et al. 1962, Schroeder and Uher 1978). P_dd1% Co shows a negative TEP hump at 20 K (Gainon and Sierro 1970); this hump becomes more pronounced and goes to lower temperatures as the concentration is decreased (Hamzi6, 1980). Below the critical concentration PdNi alloys show a strong negative hump in the TEP around 15 K which disappears once the concentration exceeds the critical value (Foiles 1978). * They can he considered to be "quasiferromagnets", i.e., systems having an overall magnetic m o m e n t but where the local m o m e n t s are each somewhat disoriented with respect to the average m o m e n t direction.

TRANSPORT PROPERTIES OF FERROMAGNETS

795

4.2. Platinum based alloys Again, Pt__Fe and Pt___Coare giant moment ferromagnets at concentrations of a few percent, but at lower concentrations the behaviour is more complicated. For Pt__Fe below about 0.8% spin glass order sets in (Ododo 1979). In the ferromagnetic concentration range there is the usual step in p(T) at the ordering temperature, but below 0.8% Fe this step disappears (Loram et al. 1972). The isotropic magnetoresistance is strongly negative at concentrations less than about 5% Fe (Hamzi6 et al. 1981). PtCo alloys below 1% Co show resistivity variations which are complex because of competing tendencies to Kondo condensation and to magnetic ordering (Rao et al. 1975, Williams et al. 1975). At concentrations above about 1% Co a step can be seen in p(T) at To. The isotropic magnetoresistance is positive at low concentrations, becoming negative by 2% Co (Lee et al. 1978, Hamzi6 et al. 1980). Both Pt__Fe and PtCo alloys show concentration independent resistivity anisotropies and extraordinary Hall angles at low concentrations (Hamzi6 et al. 1979). The low temperature thermoelectric power of PtCo alloys becomes strongly negative below about 2% Co concentration (Lee et al. 1978). This TEP is sensitive to applied magnetic fields. PtMn alloys are spin glasses (Sarkissian and Taylor 1974), and Pt___Nialloys are not magnetically ordered below 42% Ni.

5. Amorphous alloys Since the early 1970s considerable effort has been devoted to the study of the electrical and magnetic properties of amorphous alloys. The resitivity minimum observed in many systems has been subject to much controversy.

5.1. Resistivity of amorphous alloys The amorphous alloys have a very high resistivity (p ~ 100 Ixllcm) which changes relatively little as a function of temperature. Figure 22 shows that, in series of NiP alloys, the temperature coefficient changes from positive to negative as the concentration of P increases. This behaviour is well explained in the Ziman model of the resistivity of liquid metals (Ziman 1961) and its extension to amorphous alloys (Nagel 1977). In the Ziman model the resistivity turns out to be proportional to a(2kv) where kv is the Fermi wave vector and a(q) the atomic structure factor. If 2kv is close to the first peak of a(q), the resistivity is high and decreases as a function of T owing to the thermal broadening of the p~ak. In contrast, if 2kv lies well below (or well above) the peak, the resistivity is relatively low and increases as a function of T. In the NiP alloys (fig. 22) the additional conduction electrons provided by the higher concentrations of P raise 2kF to the first peak of a(q), which accounts for the experimental behaviour (Cote 1976). On the other hand, the small resistivity upturns observed in NiP at low temperature (fig. 22)

796

I.A. C A M P B E L L A N D A. F E R T n

z 03 o -i-13..

1.010

',.'

...'

'

'

'

"''

~i

' P'

...% •

e•l

•

P2s • e ••e

1.00I]

••.e

'

'

'

'

fl_ .m z

• "-..

e e e,,

••

eo

LU °% • e %°'••

_J _J

~"'4'


I->

O.9B(]

m

0.97C

.. •

P 80 20

, " t

40

. . . . . .

.

.

8

'

,

120

I

0.4

~ ~

03

.

~, ~oo

~ i °~ is ATOM]C

~)

20 ~ ~

o~

" ,

- 0.6

~_ ~2o . . . . . . . .

m

,

0.7

• crystaLLine NiP 80 20

~, .

•

0.950

-

• ~"

200

0.96C

•

OB

".

•

~

la_ o -

- 0,5

NsP15

az

-- 09

e•e •

I%

LU

2e I

•

i•

•e " Ni

,.

'

N 176 P24

Z
i--o3

r¢ >

02 £t"

I -01

280

(K)

Fig. 22. Relative resistivities of a m o r p h o u s and crystalline Ni-P alloys. Nominal compositions are indicated; (Pam/pcryst)293 ~ 3. T h e inset shows p and dp/dT as a function of the composition (after Cote 1976). Similar results are given by Boucher (1973) for N i - P d - P a m o r p h o u s alloys.

cannot be explained by the Ziman model. Such resistivity upturns, which generally give rise to a resistivity minimum, have been found in many amorphous systems. They have been found in both ferromagnetic and non-ferromagnetic amorphous alloys and, up to now, only in alloys containing transition (or rareearth) metals. Their origin has been subject to much controversy. Resistivity minima have been first found by Hasegawa and Tsui (1971a, b) in amorphous PdSi containing Cr, Mn, Fe or Co impurities (fig. 23). The classical features of the Kondo effect are observed: the resistivity varies logarithmically over a large temperature range and becomes constant in the low temperature limit; at low concentration of magnetic impurities the logarithmic term increases with the concentration, there is a negative magnetoresistance. But, surprisingly, the resistivity minimum still exists in the most concentrated alloys which are ferromagnetic. These results seem to indicate that weakly coupled moments subsist in amorphous ferromagnets and can give rise to Kondo scattering. Results on many other systems have suggested that the coexistence of ferromagnetism and Kondo effect is quite general in amorphous alloys; thus large logarithmic upturns have been observed (fig. 24) in ferromagnets of the series FeN•B, FeNiPB, FeN•PC, FeNPBS (Cochrane et al. 1978, Babi6 et al. 1978, Steward and Phillips 1978), FeNiPBA1, FeMnPBA1, CoPBA1 (Rao et al. 1979), PdCoP (Marzwell 1977); in

TRANSPORT PROPERTIES OF FERROMAGNETS

94.40

o

oO°° 94.00

o

93.60

ss

oooo° °

oO o~ooO°°°°

92.00

Fe 3 R:177Si20 co° ° ° ° o o

O_.-

cooo o

~o °°°

? ° ~

o m°

°°

o°°°° Fe oOO°

~

117. 20

Pd?$Si20 5

ooo ° °

132,10

~18,00

ooOO o °

o° ° °

91,20.~ ~'~

Cl

133.70

oo o oo

o

o oooeo °°

£0

.93.20 i34.50

ooO°°°ge 1Pd?9Si20

92.80

oOo

o°

135.40

o o° _

116.00

oooo °° Fe 7 Pd73Si20

o°°°°

o~o~

797

134.60 ~n 134.20

o°°°

03 UJ

~°

r,,-'

133.'~0

g o

133,40 o oo 69

132.60 131.80

i

,

0

40

133.00

o

1322O i

i

,

,

J

,

i

~

,

80 120 160 200 TEHPERATURE (OK)

240

Fig. 23. Resistivity versus temperature for FexPds0-xSi20 alloys. Tc = 28 K for x = 7 (after Hasegawa and Tsuei 1970b).

A A

a ,~AAt,~,A8 A

A

Aa

%,, oooooooo

~a

°o

144.3

e°o o

A

& t,

1442

162.0

A

•

\ E

162.1

A

O

a

161.9

% g ~'

O

°o o

o._, 144.1

o

% o ~

1/..4.0 143.9 Q01

% I

0.1

o o oo

I

1.0

1()

100

T(K) Fig. 24. Resistivity versus log T plot for two ferromagnetic amorphous alloys: (A) Fe75P16B6A]3 and (O) Fe60NilsP16B6AI3 (after Rapp et al. 1978).

798

I.A. CAMPBELLAND A. FERT

many cases the addition of small amounts of Cr strongly enhances the resistivity upturn. On the other hand, Cochrane et al. (1975) found that the logarithmic resistivity upturn of several amorphous alloys was field independent, in contrast to what is generally observed in Kondo systems. They also noticed a logarithmic upturn in NiP alloys with high P concentration in which the Ni atoms were not supposed to carry a magnetic moment. On the basis of these observations they ruled out the explanation by the Kondo effect and proposed a non-magnetic mechanism. Their model treats the electron scattering by the two level systems which are supposed to be associated with structural instabilities in amorphous systems; a variation of the resistivity in - l n ( T 2 + A2) is predicted, where A is a mean value of the energy difference between the two levels. The resistivity curves of several amorphous alloys fit rather well with such a variation law. At the present time (1979) however the trend is in favour of an explanation of the resistivity minima by the Kondo effect rather than by a non-magnetic mechanism. Clear examples of logarithmic resistivity upturns in non-magnetic systems are still lacking: alloys such as NiP or YNi c a n be suspected to contain magnetic Ni clusters (Berrada et al. 1978). On the other hand, systematic studies of the resistivity of FeNiPB (BaNd et al. 1978), FeNiPBAI, FeMnPBA1 (Rao et al. 1979) have shown definite correlations between the resistivity anomalies and the magnetic properties (logarithmic term large when Tc is small, etc.); it has been also found in several systems that the logarithmic upturn is lowered by an applied field. Finally, M6ssbauer experiments on FeNiCrPB alloys have found very small hyperfine fields on a significant number of Fe sites, which seems to confirm the coexistence of ferromagnetism and Kondo effect (Chien 1979). What we have written up to now concerned the metal-metalloid alloys which have been the most studied amorphous alloys. Studies of metal-metal amorphous alloys of rare-earths with transition or noble metals have been also developed recently. Resistivity minima have been again observed in these systems but appear to be generally due to contributions from magnetic ordering and not to Kondo effect. In Ni3Dy (fig. 25) the resistivity increases either if a magnetic field is applied or if the temperature is lowered below the ordering temperature To. This suggests a positive contribution from magnetic ordering to the resistivity, in contrast to what is observed in crystalline ferromagnetics. This has been ascribed by Asomoza et al. (1977a, 1978) to coherent exchange scattering by the rare-earth spins (Ni has no magnetic moment in these alloys). The model calculation predicts a resistivity term proportional to m(2kv) where re(q) is the spin correlation function 1

m ( q ) = NCelj( J + 1) R , ~ , exp[iq • ( R - R')IJR " JR'.

Here C1 is the concentration of magnetic ions, having local moments J and placed at R, R ' ; the sum is over the pairs of magnetic ions. The resistivity will depend on the magnetic order through m(2kv); for example,

TRANSPORT PROPERTIES OF FERROMAGNETS I

I

t

I

1

I

799

I

1

I

I

I

I

100

150

200

250

I

I

I 80

I

I

D y Ni 3 oH:O

296

~H:

kG 8kG

H: 2OkG o H:3OkG

295

u

294

> u~

I

293

Xx

"g~

•

Q~ 300~_

292

/

//

/

/ 292

291

50

t

I

/20I

|

I

40

I

60

I

T ( K)

Fig. 25. T h e resistivity of a DyNi3 a m o r p h o u s alloy in several applied fields is plotted as a function of temperature (after A s o m o z a et al. 1977).

ferromagnetic correlations will increase or decrease p according to whether the interferences are constructive or destructive. The Ni3-RE alloys should correspond to the case of ferromagnetic correlations and constructive interferences. The A g - R E , A u - R E and A I - R E amorphous alloys also show a clear contribution from magnetic ordering to the resistivity, but the interpretation seems to be a little more complicated than for the Ni3-RE alloys (Asomoza et al. 1979, Fert and Asomoza 1979). Finally, alloys of the series F e - R E and C o - R E generally show a monotonic decrease of the resistivity from the helium range to room temperature (Cochrane et al. 1978, Zen et al. 1979). In these alloys of high Tc the variation of the resistivity due to magnetic ordering must be displayed over a wide temperature range and is certainly difficult to separate from the normal variation due to the phonons and the thermal variation of the structure factor. We believe that this normal variation should be predominant, specially at low temperature. Similarly, in the alloys such as FeNiPB discussed above, a contribution from magnetic ordering to p(T) certainly exists but is likely covered up by other contributions (Kondo or structural effects) at low temperature.

800

I.A. CAMPBELL AND A. FERT

5.2. Hall effect and resistivity anisotropy of amorphous alloys The amorphous ferromagnetic alloys have a very large extraordinary Hall effect which generally covers up the ordinary Halt effect. This is because the extraordinary Hall resistivity, in contrast to the ordinary one, is an increasing function of the scattering rate (the contributions from skew scattering and side-jump are roughly proportional to p and p2 respectively). Thus pi~(B) is practically proportional to the magnetization in many systems and, for example, is frequently used to record hysteresis loops (McGuire et al. 1977a, b, Asomoza et al. 1977b). The extraordinary Hall effect of ferromagnetic alloys of gold with nickel, cobalt or iron has been studied by Bergmann and Marquardt (1979) and ascribed to skew scattering; the change of sign of pn between Ni and Fe has been accounted for by a model based on a virtual bound state picture of the 3d electrons. On the other hand, the extraordinary Hall effect of FeNiPB alloys rather suggest a side-jump mechanism (Malmhfill et al. 1978). The extraordinary Hall effect has been also studied in amorphous alloys of transition metals with rare-earths and related to the magnetization of the transition and rare-earth sublattices in phenomenological models (Kobliska and Gangulee 1977, McGuire et al. 1977, Asomoza et al. 1977b). The spontaneous resistivity anisotropy is rather large in amorphous alloys of gold with nickel or cobalt (/911-p± -~ 1 ix12cm) and has been interpreted in a model of virtual bound state for the 3d electrons (Bergmann and Marquardt 1979). The resistivity anisotropy seems to be smaller in alloys of the FeNiP type (Marohnid et al. 1977). The resistivity anisotropy has been also studied in amorphous alloys of nickel or silver with rare-earths and turns out to be mainly due to electron scattering by the electric quadrupole of the 4f electrons (Asomoza et al. 1979).

Reference Abelskii, Sh. and E.A. Turov, 1960, Fiz. Met. Metalloved. 10, 801. Abromova, L.I., G.V. Fedorov and N.N. Volkenshteyn, 1974, Fiz. Met. Metalloved. 38, 90. Amamou, A., F. Gautier and B. Leogel, 1975, J. Phys. F 5, 1342. Anderson, J.R. and A.V. Gold, 1963, Phys. Rev. Lett. 10, 227. Armstrong, B.E. and R. Fletcher, 1972, Can. J. Phys. 50, 244. Asomoza, R., A. Fert, I.A. Campbell and R. Meyer, 1977a, J. Phys. F 7, L 327. Asomoza, R., I.A. Campbell, H. Jouve and R. Meyer, 1977b, J. Appl. Phys. 48, 3829. Asomoza, R., I.A. Campbell, A. Fert, A. Li6nard and J.P. Rebouillat, 1979, J. Phys. F 9, 349.

Baber, W.G., 1937, Proc. Roy. Soc. A 158, 383. Babic, E., Z. Marohnic and J. Ivkov, 1978, Solid State Commun. 27, 441. Bailyn, M., 1962, Phys. Rev. 126, 2040. Basargin, O.V. and A.I. Zakharov, 1974, Fiz. Met. Metalloved. 37, 891. Beitcham, J.G., C.W. Trussel and R.V. Coleman, 1970, Phys. Rev. Lett. 25, 1970. Beitel, F.P. and E.M. Pugh, 1958, Phys. Rev. 112, 1516. Beilin, V.M., T.I. Zeinalov, I.L. Rogel'berg and V.A. Chernenkov 1974, Fiz. Met. Metalloved. 38, 1315. Berger, L., 1970, Phys. Rev. B 2, 4559. Berger, L., 1972, Phys. Rev. B 5, 1862. Berger, L., 1978, J. Appl. Phys. 49 (3), 2156. Berger, L. and S.A. Friedberg, 1968, Phys. Rev. 165, 670.

TRANSPORT PROPERTIES OF FERROMAGNETS Berger, L. and A.R. de Vroomen, 1965, J. Appl. Phys. 36, 2777. Berrada, A., N.F. Lapierre, L. Loegel, P. Panissod and C. Robert, 1978, J. Phys. F 8, 845. Bergmann, G. and P. Marquardt, 1978, Phys. Rev. B 18, 326. Birss, R.R., 1964, Symmetry and magnetism (North-Holland, Amsterdam). Blatt, FJ., D.J. Flood, V. Rowe, P.A. Schroeder and J.E. Cox, 1967, Phys. Rev. Lett. 18, 395. Blatt, F.J., 1972, Can. J. Phys. 50, 2836. Boucher, B., 1973, J. of Non-Cryst. Sol. 7, 277. Bozorth, R.M., 1951, Ferromagnetism (Van Nostrand, Princeton). Cadeville, M.C., F. Gautier, C. Robert and J. Roussel, 1968, Solid State Commun. 7, 1701. Cadeville, M.C., 1970, Solid State Commun. 8, 847. Cadeville, M.C. and C. Lerner, 1976, Phil. Mag. 33, 801. Cadeville, M.C. and B. Loegel, 1973, J~ Phys. F 3, L 115. Cadeville, M.C. and J. Roussel, 1971, J. Phys. F 1, 686. Campbell, I.A., 1974, J. Phys. F 4, L 181. Campbell, I.A., 1979, J. Magn. Magn. Mat. 12, 31. Campbell, I.A., A. Fert and A.R. Pomeroy, 1967, Phil. Mag. 15, 977. Campbell, I.A., A. Fert and O. Jaoul, 1970, J. Phys. C 3, S 95. Carter, G.C. and E.M. Pugh, 1966, Phys. Rev. 152, 498. Cheremushkina, A.V. and R.P. Vasil'eva, 1966, Sov. Phys. Solid State, 8, 659. Chien, C.L., 1979, Phys. Rev. B 19, 81. Chouteau, G. and R. Tournier, 1972, J. de Phys. 32, C1-1002. Clark, A.L. and R.L. Powell, 1968, Phys. Rev. Lett. 21, 802. Cochrane, R.W., R. Harris, J.O. Str6m-Olsen and M.J. Zuckermann, 1975, Phys. Rev. Lett. 35, 676. Cochrane, R.W. and J.O. Str6m-Olsen, 1977, J. Phys. F 7, 1799. Cochrane, R.W., J.O. Str6m-Olsen, Gwyn Williams, A. Lirnard and J.P. Rebouillat, 1978, J. Appl. Phys. 49, 1677. Coleman, R.V., 1976, AlP Conf. Proc. 29, 520. Coleman, R.V., R.C. Morris and D.J. Sellmeyer, 1973, Phys. Rev. B 8, 317. Coles, B.R., 1958, Adv. Phys. 7, 40.

801

Coles, B.R., H. Jamieson, R.H. Taylor and A. Tari, 1975, J. Phys. F 5, 572. Colp, M.E. and G. Williams, 1972, Phys. Rev. B 5, 2599. Connelly, D.L., J.S. Loomis and D.E. Mapother, 1971, Phys. Rev. B 3, 924. Cote, P.J., 1976, Solid State Commun. 18, 1311. Craig, P.P., W.I. Goldberg, T.A. Kitchens, and J.I. Budnick, 1967, Phys. Rev. Lett. 19, 1334. Dedir, G., 1975, J. Phys. F 5, 706. De Gennes, P.G. and J. Friedel, 1958, J. Phys. Chem. Solids, 4, 71. Der Ruenn Su and T.M. Wu, 1975, J. Low Temp. Phys. 19, 481. D6ring, W., 1938, Ann. Phys. 32, 259. Dorleijn, J.W.F., 1976, Philips Res. Repts, 31, 287. Dorleijn, J.W.F. and A.R. Miedema, 1975a, J. Phys. F 5, 487. Dorleijn, J.W.F. and A.R. Miedema, 1975b, J. Phys. F 5, 1543. Dorleijn, J.W.F. and A.R. Miedema, 1976, AIP Conf. Proc. 34, 50. Dorleijn, J.W.F. and A.R. Miedema, 1977, J. Phys. F 7, L 23. Dreesen, J.A. and E.M. Pugh, 1960, Phys. Rev. 120, 1218. Dugdale, J.S. and Z.S. Basinski, 1967, Phys. Rev. 157, 552. Durand, J. and F. Gautier, 1970, J. Phys. Chem. Sol. 31, 2773. Durand, J., 1973, Thesis (Strasbourg) unpublished. Dutta Roy, S.K. and T.M. Wu, 1975, J. Low Temp. Phys. 19, 481. Erlich, A.C., J.A. Dreesen and E.M. Pugh, 1964, Phys. Rev. 133, A, 407. Etin Wohlman, O., G. Deutscher and R. Orbach, 1976, Phys. Rev. B 14, 4015. Farrell, T. and D. Greig, 1968, J. Phys. C, 1 sur 2, 1359. Farrell, T. and D. Greig, 1969, J. Phys. C, 2 sur 2, 1465. Farrell, T. and D. Greig, 1970, J. Phys. C, 3, 138. Fawcett, E., 1964, Adv. Phys. 13, 139. Fert, A., 1969, J. Phys. C, 2, 1784. Fert, A. and R. Asomoza, 1979, J. Appl. Phys. 50, 1886. Fert, A. and I.A. Campbell, 1968, Phys. Rev. Lett. 21, 1190. Fert, A. and I.A. Campbell, 1971, J. de Phys. (Paris) 32, Sup. no. 2-3, C1--46.

802

I.A. CAMPBELL AND A. FERT

Fert, A. and I.A. Campbell, 1976, J. Phys. F 6, 849. Fert, A. and O. Jaoul, 1972, Phys. Rev. Lett. 28, 303. Fert, A., I.A. Campbell and M. Ribault, 1970, J. Appl. Phys. 41, 1428. Fert, A , R. Asomoza, D. Sanchez, D. Spanjaard and A. Friederich, 1977, Phys. Rev. B 16, 5040. Fischer, M.E. and A. Aharony, 1973, Phys. Rev. Lett. 30, 559. Fisher, M.E. and J.S. Langer, 1968, Phys. Rev. Lett. 20, 665. Foiles, C.L., 1978, J. Phys. F 8, 213. Friedel, J., 1967, Rendicanti della Scuola Intern. di Fisica '°Enrico Fermi" XXXVII Corso (Academic Press, New York). Fulkesson, W., J.P. Moore and D.L. McElroy, 1966, J. Appl. Phys. 37, 2639. Fujii, T., 1970, Nippon Kinsoku Gakkaishi (Japan) 34, 456. Gainon, D. and J. Sierro, 1970, Helv. Phys. Acta, 43, 541. Geldart D.I.W. and T.G. Richard, 1975, Phys. Rev. B 12, 5175. Genicon, G.L., F. Lapierre and J. Soultie, 1974, Phys. Rev. B 10, 3976. Goodings, D.A., 1963, Phys. Rev. 132, 542. Grannemann, G.N. and L. Berger, 1976, Phys. Rev. B 13, 2072. Greig, D. and J.P. Harrisson, 1965, Phil. Mag. 12, 71. Gurevich, L.E. and I.Y. Korenblit, 1964, Sov. Phys. Solid State, 6, 1960. Guenault, A.M., 1974, Phil. Mag. 30, 641. Hamzid, A., 1980, Thesis (Orsay). Hamzid, A. and I.A. Campbell, 1978, J. Phys. F 8, L33. HamziG A. and I.A. Campbell, J. Phys. (Paris) 42, L17. Hamzid, A., S. Senoussi, I.A. Campbell and A. Fert, 1978a, J. Phys. F 8, 1947. Hamzid, A., S. Senoussi, I.A. Campbell and A. Fert, 1978b, Solid State Commun. 26, 617. Hamzid, A., S. Senoussi, I.A. Campbell and A. Fert, 1980, J. Magn. Magn. Mat. 15-18, 921. Hasegawa, R. and C.C. Tsuei, 1971a, Phys. Rev. B 2, 1631. Hasegawa, R. and C.C. Tsuei, 1971b, Phys. Rev. B 3, 214. Hayakawa, H. and J. Yamashita, 1976, Progr. Theor. Phys. 54, 952. Herring, C., 1967, Phys. Rev. Lett. 19, 1131. Hiraoka, T., 1968, J. Sci. Hiroshima Univ. 32, 153.

Hirsch, A.A. and Y. Weissmann, 1973, Phys. Lett. 44A, 230. Hodges, L., D.R. Stone and A.V. Gold, 1967, Phys. Rev. Lett. 19, 655. Houghton, R.W. and M.P. Sarachik, 1970, Phys. Rev. Lett. 25, 238. Hugel, J., 1973, J. Phys. F 3, 1723. Howarth, W., 1979, Thesis, London. Huguenin, R. and D. Rivier, 1965, Helv. Phys. Acta, 38, 900. Hurd, C.M., 1972, The Hall Effect (Plenum Press, New York). Hurd, C.M., 1974, Adv. Phys. 23, 315. Ivanova, R.P., 1959, Fiz. Met. Metalloved. 8, 851. Jan, J.P., 1957, Solid State Phys. 5, 1. Jaoul, O., 1974, Thesis (Orsay), unpublished. Jaoul, O., I.A. Campbell and A. Fert, 1977, J. Magn. Magn. Mat. 5, 23. Jayaraman, V. and S.K. Dutta Roy, 1975, J.P.C.S. 36, 619. Kasuya, T., 1956, Progr. Theor. Phys. 16, 58. Kasuya, T., 1959, Progr. Theor. Phys. 22, 227. Kaul, S.N., 1977, J. Phys. F 7, 2091. Kawatra, M.P., S. Skalski, J.A. Mydosh and J.I. Budnick, 1969, J. Appl. Phys. 41), 1202. Kawatra, M.P., J.I. Budnick and J.A. Mydosh, 1970, Phys. Rev. B 2, 1587. Kawatra, M.P., J.A. Mydosh and J.I. Budnick, 1970, Phys. Rev. B 2, 665. Kittel, C., 1963, Phys. Rev. Lett. 10, 339. Kittel, C. and J.H. Van Vleck, 1960, Phys. Rev. 118, 1231. Klaffky, R.W. and R.V. Coleman, 1974, Phys. Rev. B 10, 2915. Kobliska, R.J. and A. Gangulec, 1977, Amorphous Magnetism II, eds., R.A. Levy and R. Hasegawa (Plenum, New York). Kolmets, N.V. and M.V. Vedernikov, 1962, Sov. Phys. Sol. St. 3, 1996. Kondorskii, E.I., 1964, Sov. Phys. JETP, 18, 351. Kondorskii, E.I., 1969, Sov. Phys. JETP, 28, 291. Kondorskii, E.I. and R.P. Vasil'eva, 1964, Sov. Phys. JETP, 18, 277. Kondorskii, E.I., A.V. Cheremushkina and N. Kurbaniyazov, 1964, Soy. Phys. Sol. St. 6, 422. Kondorskii, E.I., A.V. Cheremusbkina, R.P. Vasil'eva and Y.N. Arkipov, 1972, Fiz. Met. Metalloved. 34, 675. Kooi, C., 1954, Phys. Rev. 95, 843.

TRANSPORT PROPERTIES OF FERROMAGNETS Korenblit, I.Y. and Y.P. Lazarenko, 1971, Sov. Phys. JETP, 33, 837. K6ster, W. and W. Gm6hling, 1961, Zeit. Met. 52, 713. K6ster, W. and O. Romer, 1964, Zeit. Met. 55, 805. Kraftmakher, Y.A. and T.Y. Pinegina, 1974, Sov. Phys. Sol. St. 16, 78. Laubitz, M.J., T. Matsumara, 1973, Can. J. Phys. 51, 1247. Laubitz, M.J., T. Matsumara and P.J. Kelly, 1976, Can. J. Phys. 54, 92. Lavine, J.M., 1961, Phys. Rev. 123, 1273. Lee, C.W., C.L. Foiles, J. Bass and J.R. Cleveland, 1978, J. App. Phys. 49, 217. L6onard, P., M.C. Cadeville and J. Durand, 1969, J. Phys. Chem. Sol. 30, 2169. Loegel, B. and F. Gautier, 1971, J. Phys. Chem. Sol. 32, 2723. Loram, J.W., R.J. White and A.D.C. Grassie, 1972, Phys. Rev. B 5, 3659. Luttinger, J.M., 1958, Phys. Rev. 112, 739. Lyo, S.K. and T. Holstein, 1972, Phys. Rev. Lett. 29, 423. MacDonald, D.K.C., W.B. Pearson and I.M. Templeton, 1962, Proc. Roy. Soc. A 266, 161. McGuire, T.R. and R.I. Potter, 1975, IEET Transactions on Magnetics, Vol. Mag. 11, 1018. McGuire, T.R., R.J. Gambino and R.C. Taylor, 1977a, J. Appl. Phys. 48, 2965. McGuire, T.R., R.J. Gambino and R.C. Taylor, 1977b, I.E.E.E. Transactions on Magnetism M A G 13, 1977. Majumdar, A.K. and L. Berger, 1973, Phys. Rev. B 7, 4203. Malmh~ill, R., G. B~ickstr6m, K. Rao, S. Bhagat, M. Meichle and M.B. Salamen, 1978, J. Appl. Phys. 49, 1727. Mannari, J., 1959, Prog. Theor. Phys. 22, 335. Marohnic, Z., E. Babic and D. Pavuna, 1977, Phys. Lett. 63A, 348. Marzwell, N.I., 1977, J. Mag. Mag. Mat. 5, 67. Matveev, V.A., G.V. Fedorov and N.N. Voltenshteyn, 1977, Fiz. Met. Metalloved. 43, 1192. Matsumoto, H., H. Saito, M. Kikuchi, 1966, J.J. Inst. Meta. 30, 885. Miedema, A.R. and J.W.F. Dorleijn, 1977, J. Phys. F 7, L 27. Mills, D.L., A. Fert and I.A. Campbell, 1971, Phys. Rev. B 4, 196. Miyata, N. and Z. Funatogawa, 1954, J. Phys. Soc. Japan, 9, 967. Mott, N.F., 1936a, Proc. Roy. Soc. 153, 699.

803

Mott, N.F., 1936b, Proc. Roy. Soc. 156, 368. Mott, N.F., 1964, Adv. Phys. 13, 325. Nagel, S.R., 1977, Phys. Rev. B 16, 1694. Nieuwenhuys, G.J., 1975, Adv. Phys. 24, 515. Nozi6res, P. and C. Lewiner, 1973, J. de Phys. 34, 901. Okamoto, T., H. Tange, A. Nishimura and E. Tatsumoto, 1962, J. Phys. Soc. Japan, 17, 717. Ododo, J.C., 1979, J. Phys. F 9, 1441. Parks, R.D., 1972, AIP Conference, 5, 630. Pugh, E.M., 1955, Phys. Rev. 97, 647. Ramaman, R.V. and L. Berger, 1978, Proc. Int. Conf. Physics of Transition Metals (Toronto 1977), Institute of Physics, Conf. Ser. No. 39. Rao, K.V., O. Rapp, C. Johannesson, J.I. Budnick, T.J. Burch and V. Canella, 1975, AIP Conf. Proc. 29, 346. Rao, K.W., H. Gudmundsson, H.U. Astr6n and H.S. Chen, 1979, J. Appl. Phys. 50 (3), 1592. Rapp, O., J.E. Grindberg and K.V. Rao, 1978, J. Appl. Phys. 49, 1733. Rault, J. and J.P. Burger, 1969, C.R.A.S., 269, 1085. Reed, W.A. and E. Fawcett, 1964a, J. Appl. Phys. 35, 754. Reed, W.A. and E. Fawcett, 1964b, Phys. Rev. 136 A, 422. Richard, T.G. and G.J.W. Geldart, 1973, Phys. Rev. Lett. 30, 290. Ross, R.N., D.C. Price and Gwyn Williams, 1978, J. Phys. F, 8, 2367. Ross, R.N., D.C. Price and Gwyn Williams, 1979, J. Mag. Mag. Mat. 10, 59. Ruvalds, J. and L.M. Falicov, 1968, Phys. Rev. 172, 508. Sakissian, B.V.B. and R.H. Taylor, 1974, J. Phys. F 4, L 243. Sandford, E.R., A.C. Erlich and E.M. Pugh, 1961, Phys. Rev. 123, 1947. Schroeder, P.A. and C. Uher, 1978, Phys. Rev. B 18, 3884. Schwerer, F.C. 1969, J. Appl. Phys. 40, 2705. Schwerer, F.C., 1974, Phys. Rev. B 9, 958. Schwerer, F.C. and L.J. Cuddy, 1970, Phys. Rev. B 2, 1575. Schwerer, F.C. and J. Silcox, 1968, Phys. Rev. Lett. 20, 101. Schwerer, F.C. and J. Silcox, 1970, Phys. Rev. B 1, 2391. Skalski, S., M.P. Kawatra, J.A. Mydosh and J.I. Budnick, 1970, Phys. Rev. B 2, 3613. Shacklette, L.W., 1974, Phys. Rev. B 9, 3789. Shumate, P.W., R.V. Coleman and R.C. Eiwaz, 1970, Phys. Rev. B 1, 394.

804

I.A. CAMPBELL AND A. FERT

Simons, D.S. and M.B. Salomon, 1974, Phys. Rev. B 10, 4680. Smit, J., 1951, Physics, 17, 612. Smit, J., 1955, Physica, 21, 877. Smith, T.R., R.J. Jainsh, R.N. Shelton and W.E. Gardner, 1975, J. Phys. F 5, L 96. Softer, S., J.A. Dreesen and E.M. Pugh, 1965, Phys. Rev. 140, A 668. Sousa, J.B., M.R. Chaves, M.F. Pinheiro and R.S. Pinto, 1975, J. Low Temp. Phys. 18, 125. Souza, J.B., M.M. Amado, R.P. Pinto, J.M. Moreira, M.E. Brago, M. Ausloos, J.P., Leburton, P. Clippe, J.C. van Hay and P. Morin, 1979, J. de Phys. (Paris) 40, sup. no. 5, *C5--42. Star, W.M., S. Foner and E.J. McNift, 1975, Phys. Rev. B 12, 2690. Steward, A.M. and W.A. Phillips, 1978, Phil. Mag. B 37, 561. Su, D.R., 1976, J. Low Temp. Phys. 24, 701. Swartz, J.C., 1971, J. Appl. Phys. 42, 1334. Tang, S.H., F.J. Cadieu, T.A. Kitchens and P.P. Craig, 1972, AIP Conf. Proc. 5, 1265. Tang, S.H., T.A. Kitchens, F.J. Cadieu, P.P. Craig, 1974, Proceedings LT 13 (Plenum Press, New York) 385. Tari, A. and B.R. Coles, 1971, J. Phys. F 1, L 69. Taylor, G.R., Acar Isin and R.W. Coleman, 1968, Phys. Rev. 165, 621. Thomas, G.A., K. Levin and R.D. Parks, 1972, Phys. Rev. Lett. 29, 1321. Tsui, D.C., 1967, Phys. Rev. 164, 669. Turner, R.E. and P.D. Lond, 1970, J. Phys. C 3, S 127. Turov, E.A., 1955, Isv. Akad. Nauk SSSR, Ser. fiz. 19, 474. Turov, E.A. and A.N. Volshinskii, 1967, Proc. 10th Intern. Conf. Low Temperature Phys., Izd. Viniti, Moscow. Tursky, W. and K.M. Koch, 1970, Zeit. Nat. 25A, 1991. Tyler, E.H., J.R. Clinton, H.L. Luo, 1973, Phys. Lett. 45A, 10. Ueda, K. and T. Moriya, 1975, J. Phys. Soc. Japan, 39, 605. Van Elst, H.C., 1959, Physics, 25, 708. Van Peski Tinbergen, T. and A.J. Dekker, 1963, Physica, 29, 917. Vassilyev, Y.V., 1970, Phys. St. Sol. 38, 479. Valil'eva, R.P. and Y. Kadyrov, 1975, Fiz. Met. Metalloved. 39, 66. Vedernikov, M.V. and N.V. Kolmets, 1961, Sov. Phys. Sol. St. 2, 2420. Visscher, P.B. and L.M. Falicov, 1972, Phys. St. Sol. B 54, 9. Volkenshtein, N.V., G.V. Fedorov and V.P.

Shirakovskii, 1961, Fiz. Met. Metalloved. 11, 152. Volkenshtein, N.V. and V.P. Dyakina, 1971, Fiz. Met. Metalloved. 31, 773; The Phys. of Met. and Metallog. 31, no. 4, 101. Volkenshtein, N.V., V.P. Dyakina and V.C. Startsev, 1973, Phys. St. Sol. (b) 57, 9. Vonsovskii, S.V., 1948, Zh. Eksper. Teor. Fiz. 18, 219. Vonsovskii, S.V., 1955, Izv. Akad. Nauk 555 B, Ser. fiz. 19, 447. Bull. Acad. Sc. USSR, 19, 399. Weiss, R.J., A.S. Marotta, 1959, J. Phys. Chem. Sol. 9, 3202. Weiser, O. and K.M. Koch, 1970, Zeit. Nat. 25A, 1993. White, G.K. and S.B. Woods, 1959, Phil. Trans. Roy. Soc. (London) A 251, 273. White, G.K. and R.J. Tainsh, 1967, Phys. Rev. Lett. 19, 105. Williams, G., 1970, J. Phys. Chem. Solids, 31, 529. Williams, G. and J.W. Loram, 1969a, J. Phys. Chem. Solids, 30, 1827. Williams, G. and J.W. Loram, 1969b, Solid State Commun. 7, 1261. Williams, G., G.A. Swallow and J.W. Loram, 1971, Phys. Rev. B 3, 3863. Williams, G., G.A. Swallow and J.W. Loram, 1973, Phys. Rev. B 7, 257. Williams, G., G.A. Swallow and J.W. Loram, 1975, Phys. Rev. B 11, 344. Yamashita, J. and H. Hayakawa, 1976, Progr. Theor. Phys. 56, 361. Yamashita, J., S. Wakoh and S. Asano, 1975, J. Phys. Soc. Jap. 39, 344. Yao, Y.D., S. Arajs and E.E. Anderson, 1975, J. Low Temp. Phys. 21, 369. Yelon, W.B. and L. Berger, 1970, Phys. Rev. Lett. 25, 1207. Yelon, W.B. and L. Berger, 1972, Phys. Rev. B 6, 1974. Yoshida, K., 1957, Phys. Rev. 107, 396. Zen, D.Z., T.F. Wang, L.F. Liu, J.W. Zai, K.T. Sha, 1979, J. de Phys. 40, C5-243. Ziman, J.M., 1960, ELectrons and Phonons (Clarendon Press, Oxford) p. 275. Ziman, J.M., 1961, Phil. Mag. 6, 1013. Zoric, I., G.A. Thomas and R.D. Parks, 1973, Phys. Rev. Lett. 30, 22. Zumsteg, F.C. and R.D. Parks, 1970, Phys. Rev. Lett. 24, 520. Zumsteg, F.C. and R.D. Parks, 1971, J. de Phys. 32, C1-534. Zumsteg, F.C., F.J. Cadieu, S. Marcelja and R.D. Parks, 1970, Phys. Rev. Lett. 15, 1204.

SUBJECT INDEX abbreviation, see phases absorption coefficient, a, of BaO-6Fe203 as a function of wavelength 359 AC magnetization of the alnicos 18l activation energy 101, 103 of pinned wall 103 of thin wall 104 additives 462-464, 468, 476, 499, 500, 514, 522 after-effects dielectric relaxation 276 elastic relaxation 286 magnetic, spinels 249ff aging, see stability air gap 44, 46 amorphous alloys 795ff ribbons 524 Anderson localization 268 anhysteretic magnetization of the alnicos 179 anilin process 465 anisotropy C O 2+ contribution 236, 240, 247, 251 exchange 52 induced 246ff experimental data for spinels 251ff magnetic 49ff, 55 magnetocrystalline 50, 53ff, 56, 57, 102, 120, 133 magnetocrystalline constant BaCox/2Tix/2Fe12-x019 379 BaCu~Fe12-~O19-xFx 386 BaInxFel2-xO~9 376 BaNixFe12-xOa9-xFx 386 BaO.6Fe203 329-332, 376, 386 LaFe12Oi9 367 LaFeZ+Fe~-O19 367 Na0.sLa0.sFe12019 367 PbO.6Fe203 329-332 SrO-6Fe203 329-332

temperature dependence of BaScxFe12-xO19 375 magnetocrystalline, formulae 233 shape 50, 52ff alnicos 1-4, 113-120 alnico 5 and alnico 5 D G (alnico 5-7) 121-133, 149 alnicos 8 and 9 145, 149 Fe2NiA1 120, 133 single ion, spinels 235ff surface 52 uniaxial 50 anisotropy constant 67 anisotropy energy 49, 62, 85, 96 anisotropy field 49ff, 50, 446, 493, 499, 537 BaAlxFe12-xO19 373 BaCox/2Tix/2Fe12-x019 378 BaCrxFe12-xO19 373 BaGaxFe12-xO19 373 Ba(TiCo)xFe12_xO19 379 BaO.x(TiCoO3)-(6- x)Fe203 347 BaO.6Fe~O3 332-335, 349, 381 BaZnx/2Ge~/zFe12-xO19 380 B aZn:,/2Irx/2Fe12-~O19 381 BaZn2x/3Nbx/3Fe12_xO19 380 BaZn2x/3Tax/3Fe12-x019 380 BaZnx/2Tix/2Fe12-x019 347, 381 BaZr~Tir Mnz Fea2-x-r_z O19 380 BaZn2x/3Vx/3Fe12-x019 380 CaO--A1203-Fe203 375 PbO.6Fe203 332-334 SrAlxFe12-xOt9 373 SrO-xA1203.(6- x)Fe203 347 SrO-6Fe203 332-334, 374 temperature dependence of BaO.6Fe203 333 PbO-6Fe203 333 SrO.6Fe203 333 W-type compounds 433 833

834

SUBJECT INDEX

Y-type compounds 432 Z-type compounds 433 antiferromagnetic 52, 89 antiferromagnetism oxide spinels 224 antiparallel coupling 89 application of hard ferrites 535, 581, 582 plastoferrites 585, 586, 592 assemblage 463, 484 atomizer 469, 483 attritor 469, 481, 483, 485 (BH)m,x value

angular dependence 561, 564 (BpH)max value 579, 580 binder 463, 471, 483, 484, 527 blending, see raw materials, mixing Bloch wall thickness of PbO.6Fe203 358 Boltzmann constant 101 Brown's paradox 60 bubble memory 23 bubbles 21 bulk modulus K, variations with temperature BaO.6Fe203 360, 361 calcination, see reaction sintering calendering, see rolling calenders 585 calibration 510, 517 charge-density waves (in CuV2S4) 624 chemical analysis BazZn2Fe12022 (Zn2Y) 436 chemical vapour deposition 534 cobalt, effects of in alnicos 154 coercive force 334-342 angular dependence of BaO.6Fe203 361 effect of milling time on BaO.6Fe603 337 effect of packing factor on BaO.6FeeO3 336 effect of particle size on BaO-6Fe203 338 temperature dependence of (Ba or Sr)(Cu+ Ge)xFe~2-xOx9 383 (Ba or Sr)(Cu + Si)xFe12-xO19 383 (Ba or Sr)(Cu + Ta)xFe12-xO~9 383 (Ba or Sr)(Cu+ V)xFe12-xO19 383 coercivities of alnicos 1-4 112-114 alnicos 5-9 127, 131, 133 alnico 8, extra high 141 coercivity 49, 50, 59, 60 angular dependence 561, 564-566 flux 42 magnetization 41

magnetocrystalline anisotropy 66ff of antiphase boundary 92-94 of buckling mode 63 of curling mode 61, 63 of discrete sites 100 of fanning mode 65 of planar defect 87 , 88 of powder 486, 553, 566 of thin wall 94ff of twisting mode 63 of wall pinned by cavities 76, 77, 79 of whiskers 64 particle packing density 62 shape anisotropy 60ff temperature dependence 447, 551-554, 579, 580 uniform rotation 61, 63 columnar crystallization of alnico 9, 142 compass 4 compaction anisotropy 492, 540, 561 compensation material 560 complex permeability, temperature dependence of BaO.6FeaO3 344 compressive strength BaO-6Fe203 361 core loss 12 creep, by compressive deformation BaO.6FezO3 361 critical behaviour 773 stress intensity factor 573 volume for thermal stability 102 critical radius 77 cylinder 59, 63 fine particles 55ff resistivity phenomena 773ff sphere 62 upper and lower bounds 55, 59 crystal field splitting of 3d n ions in oxide spinels 202ff crystal field transitions of Cr 3+ (in CdCr2S4) 659ff of Co 2+ (in CoCr2S4) 713, 718 crystal growth, see grain growth crystal structure U-type and other compounds 402 W-type compounds 396 X-type compounds 401 Y-type compounds 397 Z-type compounds 400 crystallographic texture of alnicos and effects on magnetic properties 161 Curie constant 343 Curie temperature 74, 113, 126, 155, 156, 550

SUBJECT INDEX Ag0.sLa0.sFe12019 367 BaAlxFe12-xO19 371, 372 BaCoxFea2-xO19-xFx 386 BaCrxFelz-xO19 372 BaCuxFe12-xO19-xFx 386 BaGaxFe12-~O19 371, 372 BalnxFe12-xO19 376 Bal-~(K or Bi)x(Cu, Ni or Mn)xFe12-xO~9 383 BaNixFe12-x O19Fx 386 BaO.6Fe203 326, 327, 386 Ba(TiCo)xFe12 xO19 379 BaZnx/2Irx/2Fe12 xO19 381 BaZnx/2Tix/2Fe12-xOa9 381 Ca0.88La0.14Fe12019 367 LaFe2+Fe3~ O19 367 LaFe12019 367 Na0.sLa0.sFe12019 367 Nrel theory 222 oxide spinels 225, 296 PbO-6Fe203 326, 327 SrAI4.sFeT.2019 374 SrAlxFe12-xO19 371,372 SrO.6Fe203 326, 327 cutting 463, 584 cyclic heat treatment of alnico 5 129

DC electrical conductivity oxide spinels 260ff deagglomeration 463 Debye temperature Ba-6FezO3 361 spinel ferrites 289 demagnetization 510-512 curves 535, 539, 588, 589 curves, comparison of various materials 578, 579 curves, temperature dependence 555-557 factor 49, 53 influence of method 512 mode 56 demagnetizing field 42, 44, 53, 60 at conical pit 80 at surface defects 59 density 322, 326, 349, 384 apparent powder 464, 466, 471 green 490, 514 sintered 498, 502 tap 465, 471 uniformity 491 X-ray 575 designation, see phases dewatering 482, 494

die 489 pressing 489, 513, 584, 585 dielectric behaviour 569 dielectric constant BaNizAlxFe16-xO27 (NiA1)W 435 oxide spinels 275ff dielectric constant, real part temperature dependence of BaO-6Fe203 365 diffusion couples 472, 534 dilute ferromagnets 793 dipole 55 directional ordering 54 dispersants 483 domain observation BaO.6Fe403 354-358 domain wall detachment 92ff nucleation 59, 66, 67, 81 180 degrees 67ff, 84 pinning 59, 67, 81 thickness 62, 67ff domain wall energy 59, 67ff, 68, 334, 335 BaO.6Fe203 335, 355 PbO-6FezO3 335 SrO.6Fe203 335 domain wall mobility BaFeH.3AI0.7019 358 BaO-6Fe203 358 domain width BaO.6Fe203 355, 358 PbO-6Fe203 358 SrO.4.2Fe203-1.8A1203 355 SrO.4.5Fe203.1.5A1203 355 domain width effect of crystal thickness on BaO.6Fe203 357-358 PbO-6Fe203 357-358 SrO'6Fe303 357-358 SrO.(6- x)Fe203-xA1203 357 domain width effect of magnetic field on BaO-6Fe203 355-356 SrO-4.2Fe203-1.8A1203 355 SrO.4.5Fe203-1.5A1203 355 DS processes 519, 525 dynamic excitation of alnicos 180 easy axis 49 economic aspects of magnetism 6, 7 effects of y-phase in alnicos 138-140 elastic constants of oxide spinels 285ff elastic moduli 572 BaFe12019 361 electric conductivity ferroxplana-type compounds 434

835

836

SUBJECT INDEX

electric conductivity, temperature dependence of BaO.6Fe203 364, 365 PbO-6Fe203 364 electric steels 9-11 electrical properties of sulpho- and selenospinels 607ff ellipsoid 53 energy anisotropy 49, 57, 62, 85, 96 conversion capability 579 coupling 90 domain wall 59 exchange 57, 62, 68, 78, 85, 90, 96 interaction between magnetized bodies 47 magnetocrystalline anisotropy 56, 78 magnetostatic 49, 55, 57, 59, 62, 96 energy product 27, 42 maximum 44 of alnicos 112-114 ESR Camll2 xFexO19 370 Euler's equation 68, 84 eutectic composition 455, 458, 524 temperature 455, 458 exchange biquadratic 218, 230 constant of PbO.6Fe203 335 coupling 56 energy 57, 62, 68, 78, 85, 90, 96 coefficient 68, 69ff of body-centred cubic lattice 70, 73 of face-centred cubic lattice 71, 73 of hexagonal close-packed lattice 71, 73 of simple cubic lattice 71, 73 integrals, values in oxide spinels 218ff resonance frequency 256 striction spinels 244 exchange interaction 55, 60 between Cr 3+ ions in semiconducting sulphoand selenospinels 647ff, 701if, 728ff in metallic sulpho- and selenospinels 608, 632ff, 644ff existence range 449 extrusion 513, 515, 526, 527, 532, 584 fanning asymmetric 65 symmetric 64 far infrared absorption data oxide spinels 284 Faraday rotation BaO-6Fe203 358, 359

feed materials, s e e raw materials ferrimagnetism 216ff collinear, s e e Nrel configuration effect of diamagnetic substitution, spinels 227ff effect of magnetic field 224, 229 spiral 223ff theory, spinels 221ff triangular arrangement, s e e Yafet-Kittel configuration ferrite(s) 12 components 19 electrical properties 262ff ferromagnetic resonance data 258ff magnetization data 294ff magnetocrystalline anisotropy data 292ff magnetostriction data 294ff survey of intrinsic magnetic properties 296 ferromagnetic resonance, s e e FMR 101 ferromagnetism oxide spinels 224 ferroxdure 28 fibre texture 473, 526, 562 field anisotropy 50, 53, 60, 64 demagnetizing 42, 44, 53, 60 nucleation 66, 81 Weiss 60 filter press 469 fine particles 55ff Fisher sub-sieve-sizer 485 fluidized bed 466, 513, 525 flux density, magnetic 445 fluxes 522 FMR BaO-6Fe203 345-347 BaO-x(TiCoO3).(6- x)Fe203 347 BaZnx/2Irx/2Fe12-xO19 380-381 B aZnx/2Tix/2Fe12-xO19 380-381 SrO.xAI203(6- x)Fe203 347 FMR effect of DC field on the frequency of BaO.6FezO3 345, 346, 348 SrO-6Fe203 348 formation kinetics ferroxplana-type compounds 402 formation process BaO.6FeaO3 315-317 PbO-6Fe203 315-317 SrO-6Fe203 315-317 fracture surface energy 574 free energy magnetic 46ff reversible change 47 free drying 518

SUBJECT INDEX gangue 464 garnets 20 geometric defects 509 glass melt process 523 glassy phase 457, 499 grain growth 462, 480, 497, 498, 505-507 anisotropic 475 discontinuous 472, 498, 501, 505, 506, 517 inhibition 457, 459, 499 granulate 462, 469-471, 478, 484, 492 granulation 463, 468, 471, 472 grinding 463, 508, 513, 573, 579, 580, 584 mechanism 484, 509 gyromagnetic factor g BaO-6Fe203 348 SrO-6Fe203 348 gyrator 15 gyromagnetic ratio 102 effective 256

Hall coefficient extraordinary 752, 754, 783ff, 793 ordinary 752, 778 Hall effect 751ff extraordinary definition 754 of dilute ferromagnets 794 theory and experimental data 793 ordinary 778 planar 754 hard ferrite particles aligning 462, 463, 479, 482, 492-494, 497, 583 grain size determination 485 shape anisotropy 475, 485, 514, 518, 583 hard ferrites 443 annual mass production 577, 592 bonded 582 hardness 502, 574, 575 H - C process 519 heat capacity BaO.6Fe203 361, 362 heat treatment of alnicos annealing 112, 118, 119, 121-123, 138, 141, 142 homogenization 111, 112, 121, 123, 125, 138, 141, 142 thermomagnetic 121, 125, 130, 137, 138, 141, 142 Heisenberg model 73 hematite, s e e iron oxide, natural hexaferrites, s e e hard ferrites hexagonal ferrites 443, 454, 473

837

high field behaviour 765 history of ferrites 12 garnets 20 iron silicon alloys 10 magnetism 3 permanent magnets 24 homogeneity range 451, 454, 457, 459 homogeneous nucleation 81 honeycomb domain, stability against ternperature BaO-6Fe203 358 PbO'6Fe203 358 hot deformation techniques 525, 526, 530 pressing 489, 513, 518, 525, 528 hydrothermal method 518 hyperfine fields Fe 57 in oxide spinels 298 hyperfine magnetic field BaMg2Fe16027 423 hysteresis loop(s) 41, 44, 48, 50, 51, 67, 541543 after annealing 81, 82 after polishing 81, 82 ilmenite 467 impurities 464, 499 indirect shaping 463, 510 induction (magnetic) 445 injection moulding 484, 585 interaction domain wall with cavities 74ff domain wall with crystal lattice 81ff exchange 55, 60 magnetostatic 54 interracial energy of al and a2 phases 117 intermediate product 457, 472, 473, 476, 477, 522 internal field, temperature dependence of LaO.6F~O3 354, 368 SrO.6Fe203 352 ionic radii, list of several ions 317 iron oxide natural 465-467 synthetic 465, 468, 469 isomer shift, temperature dependence of SrO.6Fe203 352 isotropic pressing 489 Jahn-Teller effect cooperative in oxide spinels 213ff elastic constants 285

838

SUBJECT INDEX

far infrared spectra 284, 286 in Ba2Cu2Fex2022 (Cu2Y) 435 in FeCr2S4 701, 707 magnetic anneal 249, 255 Kerr rotation, as a function of wavelength BaO.6Fe203 358, 359 (K1)m/M~, temperature dependence BaO.6Fe203 339 kilns 470, 478-480, 507, 508 rotary 478, 479 kneaders 585 Kondo effect 796 Kopp's rule 288 lattice constant(s) 575 Ag0.sLa0.sFe12019 366 BaA112019 370, 385 BaAlxFe12-xO19 369 BaCozA112 xO19-xFx 385 BaCoxFelz-xO19-xFx 385 B aCo0.sZnzA19.5O16.5F2.5 385 BaCoZnAI10OlyF2 385 BaCrsFe4019 370 BaCr~Felz-xO19 369 BaCuxFelz_xO19 xFx 385 BaFe22+Ni0.58Fels.~2018.42F0.58 385 BaGa12019 370 BaGaxFelz_~O19 369 BalnxFea2-xO19 376 BaNixAl~2-xO19 xFx 385 BaNixFex2-xO19-xFx 385 BaNi0.sZn2A19.5016.sF2.5 385 BaO.6Fe203 322, 376 BaScxFe~2-xO19 376 Bal-xSr~Fe12019 368 BaZn~/zlrx/2Fe12 ~O19 380 Ca(AIFe)12019 369-370 CaA112019 369-370 Ca0.ssLa0.14Fe12019 366 LaMgGa11019 369-370 Pbl-~Ba~Fex2019 368 PblnLgFe10.1019 376 PbO-6Fe203 322 SrAl12Ot9 370 SrAl~Fe12-xO19 369 SrCr6Fe6019 370 SrCr~Fe12-xO19 369 SrGa12Ox9 369-370 SrO.6Fe203 322 Sra-xPbxFe~2019 368 temperature dependence of BaO-6Fe203 363

of

lattice defects 59, 60 leakage factor 46 light switching matrix 34 linear thermal expansion 569-571,580 liquid phase 476, 499 epitaxy 534 lodestone 4 Lorentz microscopy 94 lubricants for milling 483 pressing 492 Lurgi process 466 machining, see grinding Madelung constant oxide spinels 207 magnetic after-effect 569 of BaO-6Fe203 344 anneal 245 constant ~0 445 domain of ferroxplana-type compounds 436 hardness 443 pressure 98 viscosity 101, 102 of the alnicos 173 magnetic properties dependence on sintering temperature 503, 504 of isotropic magnets 457, 459 of powder 479 of pressed parts 491 of sulpho-, seleno- and tellurospinels 607ff primary 459, 462 magnetic structure BaCoxFelz-x O19 384 BaO'6Fe203 323-325 BaScxFe12-xO19 377 magnetization (quantity) 445 magnetization (remagnetization) 463, 510, 512, 541, 584 magnetization buckling 62, 65 changes coherent reversal 518 irreversible 550, 557-560 reversible 550, 554, 557-559, 579 curling 62, 63 in the alnicos 169 curve, initial 41 fanning . 64 field dependence of BaO-6FeeO3 330 PbO.6Fe203 329, 330

SUBJECT INDEX remanent 41, 42, 44 saturation 41 twisting 62 uniform 57 magnetizing process 341 magnetocrystalline anisotropy 120, 133 ferroxplana-type compounds 412 magnetomotoric force 46 magnetooptical effects of oxide spinels 282ff magnetooptical properties, of sulpho- and selenospinels 663, 685, 687, 711, 713, 718 magnetoresistance 776ff, 793 in sulpho- and selenospinels 607, 651ff, 657ff, 679ff, 691, 692, 708ff, 712, 715, 718, 727 ordinary 776 magnetoresistive element 32 magnetostatic energy 49, 55, 57, 59, 62, 96 of cavity 76 interaction domains in the alnicos 170 magnetostriction 54, 567 alnico 5 133, 134 alnico 5DG (alnico 5-7) 133, 134 dipole-dipole 242 linear, basic relations 234 single ion 238ff BaFe2FelrOz7 (Fe2W) 425 BaO-6Fe203 360 magnons, dispersion relation for spinels 231ff main components 464 manufacturing process hard ferrite, usual 462, 463 hard ferrite, special 513 plastoferrite 583, 584 mass efficiency 579, 580 material length l BaFe12019 358 PbFe12019 358 Maxwell's equations 43 mechanical properties of BaO-6Fe203 361 work 47 melting congruent 453 incongruent 457 point 455 techniques 519 memory cores 17 micromagnetic 55, 57, 60, 81, 84 microstructure alnicos 1--4 113 alnico 5 134, 136 alnico 8 146

839

alnico 9 146 FezNiAI 113, 118, 120 microwave linewidth W-type compounds 432 Y-type compounds 431 Z-type compounds 431 milling particle size after 484 reaction with water 488 wet 463, 472, 481,485 mills 469, 481-483 miscibility 461 mixers 585 mixing, s e e raw materials Mott's formula for variable range hopping 264 Mrssbauer effect ferroxplana-type compounds 421 AI, Cr, ZnTi, ZnGe, ZnSn, ZnZr, CuTi, CoTi, CoCr and NiTi substituted M-type compounds 353354 BaAIxFe12 xO19 370 BaO.6Fe203 351-354 BaZnxTir Mnz Fe12_x_y-zO19 380 CaAllz-xFexO19 370 LaO-6Fe203 354 PbO-6Fe203 351-354 SrAlxFea2-xOl9 370 SrO-6Fe203 351-354 Tl05La0.sFelzO19 368 M6ssbauer spectra of n9I (in CuCr2Te3I) 645 57Fe in sulphospinels 707, 715, 716, 720, 724-726, 729, 730, 733 119Sn in sulphospinels 634, 641, 711, 7'14 M6ssbauer spectroscopy of the alnicos 148 moulded alnico 149 multipole 55

Nrel configuration 222 stability conditions, spinels 222, 224 temperature, oxide spinels 225 neighbouring phases 454, 455, 458, 461 Nernst-Ettinghausen effect 792 neutral zone 491 neutralization 511 notched-bar impact test, s e e strength values, impact NMR (nuclear magnetic resonance) Y-type compounds 427 frequency temperature dependence of BaO.6Fe203 350 spin-echo amplitude versus resonance frequency, BaO.6Fe203 350

840

SUBJECT INDEX

of BaO.6Fe203 347-351 of nl'n3Cd in semiconducting sulpho- and selenospinels 666, 691 of 59Co in sulphospinels 625, 713, 736 of 53Cr in metallic sulpho- seleno- and tellurospinels 632, 636, 641, 642 of 53Cr in semiconducting sulpho- and selenospinels 666, 669, 690, 694, 710, 713 of 63'65Cu in metallic sulpho-, seleno- and tellurospinels 622, 623, 625, 626, 630, 632, 636, 641, 642 of 63'65Cu in semiconducting sulpho- and selenospinels 700, 721, 733 of 119'2°1Hgin sulpho- and selenospinels 669, 694 of rain in sulpho- and selenospinels 700 of 77Se in selenospinels 641, 691, 694 of ~2STein tellurospinels 642 of 51V in sulphospinels 624 nucleation field 66, 81 reverse domains 66, 67, 89 wall 80, 93 olivine 198 operating point 43 optical properties BaO-6Fe203 358-360 PbO.6Fe203 358-360 sulpho- and selenospinels 607, 645, 653, 659ff, 668, 673, 682ff, 692, 696, 713, 718 optical transition in oxide spinels 277ff

paramagnetic properties 342, 343 paramagnetic susceptibility, temperature dependence of BaM 342 PbM 342, 343 SrM 342 particle(s) accelerator 17 fine 55ff interactions 164--166 misalignment, effects on coercivity 163 remanence 161 orientation determination 563, 564 Peierls force 98 pellet density 471 peritectics 461 peritectoid reaction temperature 455 permanent magnet materials 443

permeability 565 permanent magnet characteristics 536, 540 influence of mechanical stress 565, 567 influence of neutron irradiation 567 optimum values 538, 585, 587, 588 temperature dependence 550 perovskite 477 phase diagram(s) 449 BaO-Fe203 310-313 BaO-MeO-Fe203 308 PbO-Fe203 313-315 SrO-Fe203 312-314 phases abbreviations 450 designations 451 phenacite 198 photoluminescence BaGaa2019 375 LaMgGa11019 375 MgGa204 375 SrGa12019 375 photon structure of sulpho- and selenospinels 664, 668, 675, 689, 692, 696, 705, 711, 713 photomagnetic effect oxide spinels 250 selenospinels 678ff, 696 pinning force 75, 79 plasticising agents 515, 527 plastoferrites 443, 479, 486, 582 Poisson's number 572 ratio of BaFe12019 361 polarization (magnetic) 445, 492 porosity 502 pot cores 14 potential energy of magnetic field 44 precursor phases, s e e intermediate product preferred direction 462, 473, 510 press forging, s e e hot deformation techniques pressed alnicos 149 presses 494, 496, 497 pressing 489 dry 463, 495, 517 orienting field 489 wet 517 pressure filtration, s e e compression moulding, wet pressure sintering, s e e hot pressing P - T diagram BaO.6Fe203 311 Fe304 311 2FeO.BaO.8Fe203 311 2FeO.SrO-8Fe203 311 pyrite 465, 467

SUBJECT INDEX quadrupole splitting, temperature dependence of SrO.6Fe203 352

raw materials 462-465, 499 coprecipitation 473, 477, 518 mixing 468, 469, 471, 472 precipitation 513, 517 reaction kinetics 462, 476 layers 473 mechanism 473, 476 model 475 product 462, 472 sequence 472, 476, 477 sintering 462, 463, 472, 477 thermal quantities 476, 477, 498 recording heads, integrated 33 reflectance spectra BaCo0.sGall.5Oas.sF0.5 386 BaNil.sAI10.5017.sF1.5 386 B aNi0.sGan.5018.sF0.5 386 relaxation, see after-effect resonance linewidth, oxide spinels 257 slowly relaxing ions (impurities) 257 reluctance 46 remanence angular dependence 510, 511, 561-563 calculation from texture 540, 562, 563 remanence, temperature dependence 551, 579, 580 of alnicos 112 of (Ba or Sr)(Cu+ Ge)xFe12-xO19 383 of (Ba or Sr)(Cu + Nb)xFel2-xO19 383 of (Ba or Sr)(Cu + Si)~Fe12-~O19 383 of (Ba or Sr)(Cu + Ta)~Fea2-xO19 383 of (Ba or Sr)(Cu + V)xF'elz-~O19 383 remanent magnetization 41, 42, 44 resistance factor 46 resistivity 751, 752ff, 762, 793, 795 anisotropy 752, 753, 779ff, 800, 850 high field 765 low temperature 762 of alloy 766ff, 793ff of amorphous alloys 795 of magnons 757 of pure ferromagnets 762 of single crystals 755 minimum 7 9 5 f f residual 764, 766 tensor 752 reversal mode 55 reverse domain at surface defect 80

841

nucleation 66, 67, 89 of cavity 78 Righi-Leduc effect 756 rigidity modulus, temperature dependence of BaO.6Fe203 360, 361 rolling techniques 513, 515, 527, 532, 584 rotational hysteresis in alnicos 177 rubber 584, 585 Ruthner process 465, 466 salt bath process 513, 523 saturation magnetization 41 ferroxplana-type compounds 404 Ba/MxFe12-~O19 370-372, 374 BaCoxFe12-xO19-xFx 384, 386 BaCrxFe12-xO19 370-372 BaCuxFel2-xO19-xFx 386 BaFz-2FeO-5Fe203 384 BaGaxFe12-xO19 370-372 BalnxFe12_xO~9 376 Bal-x(K or Bi)x(Cu, Ni or Mn)xFe12-~Oa9 383 BaNixFe12-xO19-xFx 386 BaO-6Fe203 325-328, 335, 349, 376, 384, 386 Ba(TiCo)xFela-~ O19 379 BaZnx/2Irx/2Fe12-x019 381 Ca0.88La0.14Fe12019 366 CaO-AI203--Fe203 375 LaFe2+Fe~O19 366 LaFe12019 366 Na0.sLa0.sFe12019 366 PbO.6Fe/O3 325-328 SrAI4.sFe7.zO19 374 SrAlxFe11-~O19 370-371, 374 SrCrxFelzOi9 370-372 SrO.6FezO3 325-328, 335 saturation magnetization, temperature dependence of BaO.6Fe203 326-328, 382 BaSb0.sFe 2+ 1.0Fe3+ 10.5019 382 Ba(SbFe)12019 382-383 BaSc~Felz-x O19 375 B aTi0.8Fe2+6Fe3~.8019 382 BaTiO3.5Fe203 382 BaZnxTiyMn~Fel~-~-y-~019 380 PbO'6Fe203 326-327 Sr(AsFe)12019 382-383 saturation polarization, magentic 445, 446, 462, 499, 536 of powder 487, 488 temperature dependence 446, 551 Seebeck coefficient values for spinels 269ff

842

SUBJECT INDEX

segment magnets 494, 509, 535 self cleaning effect 517 shape anisotropy of alnicos 1-4 11%120 alnico 5 and alnico 5DG (alnico 5-7) 131133, 145, 149 alnicos 8 and 9 120 FezNiA1 148 shrinkage 462, 463, 497, 507, 508, 514 ratio 502 temperature dependence 502 single crystals 755, 765, 778, 783 shunt 560 single domain particle, critical diameter of BaO.6Fe203 335, 355 BaZnx/zGex/aFetz-x Oa9 380 BaZn2x/3Nbx/3Fetz-x019 380 BaZn2x/3Tax/3Felz-xOt9 380 BaZnzx/sVx/3Felz-x019 380 PbO.6FezO3 335 SrO.6Fe203 335 single sintering techniques 513, 514 sintered alnicos 148 sintering 463, 480, 497, 513 promotion 457, 459, 514 slurry 469 small-defect-width approximation 87, 88 small-deviations approximation 85, 88 small-field approximation 87, 88 solid solution 458, 461 solid state reaction 468 solubility range, see homogeneity range specific heat 572 of sulpbo- and selenospinels 624, 626, 628, 672, 700, 708 specific resistivity 568, 569, 580 specific surface 465 spheroid, prolate 60 spin disorder scattering 757ff spin dependent Raman scattering 665ff, 689ff spin Hamiltonian 3d" ions with orbital singlets 235 values of parameters, oxide spinels 242 spin mixing 759 spinel crystal structure 609ff cation-anion distances in spinel compounds 613ff, 618 lattice parameters of spinel compounds 610ff polymorphism in spinel compounds 608 spinel structure cation distribution 208ff cation ordering 211ff crystal energy 206ff

description 191 inverse 193 ionic radii 194ff normal 193 thermodynamic properties 196ff spinodal decomposition in alnicos 1-4 115, 116 alnico 5 126 alnico 8 146 alnico 9 146 FezNiA1 115, 116 spontaneous resistivity anisotropy 752, 800 splat-cooling 522 spray drying 524 wasting 464, 525 stability chemical 445, 448, 575-577 magnetic 510, 578, 579 natural 545, 549 structural 445, 448, 550 thermal 453, 461, 545 standardization 541,545-546, 590 Stoner-Wohlfarth theory of hysteresis in alnicos 166 strength values 573, 580 substitution 450, 461 of M-type compounds with anions 384-386 suitability criterion 42ff super-exchange interactions in spinels 217ff superconductivity in sulpho- and selenospinels 623, 626, 627 superparamagnetic crystals 487 temperature compensation 560 dependence of magnetic properties of alnicos 180 influence of 100ff tensile strength, BaFex2019 361 thermal activation of wall displacement 102 agitation 101 conductivity 572, 792 excitation 101 expansion, BaO-6Fe203 362, 363 fluctuation 100 hydrolysis of salts 518 properties, oxide spinel data 288ff thermoelectric behaviour 569 effect 756, 790 thermomagnetic treatment Cahn theory of 173

SUBJECT INDEX dependence of magnetic properties on field direction 151 effects on al particles shape anisotropy 149 N6el-Zijlstra theory of 172 of alnicos 121, 125 of alnico 5DG (alnico 5-7) 129 of alnico 8 137 of alnico 8 (extra high coercivity) 141 of alnico 9 142 relationship between field direction and preferred direction of magnetization 151 thermoplastics 584 thermosettings 584, 585 thin layer techniques 534, 535 ticonal 26 titanium, effects of in alnicos 155 topotactic mechanism 475 trade marks 541, 544, 591 transport 751ff trends in magnetism research 31 two-current model 758ff two-domain state 56ff uniform rotation 49-51, 55, 60, 63, 93 units (SI, cgs) 443 valency of copper ions in sulpho- and selenospinels 618ff variational calculus 68, 91 Verwey transition 264ff volume efficiency 579, 580 volume functions of the Fe-Co rich c~l phase particles determination of the optimum value 164 in alnico 5 135, 136 in alnico 8 146

843

volumetric feeding 492 vulcanization 584, 585

wall creep 100, 104 wall energy at anti-phase boundary 90 in applied field 91ff, 95 wall nucleation at antiphase boundary 93ff at surface defects 80 wall pinning 81 at antiphase boundary 88ff at discrete sites 98ff at large cavities 76ff at line defects 99 at planar defects 83ff at point defects 99 at small cavities 78ff wall thickness 94 parameter 96 Weiss field energy 73 model 69 wettability 583 whiskers 64 working point 44, 46 X-ray absorption of Co ions 714, 721, 735 of Cu ions 620, 632, 642, 721, 735 X-ray photoelectron spectra of sulpho- and selenospinels 618, 637, 653, 719 Young's modulus E, temperature dependence of BaO.6Fe203 360-361

MATERIALS INDEX * Me = divalent metal ion, M = magnetoplumbite type compound Agl/2All/2Cr2S4 698ff AgxCdl xCr2Se~ 67%681 AgmGamCr2S4 698ff AgxHgl-~Cr2Se4 691,692. AgmlnmCr2S4 698ff AgmlnmCr2Se4 698ff Ag0.sLa0.sFe12019 366-367 AI substituted M-type compound 354, 368374, 385 alnico 39, 53, 54, 63, 64, 102, 445, 448, 578-580, 582 alnicos 1-4 111 alnico 5 121 alnico 5DG (alnico 5-7) 129 alnico 6 137 alnico 8 137, 141 alnico 9 137, 142 A1203 204, 205, 462, 464, 499, 500, 519, 522, 526, 528, 531 A1203-BaO-Fe203 454 A1EO3-BaO-Fe203-SrO 461 AI203-Fe2Oa-SrO 458 All/2CumCrzS4 698ff All/2Cul/2Cr2Se4 698ff A15/2Lil/204 614 ec-FeaO3, see Fe203 amorphous alloys 795ff B, see BaO, BxFy and BaO-Fe203 fl-A1203 444 BF 449-456, 458, 461, 473, see also BaFe203 and BaO.Fe203 BF2 450, 454, 455, see also BaO.2Fe203 and T B2F 449-451, 473, see also Ba2Fe205 B2F3 453-455, 473 BsF7 453

B7F2 450 B203 498-500, 514, 522-524, 529, 534 B203-BaO-Fe203-GeO2 524 BzO3-Fe203-GeOz-PbO 524 B203-FezO3-SiOz-SrO 524 BSF2 461 BaAll2019 370, 385 BaAlo.TFelL3019 358 BaAlxFelz-xOl9 368-375 Ba(CH3COO)2 468, 519, 521 BaCO3 444, 463, 467, 471-473, 499, 501, 515, 516, 519, 520, 522-525, 533, 534 BaC12 520 BaCoFe12-xO19-xFx 385 BaCoOaal.5018.sF0.5 386 BaCox/2Tix/2Fel2-xO19 378-379 BaCo0.sZn2AI9.sO~6.sFz5 385 BaCoZnAIa0017F2 385 Ba-Co--Zn-W 317 Ba-Co--Zn-Z 317 BaCo2Fe16027 (Co2W) 403, 434-436 Ba2Co2Fe12022 (C@Y) 406, 407, 410, 411, 414, 425, 427, 429 Ba2Co2Fee80~ (Co2X) 409, 414, 418 Ba2CoZnFe120~ (CoZnY) 403, 413 Ba2CoZnFez8046 (CoZnX) 418 Ba3CozFe24041 (Co2Z) 407, 408, 411, 414, 424, 425, 428, 436 Ba3CoL75Zn0.~Fe24041 (Coa.75Zn0.25Z) 414 BaCrsFe4019 370 BaCrxFe12-xO19 353, 354, 368-375 Ba(Cu+Ge)xFe12_xO19 383 Ba(Cu + Nb)xFe12-xO19 383 Ba(Cu+Si)xFe12_xO19 383 Ba(Cu + Ta)xFe12-xO19 383 Ba(Cu + V)xFei2-xO19 383 BaCuxFe12-xO19~ ~Fx 385 Ba2Cu2Fe12022 (Cu2Y) 435 BazCu2Fe~O4~ (Cu2X) 411 845

846

MATERIALS INDEX

Ba3Cu2Fe24041 (Cu2Z) 411 BasCuNiTi3Fe12031 (CuNi-18H) 411,420, 421 BaFeO3_x 308 BaFe204 453, 454, 518, 534, see also BF and BaO.Fe203 3+ BaFe22+Nlo.58Fe15.42018.42Fo.s8 385 BaFe2Fet6027 (Fe2W) 403, 406, 407, 411, 422, 425-427, 434 BaFe42A17.8019 454 BaFelo.92017.38 568 BaFe12019 433-448, 451, 452, 454, 455, 457, 479, 519, 522-524, 534, see also, BaO.6Fe203, BaM and M BaFe12Olg-Na20 524 BaFe12.59019.89 568 BaFe15023 453, see also BaO.FeO.7Fe203, BaO-MeO.7Fe203 and X Ba2Fe2Os 534, see also B2F BaGa12019 370, 375 BaGaxFe12-xO19 368-375 Ba-hexaferrite 55 BaInxFe12-xO19 375-378 Bal_x(K or Bi)x(Cu, Ni or Mn)xFe12-x019 383 Bal_xLaxMnO3 616 BaM 450, 536, 537, 551-553, 556-575, see also BaFe12019, BaO-6Fe203 and M Ba-Me-U 307, 309 Ba-Me-W 307, 309, 311 Ba-Me-X 307, 309, 312 Ba-Me-Y 307, 309 B a - M e - Z 307, 309 BaMg2Fe16027 (Mg2W) 405, 421-423 BaMn2Fe16027 (Mn2W) 411 Ba2Mg2Fe12022 (Mg2Y) 406, 407, 411, 414, 429 Ba2Mn2Fe12Oz~ (Mn2Y) 406, 407, 411 Ba2MnZnFe12022 (MnZnY) 407, 425 BasMg2Ti3Fex2031 (Mgz-18H) 410, 411, 420, 421 BasMgZnTi3Fe12031 (MgZn-18H) 420 Ba(NO3)2 468, 520, 521, 528 BaNil.sAlmsO17.sF15 386 BaNio 5Gan.sOls.sFo5 386 BaNio.sZn2A19.5016.sFz5 385 BaNixAl12-xO19-~Fx 385 BaNixFel2 xO19-xFx 385 BaNi2Fe16027 (Ni W) 405 BaNi2Al~Fe16-xO27 (NiA1W) 435 BaNiFeFe16027 (NiFeW) 406, 411 BaNio.sZno5FeFea6027 (Nio.sZno5FeW) 406 Ba2NiZnFe12022 (NiZnY) 413 Ba2Ni2Fe120~ (Ni2Y) 406, 411, 414 BaO 449, 450, 454, 455, 467, 468, 472, 473, 488, 522-524 BaO.4.6AI203 535

BaO-6AI203 444, 535 BaO.6.6A1203 535 BaO-CaO-Fe203 454 (BaO)x (CaO)l-x- nFe203 457 BaO-Fe203 449, 451~454, 458, 522 BaO-FeO-Fe203 454 BaO-FeO-7Fe203 308, 453, 454, 456, see also BaFelsO23, BaO-MeO.7Fe203 and X 3BaO.4FeO- 14Fe203 454 BaO.FeO.3Fe203 308 BaO.Fe203 (B) 308-310, 449-454, 456, 458, 468, 472, 474, 488, 522, see also BaFe204 and BF BaO.2Fe203 (T) 308, 309, 316, 321, 456, see also BF2 and T BaO.4.5Fe203 452 BaO-5Fe203 452 BaO-5.3Fe203 498 BaO@Fe203 453 BaO.5.5Fe203 529 BaO-5.6Fe203 484 BaO.5.9Fe203 498 BaO.6Fe203 30%366, 444, 449-453, 456, 461, 464, 468, 472, 475, 488, 522, see also BaFe12019 and BaM BaO-nFe203 449, 453 2BaO.Fe203 308 2BaO.3Fe203 308, 312, 313 3BaO.Fe203 308 5BaO.Fe203 308 5BaO.TFe203 308 7BaO.2Fe203 308 3BaO.4FeO. 14Fe203 308 BaO.Fe203-Fe203-S 456 BaO-Fe203-MeO 454, 456 BaO-Fe203PbO--SrO 461 BaO-Fe203-SiO2 457 BaO-Fe203-SrO 461 BaO-Fe203-ZnO 454 BaO-2Fe203-8Fe203 (Ba-Fe-W) 308, 311,312 BaO2 468 Ba(OH}2 468, 488, 517, 519, 521 BaO-MeO-Fe203 307, 308 BaO.MeO-3Fe203 456, see also Y BaO.MeO.7Fe203 456, see also X BaO.2MeO-8Fe203 456, see also W 2BaO-MeO-9Fe203 456, see also U 2BaO.MeO- i3Fe203 456 3BaO-MeO- 19Fe203 456 3BaO.2MeO.12Fe203 456, see also Z BaO-PbO-Fe203 367, 368 BaO-SrO-Fe203 367, 368 BaSO4 519, 523 Ba(SbFe)12019 382

MATERIALS INDEX B aSbo.sFeZ+oFe3~.5Oa9 382 BaSc~Fe~z-xO19 375 Bao.2Sro.sFe12019 575 Bao.4Sro.6Fea2019 575 Bao.6Sro.4Fe12Oa9 575 Bao.vsSro.zsFe12O19 367 Bao.sSr0.2Fe12019 575 Bal-xSr~Fea2Oa9 443, 461 (Ba, Sr)(Fe, A1, Ga)12019 535 BaTiO3-5Fe203 380 • 2+ + BaT10.6Fe 0.?,Fe310.8019 382 BaZn2A12Fe12027 405 BaZn2AIxFe12-~O27 405 BaZn2Fe16027 (Zn2W) 404, 412, 422 BaZnFeFe16027 (ZnFeW) 406, 411 Ba2Zn2Fe1202z (Zn2Y) 404, 407, 410, 411, 414, 425, 427, 429 Ba3Zn2Fe24041 (ZnzZ) 407, 408, 411, 429, 430, 433 Ba2Zn2Fe28046 (Zn2X) 409, 411,414, 416, 418, 433 Ba4Zn2Fe36Oeo (ZnzU) 409, 410, 414, 419, 430, 433 Ba4Zn2Fe52084 401 BaZn2GaFexsO27 405 BaZn2Ga3Fe13027 405 BasZn2Ti3Fe12031 (Zn2-18H) 410, 411, 419421 BaZn~/2Gex/2Felz-x019 380 BaZn~/2Ir~/2Fe12-~O19 380, 381 BaZnz~/3Nb~/3Fe~z xO19 380 BaZnzx/3Tax/3Felz-xOa9 380 BaZn~/zTi~/2Fe12 ~O19 381 BaZnxTiyMn~Felz-x-r-zO~9 380 BaZn2~/3V~/3Fea~-~O19 380 Ba-Zn-W 317 Ba-Zn-Y 317 Ba-Zn-Z 317 Bi~O3 500, 519, 522 C-steel 45 CO 477 CsH~2 477 CaAI~20~9 370 Ca(AIFe)~20~9 370 CaFesO13 454, 459 Cao.88Lao.~4Fe~zO~9 366, 367 Ca~_xLaxMnO3 616 CaO 461, 467, 519 CaO-6AI~O3 444, 475 CaO-AI~O3-Fe203 375 CaO-Fe~O3 462 CaO-Fe~O3-SrO 458 (CaO)~_~(SrO)x •nFe~O3 459

847

CaSiO3 503 CdxCol-xCr2S4 717 CdCr2S4 607, 612-615, 647,-650-654ff, 675 CdCr2Se4 697, 608, 613-615, 641, 647, 650653, 675ff CdCr2(S~-xSe~)4 696 CdCrz-xlnxS4 656 CdCrl.sTi0.2S4 656 CdCrI.sV0.2S4 656 Cdl-xCuxCr2Se4 679 CdFe204 260, 286 CdxFel-xCr2S4 656, 707, 715-717 Cdx_xFexCr2Se4 677 Cd0.98Ga0.02Cr284 657 Cdl-xGaxfr2Se4 678, 679, 682 Cdl-xHgx Cr2S4 694 Cdl-xHg~Cr2Se4 696 Cdln2S~: Cr3+ 659, 662 Cdl-xlnxCr2S4 655, 656 Cdl_xlnxCr2Se4 652, 675, 680-683, 686 Cdo.sluo.2Cr1.80C00.2S4 656 Cdo.8In0.2Cra.80Ni0.2S4 656 CdMnzO4 215 CdxZn~-xCr2Se4 695 CI 465, 466 Co 52, 762ff, 773, 776ff, 789, 790 Co alloys 766, 768, 771,772, 776, 799 Co-steel 45 Co~ 467, 472, 473, 476, 477, 498, 501, 518, 520, 523 Co-Cr, Co-Ti and Cu-Ti substituted M-type compounds 353, 354 COA1204 225, 261 CoCo2-2xMn2xOa 216 CoCrz-xlnxS4 725 CoCr2-2xMnzxO4 216 CoCr204 284, 286 CoCrxRh2-xS4 729-731 CoCr2S4 611, 613-615, 701, 703, 711ff CoCr2S4-xSex 726 ColaCrl.sSn0.1S4 714 COl_xfuxfr2S4 721,728 Coi-x (CUl/2Fel/z)xCr2S4 718 COl-xCuxRh2S4 728, 734, 735 Co~Fex-~Cr2S4 707, 714 CoFe204 196, 197, 220, 231, 242, 258, 276, 286, 288, 289, 291,296, 298 CoxFe3-xO4 248, 250-252, 269, 273, 282, 294 CoFe204 :Ti 270, 271 COl-xFe~Rh2S4 729, 730 CoFeVCr 578, 582 Co2GeO4 195, 197, 199 Coln2S4 723 CoMn204 215

848

MATERIALS INDEX

CoxMnl-xFe204 244 CoNiZn ferrite 251 COl-xNixCrzS4 722 Co304 220, 614, 626 CoRhl.5Feo.504 284 CoRh2S4 608, 612, 614, 615, 728 Co354 612, 614, 728, 736 CoS7 616 Co7/3Sb2/304 195 CozSiO4 199 CozTiO4 197 Co0.zZnl.sSnO4 205 Coo.2Znl.sTiO4 205 Cr substituted M-type compounds 353, 354, 368-375 CrAI2S4 656 CrFeCo 578, 579, 582 Crln2S4 656 CrMn204 213 CrO2 638 CrTe 616 Cu 620 CuA1Sz 618 CuA1204 205 CuCO3 620 CuC1 620 CuC12.2H20 620 CuCozS4 612, 614, 615, 619, 624ff, 736 CUCOxRhz-xS4 626ff CuCoTiS4 624ff CuCr204 215, 224, 286, 618, 620 CuCr2S4 607, 608, 611-615, 618-620, 630ff, 701 CuCr2S4-xClx 644 CuCr2S4_~Se~ 643 CuCr2Se4 607, 608, 612-615, 618-620, 630, 631, 636tt CuCr2Se4-xBr~ 645, 673 CuCr2Sea-xClx 644 CuCr2Se4_~Te~ 644 CuCr2Te4 607-609, 613-615, 618-620, 630, 631, 637, 641ff Cu~+~Cr2Te4 641ff CuCr2Te4_~I~ 645 CuCr2-~RhxSe4 636ff CuCr0.3Rhl.7-xSn~Se4 636ff Cufr2-x SnxS4 630ff CUfl'l.9Sn0.1Se4 641 CuCr2 ~TixS4 630tt CuCr2-~V~S4 630ff CuFe204 213, 215, 243, 258, 259, 269, 289, 291, 296, 618 CuFel.vCr0.304 213 Cu~Fel xCr2S4 698, 710, 718ff, 728, 732, 733 Cul/2Fel/2Cr2S4-~Se~ 726

CuxFea-xRh2S4 608, 698, 701, 728, 732, 733 Cul/zGamCr2S4 698ff Cul/zGal/zCrzSe4 698ff CuGa204 2O5 ChaxHgl-xCrzSe4 691 CumInmCr2S4 622, 698ff, 715 Cu0.5+xIn0.5-xCr2S4 700 CumInmCr2Se4 641, 698ff (C'umlnl/2)xFel_xCr2S4 715 CuxMl-xCr204 (M = Cd, Co, Mg, Zn) 216 CuMg0.sMnl.504 225 CuxMnl-~Cr2S4 718 Cul-xNixCr2S4 722 CuNiFe 578, 582 CuNi0.sMnl.504 195, 225 CuO 620 Cu20 620 CuRhMnO4 195 CuRh204 215, 225 CuRh2S4 612, 614, 615, 618, 619, 625, 626ff, 641 CuRh2Se4 613-615, 618, 619, 615~17ff, 641 CuRh2(Sl_xSe~)4 626 CuRh2_~SnxSe4 624, 627ff CuSO4-5H20 620 Cu2Se 620 CuTi2S4 610, 614, 615, 619, 620tt, 623, 625 CuV2S4 610, 614, 615, 618, 619, 621, 622ff, 625 Cu0.2Zn0.4Cd0.4Al204 205 Cu~Znl_xCr2Se4 672, 673 CuZn ferrite 275 CuZnGeO4 205 Dy 98 DyNi3 799 Dy3A12 98 F, see Fe203, BxFy, and PxFy Fe 53, 56, 63, 64, 77, 78, 80, 762ff, 773, 775, 776tt, 788, 790, 792 Fe alloys 766, 769, 771, 772, 779, 783, 787ff, 797tt Fe(CI-I3COO}2 519, 521 FeC204 519, 521 Fe(CO)5 467, 534 FeCI2 464 FeCI3 520, 524 FeCo 64 Fe~Col_~Cr204 216 FeCr2-xInxS4 724, 725 FeCr204 215, 285, 287 Fe3-xCrxO4 214 FeCrzS4 607, 608, 611,613-615, 701, 702, 706ff Fel+xCr2-xS4 726

MATERIALS INDEX FeCr2S4-xSex 726 FeCrxRh2_x$4 730 FeL1CrI.sSn0.1S4 711 Fel-sCusFel+sCuz~Ml-2~-804 (M= Co, Mg, Ni) 216 Fe2GeO4 199, 286 FeIn2S4 723 FeMnzO4 215 Fe(NO3)3 519-521 Fe-Ni-A1 alloy 45 Fe2NiA1 111 Fel-~Ni~CrzS4 722 FeO 201 FeO2 459 FeOOH 515, 521, 525 Fe203 195, 201, 444, 448-469, 471-477, 487, 499, 514-516, 519, 520, 522-525, 528, 533, 534 Fe203-2(FeO2)-SrO 459 Fe203-MeO-SrO 458 Fe203-PbO 449, 459-461, 522 Fe203-SiO2-SrO 459 Fe202~SrO 449, 457, 458, 522 Fe203-SrO-ZnO 458 Fe304 196, 197, 200, 201, 212, 213, 220, 231, 232, 235, 242, 258, 259, 262ff, 269, 270, 277, 278, 286, 287, 289, 291, 292, 296, 311, 451, 452, 457, 458, 462 Fe304: Mn 255 Fe304 : Zn 254 FeRhzS4 612, 729 FeS2 465, 467, 701 FeSO4 525 Fe2SiO4 199 Fe3S4 726 FeTiO3 467 Fe2TiO4 195, 227 Fe3-xTixO4 244 FeVzO4 196, 215, 262 Gal/2Li1/2Cr284 698ff Gd 775 GeCo204 224 GeFe204 206, 224, 225 GeNi204 224, 225 HC1 464-466, 471 H2504 466 hexaferrite 39, 49, 55 HgCr2S4 607, 612-615, 650, 652, 666ff HgCr2Se4 607, 613-615, 650, 652, 691ff HgCrz-xInxSe4 691, 692 Hgl xInxCrzSe4 692 HgxZnl xCr2Se4 696

Inl/2LimCr2S4

849 698ff

KCI 523, 524 KOH 524 K2SO4 522, 523 La(Co, Ni)5 98 LaFe2+Fe3i~O19 366, 367 LaFe12019 354, 366, 367, 368 LaMgGanO19 369, 370, 375 La203 462 LaxSrl_xMnO3 616 Lio.sAlzsO4 204, 219, 286 LiCO3 500 LiF 476 Lio.5Feo.sCr204 212 LiFeO2 476 LiFesO8 476 Lio.sFezsO4 195, 212, 220, 229, 231, 235, 238, 242, 251, 257, 260, 269, 271, 277, 282, 283, 287-289, 291, 296, 298 Lio.sFe2.504:Mn 255 Lio.sGazsO4 206, 219 Lio5Mnz504 195 LiV204 195, 261, 262 M 449-458, 460, see also BaFel2019, SrFe12O19 and PbFe12019 MS 456, see also W M2S 456, see also X MaS 456 M6S 456 MY 456, see also Z M2Y 456, see also U 2MeO-BaO-8F~O3 (2MEW) 307, 312, 316 2MeO.2BaO.6FezO3 (3MeY) 307, 309, 316 2MeO.3BaO.12Fe203 (2MeZ) 307, 309, 316 2MeO.2BaO-14Fe203 (3MeX) 307, 309, 312 2MeO.4BaO.18FezO3 (MeU) 307, 309 MeO.Fe203 309, 321,456 MgAI204 191, 197, 204, 206, 219, 260, 261, 284, 286, 287, 289, 295 MgCr204 225, 245, 648 Mga-xFexAleO4 290 Mg ferrite 252, 253, 270, 295 MgFe204 197, 209, 210, 220, 239, 242, 251, 257-259, 277, 279, 283, 288, 289, 291, 296, 298 MgFe204 : Mn 272 MgGa204 375 MgxMno.6Fez4 xO4 239, 242 MgMn204 210, 215, 269 MgO 201, 205, 499 Mg2SiO4 199

850

MATERIALS INDEX

Mg2TiO4 196, 204 MgV204 225, 262 Mg2VO4 199 MnA1 55, 89, 94 MnAIC 578, 580 MnA1204 220, 225 MnBi 578, 579 MnCr ferrite 255 MnCr204 196, 230 Mnl+2xCr2_2xO4 214, 216, 246 IVlnCrz-xInxS4 723 MnCr2S4 607, 611, 613-615, 701ff, 724 MnCr2S4-xSe~ 726 MnCr2-~VxS4 725 MnFeCrO4 230 MnFe204 196, 197, 209, 210, 230, 233, 242, 258, 259, 269, 276, 286, 289, 291, 296, 298 Mn~Fe3-xO4 213, 220, 238, 250, 253-256, 259, 260, 269-271, 273, 278, 280, 282, 293, 294 Mnln2S4 722, 723 MnMg ferrite 255, 259 Mnl-xNixCrzS~ 721,722 Mn203 195, 215, 466 Mn304 215, 224, 286 MnRh204 225 MnSb 616 MnV204 245, 262 Mn0.6Zn0.4Fe204 220 MnZn ferrite 255, 258, 259, 275 MoAg204 195 NH3 518, 520 NI-I40H 517, 519, 520 (NH4)2CO3 517, 519, 520 Na2CO3 517, 519, 510, 522, 523 NaC1 523, 524 NaF 476 NaFeO2 522, 523 Na20 524 Na0.sLa0.sFe12019 366, 367 Na2Mn2Si207 204 Na20.11AIzO3 444 NaOH 517, 520, 521, 524 NaSO4 522, 523 NazWO4 261 Nd203 462 Ni 762ff, 764, 773-776ff, 783, 788, 790, 792 Ni alloys 766ff, 772, 775, 777ff, 781ff, 786ff, 791,796ff NiAI204 261 NiCo ferrite 251 NiCo.eS4 612, 614, 736 NiCr2-xInxS4 725 NiCr204 205, 215, 285, 287

NiCrxRh2 xS4 731, 732 NiFeCo ferrite 251, 272 NiFe, Cr2_~O4 213 NiFe204 195-197, 235, 242, 257-259, 275-277, 279, 281, 286, 288, 289, 291, 296, 298 NixFe3-xO4 252, 253, 258, 259, 269-271, 282, 292, 293 NiFe2 xVxO4 228 Ni2GeOa 199, 286 Niln2S4 723 NiMn204 210 NiO 281, 499 NiRh204 215, 225 NiRh2S4 612 Ni2SiO4 199 Ni-Ti substituted M-type compound 354 NiZnCo ferrite 251 NixZnl-xCr204 285, 287 NixZnl-xCr2S4 721, 722 NiZn ferrite 243, 270, 271, 275-277, 290 PbO and PxFr PF2 460, 461, 477 PzF 460, 461, 477 PbAlxFe12-xO19 374 Pb(C2H5)4 534 PbCO3 529, PbF2 529 PbFe7.sMn3.sAlii.sTi0.sO19 444, 574 Pb2FelsMn7(A1Ti)O38 307 PbFe12019 443, 534, s e e a l s o PbO-6Fe203, PbM and M PbM 450, 536, 537, 551, 569, 574, 575, s e e a l s o PbFe12019, PbO.6FezO3 and M Pb(NO3)2 520 PbO 449, 450, 460, 461, 468, 471, 477, 507, 514, 522, 529 PbO-2Fe203 313, 315 2PbO.2Fe203 314, 315 PbO.2.5Fe203 461 PbO.!~Fe203 461 PbO-5Fe203 315, 459, 461,501 PbO.6Fe203 307-366, 444, 449, 450, 461, 464, 477, 527, 532 PbO-nFe203 449 Pd 790 Pd based alloys 775, 793ff Pt based alloys 795 PtCo 578, 579 P, see

RE-alloys 49 RE-Co 580, 582 RECo5 578, s e e a l s o SmCos RE(Co, Cu, Fe, Mn)x 578, 579

MATERIALS INDEX S 456, s e e SrO and SxFy SF 458, 459, 476 SF6 459, s e e a l s o SrFe12019 and SrO.6Fe203 S2F 457, 459, 476 S3F 457, 459 $3F2 458, 459 $4F3 457-459, 477 87F5 457-459, 461,477, 522 SO2 467 SiC 526, 531 Si3N4 527 SiO2 457, 459, 462, 464, 465, 467, 498-503, 514, 519, 522 SmCo5 45, 55, 67, 81, 83, 88, 103, 490 SmCo5.3 81 Sm2Co17 83 Smz(Coo.85Feo11Mn0.04)17 45 SnO2 499 SrAI3.8Fes.20|9 374 SrAl4.aFe7.2Ol9 374 SrAl12019 370, 458, s e e a l s o SrO-6A1203 SrAlxFe12 1019 355, 368-375 Sr(AsFe)12019 382 SrCH3(CH2)10COO2 477, 519 SrCO3 463, 467, 476, 477, 515, 516, 519, 520, 522-525, 533 SrCr6Fe6019 370 SrCrxFe12-xO19 368-375 Sr(Cu + Ge)xFe~2 xO19 383 Sr(Cu+Nb)xFe12_xO19 383 Sr(Cu+ Si)~Fe12-xOa9 383 Sr(Cu+Ta)~Fe12-xOa9 383 Sr(Cu+V),Fe12 xO~9 383 SrFeO3 x 314, 458, 459, 476, 477 SrFesA14019 535 SrFel2019 443, 448, 457-459, 479, 519, 522524, s e e a l s o SrO-6Fe203, SrM and M SrFe18027 457, 458, s e e a l s o W Sr-Fe-W 311, 313, 314 Sr-Fe-X 313, 314 Sr2FeO4-/ 459 Sr3Fe207-~ 459 Sr4Fe3Om-x 459 SrGaxFe12-~O19 368-375 SrGal2019 370, 375, 535 Sr-hexaferrite 55 SrM 450, 536, 537, 551-553, 566, 570, 571, 573-575, s e e a l s o SrFe12019, SrO-6Fe203 and M Sr(NO3)2 519, 520 SrO 449, 450, 457-459, 467, 468, 519, 522 SrO.6A1203 4 4 4 , s e e a l s o SrAl12019 SrO.2FeO-8Fe203 311-314, 457, s e e a l s o W SrO-FeO.7Fe203 458, s e e a l s o X

851

SrO.4.2Fe2Oy 1.8AlzO3 355 SrO-4.5Fe203.1.5A1203 355 SrO.5.5Fe203 501 SrO.5.9FeeO3 501 SrO-6Fe203 307, 366, 444, 449, 461, 464, 476, 522, s e e a l s o SrFe12019, SrM and M SrO.nFe203 449 3SrO.2Fe203 313, 314 Sr0.75Pb0.25Fe12019 368 SrO-PbO-Fe203 367, 368 SrSO4 519, 520, 523 Sr(SbFe)12019 382 T 456, s e e a l s o BaO.2Fe203 and BF2 Th(Co, Ni)5 98 Ticonal G 45 Ticonal GG 45 Ticonal II 45 Ticonal XX 45, 54 TiFe204 235, 285, 287 TiO2 464, 499, 519 T10.sLao.sFe12019 366-368 U

454, 456, 473,

see

2MeO.4BaO. 18Fe203

V205 499 W

450, 451, 454, 456-458, 2MeO-BaO-8Fe203 W-steel 45 X 450-454, 456-458, 461, 2MeO.2BaO- 14Fe203

461,

see

also

see also

Y

454, 456, 461, 473, s e e a l s o 2MeO-2BaO.6Fe203 Y(Co, Ni)s 98 YCos 81 Y3AI5012 204 Y3FesO12 251, 277-279, 281-283 Z

454, 456, 473, s e e a l s o 2MeO-3BaO. 12Fe203 ZnAlxCr2 xO4 285 ZnA1204 242, 260, 261 ZnCo204 626 ZnCr204 196, 285, 287, 608, 614, 647 ZnCr2-2,Mn2xO4 216 ZnCr2S4 608, 611, 613-615, 647, 652, 653ff ZnCr2Se4 608, 613-615, 647, 649, 650, 652, 653, 669tt ZnCr2(Sl-xSex)4 696 ZnCr2(Sea-xTe,)4 696 ZnFe2-2xMn2xO4 216

852

MATERIALS INDEX

ZnFe204 195--197, 225, 260, 285, 286, 288, 289, 298 ZnxFe3 xO4 270, 271 ZnGa204 204, 206, 219, 242, 284 ZnGa204 : Cr 3+ 648, 651 Zn-Ge, Zn-Ti and Zn-Zr substituted M-type compounds 353, 354 Zn2GeO4 198, 199 ZnLiSbO4 212 ZnxMl-xFe203 (M=Co, Fe, Li0.sFe0.5, Mn, Ni) 228

Zn~-xMnxCr2Se4 673 ZnMn204 215, 225, 286 ZnMn2Te4 609 ZnNbLiO4 195, 212 ZnNiSnO4 205 ZnO 534 ZnRh204 285 Zn2TiO4 204 ZnV204 262 ZrO2 526, 529, 530