Handbook of Magnetic Materials, Volume 6

Handbook of Magnetic Materials, Volume 6 Elsevier, 1991 Edited by: K.H.J. Buschow ISBN: 978-0-444-88952-2 by kmno4 PR...

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Handbook of Magnetic Materials, Volume 6 Elsevier, 1991 Edited by: K.H.J. Buschow ISBN: 978-0-444-88952-2

by kmno4

PREFACE TO VOLUME 6 The Handbook of Magnetic Materials has a dual purpose. As a textbook it is intended to help those who wish to be introduced to a given topic in the field of magnetism without the need to read the vast amount of literature published. As a work of reference it is intended for scientists active in magnetism research. To this dual purpose, the volumes of the Handbook are composed of topical review articles written by leading authorities. In each of these articles an extensive description is given in graphical as well as in tabular form, much emphasis being placed on the discussion of the experimental material in the framework of physics, chemistry and materials science. The original aim of Peter Wohlfarth when he started this Handbook series was to combine new developments in magnetism with the achievements of earlier compilations of monographs, to produce a worthy successor to Bozorth's classical and monumental book Ferromagnetism. It is mainly for this reason that Ferromagnetic Materials was initially chosen as title for the Handbook series, although the latter aims at giving a more complete cross-section of magnetism than Bozorth's book. Here one has to realize that many of the present specialized areas o1' magnetism were non-existent when Bozorth's book was first published. Furthermore, a comprehensible description of the properties of many magnetically ordered materials can hardly be given without considering, e.g., narrow-band phenomena, crystal-field effects or the results of band-structure calculations. For this reason, Peter Wohlfarth and I considered it desirable that the Handbook series be composed of articles that would allow the readers to orient themselves more broadly in the field of magnetism, taking the risk that the title of the Handbook series might be slightly misleading. During the last few years magnetism has even more expanded into a variety of different areas of research, comprising the magnetism of several classes of novel materials which share with ferromagnetic materials only the presence of magnetic moments. Most of these areas can be regarded as research topics in their own right, requiring a different type of expertise than needed for ferromagnetic materials. Examples of such subfields of magnetism are quadrupolar interactions and magnetic superconductors. Chapters dealing with these materials were included in Volume 5 of this handbook series, which appeared in 1990. In the present Volume it is primarily

vi

PREFACETO VOLUME 6

the Chapter on quasicrystals that has not much in common with ferromagnetism. Magnetic semiconductors, to be considered in Volume 7, is a further example of a class of materials with properties distinctly different from those of ferromagnetic materials, and the same can be said of substantial portions of the materials considered in the remaining Chapters of Volume 6. This is the reason why the Editor and the Publisher of this Handbook series have carefully reconsidered the title of the Handb o o k series and have come to the conclusion that the more general title Magnetic Materials is more appropriate than Ferromagnetic Materials. At the same time this change of title does more credit to the increasing importance of materials science in the scientific community. The task to provide the readership with novel trends and achievements in magnetism would have been extremely difficult without the professionalism of the NorthHolland Physics Division of Elsevier Science Publishers and I would like to thank A. de Waard and P. Hoogerbrugge for their great help and expertise. K.H.J. Buschow

Philips Research Laboratories

CONTENTS Preface to V o l u m e 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents

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

C o n t e n t s o f Volumes 1-5 List o f c o n t r i b u t o r s

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

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

1. M a g n e t i c P r o p e r t i e s o f T e r n a r y R a r e - e a r t h T r a n s i t i o n - m e t a l C o m p o u n d s H.-S. L I a n d J . M . D . C O E Y . . . . . . . . . . . . . . . . . . . . . . . . . . 2. M a g n e t i c P r o p e r t i e s o f T e r n a r y I n t e r m e t a l l i c R a r e - e a r t h C o m p o u n d s A. S Z Y T U L A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. C o m p o u n d s o f T r a n s i t i o n E l e m e n t s with N o n m e t a l s O. B E C K M A N a n d L. L U N D G R E N .................... 4. M a g n e t i c A m o r p h o u s A l l o y s P. H A N S E N . ..................... . ........... 5. M a g n e t i s m a n d Q u a s i c r y s t a l s R.C. O ' H A N D L E Y , R . A . D U N L A P a n d M . E . M c H E N R Y . . . . . . . . 6. M a g n e t i s m o f H y d r i d e s G . W l E S I N G E R a n d G. H I L S C H E R ....................

v vii ix xi

1 85 181 289 453 511

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

585

Subject I n d e x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

635

Materials Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

643

vii

CONTENTS OF VOLUMES 1-5 Volume 1 I. 2. 3. 4. 5. 6. 7.

Iron, Cobalt and Nickel, by E.P. Wohlfarth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dilute Transition Metal Alloys: Spin Glasses, by J.A. M y d o s h and G.J. Nieuwenhuys . . . . . . Rare Earth Metals and Alloys, b y S. Legvold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rare Earth Compounds, b y K . H . J . Buschow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Actinide Elements and Compounds, b y W. Trzebiatowski . . . . . . . . . . . . . . . . . . . . . . . . Amorphous Ferromagnets, b y E E . L u b o r s k y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetostrictive Rare Earth-F% Compounds, by A . E . Clark . . . . . . . . . . . . . . . . . . . . .

1

71 183 297 415 451 531

Volume 2 1. 2. 3. 4. 5. 6. 7. 8.

Ferromagnetic Insulators: Garnets, b y M . A . Gilleo . . . . . . . . . . . . . . . . . . . . . . . . . . . . Soft Magnetic Metallic Materials, b y G.Y. Chin and J.H. Wernick . . . . . . . . . . . . . . . . . . Ferrites for Non-Microwave Applications, b y P.L Slick . . . . . . . . . . . . . . . . . . . . . . . . . Microwave Ferrites, b y J. Nicolas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystalline Films for Bubbles, b y A . H . Esehenfelder . . . . . . . . . . . . . . . . . . . . . . . . . . . . Amorphous Films for Bubbles, b y A . H . Esehenfelder . . . . . . . . . . . . . . . . . . . . . . . . . . . Recording Materials, b y G. B a t e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ferromagnetic Liquids, by S . W . Charles and J. Popplewell . . . . . . . . . . . . . . . . . . . . . . .

1

55 189 243 297 345 381 509

Volume 3 1. Magnetism and Magnetic Materials: Historical Developments and Present Role in 2. 3. 4. 5. 6. 7. 8. 9.

Industry and Technology, by U. Enz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Permanent Magnets; Theory, b y H. Ziflstra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Structure and Properties of Alnico Permanent Magnet Alloys, b y R . A . M c C u r r i e . . . . . . Oxide Spinels, b y S. Krupidka and P. Novd*k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental Properties of Hexagonal Ferrites with Magnetoplumbite Structure, b y H. Kojima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of Ferroxplana-Type Hexagonal Ferrites, b y M . Sugimoto . . . . . . . . . . . . . . . . Hard Ferrites and Plastoferrites, b y H. Stiiblein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sulphospinels, b y R . P . van Stapele . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transport Properties of Ferromagnets, b y L A . Campbell and A. Fert . . . . . . . . . . . . . . . .

ix

1

37 107 189 305 393 441 603 747

x

CONTENTS OF VOLUMES 1-5

Volume 4 1. 2. 3. 4. 5.

Permanent Magnet Materials Based on 3d-rich Ternary Compounds, b y K . H . J . Busehow Rare Earth-Cobalt Permanent Magnets, b y K . J . Strnat . . . . . . . . . . . . . . . . . . . . . . . . . Ferromagnetic Transition Metal Intermetallic Compounds, b y J.G. Booth . . . . . . . . . . . . . Intermetallic Compounds of Actinides, b y V. Sechovsk~ a n d L. Havela . . . . . . . . . . . . . . . Magneto-optical Properties of Alloys and Intermetallic Compounds, b y K . H . J . Buschow . . .

1

131 211 309 493

Volume 5 1. Quadrupolar Interactions and Magneto-elastic Effects in Rare-earth Intermetallic Compounds, 2. 3. 4. 5. 6.

b y P. M o r i n a n d D. S e h m i t t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magneto-optical Spectroscopy of f-electron Systems, b y W. R e i m a n d J. Sehoenes . . . . . . . . INVAR: Moment-volume Instabilities in Transition Metals and Alloys, b y E . E Wasserman . Strongly Enhanced Itinerant Intermetallics and Alloys, b y P . E . B r o m m e r and J . J . M . Franse . First-order Magnetic Processes, b y G. A s t i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Superconductors, b y O. Fischer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

133 237 323 397 465

chapter 1 MAGNETIC PROPERTIES OF TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

Hong-Shuo LI and J. M. D. COEY Department of Pure and Applied Physics Trinity College, Dublin 2 Ireland

Handbook of Magnetic Materials, Vol. 6 Edited by K. H. J. Buschow © Elsevier Science Publishers B.V., 1991

CONTENTS 1. I r t r o d u c t ! o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. C o m p o u n d s w i t h s t r u c t u r e s r e l a t e d fo N a Z n 1 3 . . . . . . . . . . . . . . . . . 3. C o m p o u n d s w i t h s t l u c t u r c s r e l a t e d fo T h M n 1 2 . . . . . . . . . . . . . . . . . 3.1. O y s l a l s t r u c t u r e . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. A l l o ) s r i c h in F e o r C o . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 M a g n e t i c p r o p e r t i e s . . . . . . . . . . . . . . . . . . . . . . 3.2.1.1. N o n m a g n e t : c ~are e a r t h s . . . . . . . . . . . . . . . . . 3.2.12. M a g n e t i c r a r e e a i t h s . . . . . . . . . . . . . . . . . . . 3.2.2. Ce ercivi~y . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. A l l c y s rich in A1 . . . . . . . . . . . . . . . . . . . . . . . . . .

3 4 6 6 8 8 13 22 31 33

3.3.1. RT4AI8 . . . . . . . 3.3.2. R F e 5 A17 . . . . . . . 3.3.3. RT6A16 . . . . . . . 4. C o m p o u n d s w i t h , t l u ~ t u r e s r e l a : e d fo 4.1. R T 9 S i 2 . . . . . . . . . . 42. RTloSiCo.5 . . . . . . . . 5. C o m p o u n d s w i t h s t l u c t u r e s r e l a t e d lo 5.1. R 2 T 1 7 C 3 _ ~ . . . . . . . . 5.2. R 2 T l v N 3 - ~ . . . . . . . . 6. C o m p o u r d s w i t h s t l u c t u r e s 1elated ~o 6.1. R T 4 B . . . . . . . . . .

34 39 40 41 41 42 43 43 46 49 50

. . . . . . . . . . . . . . . . . . . . . . . . . . . BaCdl~ . . . . . . . . . . . . . . . . . . . . . . . . T h 2 Z n l v o r ~/h2Nil7 . . . . . . . . . . . . . . . . . . CaCu 5 . . . . . . . . . . . . . . .

. . . .

. . . .

. . . . . . .

. . . . . . .

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

. . . . . .

. . . . . .

. . . . . .

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

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

62. R3CollB4, R2CoTB 3 and RCoaB z . . . . . . . . . . . . . . . . . . . 6.3. C e T P t 4 (T = C u , G a , R h , F d e r P t ) . . . . . . . . . . . . . . . . . . . 7. C o m p o u n d s w i t h ~,tJuctures l e l a t e d fo C e N i 3 . . . . . . . . . . . . . . . . . 8. C o m p o u n d s w i t h | e r n a r y s t r u c l r r e t y p e s . . . . . . . . . . . . . . . . . . . 8.1. R 3 F e 6 2 B 1 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. R C o l 2 B6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3. R 2 T 2 3 B 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4. R 2 T 1 4 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5. R T 6 S n 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6. R1 +~T4B4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7. R 6 T l l G a 3 ~ n d N d 6 F e 1 3 S i . . . . . . . . . . . . . . . . . . . . . . 8.8. R 2 T l z P 7 a n d R C o s P 5 . . . . . . . . . . . . . . . . . . . . . . . 8.9. R A u N i 4 a r d C e l + x l n l _ x P t 4 . . . . . . . . . . . . . . . . . . . . . 9. C o n c l r s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54 55 55 56 56 56 57 58 64 65 67 69 71 71 75

1. Introduction

The magnetism of pure elements concerns the properties of about 20 metals, mostly from the 3d or 4f series. Binary intermetallic compounds are much more numerous. Magnetic binaries may involve one or both elements with magnetic moments (and even a few examples where both constituents are individually nonmagnetic, e.g., ZrZn/). Composition adds a further dimension, with many binary diagrams exhibiting ranges of solid solubility and a number of intermetallic phases, each with its particular structure. Sometimes, the distinction is a matter of site preference, e.g., ordered substitution of one quarter of the sites of the fcc structure leads to a Cu3 Autype structure (space group Pm3m) compound, whereas complete disorder produces an A75B25 fcc solid solution. The magnetic properties of binary intermetallic compounds, usually involving a 3d or 4f element, and sometimes both, have been reviewed by many authors (Taylor 1971, Wallace 1973, 1986, Buschow 1977, 1979, 1980, Kirchmayr and Poldy 1979, Buzo et al. 1991). Ternaries are at another level of complexity, with three elements and two composition variables. In magnetic ternaries, usually one or two of the constituent elements are magnetic. The structure is sometimes a specific ternary structure, unrelated to any known binary structure type (e.g., NdzFe14B). Otherwise, the ternary may be related to a binary by preferential occupation of one of the sites (e.g., CeCo3B/is related to CaCus by substituting B on the 2c sites of the latter structure). Degrees of preferential ordering of elements over the sites are possible; the extreme is a pseudo-binary, where two of the elements substitute at random over a set of sites, while the third has a unique site occupancy. Another way of generating a ternary structure from a binary is by introducing small interstitial atoms X, such as carbon or nitrogen in YzFe17X3_~, which are interstitial ternary phases. In the search for novel compounds, theories predicting the stability of intermetallic phases, like Miedema's 'macroscopic atom model' (de Boer et al. 1988c), Pettifor's structure maps (Pettifor 1988), and the structural stability diagrams of Villars (1985a,b) provide helpful guidelines. The parameter values which are assigned to the elements in these models give an impression of the chemical similarity of the elements. They are useful when trying substitutions in well-known compounds. Out of approximately 100 000 possible ternary systems, phase diagram information is available on fewer than 6 000 of them. Often, this information is far from complete, relating to only a single isothermal section or a limited compositional field. Therefore, it is

4

H.-S. LI and J. M. D. COEY

reasonable to suppose that many novel ternary structure types are still awaiting discovery. In the circumstances, it is inevitable that our knowledge of the magnetic properties of ternary compounds is far from complete. Some systems have been studied in great detail, others hardly at all. The systems of most interest magnetically involve a 3d element, and a 4f element, the other component being a metal or metalloid, particularly boron or carbon. Oxides and chalcogenides are generally nonmetallic, and they are treated elsewhere. Compounds with the Nd2Fe~4B structure are of particular importance, and they have already been discussed by Buschow (1988c). Here, in sections 2-7, we present in order of decreasing transition-metal content the magnetic properties of ternaries with structures related to a binary structure type. The true ternary compounds are discussed in section 8. Work on the magnetism of these compounds has often been inspired by the search for new materials for highperformance permanent magnets. The iron-rich ThMn12-structure compounds, the interstitial R2T17X 3_~ carbides and nitrides and the R 2 T~4C ternaries have all been studied with this in mind. Other ternary compounds of comparatively low transition-metal content are discussed by SzytuIa, chapter 2 in this volume.

2. Compounds with structures related to NaZn13 The cubic NaZnla structure (space group Fm3c) has Na on 8a, and Zn on 8b and 96i sites. The only rare-earth-transition-metal binary with this structure is LaCo13, which is ferromagnetic with a cobalt moment of 1.58#B and Curie temperature Tc = 1290K (Buschow and Velge 1977). Among the rare-earth-3d compounds it has the highest 3d-metal content and is of potential interest for application. The structure type can be stabilized for other 3d elements, including Fe and Ni, by substituting Si or A1. The cubic La(Fel_xSix)~3 phase is found to be formed for 0.12 < x < 0.19 (see table 2.1). Magnetic studies showed that Tc increases with x in this range (Palstra et al. 1983). For La(Fet~Sia) (x = 0.15), Tc is 230K and the average iron moment is 1.95#B. There is apparently no site preference of iron or silicon for the 8b site, so these alloys should be regarded as pseudo-binaries rather than ternaries. La(Nil~ Si2) is a Pauli paramagnet. La(Fet -xAlx)~3 compounds can be stabilized with x between 0.08 and 0.54 (Palstra et al. 1985). At high x values (0.38 < x ~5.0 [4] [9] [9] [9] [4,21] 2.8 [4, 21] [4] [21]

12

H.-S. LI and J. M. D. COEY TABLE 3.1 (continued)

Compounds Yl.lFel0Mo2 CeFexo Feao Mo 1.~ NdFeloMol. 5 SmFeloMol. s GdFelo Mot.5 DyFeloMoa.5 ErFeao Moa.5 YFeloMol. 5 SmFesCo/Mo z

a (•)

c (A)

8.568

4.790

SmFelo.5 W1.5 GdFelo.sWx.2 GdFelo.5 W1.5 GdFelo.4Wo.sMs.s GdFelo.sWo.5 Mo YFe~o.sW1.5 YFelo.sW1.2 YFeloW2 NdzFejoW/ SmFeloW 2 GdFeloW2

8.557 8.540 8.565 8.561 8.569 8.516

4.791 4.773 4.777 4.780 4.786 4.763

8.548 8.553 8.549 8.549

4.779 4.740 4.780 4.780

GdFeloMnz Nd2FeloMn2 Nd(Coo.s Mno.5)12 Nd(Coo.6 Mno.4)a2 Nd(Coo.7 Mno.3)~e

8.494 8.604

4.759 4.695

GdFesA14 GdFeloA12

8.57 8.49

Tc (K) 360 358 458 475 478 415 381 408 490 520 570 550 550 500 500 500 500 547 532 569

*at 77K. "~References: [1] Hu et al. (1989a). [2] Liu et al. (1988). [3] Yang et al. (1989a). [4] Christides et al. (1988). [5] Yang et al. (1989b). [6] Kaneko et al. (1989). [7] Solzi et al. (1989). [8] Chin et al. (1989a). [9] Buschow and de Mooij (1989). [10] Chin et al. (1989b). [11] Yang et al. (1988a). [12] Xing and Ho (1989). [13] Yang et al. (1988b). [14] de Boer et al. (1987). [15] Ohashi et al. (1988a). [16] Wrzeciono et al. (1989). [17] Ho and Huang (1989). [18] Chin et al. (1989b).

13.5

12.7 15.32

20.82 14.5 11.29

[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]

/~oHa (T) 293K

Ref.1" [4] [33] [33] [33] [33] [33] [33] [33] [35]

[9] [9,22] [9] [9] [9] [9] [22,23] [9] [18] 2.47 [8] 2.52 [8]

7.81 9.5

2.17 [8] [18] [26] [26] [26]

6.07 10.6

[19] [19]

0.37 5.14 11.16

385 498

4.2K

2.1

445 5 128 370

4.95 4.89

M~(/tB/f.u.) 4.2K 293K

Wang et al. (1988). Cochet-Muchy and Pai'dassi (1989). Christides et al. (1989a). Verhoef et al. (1988). Buschow et al. (1988a). Sinha et al. (1989a). Yang and Cheng (1989). Allemand et al. (1989). Yang et al. (1990a). Yang et al. (1990b). Jurczyk and Chistyakov (1989). Christides et al. (1990). Christides et al. (1989b). Baran et al. (1990). Mfiller (1988). Zhang and Wallace (1989). Christides (1990). Coey et al. (1991c).

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS

13

approximately 2.0 T, except for the Sm compounds which have a room-temperature anisotropy field around 10T. This large anisotropy field in SmFellTi is due to an unusual increase of A20 compared to other rare-earth compounds, which is only partly explained by J-mixing effects for the Sm 3 + ion (Li et al. 1988b, Kaneko et al. 1989, Moze et al. 1990a). The sign of A2o is changed by the presence of interstitial nitrogen (Yang et al. 1991, Coey et al. 1991c) or carbon (Hurley and Coey 1991). (e) These series show a variety of spin reorientations when there are contributions to the anisotropy from the iron sublattice and the rare-earth sublattice of comparable magnitude and opposite sign. Figure 3.3 summarizes the magnetic structure diagram for the R(Fet~Ti) series (Hu et al. 1989a). As these spin reorientations reflect the different thermal variations of crystal-field terms of different order acting on the rare earth, they can be used to determine the crystal-field parameters in an accurate way. 3,2.1.1. Nonmagnetic rare earths. The magnetic moments of 3d transition elements depend in a complex way on the local density of electronic states, reflecting the nature, number, distance and spatial configuration of the neighbouring atoms. These features are taken into consideration in band-structure calculations based on the real structure and site occupancies. Calculations using the augmented spherical wave method (neglecting spin-orbit coupling) have been performed by Coehoorn for the hypothetical YFe12 end-member and YFesM4 (M = Ti, V, Cr, Mn, Mo or W) R(Fe]l Ti ) V

I

Nd

ilililiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiilililililil

1

I

Sm Gd

ilililililili i i iliSi i!i i2i i i i i i i i i!i i i i i i i I iiiii!i!i!iiiiiliiiiiiiiiiiiiiii!iiiill Dy Tb

Ho Er

!iiiiiiiiilililil

I I I

Tm Lu I

i

i

0

200

400

I I

I

I

I

i~

600

T(K)

bl II c-axis

Iv[a. c-axis

complex

Fig. 3.3. Temperature dependence of magnetic phases for RFellTi series, results by Hu et al. (1989a).

14


TABLE 3.2 Fe moment on the three different crystallographic sites of the ThMn12 structure, determined by neutron diffraction and 57Fe M6ssbauer spectroscopy (conversion factor was taken as 15.7T//tB). The theoretic results are included as well. Compound

Method

#Ve(#B) at 4.2K 8f

8i

8j

1.53(5) 1.80 1.32(3) 1.23(3)

1.70(9) 1.92 1.74(3) 1.67(3)

1.16(11) 2.28 1.51(3) 1.43(3)

Re~t

[1] [2] [3,4] [3,4] [5]

YFeloV2 YFellTi YFellTi LuFellTi YFe~oMo2

Neutron Neutron M6ssbauer M6ssbauer M6ssbauer

1.83(7)

1.95(13)

1.50"(3) 1.43"(3) 1.16

1.97"(3) 1.75"(3) 1.90"(3) 1.67"(3) 1.92 1.55

YFeloV 2 YFexoV2

M6ssbauer Calculation

1.25 1.68

1.75 2.1

1.47 1.99

[5] [6]

YFeloCr 2 YFeaoCr 2

M6ssbauer Calculation

1.20 1.77

1.82 2.23

1.57 2.08

[5] [6]

YFe 12 YFe12

Extrapol. Calculation

1.77 1.86

2.31 2.32

2.17 2.26

[5] [7]

YFe8 V4 YFesV4

Extrapol. Calculation

0.75 1.41

1.24 -0.57

0.81 1.48

[5] [7]

*at 77K t References: [1] Helmholdt et al. (1988). [2] Yang et al. (1988c). [3] Hu et al. (1989a). [4] Hu et al. (1989b).

t.52(16)

#Fe(PB) at room temperature 8f 8i 8j

[5] Denissen et al. (1990). [6] Jaswal et al. (1990). [7] Coehoorn (1990a).

(Coehoorn 1988, 1990b), and by Jaswal et al. for Y F e l o M 2 (M = V or Cr) (Jaswal et al. 1990). M o m e n t s are 1.86pB, 2.32#R and 2.26#B for 8f, 8i and 8j sites in YFe12 (table 3.2), respectively. All binary Y - F e c o m p o u n d s are weak ferromagnets, meaning that both 3d T and 3d ~ states are occupied at the Fermi level. The formation of magnetic m o m e n t s in alloys, both crystalline and a m o r p h o u s , of the transition metals Fe and Co was interpreted by Friedel (1958) and developed by Terakura and K a n a m o r i (1971, T e r a k u r a 1977), Williams et al. (1983) and M a l o zemoff et al. (1984). W h e n b a n d calculations are impracticable, some pointers are provided by the magnetic valence model (Williams et al. 1983, M a l o z e m o f f et al. 1984), which assumes strong ferromagnetism (i.e., only 3d ~ states lie at the Ferni level) and ignores details of the crystallographic environment. The magnetic m o m e n t depends only on the composition, via the total n u m b e r of electrons. The magnetic valence of an a t o m Z m is defined as 2N~o-Z, where N~ is supposed to be 5 for the late 3d elements (Fe, Co and Ni), but it is zero for the early transition elements, the rare earths and the metalloids, e.g., B, C, A1 or Si. Z is the chemical valence. The average atomic m o m e n t is given by a simple formula < # ) = Uo6 + N~(A~ U 6 + A 6 4 U 6 - , ) ,

(13)

where the numerical factors {N~} are N O= Gk

(3 IIC (~° 113>,

N[ = (Gk/~/2 c~ql)(3 IIC (k)II3),

(14)

TERNARY RARE-EARTHTRANSITION-METALCOMPOUNDS

31

and the crystal-field coefficients {Ag}, defined by eqs. (13) and (14), are related to {At) } by

A ° = Ako, A~=(-1)q(A~ ) --LCXkql,;A(S)] ( q > 0). A~q = [A(e) ~,-O-kq±T ;A(s)'~ J,Z~-kq)

(15)

The matrix elements for Racah operators are (Wybourne 1965)

< 4f"LSJMIUkl4fnL'S'J'M'> = (--1)S-M+L+S+J'+kE(2J "4- 1)(2J' + 1)] 1/2 x ( JkJ' k-MqM'

"~L'Lk / [ J J ' S J 7.0

8.056

22.78

* Values at maximum applied field of 7 T ? References: [1] Li et al. (1990). [2] Allemand et al. (1990).

14.2 16.1 15.6

2.3 2.7 5.5

(Bhf) (T) 8.9 12.4 22.8

#Fe (/~B) Ref.'[ 0.60 0.84 1.54

[1] [1] [1] [2]

TERNARY RARE-EARTH TRANSITION-METAL C O M P O U N D S

15

69

Pr~

R=Sm

112 :::L

T = 300 K 0

20

10 T

0

Sm

,

I

2

,

L

4

,

I

,

.

6

~o H (X) Fig. 8.11. Magnetization curves on magnetically aligned R 6Ga 3 Fell (R = Pr, Nd or Sm) powder samples. External fields were applied perpendicular to the alignment direction (Li et al. 1991).

8.8. R2TleP 7 and RCosP5

The ternary system of R - T - P (T = Fe, Co or Ni) contains many compounds which crystallize with about a dozen different structure types (Reehuis and Jeitschko 1989). Systematic investigations of the magnetic properties were reported by Jeitschko, Reehuis and their co-workers on the series RT2P2 (Jeitschko and Reehuis 1987, Reehuis and Jeitschko 1987, M6rsen et al. 1988, Reehuis et al. 1988b), RCo8P5 (Reehuis et al. 1988a) and R2 T12 P7 (Reehuis and Jeitschko 1989). Among these rareearth-transition-metal phosphide ternary series, R2TIEP 7 and RCosP5 are richest in transition metal and rare earth. R2 T12 P7 compounds crystallize in the Zr2 Fe12 PT-type structure (space group P6) (Jeitschko et al. 1978), see table 8.8. Rare-earth atoms occupy the two Zr crystallographic sites, which have very similar local environments. The transition-metal atoms are distributed over four different crystallographic sites. The iron atoms carry essentially no magnetic moment and Lu2 FelfP7 is weakly paramagnetic with a minimum of the susceptibility of X = 4.3 x 103 m~ 3 mo1-1 at about 100K. The magnetism of these compounds is, thus, dominated by the magnetic properties of the R atoms. In contrast, all cobalt compounds order ferromagnetically with Curie temperatures of between Tc= 142K (Pr2Fe~2P7) and Tc = 160K (Ho2FelEPT). The magnetic moment per Co atom deduced from LUECO12P7 is 1.14 +_0.02/zB, similar to the value (1.44#B) obtained for the cobalt atoms in RCo2P2 (Mrrsen et al. 1988). It is worth

H,-S. LI and J. M. D. COEY

70

TABLE 8.8 Structural and magnetic data for R2TI2P7 (T = Fe or Co) compounds, results by Reehuis and Jeitschko (1989). Compound

a (A)

c (A)

Ce2 Fe12 P7 Pr2Fe12P 7 Nd2Fe12P7 Sm2Fe12P7 Gdz Fex2 P7 Tb/Fe12 P7 Dyz Fe12 P7 Ho2 Fe12 P7 Er 2Fexz P7 Tin2 Fe12 P7 Yb2 Fe12 P7 Lu2 Fe12 P7

9.132 9.198 9.190 9.167 9,140 9.129 9.118 9.109 9.100 9.098 9.091 9.083

3.6728 3.689 3.683 3.6670 3.6562 3.6428 3.6393 3.6363 3.6293 3.6250 3.6210 3.6146

Ce2 Co12 P7 Pr2Co12P v Nd2 Co12 P7 Sm2 Co1~ P7 Eu2 Co12 P7 Gd2Co12P7 Tb2 Colz P7 DY2Co12 P7 Ho 2Co 12P7 Er2 Co12 P7 Tm2 Colz P7 Yb2 Co 12P7 Lu2 Co12 Pv

9.077 9.129 9.109 9.083 9.078 9,068 9.049 9.046 9.043 9.032 9.025 9.020 9.018

3.651 3.665 3.649 3.628 3.6265 3.617 3.609 3.603 3.5997 3.5918 3.5859 3.5793 3.576

Tc(K)

/~3d(PB)

Pgf (#B)

0 (K)

3.8 3.8 2.0 7.8 9.7 10.6 10.9 9.5 7.5 4.5 48 136 140 148 151 145 150 152 152 146 147 134 150

10 3 3 5 5 4 3 7 0

1,21

56 142 147 153 156 154 158 159 160 155 155 142 158

3.5 3.5 1.9 4.1 8.1 9.9 10.5 10.4 9.5 7.4 4.2 1.14

noting that the maximum Curie temperatures occur for the rare earth with the highest moment, Dy2FelePT and HozFe12PT. A similar correlation was observed in the ternary carbide series R 2 Cr2C3 (Jeitschko and Behrens 1986). RCo8 P5 compounds for R = La, Pr or Eu are found to crystallize in the LaCo8 P5type structure (space group Proton), see table 8.9. The rare earth occupies one crystallographic site and the cobalt atoms occupy five inequivalent sites (Reehuis et al. 1988a). The cobalt atoms are not magnetic and LaCo8Ps is a Pauli paramagnet. The susceptibility of LaCos P5 exhibits Curie-Weiss type behaviour, and indicating ferromagnetic order of the praseodymium atoms at below 20K. Europium in LaCo8 Ps is divalent. TABLE 8.9 Structural and magnetic data for RCosP 5 compounds (Reehuis et al. 1988a). Compound

a (•)

b (A)

c (/~)

LaCosP 5 PrCos Ps EuCo s Ps

10.501 10.479 10.526

3.596 3.570 3.559

9.342 9.295 9.321

/~eff(#B)

0 (K)

Z = 1.62 x 10 -9 m3/f.u. (300K) 3.67 (3) 20 (1) 7.70 (8) 6 (I)

TERNARY RARE-EARTH TRANSITION-METAL C O M P O U N D S

71

8.9. RAuNi4 and Cel+xlnl-xPt4 The RAuNi4 compounds (R = heavy rare earths) and Cel + x l n l _ x P t 4 (0 ~<x y ~>z, x + y + z = 1) occur only for x ~0.05. (2) From a magnetic point of view, solid solutions between isostructural end members and the existence of long isostructural series with many rare-earth elements, permit a more systematic approach to the experimental study of magnetism than is possible for simpler structures. Ternary compounds with useful magnetic properties (i.e., those that are ferromagnetic with Tc > 300 K) are found only when the concentration of Fe, Co or Ni is sufficiently large. Alloying, whether with rare earth and early transition metals or metalloids tends to destroy the 3d moment. The magnetic valence model (presented in section 3.2.1.1) relates the average atomic moment to the electron concentrations via the average magnetic valence, assuming strong ferromagnetism. All the data collected in fig. 9.1 show the general tendency predicted by the model for Nsp ~ 0.6-0.8. In particular, all the cobalt-rich alloys appear to be strong ferromagnets, whereas a number of the iron-rich compounds, including ~-Fe, R2Fe17, RFeuTi, RFeioM2 and RFeloSiCo.s, are weak. Increasing (y + z) pushes the iron compounds towards strong ferromagnetism, but dilutes the magnetization in all cases except for R2 Fei7 Cx and R2 Fe~7Nx. (3) As in binaries, there is a tendency for cobalt-rich compounds to have higher Curie temperatures than either iron or nickel counterparts. In fact, the Co-Co exchange tends to be rather independent of structure or cobalt moment, in the range 130K < J < 150K. By contrast, the iron-iron exchange is unpredictable. In some structures such as 2:17, where it is unusually low, it may be greatly increased by interstitial modification. (4) The 3d magnetocrystalline anisotropy in uniaxial crystals is generally opposite in sign for isostructural iron and cobalt compounds. (5) The magnetocrystalline anisotropy of rare-earth-transition-metal intermetallic compounds is frequently dominated by the rare-earth contribution. When the rareearth ion possesses an orbital moment, the crystal-field parameters of the rare-earth sites are then the key to understanding magnetocrystalline anisotropy. There has been some progress towards calculating these parameters accurately in metals from first principles (Coehoorn 1990a,b). Also, Coehoorn has shown that a qualitative estimation of the sign and magnitude of A2o is better obtained from values of the charge density at the boundaries of the cell surrounding the rare-earth atom than from traditional point charge calculation, which fail in metals because the electric field gradient is mainly created by the rare earth's own 6p and 5d electrons. The charge density at the edge of the atomic Wigner-Seitz cells is described by the Miedema parameter nws, which generally shows n o simple correlation with the electronegativity (fig. 9.2). It is concluded that -~2o is positive if neighbours with highest nw~are on the z-axis through the R-atom and that -~2o is negative if they are in the x-y-plane around the R-atom. Experimental methods for determining the crystal-field coefficients include the single-crystal magnetization or torque measurements, inelastic neutron scattering and measurements of rare-earth hyperfine interactions, particularly by M6ssbauer spectroscopy. The last technique provides only the leading, second-order terms -42o and ~22~-(c)from the electric field gradient

TERNARY RARE-EARTH TRANSITION-METAL COMPOUNDS i

i

i

i

73

L it it

Y (Fe0.30-o0.7) 11Ti Y (Fe0.5C°0.5) 11Ti X (Fe0.7C°0.3) 11Ti 4 x (Fe 0 .8Co0.2) 11 Ti 1

i

2 3

2.5

/ it

2NTsp = 0.8/"

5 Y (Fe0.9C°0.1) 11 Ti

6

i

,,/

t

/

,/0.6 /

Y (Fe0.92Ni0.08) Ii Ti

7 X (Fe0.8Ni0.2) 11 Ti

/

8 Y (¥e0.7Ni0.3) 11 Ti

I /

9 YFe8.5V3.5

2.0

tl ,i

/

I0 ~ez0v2 11 YFeg. 4V2.6

/ i ,

Ct~

i•

I'

(I

'

Fe

/ tI i i

/ t /

/ b Lu2FeI4B

YFel0. sWI.~'A ff'ALu2Fel4C / '~,~ 5

1.5 A -A V

///'-~

Y2co14~// ~//

,'

,'

~'Z/

1.0

8

~ez0.5vL

"

• c,,r~losieo.5

7./,o' .1/

0.5

5

. YFel0Si2

o.

14 Yg.l.sC02.sB

/'Ni

t~ / / YCo~B y Co~I2B6, '

15 LuFe2Co2B 16 LuFe3CoB

tt t• i i iI tI iI

0.0

iI

iI /

-015

010

015

1.'0

115

2.0

Fig. 9.1. Plot of the average atomic moment (#) against the average magnetic valence (Zm) for some ternary R-T-X (T = Fe, Co or Ni and X = B or C).

(EFG) at the nucleus. Many ternary alloys have been examined using 155Gd M6ssbauer spectroscopy, which has the advantage that there is no 4f orbital contribution to the field gradients, so the results are only from the contributions of the lattice, including conduction electrons, and is, therefore, proportional to the electric field gradient acting on the 4f electrons, which produces the second-order crystal field interactions. "~20 and x(o) ~22 are related to the principal component of EFG by the following expressions A2o

=

--

¼lelV=/(1

__

y~);

-

-(c)

[A2o/Az21

=

rh

(18)

74


where -lel is the electronic charge and ?o is the Sternheimer antishielding factor [7~o = - 9 2 for 155Gd (Bog6 et al. 1986)]. Table 9.1 lists the values of-~2o which are deduced without taking any account of the screening effects due to outer electronic shells. The true second-order crystal-field coefficients A2o and ~22A(c)experienced by 4f electrons are often related to ~t~) -'~-2m by A~) 2m - tl ~x -

-

-

-

.. ~X~)

(~ = c. s),

u2t,,Zt2m

(19)

where the value of the screening factor 0-2 (Sternheimer et al. 1968, Blok and Shirley 1966) is normally taken to be about 0.5. Values of V~z and A20 deduced from the 155Gd M6ssbauer spectroscopy (table 9.1) indicate that there is a variation of a factor 80 between the most and least anisotropic rare-earth sites. Of the compounds listed, only Gd2 FeI4B and related materials turn out to have a positive sign for Jzo, which is an important fact for permanent magnet applications because Nd and Pr (which show uniaxial magnetocrystalline anisotropy when A2o > 0) are more abundant than Sm, for which the opposite is true. Note that Azo is only about half as large as A2o listed in table 9.1. (6) The giant coercivity ( # o i H e = 5.03 T) obtained in Sm z F e 7 Ti magnets (made by mechanical alloying) is among the highest measured in permanent magnets at room temperature, but the comparatively low saturation magnetization (~ by the crystal field will depend on both the rare-earth ion and the crystal structure considered. Usually, it is of the order of a few hundredths of a Kelvin, thus, the CEF is a very important contribution for determining the magnetic anisotropy. The values of the B~ coefficients can be determined from experimental data such as magnetic susceptibility, magnetization, heat capacity, inelastic neutron scattering, spin-disorder resistivity and the M6ssbauer effect. 3.4. Magnetic anisotropy

In this section, we want to emphasize the importance of the relative strength of the crystal field (Hcf) and the magnetic interactions (H~x) in determining the anisotropy, i.e., the momentum direction. This problem can be treated in a purely one-ion approach, and will depend very much on the relative ratio of Her and H~x. 3.4.1. The case Hox > Hcf

This situation occurs when the exchange interaction is very large, or when the CEF splitting is very small. In that case, Hcf can be treated as a perturbation in comparison with H~x, and the anisotropy can be expressed by the classical formulation as E A = K 1 sin20 + K 2 sin40 + ....

(10)

The magnetic moment reaches the maximum value g j J . The preferred magnetization direction depends on the crystal structure via the CEF parameters B~' and the shape of the 4f electron charge cloud via the so-called Stevens coefficients. In the case of uniaxial crystal structures the lowest-order parameters are B ° and c~s, respectively. 3.4.2. The case Hox < Her

This situation applies usually to ionic rare-earth compounds, but it also occurs very often in rare-earth intermetallics that have a low ordering temperature (RossatMignod 1983). We must define two parameters: 6 which is the energy of the first excited CEF level and A which is the total CEF-splitting. A simple and more common situation corresponds to the case where the magnetic

TERNARY INTERMETALLICRARE-EARTHCOMPOUNDS

97

interactions are lower than 6. Then, the Hamiltonian He, can be projected on the crystal-field ground level. In this case, the CEF anisotropy may lead to noncollinear magnetic structures. For rare-earth compounds in which the magnetic interactions are smaller than the energy 6 of the first excited CEF level, the magnetic behaviour is dominated by the CEF anisotropy.

3.4.3. The case Hex Hcf When Hex "~ Hcf, no simple approximation can be made and the complete Hamiltonian H~x + Hcf must be diagonalized. The problem is then much more complex, but qualitative results can be obtained by using also a semiclassical description. By decreasing the temperature, the population of excited levels decreases and a rotation moment may occur due to the competition between the CEF anisotropy and the entropy. Such a rotation moment has been observed, e.g., in HoA12 (Barbara et al. 1979). In that case, it is not possible to formulate general trends, the magnetic properties depending very much on the strength of both CEF and exchange terms. The symmetry of the rare-earth site remains always an important parameter, but a large variety of anomalous magnetic behaviours can occur. "~

4. Magnetic properties of ternary compounds The variation in magnetic properties of rare-earth intermetallic compounds through several systems has been discussed briefly before. The data discussed in this section were obtained mostly for polycrystalline samples. Only in a few cases, single-crystals were available for measurements of the magnetic anisotropy.

4.1. R T X phases A large number of equiatomic ternary rare-earth intermetallic compounds with the general formula RTX (R = rare earth, T = transition element and X = metalloid) are known to exist (Hovestreydt et al. 1982, Ba~ela 1987). These compounds crystallize in several different types of structure, such as MgCu2, MgAgAs, ZrOS, Fe2 P, A1B2, Ni2 In, LaPtSi, LaIrSi, PbFC1, MgZn2, TiNiSi and CeCu2. The two crystal structure parameters a/c and (a + c)/b can be used for grouping the various RTX type structures. This is illustrated in fig. 5. Each group of RTX metallic phases has different values of these parameters. Shoemaker and Shoemaker (1965) and Rundqvist and Nawapong (1966) found that the a/c ratio contains information on the number of nearest neighbours. The length of the short b-axis parameter is a further quantity determining the coordination number. A convenient expression for the coordination number is the ratio (a + c)/b. This section is on the systematics in the magnetic properties of a large family of RTX rare-earth intermetallic compounds.

4.1.1. Compounds with the MgCu2-type structure The ternary RMnGa (R = Ce or Ho) compounds have a crystal structure of high symmetry. It belongs to the cubic Laves phases (C15, fcc structure, MgCu 2 type,

98

A. SZYTULA

2.O a/c 1.8

~

Fe2P (ZrNiAt}

=,,

1.6 1.4 1.2

MgCu2 MgAgAs ", ZrOS Ata 2 ~,

1.C

.•NiTiSi E° ~-

0.8

CeCu2 Coin2 •~t, MgZn2 PbFC[q..... Ni21 n

O.B

0.t

LaPtSi a.

0.2 0.0 1.0

I

I

2.0

I

I

3.0

I

I

4.0

I

I

5.0

(o*c)/b Fig. 5. Grouping of RTX compounds according to their axial ratios.

space group Fd3m). This structure is depicted in fig. 6a. In this type of structure, the R atoms occupy the 8a site, while the Mn and Ga atoms are randomly situated in the 16d site (Tagawa et al. 1988). The temperature dependence of the electrical resistivity and the magnetic susceptibility of the compounds with R = Ce, Pr or Nd in the temperature range 4.2-300 K indicate spin glass-like behaviour (Tagawa et al. 1988). The neutron diffraction, the electric resistivity and the magnetic measurements for the D y M n G a compound show a spin glass state with a spin glass temperature T~g= 40 K (Sakurai et al. 1988). The TbMnA1 and ErMnA1 compounds are antiferromagnets with a N6el temperature TN = 34 K and 15 K, respectively (Oesterreicher 1972). Neutron diffraction data for TbMnA1 suggesting a modulated magnetic structure similar to that found in TbMn2 (Corliss and Hastings 1964).

4.1.2. Compounds with the MgAgAs-type structure Only a small number of RTX compounds crystallize in the cubic MgAgAs-type structure (space group FT~3m) in which the R atoms occupy the corners of a regular tetrahedron, as may be seen in fig. 6b. Such a structure is frequently found in transition-metal intermetallic compounds (e.g., NiMnSb). It is closely related to the structure of ordinary Heusler alloys of the X2YZ type, to be discussed in section 4.3.2. Both structures can be described by means of four positions: v n 1 h v ta 3 3x

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS

ol

99

c)

b)

I,

OR

oT, X

OR

e)

oT

oX

OR

o'r2- oX

g)

f)

OR

oT

oX

h) or oX

oR

OR

OT, X

ox

oT, X

j)

.LL_ Z_-_°_-_## . . . . . . . . . q,¢ OX

OR

,.(

oT OR

OT

o X

OR

oT, X

Fig. 6. The structure of (a) cubic MgCu2, (b) cubic MgAgAs, (c) cubic LalrSi, (d) hexagonal Fe2P , (e) hexagonal MgZn2, (f) hexagonal Cain2, (g) hexagonal Ni2In, (h) tetragonal LaPtSi, (i) tetragonal PbFCI, (j) orthorhombic TiNiSi and (k) orthorhombic CeCu2.

Y(000) and z.42221.7/-111~In the case of RTX compounds, the R, T and X atoms occupy the X~, Y and X2 positions, respectively. The Z sites remain vacant again. The magnetic and other bulk properties of RNiSb compounds were reported by Aliev et al. (1988). For RNiSb compounds in which R = Ho, Er, Tm or Yb, there is no magnetic ordering observed above 5 K. The magnetic susceptibility of YbPdX (X = Sb or Bi) satisfies the Curie-Weiss law in the temperature range 4.2-300 K (Dhar et al. 1988). GdPtSn is a paramagnet with a paramagnetic Curie temperature 0p = 24 K and the effective magnetic moment equals #eff 8.28/~B (de Vries et al. 1985). =

4.1.3. Compounds with the LalrSi- (ZrOS-) type structure The RTSi compounds, in which R is a light rare-earth atom (La-Eu) and T represents Rh or Ir, crystallize in a primitive cubic structure (space group P213). In the crystal structure of the LaIrSi (ZrOS) type, the R, T and Si atoms are placed on the fourfold 4e sites of the P213 group. Its crystal structure is shown in fig. 6c. LaRhSi and LaIrSi exhibit a superconducting transition at 4.35 K and 2.3 K, respectively. Above the superconducting transition temperature, T~, the measured susceptibility is positive and almost temperature independent (Chevalier et al. 1982a).

100

A. SZYTULA

NdlrSi has a spontaneous magnetization below the Curie temperature, Tc = 10 K. The fact that the magnetic saturation is not reached up to 20 kOe suggests that a noncollinear magnetic ordering occurs below Tc. A hysteresis loop was obtained at 4.2 K with a coercive field of 0.5 kOe. Above Tc, the magnetic susceptibility obeys the Curie-Weiss law with a positive value of the paramagnetic Curie temperature, 0p = 12K, and the paramagnetic moment is equal to #elf = 3.62#B (Chevalier et al. 1982a). EuPtSi and EuPdSi are isomorphous with the LaIrSi-type structure. The magnetic susceptibility for both compounds obeys the Curie-Weiss law between 10-300 K with an effective paramagnetic moment close to the free E u 2 + ion value. At 4.2 K, a symmetric unresolved hyperfine split M6ssbauer spectrum is observed in EuPtSi, indicating the onset of magnetic ordering. For EuPdSi, at T = 4.2 K only a single M6ssbauer line is observed (Adroja et al. 1988b).

4.1.4. Compounds with the Fe2P- (ZrNiA1-) type structure The hexagonal structure of the F e 2 P type has the space group P6m2. In the ternary RTX compounds, the T atoms occupy the phosphorus sites and the R and X atoms are situated in the two inequivalent iron sublattice sites, as seen in fig. 6d. Compounds of the type RNiA1 and RCuA1 crystallize in the hexagonal Fe 2 P-type structure (Dwight et al. 1968). They are ferromagnets at low temperatures. The magnetic data obtained for these compounds are summarized in table 2 (Buschow 1980). TABLE 2 Magnetic data for RTX compounds. Compound

Crystal structure

Type of magnetic ordering

TC,N(K)

NdMnGa DyMnGa TbMnA1 ErMnA1 GdPtSn YbPdSb YbPdBi NdlrSi PrNiA1 NdNiA1

MgCu2 MgCu 2 MgCu2 MgCu2 MgAgAs MgAgAs MgAgAs ZrOS Fe2 P Fe2P

Spin glass Spin glass AF AF

10 40 34 15

GdNiA1

Fe2P

TbNiAI DyNiA1 HoNiAI ErNiA1 TmNiA1 LuNiAI PrCuA1 NdCuA1 GdCuA1

FezP Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P Fe2P

F

10

F 15-17 F 61-70 F 57-65 F 39-47 F 25-27 F 15-16 F 4.2, 12 Pauli paramagnetic F 36 F 25 F 67-90

0p(K)

,t/err(b/B)

- 11 0-18

10.6

+ 24 - 9 - 9 + 12 - 10 +5 53-70 45-52 30 11-12 -1-0 -11

8.28 4.39 4.04 3.62 3.73 3.84 8.5-8.9 10.1-10.2 11.0-11.1 10.6-10.8 9.8-9.85 7.8

55-90

8.2

PR(Pn)

1.5 1.6 7.38-7.42 7.48-8.01 7.38-7.82 7.25-8.86 7.39-7.4 4.72 1.7 1.8 7.01

Ref.*

[I] [2] [3] [3] [4] [5] [5] [6] [7, 8] [7, 8] [7-10] [7-10] [7-10] [7-10] [7-10] [7, 10] [7, 10] [7, 10] [7,10] [7-10]


101

TABLE 2 (continued) Compound

Crystal structure

Fe2P Fe2 P Fe2P Fe2P FezP Fe2 P Fez P Fe2 P Fe2P FezP Fe2P Fe2 P Fe2P Fe2P FezP MgZnz MgZnz MgZn2 MgZnz MgZn 2 MbZn2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 MgZn2 AIB2 A1B2 A1Bz A1B2 A1B2 Ni2In A1B2 HoCuSi Nizln TmCuSi A1B2 CeZnSi A1Bz NdZnSi AIBz GdZnSi A1B2 TbZnSi A1Bz HoZnSi GdCuGe A1B2 A1Bz NdAgSi EuAgo.67 Sil.33 AIBz NdNio.67 Si1.33 A1B2 A1Bz CeCoo.4Sil.6 A1Bz NdNio.4Sil.6 SmFeo.4.Sil.6 A1Bz GdCoo.4.Sil.6 A1B2 A1Bz GdFeo.4Sil.6

TbCuA1 DyCuA1 HoCuA1 ErCuA1 TmCuA1 YbCuA1 LuCuA1 GdNiIn GdPdIn GdCuA1 GdPtSn GdCuIn CePtIn CePdIn CeAuIn YFeA1 GdFeAI TbFeA1 DyFeA1 HoFeA1 ErFeA1 TmFeA1 LuFeA1 TbCoA1 DyCoA1 HoCoA1 ErCoA1 CeCuSi PrCuSi NdCuSi GdCuSi TbCuSi


Tc,N(K)

F 52 F 35 F 23 F 17 F 13 No C.-W. Pauli paramagnetic F 83 F 102 F 90 AF 30 AF 20 AF AF F F F F F F F F F F F F F F

1.8 5.7 38 260 195 125-144.5 92 56 38 39 48 47 34 25 15.5 14

F F AF

49 47 16

F

AF F F F

0p(K)

+42 + 29 +13 +3 -8

80 103 90 20 -73 -15 -10

+ 36

,Ueff(/AB)

]2R(~B )

10.1 11.0 10.9 10.0 7.6

7.41 8.66 8.59 7.27 4.71

7.28 7.73 8.56 7.99 7.90 2.58 2.56 2.1

10.9

-30 +8 - 45 30-58 + 52

10.4 3.3 3.39 4.2 7.0-8.32 9.62

+ 30

10.2

+ 12 + 30 + 63 +40 +50

2.54 3.62 7.94 9.72 10.61

+17 +21 +12 -- 9 0 0 0 -30

3.62 7.94 3.68 4.9 4.9 5.75 9.0 9.06

9

16 20 34 23

0.1 5.81 6.44 7.12-7.6 8.11 6.32 2.93 0.1 6.42 6.55 8.54 8.3 1.25 2.02 6.9 7.3 8.7 6.1

0.2 0.2 1.0

Ref.*

[7,10] [7,10] [7,10] [7,10] [7,10] [7,10] [7, 10] [4,9-11] [4,9-11] [4] [4] [4]

[12] [12] [13] [14] [14] [14] [14-16]

[14] [14] [14]

[14] [17] [18, 19] [17]

[20] [2 I,22] [23]

[21] [21,23] [23] [24] [21] [25] [26] [26] [26] [26] [26] [27] [28] [28] [283 [28] [283 [28] [293 [29]

102

A. SZYTULA TABLE 2

(continued)

Compound

Crystal structure


Tc,N (K)

0p(K)

SmFeo.67 Gel.a3 NdA1Ga TbA1Ga DyA1Ga HoA1Ga ErA1Ga CeCuSn GdCuSn GdAuSn CePtSi NdPtSi SmPtSi YMnSi LaMnSi GdMnSi DyMnSi HoMnSi GdCoSi YNiSi LaNiSi CeNiSi PrNiSi NdNiSi SmNiSi GdNiSi TbNiSi DyNiSi HoNiSi ErNiSi TmNiSi YbNiSi LuNiSi TbCoSn DyCoSn HoCoSn ErCoSn TmCoSn LuCoSn CeRhGe CeIrGe GdAuGa TbAuGa DyAuGa HoAuGa ErAuGa TmAuGa CePdSn GdPdSn CePtGa

A1B2 A1B2 A1B2 AIB 2 " A1Ba A1B2 Cain 2 Cain 2 Cain2 LaPtSi LaPtSi LaPtSi PbFC1 PbFC1 PbFC1 PbFC1 PbFC1 PbFCI TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi TiNiSi

AF AF AF AF AF AF AF AF AF

26 2.5 47, 23 51.5, 17 30, 17.8 2.8 4.2 24 35

+ 33

AF 15 AF 4 F, AF 275,130 F 295 F 314-320 AF 30 AF 36 F 250 Pauli paramagnetic Pauli paramagnetic 57 +17 -15 Pauli paramagnetic 0 -2 0 0 +5 +8 -65 Pauli paramagnetic

AF

9.3

AF

6

AF AF AF

7.5 14.6 3.2

+1

+5 - 32 -I0 -47

290 295 220-314 30 - 10 131

~¢ff([~B)

~R(~B)

0.07

10.8

0.9 6.7 6.8 8.2 4.9

2.59 2.3 1.6 2.56

2.0 7.8 10.6 11.7

1.3 0.24 5.37 6.7 7.35

Ref.*

[29] [30] [31] [32] [31] [30] [33] [34] [34] [35] [36] [36] [37] [38] [38, 39] [38] [38] [39] [40]

[40] - 57 +17 -15

2.86 3.56 3.50

0 -2 0 0 +5 +8 -65

8.12 9.83 10.4 10.4 9.53 7.58 4.57

+30 + 27 +9 +11 +5 +31 - 56 -10 8.5 -10 -4.5 +3.5 +1.5 -2.0 - 67

10.43 10.47 9.42 7.57 0.79 2.30 0.27 8.06 9.7 10.63 10.58 9.6 7.59 2.67

[40] [40]

[40] [40] [40] [40] [401 [401 [40] [40]

[40] [40] [41] [41] [41] [41] [41] [41] [42] [42]

[43] [43] [43] [43] [43] [43] [44] [44] [45]


103

TABLE 2 (continued) Compound

Crystal structure


Tc,N(K)

CePdGa GdRhSi TbRhSi

TiNiSi TiNiSi TiNiSi

DyRhSi HoRhSi ErRhSi TbRhGe CePdGe CePtGe TbNiGa PrAgGa NdAgGa GdAgGa TbAgGa DyAgGa HoAgGa ErAgGa TmAgGa EuCuGa

TiNiSi TiNiSi TiNiSi TiNiSi

AF F F AF F AF AF AF AF AF AF

1.7 100-102 55 13, 29 25 8-11 7.5-12 15 3.4 3.4 23

CeCu 2

CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCu2 CeCuz CeCu2 CeCu2

AF AF AF AF

AF

* References: [1] Tagawa et al. (1988). [2] Sakurai et al. (1988). [3] Oesterreicher (1972). [4] de Vries et al. (1985). [5] Dhar et al. (1988). [6] Chevalier et al. (1982a). [7] Oesterreicher (1973). [8] Leon and Wallace (1970). [9] Buschow (1975). [10] Buschow (1980). [11] Ba~ela and Szytuta (t986). [12] Fujii et al. (1987). [13] Pleger et al. (1987). [14] Oesterreicher (1977b). [15] Lima et al. (1983). [16] Bara et al. (1982). [17] Oesterreieher (1973). [18] Oesterreieher (1977a). [19] ~lebarski (1980). [20] Oesterreicher et al. (1970). [21] Kido et al. (1983b). [22] Gignoux et al. (1986b). [23] Oesterreicher (1976). [24] Ba~ela et al. (1985b). [25] Allain et al. (1988). [26] Kido et al. (1983a). [27] Oesterreicher (1977c).

0 v (K)

#eff(/AB)

60-90 48

7.55-7.95 9.92

11.5 10.5 -3

10,31 10.71 9.54

-37 -82

2.55 2.54

+31 +4 + 52 +20 +17 +14 +12 +9

3.18 3.65 7.95 10.03 10.6 10.43 9.43 7.38

#R(#B)

2.2 2.0 8.1 8.7-9.1 6.6 9.26

6.8

27 18 4.7 3 l0 [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53]

Felner and Schieber (1973). Felner et al. (1972). Martin et al. (1983). Girgis and Fischer (1979). Doukour6 et al. (1986). Adroja et al. (1988b). Oesterreicher (1977a). Lee and Shelton (1987). Braun (1984). Kido et al. (1985c). Nikitin et al. (1987). Kido et al. (1982). Skolozdra et al. (1984). Skolozdra et al. (1982). Rogl et al. (1989). Sill and Hitzman (1981). Adroja et al. (1988a). Malik et al. (1988). Chevalier et al. (1982b). Szytuta (1990). Ba~ela et al. (1985a). Quezel et al. (1985). Szytula et al. (1988a). Kotsanidis and Yakinthos (1989). Sill and Esau (1984). Malik et al. (1987).

Ref.*

[45] [46,47] E46] [48,49] [46] E46,48, 49] [46,48] [50] [42] [42] [51] [523 [523 [52] [52] [52] [52] [52] [523 [533

104

A. SZYTULA

Ternary GdTAI and GdTSn compounds were investigated by Buschow (1971, 1973) and found to be ferromagnets, too. A rather unusual variation of the paramagnetic Curie temperature 0p was observed in the Gdl_~ThxCuA1 series, passing through a maximum for x = 0.3. In the Gdl _xThxPdln series, a change in the sign of 0p from positive to negative was observed at about the same concentration. Taking into account the 27A1 N M R data on GdCuA1, attempts have been made to explain such behaviour in terms of the RKKY model (Buschow et al. 1971, 1973). 155Gd M6ssbauer spectra obtained for some GdTX compounds showed a magnetic ordering at 4.2 K. The analysis of these spectra indicates that the magnetic moment of the Gd atoms is oriented parallel to the c-axis in GdCuA1, GdNiln and GdPdln and has an angle of ~b= 47 ° with the c-axis in GdPdSn and GdPdA1 (de Vries et al. 1985). Also, CeTIn (T = Ni, Pd, Pt or Rh) crystallize in the Fe2 P-type crystal structure. The temperature dependence of the inverse susceptibility gg- 1 for CePdIn and CePtIn follows the Curie-Weiss law with effective moments which are in agreement with the theoretical free-ion value for the Ce 3 + ion. At low temperatures, CePdIn exhibits antiferromagnetic order below TN= 1.8 K, whereas CePtIn is a heavy fermion (Fujii et al. 1987). The temperature dependence of the magnetic susceptibility and the electrical resistivity suggests that CeNiIn is an intermediate valence compound (Fujii et al. 1987). Also, the temperature dependence of the magnetic susceptibility of CeRhIn indicates the mixed-valent behaviour of this compound (Adroja et al. 1989). The temperature dependence of the magnetic susceptibility and the specific heat of CeAuIn indicate antiferromagnetic ordering below TN= 5.7 K. Above TN, the magnetic susceptibility obeys the Curie-Weiss law with an effective moment that appears to be reduced with respect to that expected for the 4f 1 configuration of Ce (Pleger et al. 1987). 4.1.5. Compounds with the MgZn2-type structure The groups of intermetallic compounds RTA1 with T = Fe or Co have the hexagonal MgZn2- (C14) type structure (space group P6a/mmc) represented schematically in fig. 6e. This space contains three nonequivalent sets of crystal sites. The 4f sites are occupied by R atoms. The sites 2a and 6h are occupied both by T and X atoms. The magnetic measurements of RFeA1 compounds in which R is a heavy rare earth show that they are ferromagnets with a high Curie temperature (Oesterreicher 1977c). Systematic studies were only performed for DyFeA1. Neutron diffraction data indicate a ferrimagnetic structure in which the magnetic moments of the Dy atoms order ferromagnetically and are equal to 7.6(1)/~B/Dy atom. The Fe sublattice orders ferromagnetically with Fe moments equal to #(2a)= 0.8(4)#B and /~(6h)= 0.5(2)/~B. The Fe sublattice is coupled antiferromagnetically to the Dy sublattice. There is a strong reduction of the Dy moment compared to the free-ion value. The magnetic moment lies in the basal plane (Sima et al. 1983). The Lni emission spectra of iron in DyFeA1 give evidence of some charge transfer between 3dFe and 5dDy bands (Slebarski and Zachorowski 1984). The results of M/Sssbauer investigations, which indicate a more complete transfer to the 3d band by transfer of Dy 5d electrons and

TERNARY INTERMETALLICRARE-EARTHCOMPOUNDS

105

of A1 3p electrons to the iron sites, are in accordance with the observed increase in the intensity of the Lxn spectra. The total magnetic moment localized on the Dy atoms decreases at T = 4.2 K, as a consequence of an opposite polarization of the 5d and 4f bands (Bara et al. 1982, ~lebarski 1987). Also, in the case of the RCoA1 compounds (R = Tb-Er) a ferromagnetic ordering is observed at low temperatures. Magnetic data of these compounds are listed in table 2 (Oesterreicher 1973, 1977a). The neutron diffraction data for ErCoA1 indicate a ferromagnetic ordering at T = 4.2 K with magnetic moments per Er atom equal to p = 7.0#B parallel to the c-axis. No moment is observed for the Co atoms (Oesterreicher et al. 1970). 4.1.6. Compounds with the AlB 2- or Ni2In-type structure Many ternary equiatomic compounds crystallize in the two similar hexagonal structures represented by the A1B2 type with space group P6/mmm (Rieger and Parth6 1969) and the NiEIn type with space group P63/mmc (Iandelli 1983). These two structure types are shown in fig. 6g. In these structures, atoms occupy the following positions: A1 in 0, 0, 0 and B in ½, 2, ½ and 2, ½, ½ for the A1B2 type; and Ni in 2a: 1 2 37, ~, and -~, 1 1 for 0, 0, 0, and 0, 0, ½, and in 2c: 7,17,2~1 and ~,27,2~a and In in 2d: 7, Ni2 in. In the case of RTX compounds, the T and X atoms are statistically distributed in the A1B2-type structure while for Ni2In they are situated in 2c and 2d positions (Mugnoli et al. 1984, Ba£ela et al. 1985b). The difference between the two structural types is due mainly to a doubling of the periodicity along the c-axis, giving in the latter space group an ordered distribution of T and X atoms in ½, 2, ¼ and in ½, 2, ¼, respectively. On the basis of neutron diffraction data, Mugnoli et al. (1984) concluded that LaCuSi exists in two thermal modifications: a low-temperature Ni2 In type and a high-temperature A1B2 type. The magnetic properties of RCuSi (R = Y, Ce, Nd, Sm, Gd or Ho) were investigated by Kido et al. (1983b). The magnetic susceptibilities of YCuSi and SmCuSi are 102 times smaller than those of the other compounds and they show no temperature dependence. In the other compounds, the magnetic susceptibility obeys the CurieWeiss law with effective magnetic moments equal to the free-ion values (see table 2). The magnetic properties of RCuSi with R -- Pr, Gd or Tb were investigated from 4.2 to 150 K in magnetic fields up to 50 kOe. As may be seen in table 2, all these compounds order ferromagnetically (Oesterreicher 1976). The magnetic properties of CeCuSi were studied by neutron diffraction and magnetization measurements. The CeCuSi compound shows a ferromagnetic ordering below Tc -- 15.5 K, with a magnetic moment of 1.25/~B at T--2.5 K, perpendicular to c-axis (Gignoux et al. 1986a). Neutron diffraction studies of TbCuSi indicate a cosinusoidally modulated transverse spin structure below T~ = 16 _+2 K, while DyCuSi and HoCuSi remain paramagnetic down to T-- 4.2 K (Ba~ela et al. 1985b). TmCuSi is a collinear ferromagnet with Tc = 9 K and a magnetic moment #-6.1(2)/~B at T = 2.1 K oriented parallel to c-axis (Allain et al. 1988). GdCuGe is an antiferromagnet with TN----17 K (Oesterreicher 1977c). The RZnSi compounds (R = Ce, Nd, Sin, Gd, Tb or Ho) are paramagnetic in the

106

A. SZYTULA

temperature range between 77 and 300 K. Their effective magnetic moments are in good agreement with the corresponding free-ion values. YZnSi is a Pauli paramagnet. All these compounds are metallic (Kido et al. 1983a). The magnetic properties of pseudoternary RCul _xZn~Si (0 5 ~

/~"/ -T=4"2K

20t

r }JB

il I I

ill~

101 OI

O'g =I{H} H(kOe)

J

0

J_

10

J_

20

.L

30

(ernu/g) 30

40

5'0

PrFe2Gez

20

~

10

J

~

~

~ H =40koe

"-......~H=

20

~o, T(K)

lb

o

2b

4'0

3b

5b

Fig. 19. (Top) Magnetization versus applied field for PrF% G% at different temperatures. (Bottom) Magnetization versus temperature at different applied fields (Leciejewicz et al. 1983a).

Happt. (kOe) 40

I

I

I

I

!

ferri ~I

20

10

\~, af. 2

0

0

p CI rQ m.

t 10

i i 20

30

~"~afjl\\ 40

I 50 T(K)

Fig. 20. Magnetic phase diagram of GdRuzSi 2. Circles and solid lines mark phase boundaries derived from differential magnetization data (L~tka 1989, Czjzek et al. 1989). Diamonds and the broken line mark the antiferromagnetic-to-paramagnetic phase boundary according to results reported by Buschow and de Mooij (1986).


133

and 32 K in N d C o 2 S i 2 (Shigeoka et al. 1988a) and at 10 and 29.5K in N d C o 2 G e 2 (Kolenda et al. 1982). In the case of N d C o E G e 2 , measurements of the temperature dependences of the specific heat and the resistivity (see figs. 21 and 22) were also made. These measurements, however, show only one phase transition at the N6el temperature (Slaski et al. 1988). Neutron diffraction data show that all compounds at T--4.2 K are antiferromagnets with magnetic structures of the AF I-type (see fig. 23) described by the propagation vector k = (001)2~z/c. With increasing temperature, transitions to modulated magnetic structures are observed, being described by the wave vector k - - [ 0 0 1 - k=]2n/c. The corresponding values of k= are given in table 10. Also, in the P r F e 2 G e 2 compound, there is a transition from a collinear antiferromagnetic structure of the AF II-type (see fig. 23), described by the wave vector k = (00½)2re/c, to an incommensurate structure with wave vector k = (0, 0, 0.476)2n/c at T = 9 K (Szytuta et al. 1990). For all these compounds, the commensurate AF I-type (in P r C o E S i 2 , N d C 0 2 S i 2 and N d C o 2 G e 2) and the AF II-type (in PrFe2 GeE) are observed at low temperatures. An increase in temperature changes the commensurate structure into an incommensurate structure described by the wave vector k = (0, 0, k=). The particular location of the rare-earth atoms in a crystal structure of ThCr2 Si 2type is responsible for the anisotropic character of the magnetic interaction between the magnetic moments of the rare-earth atoms. The anisotropy may be understood in two ways: - t h e magnetic moments are quenched along the c-axis leading to an Ising-like behaviour, ° °°° °°°°•

°.°°°

soE

o° °°-°°°°•

..."" NdCo26e2 °° ° °°•

p

c,

°•° °•• °•°

E 2.13

. . . . ~•..°.-°"•"

.- .-""~

..1"

¢,,2

~-

O~

....

. . . . NdRu2Ge2

~,"°

°, . ° . . . , , °°•-°'"•"•" °" "°°" •°

j'"--"~ .._.....-,"

NdRu2Si2

!~f...~"~ I

"- 1.=.

I

'

1()

~

2(3

'

3(]

'

[i

IL

0 T K] 50-

Fig. 21. Electrical resistivity versus temperature for NdCo2Oe 2, NdRu2Si2 and NdRu2Ge 2 (Slaski et al.

1988).

134

A. SZYTULA 3~

3c ' ~ 25

E

c~ lC 10

20

30

'•4.0

40 T [ K ] ~u

NdRu2Si2

)

'~E3.0 "m 2.0 13. t 3 1.0

10

j

6.0

..b 4JO o

E

..2.13 (,.J

QO

s

1~)

20

30 T [ K ]

NdRu2Ge z

1~

2b

zs

3~" T[K]

Fig. 22. (a) Magnetic heat capacity versus temperature for NdCo2Ge2, (b) for NdRu2Si2, and (c) for NdRu2Ge2 (~laski et al. 1988).

- t h e exchange interaction J0 within the (001) planes is strongly ferromagnetic, whereas the coupling between planes J1, J2 .... , J, is weaker and can be antiferromagnetic. The magnetic behaviour of these compounds is similar to that observed for CeSb (Rossat-Mignod 1979). In this case, the stability of the magnetic structures is discussed on the base of the anisotropic-next-nearest-neighbour Ising (ANNNI) model. In the ANNNI model the interaction between nearest-neighbour layers is positive, J1 > 0, and the interaction between next-nearest neighbour layers is negative, J2 < 0. According to Bak and von Boehm (1980), a mean-field calculation leads to various magnetic structures as a function of the parameter - J 2 / J 1 . The calculation reveals that for Jt > 0 the ground state is ferromagnetic if J2 > - ½J1. However, if J 2 < - ½J1, the ground state is antiferromagnetic. With increasing temperatures a change to modulated periodic structures occurs, characterized by a wave vector k = (0, 0, k~). For IJ2/J11 < 1, the antiferromagnetic ordering is of the AF I-type. A modulated magnetic ordering with a wave vector k given by cosrck= -Ja/4J2 is stable if IJz/Jl[ >¼, and the AFII-type structure is stable if -J2/[Jl[> ½. In the case of TbNi 2 Si2, the temperature dependence of the magnetic susceptibility and resistivity indicate that the N6el transition occurs at TN = 15 K and an additional


135

SPIRAL AXIS

...--~-.~-

I

:~l 3 P,' AFI

~-: =,__ ~ 7 I

I I I

I i i

I i I

I

I

i

f - ~ LSW~"

LSW I

I LSW IV

LSW'~I

Fig. 23. The magnetic structure of the R sublattice in various RT2 X2 compounds. TABLE 10 Values of the wave vector k, for

RCo2X

2

compounds.

k,

Compound

Temperature

PrCo2Si 2 [1]

T < 9K 9 K < T < 17K 17K< T> TRKKY should be called nonmagnetic concentrated Kondo systems (CKS), e.g., CeTzSi z compounds (T = 3d metals). The intermediate situation where TK>> TRKKYand TN # 0 corresponds to the magnetic ground state modified essentially by the Kondo compensation of the magnetic moment of rare-earth ions. Figure 41b demonstrates the dependence of the N6el and Kondo temperatures as a function of the unit cell volume for several CeT2X2 compounds. The obtained results indicate that for large volumes

I

i

1

[

11

I

~

TK,TN(K)

I

/~

b}

/o

20

ii /

10

v..vS/" i ~"

IM

I

i II TK

3O

200

/

~, iTN o

o

i

180

,,"160 VEJ3] /'T K /

r¢ #

I--

tY uJ

/

l/

//

IM

/

~ ~ ~

TRKKY

uJ i---

Fig. 41. (a) The classification of concentrated Kondo systems (CKS) by the relation between two characteristic temperatures: TK and TRUly; TN is magnetic transition temperature. (b) Kondo temperatures T~ (©) and magnetic ordering temperatures TN (V) versus the unit cell volume for several CeTzX 2 compounds. The lines are guides to the eye.

TERNARY INTERMETALLIC RARE-EARTH C O M P O U N D S

165

the RKKY interaction between well-localized f-electrons dominates. And, in the case when the Kondo effect plays a minor role, ordinary magnets are found. For small cell volumes and low temperatures 4f-electrons are weakly localized. It was found that pressure has a considerable influence on the N6el temperature. The results for several compounds are presented in fig. 42a. The weak linear pressure dependence of TN for CeAg2Si 2 and CeAu2Si 2 (dTN/dp = +0.1 and -0.04K/kbar, respectively) confirms on the suggestion that in these materials TK is much smaller than TN. However, the strong nonlinear decrease in TN with pressure in CePd 2 Si2 and CeRhzSi2, dTN/dp = 1.4 and - 5 K / k b a r , respectively, suggests the opposite regime. Changes in TN(p) agree qualitatively with Doniach's phase diagram in which the energy of a Kondo singlet is compared with that of an RKKY-antiferromagnetic ground state (see fig. 42b).

5.3. Crystalline electric field It is well-known nowadays that the crystalline electric field (CEF) at the rare-earth site can strongly effect the magnetic properties of the ternary rare-earth intermetallics. The interaction of the CEF with the multipole moments of the electrons of the R 3 + ion is described by the CEF Hamiltonian [see eq. (6)]. For the ternary rare-earth intermetallics, a systematic study of crystal electric field was performed only for the RT2X2 compounds. The values of the Bm parameters determined for a large number of these compounds are collected in table 20. The B ° parameters seem to be dominant, since the remaining Bm parameters are smaller by an order of magnitude. At a site of the tetragonal point symmetry, the easy axis of magnetization is parallel to the fourfold c axis if B ° is negative, it is perpendicular to the e axis if B2° is positive (Hutchings 1964, Bertaut 1972, Dirken et al. 1989), provided the effect of the second-

X~b)

2.0

o) 1.2

T/W 1.51

I£ ~CePd2Si2

~ \CleRh2Si~ 2

O.8 a_ 0.~ 0.4

1.0 P

-~

0.5

I I

0.~ i I

O.C 0

,

10 P{kbar}

15

0.5

1.0J/W

Fig. 42. (a) The N6el temperature normalized to its value at p = 0 as a function of pressure in CeT2Si 2 (Thompson et al. 1986), (b) Doniach's phase diagram for the one dimensional 'Kondo necklace' model (Doniach 1977),

166

A. SZYTULA TABLE 20 Values of the B,~ crystal electric field parameters in RTzX2 compounds.

Compound

B° (K)

CeCu2 Si2

- 3.0 + 1.0 -3.1 _+ 1.2 - 8.78 -11.4 ± 2 . 6 5 -0.5 + 1.3 + 30.7 -1.08 _ 1.20 + 6.46 - 8.0 -3.99 -1.8 + 0.45 - 0.915 - 1.09 - 1.93 -4.94 - 1.8 - 1.0 - 0.22 + 0.70 +0.241 +2.53 +0.12

CeCuz Ge2 CePd2 Si2 CeAg2Si2 CePt2 Siz CeAu2 Si2 CeAlz Ge2 PrCo2 Siz PrNizSiz NdCo2Ge2 NdMn 2Ge 2 NdRh z Si2 Tb Rh 2 Si2 DyRh 2Siz DyRuzSiz DyFe2 Siz DyCo z Si 2

HoRh2 Siz ErRhz Siz TmFe2Si2 TmCuzSiz

* References: [-1] Horn et al. (1981). [2] Severing et al. (1989). [3] Knopp et al. (1989). [4] Gignoux et al. (1988b). [5] Gignoux et al. (1988a). [6] Shigeoka et al. (1989b). [7] Barandiaran et al. (1986b). [8] Fujii et al. (1988).

B° (K)

B## (K)

-0.4 _+0.1 0.25 _+0.1 +0.41 _+0.12 -6.5 +0.5 - 0.054 + 2.79 -0.0012 -3.25 + 0.7 -0.04 + 0.01 -4.0 + 0.4 + 0.93 + 19.5 + 0.34 ___0.04 -4.6 ± 0.4 - 0.09 + 0.013 - 0.0136 + 0.05 +0.0016 +0.156 0 -0.011 + 0.0057 - 0.020 + 0.189 - 0.02 - 0.0047 - 0.0085 + 0.0043 +0.0063 - 0.0039 -- 0.00 + 0.0011 - 0.002 - 0.0027 + 0.04 -0.00125 -0.00246 -0.017 +0.049 -0.0312 -0.049 [9] [10] [11] [12] [13] [14] [15]

B° (K)

+ 0.0026 +0.00013 -0.00013

B6 (K)

- 0.0024 -0.00032 -0.001

+ 0.000025 + 0.00003

0 -0.00014

+0.002 +0.00126

Ref.* [,1] [-2] [3] [2] [2] [4] [2] [5] [6] [7] [8] [9] [ 10] [ 10] [ 11] [11] [12] [ 12] [ 13] [12] [10] [14] [,15]

Shigeoka et al. (1988a). Takano et al. (1987b). Sanchez et al. (1988). G6rlich (1980). Takano et al. (1987a). Umarji et al. (1984). Stewart and Zukrowski (1982).

o r d e r t e r m i n the crystal field H a m i l t o n i a n is d o m i n a n t . T a b l e 21 c o n t a i n s the v a l u e s of B ° coefficients d e t e r m i n e d e x p e r i m e n t a l l y for a n u m b e r of R T 2 X 2 c o m p o u n d s . These d a t a i n d i c a t e t h a t the signs of the B ° coefficients a n d the c o r r e s p o n d i n g o r i e n t a t i o n of the m a g n e t i c m o m e n t s agree w i t h t h o s e d e d u c e d f r o m n e u t r o n diffract i o n e x p e r i m e n t s . H o w e v e r , it h a s b e e n s h o w n t h a t the sign of B ° d e p e n d s also o n the n u m b e r of 4f a n d n d electrons, b u t the lack of d a t a does n o t p e r m i t us to p l o t a d e t a i l e d d i a g r a m . O n l y i n s o m e c o m p o u n d s , the m o m e n t d i r e c t i o n is i n disa g r e e m e n t w i t h the C E F p r e d i c t i o n . F o r c o m p o u n d s w i t h N i a n d w i t h P d , the v a l u e s of B ° are very s m a l l c o m p a r e d to o t h e r c o m p o u n d s . T h u s , crystal field t e r m s of h i g h e r o r d e r m a y h a v e a s t r o n g effect. I n a d d i t i o n , s m a l l d e v i a t i o n s of s t r u c t u r a l p a r a m e t e r s f r o m t h o s e i n the c o r r e s p o n d i n g RT2 X2 c o m p o u n d s m a y l e a d to a c h a n g e in sign of the B ° coefficients. I n the c o m p o u n d s H o R h 2 Si2 (Slaski et al. 1983), D y R h 2 Si2 ( M e l a m u d et al. 1984),

TERNARY INTERMETALLIC RARE-EARTH COMPOUNDS TABLE 21 Values of the B ° coefficients and direction of the magnetic m o m e n t s on RT2Si2 compounds. Compound •C e M n 2 Si 2 PrMn2 Si 2 N d M n 2 Si 2 G d M n 2 Si 2 T b M n 2 Si2 D y M n 2 Si~ H o M n 2 Si2 ErMn2 Si2 T m M n 2 Si2 YbMn2 Si2 CeFe2 Si2 PrFe2 Si2 N d F e 2 Si 2

B°

- 0.7 + 0.45

Direction

Ref.*

rlc ±c 3_ c IIc

[2] [8] [ 13] [ 14] [21] [38] [26]

- 1.35 q~ ±c

- 0.63

±c

[9] [103 [13, 14] [15] [16] [9] [223 [9] [25] [9] [26] [9] [ 15] [27]

IIc

[3] [4, 5]

IIc ±c

GdFe2 Si 2 T b F e 2 Si 2

- 4.07

DyFez Si2

- 1.8

H o F e 2 Si 2

-- 0.6

ErFe2 Si 2

+ 0.67

TmFe2 Si2 YbFe 2 Si 2

+ 2.54 + 10.12

IIc IIc (p ±c

CeCo 2 Si 2 PrC02Si 2 N d C o 2 Si 2

-8.0 - 1.8

[11] /Ic Zc

GdCo2 Si 2 TbCo/Si z

- 2.24

DyC02 Si 2

- 1.0

H o C o 2 Si 2

-- 0.44

ErCo2 Si2

+ 0.44

T m C o z Si 2

+ 1.85

YbCo2 Si 2

+ 5.58

lie IIc

p[c

- 3.99

[4, 17]

±c ±c

[ 15] [4] [ 15] [23] [27]

IIc

[6]

± c ±c

[ 12] [l 3, 14]

±c

CeNi a Si z P r N i 2 Si 2 N d N i 2 Si z GdNi2 Si z

[4] [13, 14] [15] [4,5,17] [21] [23, 24] [ 15]

167

168

A. SZYTULA TABLE 21 Compound TbNi2 Si2

B°

(continued) Direction

- 0.66 I1c

DyNi2 Sia HoNi2Si2

+ 0.17 -0.13

ErNi 2 Si 2

+ 0.14

TmNi2 Si z

+ 0.55

YbNi2 Si2

+ 0.65

CeCu 2 Si 2

-

_l_c _l_c Lc 3.0

PrCu 2Si 2 NdCu 2 Si2 GdCu 2 Si2 TbCu2Si 2

1]c

+0.8, +1.3

DyCu2 Si2

+ 0.57

HoCua Si2

+ 0.175

ErCu 2 Si2 TmCuz Si2 YbCu 2 Si2

- 0.2 - 0.79 - 3.23

I c ±c lc Zc

CeRu2 Si 2 NdRu2 Si 2 GdRu2 Si2 TbRu 2 Si 2

- 8.33

DyRuz Sia

- 4.94

HoRu

--

IIc q~

II c II c 2 Si 2

1.64 IIc

ErRu2Si 2

+ 1.78

TmRuz Si2

+ 6.89

CeRh2 Si2 NdRh z Siz

- 0.9

Zc I c [kc _Lc

GdRh2 Si2 TbRhg Si 2

- 3.3

DyRh28i 2

-- 1.9

HoRh2 Si2

- 0.64

ErRh2 Si2

+ 0.7

TmRh2 Si 2

+ 0.69

II c ~o q~ ±c ic

Ref,* [ 15] [12, 17] [21 ] [15] [12] [ 15] [12] [15] E12] [15] E1] [7] [ 13,14] [15, 18] [19,20] [21] [24] [18] [19,20] E18] E18] E15] [30] [ 13,14] [15] [30] [15] [30] [ 15] [30] [15] [30] E15] [28] [31 ] [32] [13, 14] [15] E28, 33] E15] [33] E15] [33] [15] [32] [ 15] E37]

TERNARY INTERMETALLIC RARE-EARTH C O M P O U N D S TABLE 21 Compound

B2°

CePd2 Si2

- 11.4

NdPd2 Si2 GdPd2 Si2 TbPd 2 Siz

- 0.18

DyPd 2 Si2 HoPdz Si2

- 0.11 + 0.04

ErPd 2 Si 2 TmPd2 Si2

+ 0.04 + 0.15

CeOs2 Si2 NdOsz Si2 GdOs 2 Si 2 TbOs2 Si2

- 8.32

DyOs2 Siz HoOs 2 Si~

- 4.93 - 1.64

ErOs2 Si2 TmOs2 Si2

+ 1.78 + 0.88

Celr2 Si2 NdIr2 Si2 Gdlr2 Si 2 TbIr 2 Si2

- 3.9

DyIr2 Si2 HoIr2 Si2 Erlr2 Si2 Tmlr 2 Si 2

- 2.32 - 0.77 + 0.84 + 3.24

(continued) Direction

Ref.*

±c

[37] [29]

_1_c l c

±c

~o IIc

I]c _1_c

±c [Ic

* References: [1] Horn et al. (1981). [2] Iwata et al. (1986b). [3] Shigeoka et al. (1988b). [4] Leciejewicz et al. (1983b). [5] Yakinthos et al. (1984). [6] Barandiaran et al. (1986b). [7] Szytu~a et al. (1983). [8] Shigeoka et al. (1988a). [9] Noakes et al. (1983). [10] Pinto and Shaked (1973). Ell] Fujii et al. (1988). [12] Barandiaran et al. (1987). [13] Dirken et al. (1989). [14] Czjzek et al. (1989). [15] L~tka (1989). [16] Szytuta et al. (1987a). [17] Nguyen et al. (1983). [18] Budkowski et al. (1987). [19] Leciejewicz et al. (1986).

[20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38]

[ 13,14] [ 15] [34] [ 15] [ 15] [36] [ 15] [15]

E13, 14] [15] [35] E15] [ 15] [35] [35] [ 15]

[13, 14] E15] [33] [ 15] [15] [15] [15]

Pinto et al. (1985). G6rlich et al. (1989). Bourre-Vigneron et al. (1990). Leciejewicz and Szytuta (1983). Pinto et al. (1983). Leciejewicz and Szytuta (1985a). Leciejewicz et al. (1984b). Hodges (1987). Quezel et al. (1984). Steeman et al. (1988). Slaski et al. (1984). Takano et al. (1987b). Szytuta et al. (1984). ~laski et al. (1983). Szytuta et al. (1986b). Kolenda et al. (1985). Leciejewicz and Szytuia (1985b). Severing et al. (1989). Leciejewicz et al. (1990).

169

170

A. SZYTULA

TmRh2 Si2 (Yakinthos 1986b) and for HoFe2 Si2 (Leciejewicz and Szytula 1985a), the moment directions have been reported to be neither parallel nor perpendicular to the fourfold c axis. Such canting points to a strong influence of higher-order crystal field terms. Apart from its influence on the easy direction of magnetization, the CEF has also considerable influence on the magnetic transition temperatures. Taking only the second-order CEF term into account, the large deviations of TN from that predicted by the de Gennes rule can be understood (Noakes and Shenoy 1982). The observed values of the magnetic transition temperatures of RCu2 Siz compounds do not follow the de Gennes rule (see fig. 43). However, if a CEF Hamiltonian, Hof is added to the exchange Hamiltonian, the agreement with the de Gennes function improves considerably (Noakes and Shenoy 1982). Using H = -2y(g

s -

1)2Jz<Jz> + B20 [3Jz2 -- J ( J

+

1)],

(18)

the magnetic ordering temperature is given by TN = 2 J ( O ,

-

1)2 ~' Jz2 exp(s=

o Fz

3B z Jz/TN)

L J=

exp(-- 3B2 J ~ / T N )

•

_1

(19)

The values deduced for B ° are as follows: 0.8 K for Tb, 0.5 K for Dy, 0.175 K for Ho, - 0 . 1 9 9 K for Er and - 0 . 7 8 9 K for Tm (Budkowski et al. 1987).

TN[K] 15

\\ lc

•

•"\\

•\

•\

•

i \\\\\ ~I \

\

i

\\

"\~/,, GId

l'lb

Dy

HO

Er

Tm

RE

Fig. 43. Comparison of experimental(solid triangles) and calculated magnetic transition temperatures TN for RCu2Si2 compounds. The broken smooth line represents the de Gennes rule. The dotted line is for trends obtained on the basis of the molecular field model (Noakes and Shenoy 1982) including CEF effects. The solid line (open circles) represents TNpredicted by the B° model with A° as for GdCu2Si2 (L~tka et al. 1979). The dotted line (open squares) represents calculations made with the full CEF Hamiltonian using the five B,~ parameters of Stewart and Zukrowski (1982), the symbols [] represent data of Koztowski (1986),the symbol (3 refer to data of Budkowski et al. (1987).


171

All these results show that the crystal electric field has a significant effect on the magnetic properties of the RT2 X2 compounds. Of other ternary intermetallics, the CEF parameters were determined only in some cases.

In CeCuSi, the Ce a+ ions occupy positions with point symmetry 3m. For a hexagonal symmetry, 3m, the CEF Hamiltonian is given by eq. (9). The values determined for the B," parameters in CeCuSi are: B ° = 9.14 K, B ° = -0.035 K, B43= 6.56 K. The magnetic moment of the Ce atoms lies in the basal plane, which is in agreement with the sign of B °. Under these conditions, the multiplet J = ~ is split into three doublets which are mainly _+ [M s ) states (Ms = ½, ~ or ~), with a small mixing between -t- [½) _+ [~) states due to the B~ term. For the above B," parameters, the ground state in the paramagnetic regime is found to be the doublet + [½), well separated (A = 90 K) from the first excited level + J~). In the ordered state, the basal plane is then favoured as the easy magnetization direction, with an associated magnetic moment of 1.2#B at 0 K. This value is quite consistent with the experimental data (#R = 1.25/~B) (Gignoux et al. 1986a). In the rare-earth Heusler intermetallic compounds, the ordering temperatures are low and the associated magnetic energies are small. The crystalline electric field (CEF) effects, therefore, play an essential role in determining the magnetic properties. The values of the rare-earth magnetic moments determined experimentally for R T 2 X cubic compounds are smaller than the free R 3+ ion values. This result indicates the strong influence of crystal field effects. In these compounds the rare-earth ions occupy a site of cubic point symmetry, and the crystalline electric field will then lift the (2J + 1)-fold degeneracy of the freeion state. The CEF interactions are commonly described by the parametrization of Lea et al. (1962), Wx o + 504) + W ( 1 - X) (oO H,f = B4(O ° + 50~) + B6(O ° + 21064) = --~-(04 F~

210~),

(20) where W is an energy scale factor and x represents the relative weight of the fourthand sixth-order terms. The quantities F4 and F6 are numerical factors (Lea et al. 1962). The CEF parameters B,", W and x for several members in the RPd2 Sn series are listed in table 22. The results obtained indicate that the compounds with R = Dy, TABLE 22 Crystalline electric field parameters for various rare-earth ions in RPd2 Sn compounds. R Tb Dy Ho Er Tm Yb

B° [-1] (10-ZK) B° [1] (10-*K) -0.61 0.32 -0.39 -0.104 0.13

0.38 0.41 -0.60 1.48 -33.0

W(meV) I-2] x [2] +0.053 -0.036 +0.0287 -0.0450 +0.076 -0.530

-0.785 -0.509 +0.325 +0.3022 -0.513 -0.722

OES [2] 10.71 11.8 17.56 20.32 11.98 13.43

GSS [-2] M/NM M M M M/NM M

OES = overall energy splitting, GSS = ground state status, M = magnetic, NM = nonmagnetic, [11 Malik et al. (1985b), [-2] Li et al. (1989).

172

A. SZYTULA

Ho, Er or Yb have a crystal-field split ground state that is magnetic and, therefore, a magnetic ordering in these systems is expected at low temperatures. The results are in agreement with experimental data. For R = Tb or Tm (both have J = 6) the scaling values of x are located in the region of the LLW diagram (Lea et al. 1962) where the F3 and F5x energy levels are crossing, so that the separation energies between the ground state and the first excited state are small: 0.7 and 0.3 meV for R = Tb and Tm, respectively (Li et al. 1989).

Acknowledgements I am grateful to Professor J. Leciejewicz, Drs H. Hrynkiewicz and K. L~tka who spent much time in discussing many details of the manuscript. Special thanks are due to Miss G. Domoslawska for the preparation of the graphical part of this work.

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173

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Sales, B.C., and D.K. Wohlleben, 1975, Phys. Rev. Lett. 35, 1240. Sampathkumaran, E.V., and R. Vijayaragharan, 1986, Phys. Rev. Lett. 56, 2861. Sampathkumaran, E.V., R.S. Changhule, K.V. Gopalakrisharan, S.K. Malik and R. Vijayaragharan, 1983, J. Less-Common Met. 92, 35. Sampathkumaran, E.V., K.H. Frank, G. Kalkowski, G. Kaindl, M. Domke and G. Wortmann, 1984, Phys. Rev. B 29, 5702. Sampathkumaran, E.V., G. Kalkowski, C. Laubschat, G. Kaindl, M. Domke, G. Schmiester and G. Wortmann, 1985, J. Magn. & Magn. Mater. 47-48, 212. Sampathkumaran, E.V., S.K. Dhar and S.K. Malik, 1987, Proc. Int. Conf. Valence Fluctuations (Bangalore, India) p. B13. Sampathkumaran, E.V., S.K. Dhar, N. Nambudripad, R. Vijayaragharan, R. Kuentzler and Y. Dossmann, 1988, J. Magn. & Magn. Mater. 76-77, 645. Sanchez, J.P., K. Tomala and R. Kmie6, 1988, J. Phys. 49, C8-435. Sanchez, J.P., K. Tomala and K. Ltatka, 1990, to be published. Schlabitz, W., J. Baumann, G. Neumann, D. Pliimacher and K. Reggentin, 1982, in: Crystalline Electric Field Effects in f-Electron Magnetism, eds R.P. Guertin, W. Suski and Z. Zolnierek (Plenum Press, New York) p. 289. Schobinger-Papamantellos, P., and F. Hulliger, 1989, J. Less-Common Met. 146, 327. Schobinger-Papamantellos, P., Ch. Routsi and J.K. Yakinthos, 1983, J. Phys.-Chem. Solids 44, 875. Schobinger-Papamantellos, P., A. Niggli, P.A. Kotsanidis and J.K. Yakinthos, 1984, J. Phys.Chem. Solids 45, 695. Sekizawa, K., Y. Takano, H. Takigami and Y. Takahashi, 1987, J. Less-Common Met. 127, 99. Severing, A., E. Holland-Moritz, B.D. Rainford, S.R. Culverhouse and B. Frick, 1989, Phys. Rev. B 39, 2557. Shelton, R.N., H.F. Braun and E. Misick, 1984, Solid State Commun. 52, 797. Shelton, R.N., L.S. Hausermann-Berg, M.J. Johnson, P. Klavius and H.D. Yang, 1986, Phys. Rev. B 34, 199. Shigeoka, T., 1984, J. Sci., Hiroshima University, A 48/2/103. Shigeoka, T., H. Fujii, H. Fujiwara, K. Yagasaki and T. Okamoto, 1983, J. Magn. & Magn. Mater. 31-34, 209.

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179

Slebarski, A., 1980, J. Less-Common Met. 72, 231. Slebarski, A., 1987, J. Magn. & Magn. Mater. 66, 107. Slebarski, A., and W. Zachorowski, 1984, J. Phys. F 14, 1553. Stanley, H.B., J.W. Lynn, R.N. Shelton and P. Klavius, 1987, Phys. Rev. J. Appl. Phys. 61, 3371. Steeman, R.A., E. Frikkee, R.B. Helmholdt, A.A. Menovsky, J. van den Berg, G.J. Nieuwenhuys, and J.A. Mydosh, 1988, Solid State Commun. 66, 103. Steglich, F., 1989, J. Phys.-Chem. Solids 50, 225. Steglich, F., J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz and H. Schiller, 1979, Phys. Rev. Lett. 43, 1892. Steglich, F., K. Wienand, W. Klamke, S. Horn and W. Lieke, 1982, in: Crystalline Electric Field Effects in f-Electron Magnetism, eds R.P. Guertin, W. Suski and Z. Zolnierek (Plenum Press, New York) p. 341. Steglich, F., C.D. Bredl, W. Lieke, U. Rauchschwalbe and G. Sparn, 1984, Physica B 126, 82. Stewart, A.M., 1972, Phys. Rev. B 6, 1985. Stewart, G.A., and J. ~ukrowski, 1982, in: Crystalline Electric Field Effects in f-Electron Magnetism, eds R.P. Guertin, W. Suski and Z. Zolnierek (Plenum Press, New York) p. 319. Stewart, G.R., 1984, Rev. Mod. Phys. 56, 755. Suski, W., 1985, Physica B 130, 195. Szytuta, A., 1990, J. Less-Common Met. 157, 167. Szytuta, A., and J. Leciejewicz, 1989, in: Handbook on the Physics and Chemistry of rare Earths, Vol. 12, ch. 83, eds K.A. Gschneidner Jr and L. Eyring (North-Holland, Amsterdam) p. 133. Szytula, A., and S. Siek, 1979, J. de Phys. 40, C5162. Szytu|a, A., and S. Siek, 1982a, Proc. 7th Int. Conf. on Solid Compounds of Transition Elements, Grenoble, IIA1 I. Szytuta, A., and S. Siek, 1982b, J. Magn. & Magn. Mater. 27, 49. Szytuta, A., and I. Szott, 1981, Solid State Commun. 40, 199. Szytuta, A., J. Leciejewicz and H. Bificzycka, 1980, Phys. Status Solidi A 58, 67. Szytuta, A., W. Bazela and J. Leciejewicz, 1983, Solid State Commun. 48, 1053. Szytuta, A., M. Slaski, H. Ptasiewicz-Bak, J. Leciejewicz and A. Zygmunt, 1984, Solid State Commun. 52, 396.

180

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chapter 3 COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

O. BECKMAN and L. LUNDGREN Department of Technology Uppsala University Box 534, S-751 21, Uppsala, Sweden

Handbook of Magnetic Materials, Vol. 6 Edited by K.H.J. Buschow © Elsevier Science Publishers B.V., 1991 181

CONTENTS 1. I n t r c d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. T X c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 X: g r o u p ]lI; B . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1. M n B , F e B , C o B . . . . . . . . . . . . . . . . . . . . . . . 2.1.2. P s e u d o b i n a r y m o n o b o r i d e s . . . . . . . . . . . . . . . . . . . 2.2. X: g r o u p IV; Si, G e , Sn . . . . . . . . . . . . . . . . . . . . . . . 2.2.1. C u b i c F e S i 0320) s t r u c t u r e . . . . . . . . . . . . . . . . . . . . 2.2.1.1. M n S i . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1.2. F e G e , c u b i c B20 . . . . . . . . . . . . . . . . . . . . 2.2.1.3. F e l - t C o t S i . . . . . . . . . . . . . . . . . . . . . .

186 187 187 187 188 188 189 189 191 191

2.2.1.4. M n l _ t C o t S i . . . . . . . . . . . . . . . . . . . . . 2.2.1.5. C r l _ t M n t G e . . . . . . . . . . . . . . . . . . . . . 2.2.1.6. C r l _ t F e t G e . . . . . . . . . . . . . . . . . . . . . . 2.2.1.7. C r G e 1 _=Six . . . . . . . . . . . . . . . . . . . . . . 2.2.2. U C x a g o n a l C o S n (B35) s t I u c t u r e . . . . . . . . . . . . . . . . . 2.2.2.1. F e C e , hexagol~al B35 . . . . . . . . . . . . . . . . . . 22.2.2. F e S n . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3. M o n c c l i n i c C o G e ~,t~ucture . . . . . . . . . . . . . . . . . . . X: g r o u p V; P, As, 5b, Bi . . . . . . . . . . . . . . . . . . . . . . 2.3.1. P17osphides . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1.1. M n P . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1.2. F e P . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1.3. P s e u d o b i n a r y p h o s p h i d e s . . . . . . . . . . . . . . . . .

192 193 193 193 193 193 194 195 195 198 198 202 202

2.3.1.4. M n l - t C r t P . . . . . . . . . . . . . . . . . . . . . 2.3.1.5. M n l - t F e t P . . . . . . . . . . . . . . . . . . . . . 2.3.1.6. M n l _ t N i t P . . . . . . . . . . . . . . . . . . . . . 2.3.2. A r s c n i d e s . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2.1. C r A s . . . . . . . . . . . . . . . . . . . . . . . 2.3.2.2. M n A s . . . . . . . . . . . . . . . . . . . . . . . 2.3.2.3. F e A s . . . . . . . . . . . . . . . . . . . . . . . 2.3.3. F s e u d o b i n a r y a r s e n i d e s . . . . . . . . . . . . . . . . . . . . 2.3.3.1. (V, Cr)As, (Ti, Cr)•s . . . . . . . . . . . . . . . . . . 2.3.32. M n x _ t C r t A s . . . . . . . . . . . . . . . . . . . . 2.33.3. M n l _ t T i ~ A s . . . . . . . . . . . . . . . . . . . . 2.3.3.4. M n x _ t F e t A s . . . . . . . . . . . . . . . . . . . . 2.3.4. P s e u d o b i n a r y c o m p o u n d s w i t h a e o r r m e n c a t i c n . . . . . . . . . 2.3.4.1. C r A s l _:,Ix . . . . . . . . . . . . . . . . . . . . .

202 203 203 203 203 203 206 206 206 207 208 208 208 208

2.3.

182

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

COMPOUNDS 2.3.4.2. 2.3.4.3. 2.3.4.4.

OF TRANSITION

ELEMENTS

WITH NONMETALS

MnAsl_xPx . . . . . . . . . . . . . . . . . . . . . . FeAsl_~Px . . . . . . . . . . . . . . . . . . . . . . Mnl-tCrtAsl-xP~ . . . . . . . . . . . . . . . . . . .

2.3.4.5. C r A s l _ x S b x . . . . . . . . . . . . . . . . . . . . . Antimonides, including MnBi . . . . . . . . . . . . . . . . . . 2.3.5.1. C r S b . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.2. M n S b . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.3. F e l + t S b . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.4. C o S b . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.5. M n B i . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6. P s e u d o b i n a r y a n t i m o n i d e s . . . . . . . . . . . . . . . . . . . . 2.3.6.1. M n l _ t T i t S b . . . . . . . . . . . . . . . . . . . . . 2.3.6.2. C r 1 _ t C o t S b . . . . . . . . . . . . . . . . . . . . . . 2.3.6.3. M n 1 _ t C r t S b . . . . . . . . . . . . . . . . . . . . . 2.4. X: g r o u p VI; S, Se, Te . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1. CrS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2. C r S e . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3. C r 1 tTe . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4. M n S . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.5. M n T e . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.6. V1 tCr~Se . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.7. C r A s l _ x S e x . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.8. C r T e l _ ~ S e x . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.9. C r T e l x S b x . . . . . . . . . . . . . . . . . . . . . . . . . 3. T 2 X - a n d T T ' X c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . 3.1. X: g r o u p III; B . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. ( F e l _ t C o t ) 2 B . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. ( F e l _ t M n t ) 2 B . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3. (Nia tTt)zB . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. X: g r o u p IV; Si, G e , Sn . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. M n C o S i . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. M n N i G e . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3. M n ( C o l _tNit)Si . . . . . . . . . . . . . . . . . . . . . . . 3.2.4. M n C o ( S i l _ ~ G e x ) . . . . . . . . . . . . . . . . . . . . . . . 3.2.5. M n ( C o l _ ~ N i ~ ) G e . . . . . . . . . . . . . . . . . . . . . . . 3.2.6. M n N i ( S i l _ x G e x ) . . . . . . . . . . . . . . . . . . . . . . . 3.2.7. M n R h S i . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.8. C o m p o u n d s w i t h h e x a g o n a l N i z l n - t y p e s t r u c t u r e . . . . . . . . . . . 3.2.9. M n C o S n . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. X: g r o u p V; P, As, Sb . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1. P h o s p h i d e s . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.1. F e 2 P . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.2. F e z - t P . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.3. ( C r l _ t F e ~ ) 2 P . . . . . . . . . . . . . . . . . . . . . 3.3.1.4. C r F e P . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.5. ( M n l _ t F e t ) / P . . . . . . . . . . . . . . . . . . . . . 3.3.1.6. M n F e P . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.7. M n 2 P . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.8. ( F e l _ t C o t ) 2 P . . . . . . . . . . . . . . . . . . . . . 3.3.1.9. ( F e l _ t N i t ) 2 P . . . . . . . . . . . . . . . . . . . . . 3.3.1.10. ( C r a _ ~ N i t ) z P . . . . . . . . . . . . . . . . . . . . . 3.3.1.11. ( M n l _ r C o ~ ) 2 P . . . . . . . . . . . . . . . . . . . . . 3.3.2. A r s e n i d e s . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2.1. C r z A s . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.

183 208 209 209 209 210 210 210 211 211 211 212 212 212 212 212 212 212 213 214 214 214 214 215 215 215 215 217 218 218 218 219 221 221 222 222 223 223 223 224 224 225 225 231 232 232 232 233 233 233 234 234 235 237 237

184

O. BECKMAN

a n d L. L U N D G R E N

. . . .

237 239 239 239 240 240 241 241 241 242 243

3.3.3.1. F e 2 ( P l _ ~ A s x ) . . . . . . . . . . . . . . . . . . . . . 3.3.3.2. M n F e ( P ~ _ ~ A s x ) . . . . . . . . . . . . . . . . . . . . 3.3.3.3. M n C o ( P l _ x A s x ) . . . . . . . . . . . . . . . . . . . . 3.3.4. A n t i m o n i d e s . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4.1. M n / S b . . . . . . . . . . . . . . . . . . . . . . . 3.3.4.2. M n 2 _ t C r t S b . . . . . . . . . . . . . . . . . . . . . 3.3.4.3. O t h e r m o d i f i e d M n 2 S b c o m p o u n d s . . . . . . . . . . . . . 3.3.4.4. M n z S b x _ x A s x . . . . . . . . . . . . . . . . . . . . . 3.4. T T ' X c o m p o u n d s w i t h a 4 d e l e m e n t . . . . . . . . . . . . . . . . . . . 3.4.1. F e R u P . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2. F e R h P . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3. M n R u P . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4. M n R h P . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.5. M n R u A s . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.6. M n R h A s . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.7. ( C r x _ r P d t ) 2 A s . . . . . . . . . . . . . . . . . . . . . . . . 4. T X 2 c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. C r B 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. V l - t C r t B 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. M n B 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. F e G e 2 , F e S n / , M n S n 2 . . . . . . . . . . . . . . . . . . . . . . . 4.4.1. F e G e / . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2. F e S n / . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3. M n S n / . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. C r S b 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6. C r t F e l _ t S b 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7. M n S 2 , M n S e 2 , M n T e 2 . . . . . . . . . . . . . . . . . . . . . . . 4.7.1. M n S 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.2. M n S e / . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.3. M n T e 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8. C o S / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9. C o S e 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10. T e r n a r y s y s t e m s . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10.1 NiSz_~Se~ . . . . . . . . . . . . . . . . . . . . . . . . . 4.10.2. C o P x S 2 _ x , C o A s x S 2 _ x , C o S e x S 2 _ ~ . . . . . . . . . . . . . . . . 5. T 2 X 3 , T 3 X 4 , T s X 6 c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . 5.1. C r z S 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Cr2Se3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. C r 2 T % . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. C r z S a _ x T e x . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. C r 2 S e 3 _ ~ T e x . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. F e / T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7. C r t F e 2 _ t T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . .

243 243 245 245 245 246 247 248 249 250 250 250 250 251 251 252 252 252 254 254 254 254 254 255 256 256 257 257 257 258 258 259 259 259 259 259 259 260 260 262 262 262 262

3.3.3.

3.3.2.2. M n 2 A s . . . . . . . . . . 3.3.2.3. F e z A s . . . . . . . . . . . 3.3.2.4. C o z A s . . . . . . . . . . 3.3.2.5. ( C r l _ ~ M n t ) 2 A s . . . . . . . 3.3.2.6. V M n A s . . . . . . . . . . 3.3.2.7. ( M n l _ t F e t ) / A s . . . . . . . 3.3.2.8. ( F e l _ t C o t ) 2 A s . . . . . . . . 3.3.2.9. ( M n l _ t C o t ) 2 A s . . . . . . . 3.3.2.10. M n ( F e , C o ) A s a n d M n ( C o , Ni)As 3.3.2.11. ( C r l _ t N i t ) z A s . . . . . . . . Arseno-phosphides . . . . . . . . .

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

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

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

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

. . . . . . . .

COMPOUNDS

OF TRANSITION

ELEMENTS

WITH NONMETALS

5.8. C r 3 S 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9. C r 3 S e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10. C r 3 T e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11. Cr3Se4_xTe~, . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.12. C r s S 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.13. C r s T e 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. T 3 X c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. M n 3 S i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. M n 3 G e , M n 3 S n . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. M n ~ G e , t e t r a g o n a l p h a s e . . . . . . . . . . . . . . . . . . . . . . 6.4. F % Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. F e 3 _ t T t S i . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. F % G e , h e x a g o n a l D019 . . . . . . . . . . . . . . . . . . . . . . . 6.7. F % G e , c u b i c L12 . . . . . . . . . . . . . . . . . . . . . . . . . 6.8. ( F e l - t V t ) 3 G e . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.9. ( F e l _ t N i t ) 3 G e . . . . . . . . . . . . . . . . . . . . . . . . . . 6.10. F % S n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11. M n 3 P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.12. F e 3 P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. T s X 3 c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. F e s P B z a n d F e s S i B 2 . . . . . . . . . . . . . . . . . . . . . . . . 7.2. M n s P B 2 a n d M n s S i B z . . . . . . . . . . . . . . . . . . . . . . . 7.3. M n s S i ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4. M n s G e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5. M n s ( G e l _ x S i x ) 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6. F % G % . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7. ( F e t M n l _ t ) s G % . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8. ( F e t T l _ t ) s G e 3 , T = N i o r C o . . . . . . . . . . . . . . . . . . . . . 7.9. F % S i 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.10. M n s S n 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.11. F e s S n 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.12. (Fe, T ) s S n 3 , T = N i o r C o . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

185 262 262 262 263 263 264 264 264 265 266 267 268 268 268 269 269 269 269 269 270 272 272 273 273 273 274 274 275 275 275 276 276 276

1. Introduction The ferromagnetism of transition metal interrnetallic compounds has been covered by Booth (1988) in volume IV of this series. The present chapter is a supplement to Booth's chapter, since it deals with compounds of transition metals with nonmetallic and semimetallic elements. In order to keep the size of this chapter within reasonable limits, we have excluded carbides, nitrides, oxides and halides. The chapter then closely covers the scope of the combined physics and chemistry conference series International Conference of Solid Compounds of Transition Elements. However, sulfides are only treated when there is a direct connection to related selenides and tellurides. The present compilation does not exclusively deal with ferromagnetic compounds. The intention has been to cover all types of ordered magnetic structures, i.e., ferromagnetism as well as ferri-, antiferro- and helimagnetism. However, disordered magnetic systems such as spin glass and amorphous magnetism are excluded. The compounds are listed according to the stoichiometric composition. The first two sections are devoted to the large groups TX and T2X, TT'X, where T is a transition element and X a nonmetal element. Then follow sections on various Tr, Xn compounds. Within each section, the compounds are arranged according to the nonmetallic elements of the third, fourth, fifth and sixth group of the periodic table. In the chemical formulas, we have arranged the elements according to increasing atomic number. The magnetic phase diagrams are presented according to the same rule. Each section (subsection) starts with a survey of the relevant crystallographic structures. Sometimes there is an ambiguity in the literature as regards crystal settings. In those cases, we have followed Hahn (1983). In a separate table we have given a summary of lattice parameters and basic magnetic data in order to give the reader a schematic overview. Our intention has also been to present the overwhelmingly large piece of information in the literature in simplified magnetic phase diagrams compiled from several scientific papers. For more detailed information, the reader should consult the references quoted. The magnetic moment is usually given as the low-temperature saturated moment ~ts and expressed in Bohr magnetons, /~B. The paramagnetic moment, which is calculated from the slope of a 1/g versus Tcurve, is expressed as #off and occasionally as #p (= 2S). A g-factor of g = 2 is then assumed.

186

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

187

2. TX compounds 2.1. X : group III; B 2.1.1. MnB, FeB, CoB

These monoborides crystallize in the orthorhombic FeB (B27) structure; space group Prima, No. 62 (table 1). As an example, fig. 1 shows the ac projection of the FeB structure, where both iron and boron occupy the 4(c) sites (x, 1, z) with x = 0.180, z = 0.125 for Fe, and x = 0.031, z = 0.620 for B (Kiessling 1950). MnB and FeB show ferromagnetic ordering, and data by Lundqvist et al. (1962) and Cadeville (1965) on these compounds are given in table 2. Besides To, the paramagnetic Curie temperature, 0p, the effective number of Bohr magnetons ]~eff with #p = 2S, and the saturation moment #s are given. CoB exhibits diamagnetic properties. CoB was reported to be ferromagnetic by Lundqvist et al. (1962), probably because of contamination by Co2 B (Cadeville 1965). TABLE 1 Crystallographic parameters for some TB compounds. Compound

a (/~)

b (A)

c (/~)

Ref.

MnB FeB CoB

5.560 5.506 5.253

2.977 2.952 3.043

4.145 4.061 3.956

Kiessling (1950) Aronsson (1961) Aronsson (1961)

Fe

B

O ~

° 3 !4

Fig. 1. Crystal structure of FeB (orthorhombic), as projected on the

ac

plane in the Pnma setting.

TABLE 2 Magnetically ordered monoborides. Compound MnB FeB

Tc (K)

0p (K)

fleff(#B)

pp = 2S

Ps (~B)

578 572 598 582

575 600 625 646

2.71 2.70 1.84 2.43

1.89 1.88 1.09 1.63

1.92 1.84 1.12 1.12

Ref. Lundqvist et al. (1962) Cadeville (1965) Lundqvist et al. (1962) Cadeville (1965)

188

O. BECKMANand L. LUNDGREN

From M6ssbauer measurements, Bunzel et al. (1974) find an internal field of 11.8 T for FeB. They conclude that the spins lie close to the ab plane in the Pbnm setting, i.e., the ac plane in Pnma as shown in fig. 1. The M6ssbauer data indicate that the spins deviate about 20 [] from the a axis; the same angle as the Fe-Fe bonds form with the a axis. The structure should be described as canted ferromagnetism. Li and Wang (1989) performed linearized augmented plane-wave band calculations for FeB. The boron 2s a n d 2p bands, well below the Fermi surface, hybridize and form covalent B-B bonds. There is no electron transfer to iron. 2.1.2. Pseudobinary monoborides Cadeville and Meyer (1962) and Cadeville (1965) studied several pseudobinary monoborides (fig.2). (Mn, Fe)B shows a maximum Curie temperature of 789 K at Mno.sFeo.sB. The saturation magnetization decreases linearly from MnB to FeB with 0.8#s per d-electron. In (Fe, Co)B, the Curie temperature and saturation magnetization decreases linearly with 1.12#B per d-electron aiming at Tc = OK for Feo.09Co0.91B. A similar behaviour was observed for (Mn, Co)B. The saturation magnetization decreased linearly to zero for CoB with a slope of 0.96#B per d-electron. Substitution of chromium decreases Tc as well as #s (fig. 2). The latter has a slope of 3,u b per d-electron, a value that also applies to vanadium substitution. 2.2. X: group IV," Si, Ge, Sn Only a few TX compounds with group IV elements are magnetically ordered. Since the type of magnetic order is closely related to the crystal structure, it is convenient to arrange the material according to the structures presented in table 3. Table 4 gives a survey of the magnetically ordered stoichiometric TX compounds of group IV. FeGe exists in three different polymorphs (Richardson 1967a,b). The low-temperature B20 polymorph transforms at about 630°C to the B35 modification, which in

T c (K)

~t s (rt B)

1000.

. 2

500

0

0

CrB

MnB o Curie temp Tc

FeB []

CoB

Sat. morn. ~-s

Fig. 2. Curie temperatureand saturationmomentof pseudobinarymonoborides.

189

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS TABLE 3 TX (X is a group IV element) crystal structures. Compound

Structure

Space-group

FeSi CoSn CoGe

Cubic B20 Hex. B35 Monocl.

P213 P6/mmm C2/m

No 198 No 191 No 12

M=4 M=3 M=8

TABLE 4 Magnetically ordered TX (X is a group IV element) compounds. Compound

Magn. order*

Struct.

a (A)

MnSi (Fe, Co)Si FeGe

H H H AF AF AF

B20 B20 B20 Monocl. B35 B35

4.558

FeSn

b (/~)

c (A)

fl (deg)

TN (K)

Tt (K)

29.5

#s Ref.t (PB) 0.4 [a]

See text 4.700 11.838 5.002 5.300

3.937

4.9336 4.055 4.449

279 103.514 340 411 368

120

1.0 [b] I-c,d] 1.7 I-d] 1.7 l-e]

* Magnetic order: H = helix, AF = antiferromagnetism. References are only given to structural parameters. For other data, see text. "~References: [a] Shirane et al. (1983). [b] Richardson (1967b). [el Different magnetic moments for different lattice sites (Felcher et al. 1983). [d] Richardson (1967a). I-el Nial (1947).

turn transforms at 740°C to the monoclinic CoGe structure. This structure decomposes at 750°C. 2.2.1. Cubic FeSi (B20) structure The cubic FeSi (B20) structure is lacking inversion symmetry, and is, therefore, a good candidate for a long-range magnetic superstructure called a Dzyaloshinskii spiral (Dzyaloshinskii 1964). Nakanishi et al. (1980) and Bak and Jensen (1980) analyzed the cubic FeSi structure and found that a helical spin density wave along the [-100] or [111] direction will appear if the anisotropy energy is small. A helical spin structure, in fact, exists in both MnSi and cubic FeGe, as well as in some ternary (Fe, Co)Si compounds. 2.2.1.1. MnSi. The manganese and silicon atoms occupy the 4(a) site (x, x, x) with x -- 0.138 for Mn and x = 0.845 for Si (Ishikawa et al. 1977a) (fig. 3). Williams et al. (1966) and Wernick et al. (1972) reported MnSi to order magnetically at 30 K. At 1.4 K, the magnetization increases linearly with field up to a saturation value of 0.4#B at 0.62 T. This is significantly smaller than the moment of 1.4#B obtained from/~eff = 2.19#B in the paramagnetic region. Fawcett et al. (1970) measured the thermal expansion and specific heat of MnSi, and found the transition to be of second order with a change in magnetic entropy of Sm = 0.385 J/K tool (however, note the correc-

190

O. BECKMAN and L. LUNDGREN

Mn

0 Fe

Si

• Ge

Fig. 3. Crystal structure of MnSi and FeGe (cubic B20).

tion in the paper by Ishikawa et al. 1977a). From renormalization group theory, Bak and Jensen (1980) predicted the transition to be of first order in the P213 space group. As mentioned above, a theoretical analysis shows that MnSi should have a helical spin structure. This has been confirmed by ESR (Date et al. 1977), by N M R (Motoya et al. 1976, 1978a) and by neutron diffraction experiments. By means of small-angle neutron diffractometry, Ishikawa et al. (1976, 1977a,b) have shown that MnSi has a spiral magnetic structure with a long period of 180 A in the (111> direction below TN=29.5 +0.5 K. In a magnetic field larger than 0.15 T, a conical structure is stabilized with the cone angle close to ferromagnetic alignment at 0.62 T at 1.4 K. Because of the small anisotropy energy, the spiral axis will be aligned parallel to an applied magnetic field for fields larger than 0.4 T. A magnetic phase diagram has been deduced by Kusaka et al. (1976) from ultrasonic attenuation studies and by Ishikawa and Arai (1984) from small-angle neutron scattering (fig. 4). Using polarized

1

B(T)

MnSi para (induced ferro) 0.5 conical para helix 0

1'0

10

"

' T(K) 30

Fig. 4. Magnetic phase diagram of MnSi from Kusaka et al. (1976) and Ishikawa and Arai (1984). Region A is a paramagnetic (or nearly paramagnetic) phase, which penetrates into the ordered phase.

COMPOUNDS OF TRANSITIONELEMENTS WITH NONMETALS

191

neutrons, Shirane et al. (1983) have studied the helicity of the helical spin density wave. In two consecutive papers Tanaka et al. (1985) and Ishida et al. (1985) report investigations of single-crystal MnSi as regards the crystal chirality by convergent-beam electron diffraction, and the helicity of the helical spin density wave by polarized-neutron diffraction. They found a left-handed helical spin density wave in left-handed single crystals indicating a negative sign of the DzyaloshinskiiMoriya interaction. The band structure of ferromagnetic MnSi was calculated by Taillefer et al. (1986), showing good agreement with de Haas-van Alphen (DHVA) measurements. They noted very high cyclotron masses (~ 15too). Conventional Stoner theory gave a very high ordering temperature, which, however, was drastically reduced to a value close to the experimental value when the strong spin fluctuations, characteristic of MnSi, were taken into consideration. Zero-field positive muon spin relaxation (Matsuzaki et al. 1987) and thermoelectric power (Sakurai et al. 1988) studies have been performed on MnSi. 2.2.1.2. FeGe, cubic B20. The cubic polymorph of FeGe shows great similarities with MnSi as regards both crystal and magnetic structure. Iron and germanium occupy the 4(a) site (x, x, x) with x = 0.1352 and 0.8414 for Fe and Ge, respectively (Richardson 1967a), fig. 3. Lundgren et al. (1968, 1970) made magnetization measurements on powder and single crystals of FeGe. They found TN = 280 K. Data in the paramagnetic region gave #eef=2.1#R and a paramagnetic Curie temperature of 295 K. From magnetization and torsion measurements, they proposed a helical spin structure propagating in the [111] direction in zero field. Because of the small anisotropy energy, the helical axis turns parallel to an applied field already at some tens of a millitesla. With increasing magnetic field, the spins align ferromagnetically at about 0.2 T with a saturation moment of 1.0#B. W~ippling and Hfiggstr6m (1968) and Ericsson et al. (1981) confirmed from M6ssbauer measurements a spin structure directed along the [111] direction, in agreement with ESR measurements in the frequency range 3-35 GHz by Haraldson et al. (1978). A Dzyaloshinskii-type magnetic structure was observed by Wilkinson et al. (1976) in small-angle neutron diffraction experiments on powder samples, giving a repeat distance of 700 A. A magnetic field of 0.33 T made the helical spin structure collapse with the spins parallel to the field. Extended small-angle neutron diffraction by Lebech et al. (1989) have confirmed the helical spin ordering according to the theory of Bak and Jensen (1980). Lebech et al. found that cubic FeGe orders magnetically at 278.7 K into a long-range spiral with a period ~ 700 A, which is nearly independent of temperature. The propagating direction is along the [100-1 axis just below TN but changes to [111] with a pronounced hysteresis in the interval 211-245 K. In table 5, we give specific heat data for some B20 compounds, i.e., the coefficient of the linear electron term ~, the coefficient of the Debye T 3 law/~, and the Debye temperature 0 (Marklund et al. 1974). 2.2.1.3. Fe1-tCotSi. The pseudobinary compounds Fel_tCotSi with a cubic B20 structure (fig. 3) form disordered solutions in the whole concentration range. CoSi is

192

O. BECKMAN and L. LUNDGREN TABLE 5 Specific heat data for some TX, B20 compounds. Compound

7 (mJ/mol K 2)

fl (ktJ/mol K 4)

0 (K)

1.37 1.1 10.3

14.2 16.9 62.1

515 487 315

FeSi CoSi FeGe

a diamagnetic semimetal, while FeSi is a semiconductor with a small bandgap (0.05 eV). FeSi is paramagnetic with a broad maximum in susceptibility around 500 K (Jaccarino et al. 1967). The anomaly in susceptibility has been explained by Takahashi and Moriya (1979) and Gel'd et al. (1985) by taking into account the effect of spin fluctuations. As regards the pseudobinary compounds, Beille et al. (1981, 1983) have shown that Fel_tCotSi has a long-period helimagnetic structure in the region 0.05 < t < 0.80 similar to the one in MnSi and FeGe. However, in contradiction to MnSi, a right-handed helix of left-handed chirality was found in a single crystal (Tanaka et al. 1985, Ishida et al. 1985). The saturation magnetic moment and the N6el temperature show a maximum around t = 0.35 (fig. 5). Helical spin resonance and magnetization measurements by Watanabe et al. (1985) show similarities with the results obtained by Date et al. (1977) on MnSi. Motokawa et al. (1987) have made pulsed high-field magnetization measurements, but did not observe any remarkable change in magnetization. Right- or left-handed spin structures have been investigated by Ishimoto et al. (1986) by means of polarized neutrons.

2.2.1.4. Mnl_tCotSi.

Mnl_tCotSi also shows a long-period helimagnetic structure (Beille et al. 1983) for small Co concentrations. The N6el temperature decreases rapidly with increasing cobalt content. N M R and magnetization measurements have been reported by Motoya et al. (1978b).

Tc (K)

ktS (]-tB) -

50 ~

0.3 0.2 0.1

O'

D

0

i

0

FeSi

0'.5

O Curietemp.Tc

t

[] Sat.morn.P~S

CoSi

Fig. 5. Curie temperature and saturation moment of pseudobinary (Fe, Co)Si compounds.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS

193

2.2.1.5. Crl_tMntGe. CrGe is paramagnetic with an anomalous peak in the magnetic susceptibility at 45 K (Sato and Sakata 1983), indicating a nearly ferromagnetic metal. Substitution with manganese gives ferromagnetism for t/> 0.09, followed by a mixing with a spin-glass phase for t ~>0.17. For 0.24 ~ 0.03 the ordered magnetic state seems to change into a metamagnetic state, which is indicated by the shaded area in fig. 32. The local deformations of the crystal lattice caused by the vacancies result in large hysteresis effects of the magnetization curves. Zvada et al. (1988) have also studied the magnetic properties on nonstoichiometric samples.

232

O. BECKMAN and L. LUNDGREN

The great similarity between the magnetic phase diagrams for 'pressure on Fe2P', 'nonstoichiometric Fe2 P' and 'Mn substitutions in Fe2 P' is emphasized.

3.3.1.3. (Cr~-~Fet)eP. Only minute substitutions of Cr in Fe2P impose antiferromagnetism. M6ssbauer and magnetic susceptibility measurements by Dolia et al. (1988) show that only 1% Cr induces antiferromagnetism with a reduction of the transition temperature to 150 from 216 K in pure Fe2 P. Further substitutions of Cr reduces the transition temperature at a much slower rate. 3.3.1.4. CrFeP. M6ssbauer spectroscopic studies (H/iggstr6m et al. 1986a) indicated antiferromagnetic behaviour with a Nrel temperature of 265 K. The saturation magnetic hyperfine field at the Fe nuclei is only 1.0 T. 3.3.1.5. (Mnl-tFet)2P. This system has been studied extensively (Fruchart et al. 1969, Roger 1970, Nagase et al. 1973, Fujii et al. 1982, Srivastava et al. 1987, Chenevier et al. 1987, 1989). The main magnetic phase diagram is shown in fig. 34. According to Srivastava et al. (1987), the system crystallizes with the hexagonal structure for t~>0.76 and t~~0.30 is small (~0.30, the ferro-paramagnetic transitions are of first order and are accompanied by a discontinuous change in lattice parameters, without any change in the hexagonal symmetry. Figure 46 shows the temperature dependence of the axial ratio c/a for samples with various compositions. For the sample with x = 0.30, the discontinuous change in the lattice parameters are Aa/a = --0.90% and Ac/c = 1.74% with increasing temperature, i.e., a volume decrease of only 0.07%. There is some ambiguity whether this transition is to an antiferromagnetic or to a paramagnetic state. For the sample with x = 0.275, the magnetic phase transitions at 130 and 180 K do not give rise to any significant change in the lattice parameters. It was found by Zach et al. (1988) that the transition temperatures increase with the application of pressure. This observation implies that the effect of external pressure and the effect of chemical pressure are different, which emphasizes the importance of anisotropy effects.

COMPOUNDS OF TRANSITION ELEMENTS WITH NONMETALS c/a 0.58

245

MnFePl-xAs x X=0.275

~

0.30 040

0.57

I

#

i i

I I

0.56

,

!

0'550 4' 100

I

I

, 200

0.60

t

, 300

i

, T(K) 400

Fig. 46. Temperature dependence of the axial ratio c/a for some hexagonal MnFeP1-xASx compounds (after Krumbfigel-Nylund1974, Lundgren 1977, 1978). The average magnetic moment is 4.1#B in the hexagonal phase, independent of composition. The first-order transitions in MnFe(P, As) are presumably of the same origin as the occurrence of a crystallographic transition in the Fe2Pl-xAsx system (0.35 ~<x ~ -~

Fig. 19. Collinear magnetic structures in amorphous materials (Coey 1978).

a random structure into two sublattices is impossible (Simpson 1974). In crystalline materials, antiferromagnetism is defined by symmetry and requires equivalent atoms on equivalent sites. Both requirements cannot be fulfilled in an amorphous structure. The collinear ferrimagnetic structure shown in fig. 19c is observed for Gdl_xRx alloys with T = Fe, Co or Ni and thus represents a two-subnetwork structure containing two distinguishable groups of atoms. In this sense, e.g., FeNi or FeCo will not be discussed under the topic of the two-subnetwork alloys. In addition to these familiar types of magnetic order, noncollinear structures with 0 < S~Sj < IS~IISjI like speromagnetic, asperomagnetic and sperimagnetic order occur in amorphous alloys as illustrated in fig. 20. These structures involve a competing random anisotropy and exchange interaction where the local anisotropy aligns the magnetic moments along the locally varying crystalline field axis. All these structures represent arrangements of magnetic moments which are frozen at a sufficiently low temperature. The speromagnet can be considered as a random antiferromagnet and the asperomagnet as a random ferromagnet. Both represent one-subnetwork mag(a) a s p e r o m a g n e t

magnetization

~1 ¢ 0

(b) s p e r o m a g n e t

~1 = 0

(c) sperimagnet

~1 , 0

Fig. 20. Noncollinear magnetic structures in amorphous materials (Coey 1978).

MAGNETIC AMORPHOUS ALLOYS

317

netic structures. The speromagnetism was observed for Yl-xFex and Fo.75Feo.25 while anisotropy-dominated asperomagnetism was found for D y o . z l N i o . 7 9 . Other spin structures, where the ferromagnetic alignment is limited to domains of some nanometers, are discussed for amorphous Zr-Fe alloys (Rhyne and Fish 1985, Ryan et al. 1987b). Sperimagnetism occurs in two-subnetwork structures like rare-earth-transitionmetal alloys of composition Rt _xT~ where the large spin-orbit coupling of the nonS-state rare earths give rise to large local anisotropies. Two classes of alloys can be distinguished containing heavy and light rare earths. In the first case, the R and T moments are coupled antiparaUel and in the second case parallel according to Hund's rule and the exchange coupling between the spins of the R and T atoms involving negative coupling of the 5d rare-earth electrons and the 3d transition-metal electrons (Campbell 1972). The first case, representing the antiparallel alignment of the moments, is illustrated in fig. 20c and fig. 21a for a collinear T sublattice which is representative for Co-based alloys due to the strong ferromagnetic coupling of the Co sublattice. For light rare earths with a parallel alignment of R and T moments, the situation is shown in fig. 2lb. In Fe-based alloys also a distribution of the Fe moments can occur as shown in fig. 21c,d. The strength of the R - T exchange coupling depends on the R element (Beloritzky et al. 1987) and is related to the variation of the 4f-5d interaction which is larger for light rare earths because the spatial extent of the 4f and 5d electrons is reduced. The distribution of moments induced by local anisotropies is not uniquely associated with disordered structures. Rare-earth-iron garnets also show a distribution of rare-earth moments due to the high single-ion anisotropy at low temperatures (Clark and Callen 1968, Englich et al. 1985). Another possibility is the presence of an exchange interaction of both signs which Sperimognetic

a) Dy-Co

structures

b) Nd-Co

._---~ c) D y - F e

- __~ d) Nd-Fe

r a r e e a r t h moment t r a n s i t i o n meta[ moment

• . . . . . -~

Fig. 21. Sperimagnetic structures in amorphous rare-earth-transition-metal alloys containing heavy rare earths (Dy, Tb, etc.) and light rare earths (Nd, Pr, etc.) (Taylor et al. 1978). The configurations sketched in (a) and (b) represent an asperomagnetic R suhlattice and a collinear T sublattice, while in the configurations (c) and (d) both sublattices exhibit a noncollinear structure.

318

P. HANSEN

is associated with the spin-glass behavior. These materials possess a typical spinfreezing temperature defined experimentally by a sharp peak in the low-field susceptibility as shown in fig. 22a for amorphous Sbo.s0Feo.5o (Xiao and Chien 1985). The magnetic phase diagram of Sb-Fe alloys shown in fig. 22b indicates the ranges of composition and temperature where spin-glass behavior is observed. However, also speromagnets, exhibiting a random distribution of moments due to the random local anisotropy, show a spin-freezing temperature associated with the typical cusp in the low-field susceptibility and thus might be considered as a spin glass. A large variety of compositions of either crystalline and amorphous materials show spin-glass behavior (Moorjani and Coey 1984). There is a principal difference between amorphous Fe-based and Co-based alloys with respect to the magnetic structure. The former tend to spin-glass behavior or speromagnetic structures (Xiao and Chien 1987, Ryan et al. 1987a,b, 1988, Fukamichi et al. 1988, Wakabayashi et al. 1987, 1990, Kakehashi 1990a,b) while the latter in general exhibit good ferromagnetic order. This is associ10

>,

5

0

(o)

i

i

20

~0

60

T(K} 300 Sb1_ x F e x

200

/ para

o

F-

100

fe spin

o

g t a ~ s / Ie

I ,l 0,30

0.40

0.50

0,60

0.70

x

Fig. 22. (a) Low-field susceptibility (2.4 kA/m) versus temperature exhibiting the typical cusp at the spinfreezing temperature Tf for amorphous Sbo.soFeo.so and (b) the magnetic phase diagram for amorphous Sb-Fe alloys (Xiao and Chien 1985).

MAGNETICAMORPHOUSALLOYS

319

ated with the different bonding character of these alloys as it is shown by X-ray photoelectron spectroscopy (XPS) valence-band spectra (Amamou 1980, Amamou and Krill 1979, 1980) and the much higher exchange interaction of the Co alloys.

5.2. Influence of preparation conditions The structure of amorphous alloys represents no ideal statistical arrangement of atoms but depends on the particular preparation conditions leading to differences in the local atomic environments and nearest-neighbor distances, the occurrence of a typical microstructure or the incorporation of gas atoms. This gives rise to variations in the magnetic properties. The magnetic moment is less sensitive to structural differences while the Curie temperature, the coercivity, the uniaxial anisotropy and the compensation temperature occurring in ferrimagnets are strongly affected by structural changes and thus depend on the preparation parameters. The compositional variation of the specific magnetization and the Curie temperature for evaporated (Miyazaki et al. 1987a) and liquid quenched (Miyazaki et al. 1986) amorphous Sml-xFex alloys are shown in fig. 23. The magnetization data are independent of the preparation technique and agree with those of crystalline compounds indicated by the squares. The corresponding Tc variation reveals a completely different behavior for the two amorphous alloys, probably due to the higher amorphicity of the evaporated films. In the case of amorphous films prepared by sputtering, the deposition parameters are of significant importance (Niihara et al. 1985, Hashimoto et al. 1987, Heitmann et al. 1987a,b) as demonstrated in fig. 24 for the uniaxial anisotropy constant, Ku. The influence of the sputter atmosphere on Ku for magnetron sputtered Gdo.24Tbo.o4Feo.72 films (Heitmann et al. 1987a) is shown in fig. 24a, while the influence of the argon gas pressure on K~ for diode sputtered [-(Gd, Tb)l _xCox] 1_yAry films (Heitmann et al. 1987b) is shown in fig. 24b for different bias voltages. In the first case, an increasing oxidation of the rare earths causes a reduction of K~ and in the second case a change of the microstructure and resputtering effects at the growing film surface lead to the observed Ku variations. In these cases, also the compensation temperature, the Curie temperature and the coercivity are strongly affected. A very important parameter controlling the structural disorder is the effective cooling rate that can be influenced via the substrate temperature of vapor-quenched films. This is demonstrated in fig. 25, showing the variation of the coercive field, He, versus the substrate temperature, T~, of sputtered Sm~_ ~Cox films (Munakata et al. 1984). Films prepared at T~~ t~

>

o~

E c

"1-

-6

-3

0

v(mm/s)

6

k

0

I

1

I

2

I

3

Hhf (107A/m)

Fig. 31. Mrssbauer spectra of amorphous Y-Fe alloys at T = 1.6K. The corresponding hyperfine-field distributions are shown on the right-hand side of the figure, indicating a relatively increasing fraction of nonmagnetic iron (shaded area) with a decreasing iron content (Chappert et al. 1981).

330

P. H A N S E N

ity between hyperfine field and magnetic moment was established from crystalline Y-Fe alloys (Gubbens et al. 1974). The hyperfine-field distribution is shown on the right-hand side of fig. 31 and the shaded area indicates the relatively increasing fraction of nonmagnetic iron with decreasing x. The analysis of the spectra reveal an asperomagnetic order in the entire range of concentrations x > xc as demonstrated in fig. 32. This random ferromagnetism again can be attributed to a broad distribution of Fe-Fe exchange interactions including a significant fraction of antiferromagnetic bonds. The moment variation for amorphous La-Ni and Hf-Ni alloys (Buschow 1984b) is presented in fig. 33. Very similar results have been found for amorphous Y-Ni and Ce-Ni alloys (Fr6my et al. 1984). These alloys are ferromagnetic, but the onset of magnetic order takes place at much higher concentrations as compared to the corresponding Fe or Co alloys. Split bands. Valence bands of Ml-xTx alloys split into two resolvable parts at different energies when the difference in atomic number is greater or equal to two (Beebey 1964, Velicky et al. 1968). The split-band character is a consequence of polar d-d bonding and was experimentally confirmed for various amorphous alloys (Oelhafen et al. 1979, 1980). The concept of split bands, originally applied to crystal-

Yl-xFex

x=0.32 0.57

0.71

0.82

Fig. 32. Schematic representation of speromagnetic structures in amorphous Y-Fe alloys (Chappert et al. 1981).

0.6

Ml_xNix

/

"-b O.Z, ,:& 0.2 0

0.7

j ~ 0.8

M=Hf 0.9

1.0

x

Fig. 33. Concentration dependence of the average Ni moment in amorphous Hf-Ni and La-Ni alloys at T = 4.2 K (Buschow 1984b).

MAGNETIC AMORPHOUSALLOYS

331

line alloys (Berger 1977, Berger and Bergmann 1980), was extended to amorphous alloys (O'Handley and Berger 1978). The interpretation of magnetostriction (O'Handley 1978a, O'Handley and Berger 1978) and Hall effect (O'Handley 1978b) measurements for amorphous Bo.2o(FeCoNi)o.8 o alloys indicate that Fe and Ni indeed contribute to the valence-band density of states at different energies and thus a minimum in the density of states is present. This model was shown to account well for the compositional variation of the magnetostriction and spontaneous Hall effect in these alloys. Coordination bond model. This model was derived from valence-bond theory to account for the magnetic moment variation of crystalline and glassy transitionmetal-metalloid (M-T) alloys (Corb et al. 1982, 1983, Corb 1985). It assumes that the average T moment is suppressed according to the number of M neighbors and the strength of the M - T bonds. The model is based on a strong p - d bonding, causing a T moment reduction of one fifth of its moment for each 3d electron participating in the nonmagnetic covalent T - M bond. This leads to an average T moment suppressing for M1 -xTx alloys of the form fiT(X) = #° [1 -- (1 + ~--~-~)(1 -- 1)1,

(23)

representing a linear decrease of fiT with the metalloid concentration 1 - x. Z~ is the number of T atoms surrounding an M atom. This model accounts for the moment variation for various M - T alloys (Corb et al. 1982, 1983, Corb 1985, O'Handley 1987a, Stein and Dietz 1989), however, the band-gap model appears to be able to explain more general trends in a wider class of alloys (O'Handley 1987a). Although these models are contradictory in their basic origin, both lead to a linear decrease of 17 according to the relation fix(X) = #°1-1 - p(1 - x)], where the slope p differs according to the assumptions made in these models. Environment model. The third picture to interpret the moment variation is based on the structural disorder and accounts for the different environments of a transition metal (Jaccarino and Walker 1965). The probability of a T atom to have j nearest T neighbors out of a maximum number n is given by n!

P(x, k,n) - k!(n - k)!"

(24)

Assuming a minimum number j of nearest T neighbors to be necessary for a T atom to carry a moment #1 and for less than j T neighbors a moment #2, then fi(x) can be expressed in the form fi(x) = #1Pj(x) + #2 [1 - P~(x)], where Pj(x) = ~ P(x, k, n). k=j

(25)

332

P. HANSEN

In the case #1,/~2 ~ 0, no critical concentration is expected. For #2 = 0, a critical concentration can be calculated from the tangent of the turning point of/i(x) at x = xt by xc = xo/P}(xt) where xt is determined by Pj'(xt)= 0. The comparison between experimental data for amorphous Y - F e (Chappert et al. 1981, Coey et al. 1981), Y - C o (Buschow et al. 1977) and S n - C o (Teirlinck 1981) and the environment model is shown in fig. 34. The full lines represent the calculated result with j = 7 for Fe, j = 8 for Co in Y and j = 9 for Co in Sn assuming #2 = 0. This means that at least seven nearest Fe neighbors and eight or nine nearest Co 2.5 Y1-x mx

2.0

1.5

m

1.0

0.5

0

0

0.2

0.4

0.6

0.8

1.0

X

Snl_ x Co x

150

•

100 E

500 490 460 420 550 750 > 500 > 500 38 390 405 387 365 > 600 > 600 > 600 287 333, 350 351 > 900 47 250 260 290 300 375 600 > 600 > 600 > 600 > 400 15 400 Not magn. 105 < 50

T=omp(K) Amorphous

Crystalline

Gd + Tb + Tb + Tb +

Gd + Gd + 450 150 ~ 100 510 400 300 80 Gd + Tb + Tb + Tb +

Tb + Tb + 100 Dy + Dy +

500 250 Co + Dy + Dy +

Gd +

Gd + Gd + 410

230

Ho + 350 80

180 120 50 Fe + Ho + 325 270 150 Co +

Er + Tm+

Er + Tm +

Ho + 400 40

the rare earth except for Er-Co alloys. This can be attributed to the dominance of the Co-Co exchange for medium and high Co content. It should be noticed that the magnitude of Tc strongly depends on the preparation conditions affecting the structural disorder and thus the exchange coupling constants. In particular strong differences in Tc are observed for vapor-quenched and liquid-quenched alloys (Miyazaki et al. 1987a, Takahashi et al. 1988a,b), shown in fig. 23.


369

1000 RFe 2 800

600

400

. ~ -

orphous

200

a) 0 i ~ P t t t t i t ~ ~ ~ t La Ce Pr Nd P m S m Eu Gd Tb Dy Ho Er Tm Yb Lu R

200 Ro.69 C 00.31

150

100

50

0

0

De/ a Ce Pr N d P m S m Eu Gd Tb Dy Ho Er Tm Yb l u R

Fig. 59. Curie temperature for (a) crystalline(Buschow 1977)and amorphous (Heimanet al. 1976b)RFe2 alloys and (b) amorphous Ro.69Co0.31 alloys (Buschow 1980b).

5.5. Critical exponents Magnetically ordered systems undergo a second-order phase transition when passing the critical temperature. The magnetization represents the order parameter that is controlled by the reduced temperature e = (T/Tc) - 1 and the external magnetic field. The critical phenomena are discussed in terms of the static hypothesis (Domb and Hunter 1965, Widom 1965, Wilson 1974a,b), which can be expressed in the general form

I~lp +, where the signs + and - refer to T < Tc and T > To respectively. # and 6 are the critical exponents which refer respectively to the temperature dependence of M below

370

P. HANSEN

~0

0.2

0.4

x

0.6

0.8

1.0

Fig. 60. Compositional variation of the Curie temperature for amorphous R-T alloys prepared by evaporation (Hansen et al. 1989). The full symbols refer to Tc data taken from different investigators [Tb-Fe: Alperin et al. (1976), Heiman et al. (1976b), Busehow and van der Kraan (1981), Takayama et al. (1987); Tb-Co: Lee and Heiman (1975), Buschow (1980a), Busehow et al. (1980); Gd-Cu: Heiman and Kazama (1978b)]. The full lines for Dy-Fe and Ho-Fe were taken from Hansen et al. (1991).

1000 Rl-x COx oR=Sm •

p~

% ' f

• Er []z, Nd D y e /

500

O0

/m Id

i

0.20

i

0.40

i

x

i

0.60 0.80 1.00

Fig. 61. Compositional variation of the Curie temperature for amorphous R-Co alloys prepared by evaporation (Takahishi et al. 1988a,b).


371

Tc and the field variation of M at Tc according to the relations M ~ ( - e ) p ( H = 0 , T < Tc),

(61a)

( T = To, H--*0).

(61b)

M~H

1/~

The critical exponent 7 associated with the susceptibility above Tc is defined by the expression X-1 ~

(T>~ Tc).

(61c)

The critical exponent ~ is associated with the specific heat and is defined by Cn ~ e-"

(T ~> rc).

(62)

The static hypothesis, eq. (60), leads to the equalities 7 =/~(6 - 1), = 2(1 -/~) - 7.

(63a) 63b)

A comparison of the micromagnetic theory of phase transitions (Kronmfiller and F~ihnle 1980, F~ihnle and Kronmiiller 1980, F~hnle 1980, Herzer et al. 1980, 1981, Meyer and Kronmfiller 1982) with experimental data reveal that exchange fluctuations are the primary origin of the differences of the critical exponents between amorphous and crystalline materials. The examination of the critical behavior requires materials which possess values of Tc well below their crystallization temperatures. The critical exponents were determined from different representations such as Kouvel-Fisher plots, modified Arrott plots or scaling plots (Reisser et al. 1988), leading to slightly different results. Typical values of the critical exponents for some crystalline metals (Fe, Ni, Co, Gd) and amorphous alloys are compiled in table 13. The critical exponents predicted by the three-dimensional Heisenberg model are also listed in table 13. They are in reasonable agreement with the experimental data of many amorphous alloys. Also, the scaling laws are satisfied for many alloys. This can be ascribed to the longwavelength dependence of the critical fluctuations near Tc and, thus, the critical behavior is independent of the local atomic structure. This is confirmed by theoretical investigations (Harris 1974) predicting no influence of the structural disorder on the critical exponents. However, outside the critical region strong differences between amorphous and crystalline materials occur. This is obvious from the temperature dependence of the susceptibility and the effective exponent y(T) defined by (Kouvel and Fisher 1964) 7(T)-

dlnx -~ dine "

(64)

For amorphous alloys 7(T) typically shows a maximum in the temperature dependence as shown in fig. 62 for amorphous Zr-Fe (Reisser et al. 1988) in contrast to crystalline compounds where 7(T) decreases monotonically with temperature (F/ihnle

372

P. HANSEN

o

_,.- ~ o "-r. ~

izl 0

r~

"a

8 o

o

"-r. -,=,

,~ ~

~ o

~.~

~

~

~ .~ o

~f o o ~ o o I I + I +

o o o o o o o o I I I I I I I

o I

I

o o +1

+1 +1 ~

+1 +1 +1 +1

+1

,,-,1

S o'-'a ~t

4-1

I~

+1 4-1

+1 +1 r.--

4-1 +1

4-1

,,~

~ ~1 +1

~ ~ +1+1~

0 ~ ~1 ~ +1+1 +1

~1 ~

o

,-fi °

8

~1=o

"I. c~ d

"I, "I,

,-~

MAGNETICAMORPHOUSALLOYS

373

1.70 0

0

0

0

0

1.60

0

0

0

o

o

o

1,50

/

0

o 0 0 0

I.&0 Z ro.lO F eo.@o

1.30 200

i 250

i 300

i

350

&00

T(K]

Fig. 62. Temperature dependenceof the effectiveexponent7(T) for amorphous Fe-Zr with Tc= 207.5K (Reisser et al. 1988).

et al. 1983). A similar behavior for 7(T) was reported for disordered Po.25Feo.75 and Pdo.75Feo.zs alloys satisfying also the scaling laws (Seeger and Kronmiiller 1989).

5.6. Uniaxial magnetic anisotropy Amorphous magnetic alloys are expected to behave magnetically isotropic or to exhibit a low anisotropy in the case of thin films where the deposition on a substrate induces intrinsic stresses (d'Heude and Harper 1989) which may cause a stressinduced anisotropy. However, for most alloys a uniaxial anisotropy energy, E, = Ku sin 2 0,

(65)

was found with values of the uniaxial anisotropy constant, Ku, ranging between some hundred J m -a for field-induced anisotropies in metal-metalloid alloys and some hundred kJ m-3 for rare-earth-transition-metal films. 0 represents the angle between the preferred axis and the direction of magnetization. Significant larger K~ values occur for amorphous transition-metal-based alloys when the alloy is formed of two different magnetic atoms or for Co-based alloys (Ounadjela et al. 1989). The strong uniaxial anisotropies occurring in R-T films are due to the deposition process (evaporation, sputtering) causing locally an anisotropic atomic arrangement that leads to a preferred axis parallel to the film normal (K, > 0) or to an easy plane (K, < 0) of magnetization. The magnitude of K, depends on the degree of shortrange order and the magnitude of the magnetic anisotropy per atom. The former is primarily controlled by the energy of the atoms at the growing surface and the latter by spin-orbit coupling leading to high anisotropies for R-T alloys with non-S-state rare earths like Tb or Dy. Different origins were discussed to account for the observed anisotropies such as structural inhomogeneities (Graczyk 1978, Herd 1977, 1978, 1979, Katayama et al. 1977, Leamy and Dirks 1979, Mizoguchi and Cargill III 1979,

374

P. HANSEN

Yasugi et al. 1981, Kusuda et al. 1982a,b), incorporation of oxygen (Brunsch and Schneider 1978, Dirks and Leamy 1978, Leamy and Dirks 1979, Biesterbos et al. 1979, Tsunashima et al. 1980, Hoshi et al. 1982, van Dover et al. 1986, Heitmann et al. 1987a,b, Klahn et al. 1988), columnar microstructures (Suzuki 1983), stress-induced anisotropies (Tsunashima et al. 1978, Leamy and Dirks 1979, Takagi et al. 1979, Togami 1981, Labrune et al. 1982), dipolar interactions (Chaudhari and Cronemeyer 1975, Mizoguchi and Cargill III 1979, Wang and Leng 1990), pair ordering (Gambino et al. 1974, Taylor and Gangulee 1976, 1977), anisotropic exchange (Meiklejohn et al. 1987), bond orientation and anelastic deformation (Egami et al. 1987, Hirscher et al. 1990, Y. Suzuki et al. 1987). In one-subnetwork 3d-based alloys, usually low anisotropies are found originating primarily from the magnetostriction coupling the magnetization to the internal stresses (Egami et al. 1975, O'Handley 1975) or pair ordering (Luborsky 1977, Miyazaki and Takahashi 1978). The anisotropy constant of amorphous SiB-FeCo alloys in the as-quenched and field-annealed state (Miyazaki and Takahashi 1978) is shown in fig. 63. The observed anisotropies were associated with pair ordering. Typically Ku values up to 6 x 10 2 J m -3 were reached by field annealing (Luborsky 1978, Fujimori et al. 1984, Maehata et al. 1986) which is shown in fig. 64 for amorphous B-FeNi alloys. These anisotropies are associated with short-range pair ordering and interstitial or monoatomic ordering of the metalloids. However, also large anisotropies have been found in rare-earth-based one-subnetwork alloys prepared by liquid quenching as reported for Gd-Cu alloys (Algra et al. 1980). The uniaxial anisotropy in vapor-deposited rare-earth-transition-metal films strongly depends on the composition, the R and T component and the deposition parameters. The presence of oxygen leads to a selective oxidation of the R component and reduces

°'4/(a) '~

i~

0.2

Si°'lO B°'13 (Fel-× Cox)o.77

4

~ ~,

0/0

•

•

,

0.2

•

.

• ~---¢"0.4

0.6

0.8

1.0

0,6

0.8

1.0

X

O.lO

:z

0.05

0

I

I

0,2

0,4 X

Fig. 63. Compositional dependence of the room-temperature uniaxial anisotropy constant for amorphous (a) as-quenched and (b) annealed (T~ = 573K and H = 184kA/m) SiB-FeCo alloys prepared by melt quenching (Miyazaki and Takahashi 1978).


6

375

]

Bo.2o(Vex Nil->,)o.8o / ~

7o:===oo~ ' / ~ . . ~ - ' k ' k " , / = j .~_ . _ , _ L Z/'06.. ..... _'x.~\~, ... / 7°

.,

32s~...", ~ ~ . k . \ ~ . - ' t # 1i...:j ..... ...., . . . . . ".M / lillS'O.IOBo.12(FexC01-x)0.78.-#, : " ~ ~ ; ~ ,

15.oi.4" i.." {

~'. -~

/Po., 0 and x defined by eq. (72). The occurrence of a compositional and temperature compensation of 2s in CoFe-based alloys confirms the presence of these two mechanisms contributing to 2s. However, also the competition between two single-ion contributions was discussed to cause 2~ = 0 in B-CoMn alloys (du Tr6molet


383

TABLE 14 Room-temperature saturation magnetostriction for amorphous metal-metalloid alloys and rare-earthtransition-metal alloys. Alloy

2s(x 106)

Bo.zoFeo.so Po. 13Co.ovFeo.so Po.14Bo.06 Feo.40Nio.4o Bo.2oFeo.3oNio.so Po.o9Coo.ga Bo.2oCoo.so Bo.loSio.15Coo.75 Bo.2oFeo.o6Coo.v4 Bo.2oNo.4oCoo.4o Pro.2o Feo.so Smo.zoFeo.so Gdo.33 Feo.67 Tbo.2o Feo.so Tbo.33 Feo.67 DYo.aa Feo.67 Gdo.3oCoo.7o Gdo.23 C0o.77

(1)At H = 1600kA/m. (2)At H = 2000kA/m. * References: [1] O'Handley (1977b). [-2] Tsuya et al. (1975). [3] O'Handley (1976). [4] O'Handley (1978a). [5] Simpson and Brambley (1971).

31.0 31.0 11.0 8 -4.3 -4 -3 ~0 - 7 96 tl) 140~a) 20 220 ~1) 310~z) 38t2) 5 33

Refs.* [1] I-23 [3] [4] [5] [-4] [-6] I-7] [4] [8] [-8] [9] [8] [10] [10] [11] [11]

[6] Arai et al. (1976). [7] Jergel et al. (1989). [-8] Ishio (1988a). [-9] Moorjani and Coey (1984). [10] Clark (1980). [11] Twarowski and Lachowicz (1979).

de Lacheisserie and Yavari 1988). The magnetostriction arising from a disorder caused by randomly oriented easy axes follows a power law 2s(T) = 2s(0)m,(T)" with n < 3 (Cullen and del Moral 1990). The magnetostriction in amorphous rare-earth-transition-metal alloys is composed of an R and a T contribution where in the case of non-S-state rare earths 2s is primarily controlled by the strong single-ion contribution of the R atoms (Suzuki et al. 1988, del Moral and Arnaudas 1989) in accordance with the anisotropy. Alloys containing S-state rare earths are characterized by a magnetostriction which is comparable in magnitude with that of the T-based alloys. This is demonstrated in fig. 75, showing 2s versus x at T = 80 K for amorphous Y - T and G d - T alloys with T = Fe or Co (Yoshino and Masuda 1988). In the case of Y-Fe and G d - F e (fig. 75a), the variation of 2s reflects the behavior of Ms and Tc versus x. The value of 2s for G d - F e is higher than that of Y - F e alloys due to the positive Gd contribution. At the R-rich side, 2~ approaches zero for Y - F e or approaches the 2~ value for Gd in the case of G d - F e alloys because the Fe contribution vanishes at low x. At the Ferich side, 2s decreases due to the noncollinear structure of the Fe sublattice. Amorphous Y - C o and G d - C o alloys (fig. 75b) show a corresponding behavior at the

384

P. HANSEN

Bo.2o(COl_xF ex)o.eo i./~"~A\

P0.13C0.o71COl_xF ex}o.75 ,,/

g

,"•

lO

0

•

t

/..Y

2.--

S /"

/;~

/

\

"-

SIo.15Bo.lo( C%xFex)o.7s

' and the operators rt+ = rt~ _+i~r are linear combinations of the electron kinetic momentum operator defined by h n = p + 8-~5mc z [s x gV(r)].

(90)

V, is the sample volume and VV(r) is the electric field controlling the motion of the electron with spins s and momentum p. [e> and [fl> are linear combinations of wave functions with spin-up and spin-down states and the summation in eq. (89) extends over the occupied and unoccupied states. The second term in eq. (90) represents the spin-orbit contribution. Different approaches for the calculation of-'") ~ ( 2 ) were reported (Wang and ~'ik and t~ik Callaway 1973, Erskine and Stern 1973a, Singh et al. 1975, Laurent et al. 1979, Misemer 1988). In addition to the many features of the band structure, the magnitude of the spin-orbit coupling and the spin polarization are the significant parameters determining the magneto-optical effects. Some features of the measured spectra were reproduced by the theory for the crystalline metals (Fe, Ni, Co, Gd), however, parts of the spectra show a less satisfactory agreement between theory and experiment. Also relativistic band structure calculations were performed yielding only minor changes with respect to the nonrelativistic results (Ebert et al. 1988). 6.2.2. Intraband transitions

Normal electron scattering and skew scattering processes are responsible for the intraband transitions (Erskine and Stern 1973a,b, Voloshinskaya and Fedorov 1973, Voloshinskaya and Bolotin 1974, Reim et al. 1984). They contribute to the lowenergy part of the magneto-optical spectra. The frequency dependence originating from these processes yield (Erskine and Stern 1973a). cog f Q ax,=-g(a,>~f~+t/k

Fico(Y + i@-]~ ~j jj,

(91)

where f(co) = g22 + (y + ico)2. co2 = &re2N/m , and are the plasma frequency and the spin polarization, respectively. N and m* denote the concentration and the effective mass of conduction electrons, respectively. O denotes the skew scattering frequency and ~ = 1/7 is the normal scattering lifetime, t/ is proportional to the strength of the spin-orbit coupling. In the high-frequency limit, defined by (2)> 7 and (2)>>g2, eq. (91) yields t- '-rx( 1y ) - -

--

~/'] 1. The isotropic part of the magnetoresistance is displayed in fig. 100 for amorphous Dy-Ni and turns out to be positive in accordance with eq. (100) for a(2kv) > 1 and j > 0. The much smaller anisotropic part of the magnetoresistance is presented in fig. 100b. This anisotropy was ascribed to the quadrapole moment of the rare earth (Fert and Asomoza 1979, Asomoza et al. 1979a). The magnetoresistance was found to be positive for Dy-Ni, Ho-Ni (Asomoza et al. 1979b) and Ce-Co (Felsch et al. 1982) and negative for Er-Ni (Asomoza et al. 1979b) and DyGd-Ni (Amaral et al. 1988). Amorphous R - U with R = Gd or Tb reveal a sign change of Ap with temperature (Freitas et al. 1988). Below the spin-freezing temperature, an increasing portion of antiferromagnetic interactions become important, leading to a negative magnetoresistance according to eq. (100) with (Ji',lrk) < 0 in contrast to amorphous U - F e with collinear or random ferromagnetism where Ap > 0 due to a positive <Ji. Jk>. The latter is in agreement with results for amorphous Si-Fe (Shimada and Kojima 1978). Also, a negative magnetoresistance was observed in the spin-glass-like amorphous D y - U and N d - U systems (Freitas et al. 1988).

297 296

o

Dy0.2s N i 0 . 7 / /

29/. 295 ~

~ ~ 6

:zl. ~o.. 293 292

~0 kA/m

"et~z/"'-. ~ '2/.00 kA/m •" ~'H= 0 kA/m

~,.+'

291 "" Tc /

290

~ 0

q 20

i /*0

T(K}

t 60

i 80

100

Fig. 99. Temperaturedependenceof the resistivityfor amorphous Dy-Ni at differentmagneticfields(Fert et al. 1977, Asomozaet al. 1977a,b, 1979b).

420

P. HANSEN 2.5

(a} Dyo.25 Nio.75

2.0 /H=2400 kA/m 1600 k A / m 640 k A / m

1.5 C~

~1.0

0.5

I

20

10

30

40

T(K) (b)

T=I.2K 4.2 7.0 10.0

D Yo.25Nio.75 3.0

15.0 1,

(1)

where I(Ev) is the Stoner exchange integral evaluated at EF. This implies that local moment fluctuations at an icosahedral site could be either stabilized (>11) or destabilized (~ 2c. One of the important experimental observations of quasicrystal properties has

MAGNETISM AND QUASICRYSTALS

469

been the large resistivities (comparable to those of metallic glasses), and, therefore, the inferred short mean free paths [~1 A] in quasicrystals (Fukamichi et al. 1987). Sokoloff (1986) has considered the question of electron localization in quasicrystals (A1-Mn) by considering scattering from almost periodic potentials. In this work, weak pseudopotential theory and the Ziman method (Ziman 1961) are used to calculate scattering rates for a three-dimensional Penrose lattice. It was shown that the almost-periodic Penrose lattice proposed for quasicrystals did not contribute to the resistivity in any order of time-dependent perturbation theory. Thus, like perfect periodic crystals, the resistance at T = 0 K is not increased by the quasiperiodicity. Structural defects and/or large s-d resonant scattering matrix elements due to the Mn impurity states, must be introduced into the Penrose tiling to account for the large, nearly temperature-independent resistivity that characterizes QCs (Fukamichi et al. 1987). Smith and Ashcroft (1987) have used a nearly free-electron (NFE) model and an A1 pseudopotential to calculate the electronic structure for atoms on a Penrose lattice. The electronic structure exhibited band gaps associated with each reciprocal lattice vector of the QC structure which led to notable singularities in the density of states (fig. 9). The largest band gap observed was near EF, suggesting that stable icosahedral phases may be due in part to a Hume-Rothery instability like that suggested by Bancel and Heiney (1986). This nearly free-electron result with many gaps superposed on D(E)~ E 1/2 should be applicable to the A1 states in Al-based quasicrystals. Indeed the Smith-Ashcroft NFE D(E) resembles a large cluster limit of that generated by local density functional theory on A1 icosahedral clusters, see fig. 5 (McHenry et al. 1986a). Marcus (1986) has calculated the density of states for two- and three-dimensional Penrose lattices with atoms at vertex sites for the two rhombi which generate the tilings. A one-orbital tight-binding Hamiltonian was employed. A D(E) with many peaks and gaps was observed for the two-dimensional tiling, in agreement with several previous calculations (Choy 1985, Kohmoto and Sutherland 1986). However, the three-dimensional tiling was shown to yield a smooth, relatively featureless density of states in which all of the states remained delocalized. Marcus concluded that, in the three-dimensional case, there should be little signature of the QC lattice I

i

Quasiperiodic---b~ ~

1.0

0.5

!itY o

EF . . . .

o

5

, , ,

10

1,5

E (eV) Fig. 9. Density of states calculated for a nearly free-electron model of A1 atoms on a Penrose lattice. The broken line is a result for a periodic AI lattice (from Smith and Ashcroft 1987).

470

R.C. O'HANDLEY ET AL.

in the electronic structure. This conclusion is not expected for a tight-binding calculation where bonding effects are weak to begin with. A similar result (little difference in electronic structure between Ih and Oh symmetry) was obtained using local density functional theory on icosahedral Co clusters (McHenry et al. 1986b). Redfield and Zangwill (1987) have performed total energy calculations using an effective medium technique to investigate the icosahedral phase stability in A1-T binary alloys. Using a pair potential and embedding function, the total energy is calculated for various A1-T alloys. This approach views the alloy as a collection of atoms with a particular nearest-neighbor configuration, embedded in a potential reflecting the average local background electron density. These calculations are very successful in predicting various optimum stoichiometries for QC formation in AI-T systems, such as AI-Mn, A1-Cr and AI-V (Lawther et al. 1990). It is also worth mentioning the several empirical techniques which have been used to try to understand the chemical tendencies for quasicrystal formation. Bancel and Heiney (1986) have suggested the use of Hume-Rothery rules to understand the formation of quasicrystals in AI-T alloys. In this model, optimum quasicrystal compositions are determined by the conduction-electron density which allows the Fermi level to lie in a minimum in the density of states as determined by the structure factor. Another semi-empirical technique employed to understand the chemical trends in quasicrystal formation has been the use of quantum structural diagrams by Villars et al. (1986). This technique considers average valence-electron numbers and s-p orbital radii differences as coordinates to determine regions of this parameter space in which certain known alloys form stable or metastable QCs. Out of this space, new alloy systems can be projected. The technique has been used to predict new ternary alloy phases in which quasicrystals may be found with higher probability than by geometrical methods of prediction. None of the quasicrystals discussed in this chapter, except those already known in 1986 (AI-Li-Cu and A1-Mg-Zn), is among those listed by Villars et al. (1986) as possible new quasicrystals. That is not to say that their generalized coordinates would not place these new QCs in the field of likely candidates.

2.4. Global manifestations of icosahedral symmetry Up to this point, we have considered the implications of an icosahedral environment on local moment formation. We turn now to the second consequence for magnetism of icosahedral symmetry, that on a global scale. The interaction between atomic moments and the crystalline anisotropy is governed by the relative importance of the local anisotropy represented by D and the exchange energy, J (Imry and Ma 1975, SeUmyer and Naris 1985). In the case where D/J > 1, as may be the case for 4f moments (if L # 0), the local anisotropy dominates and dispersed moment structures are possible (Alben et al. 1978a) if the local anisotropy is randomly oriented (Coey et al. 1976, Coey 1978). On the other hand, if D/J < 1, as is the ease for 3d moments, then the effects of long-range exchange interactions dominate, the magnetization direction is uniform over larger distances, and it is the long-range anisotropy (or symmetry) which is more important than the local anisotropy (or symmetry). Since in known quasicrystalline materials it is 3d magnetic moments, predominantly on


471

Mn, that determine the magnetic behavior, then it is the long-range symmetry of the system that is of relevance. These effects of long-range icosahedral symmetry are, therefore, limited to icosahedral QCs and will not be observed in crystalline materials with only local icosahedral coordination, unlike the consequences of local icosahedral symmetry (section 2.2), which may be seen in icosahedral crystals. The anisotropy energy, EA, can be expanded in spherical harmonics, Y~",with l ~>6 and coefficients Kz. Lower-order terms vanish by symmetry. The leading term in this expansion for icosahedral symmetry is given as EA = K6 yO _ (~) 1/2(y65 _ Y651,

(3)

or

EA = (~5K6) [231 cos 6 0 -- 315 cos 4 0 + 105 cos 2 0 -- 5 + 42 cos 0 sin s 0 cos(5~b)], where 0 and q~ are the usual spherical coordinates. The anisotropy energy calculated along principal quaiscrystallographic directions has been calculated according to eq. (3) and is given in table 1 (McHenry and O'Handley 1987). If we assume K 6 < 0, then the twelve vertex directions (see fig. 10), given by permutations of [100000] are clearly easy directions for the magnetization. The angular proximity of the principal axes, compared with the case of, e.g., a cubic crystal, results in a larger number of possible domain-wall orientations. Further, the small anisotropy energy barrier expected between adjacent domain orientations (because of the vanishing of the lower-order anisotropy terms), could render these materials very soft magnetically. TABLE 1 Calculated anisotropy energy for principal directions in icosahedral symmetry (see fig. 2). Principal directions

0

E /K 6

(rad)

Vertex (V) Edge center (E) Face center (F)

0 0.5536 0.6524

1 -0.3125 --0.5556

V

Fig. 10. Icosahedron showing angular relations between twelve vertex (V) directions, 30 edge (E) directions and 20 face (F) directions.

472

R.C. O'HANDLEYET AL.

If, on the other hand, K6 > 0, then the twenty permutations of the [-111000] direction become the easy axes and again magnetic softness is implied.

3. AI-based quasicrystals 3.1. Al-Mg-Zn and A1-Cu-Li quasicrystals 3.1.1. Atomic structure Quasicrystals in the A1-Mg-Zn and A1-Cu-Li systems are of great interest for several reasons. The similarity of the local structure in the A1-Mg-Zn quasicrystalline phase and the (A1, Zn)49Mg32 crystalline Frank-Kasper phase has been noted by Henley and Elser (1986). The local crystalline symmetry is interesting in that it contains icosahedral units with central sites occupied and the decoration beyond the icosahedral first nearest-neighbor polyhedron is by second nearest neighbors located above the faces. Both of these features differ from the Mackay icosahedron (basis of ~-A1MnSi), which had been used as a structural model for i-A1MnSi QCs (section 3.2). Icosahedral packing is preserved to n coordination shells in (A1, Zn)49 Mg32 (Samson 1965, Pauling 1988). The A1-Mg-Zn quasicrystals are interesting in that the components all have s and p electrons as their important valence electrons with presumably little influence of the d electrons of Zn on the electronic structure, especially near the Fermi energy. Therefore, analysis of experiments which examine the electronic structure are relatively unencumbered by considerations of d states, and local moments are also unimportant in these materials. The A1-Li-Cu quasicrystals are believed to be structurally similar to the A1-MgZn system. Further, the icosahedral phase A16Li3 Cul appears to be thermodynamically stable (Cassada et al. 1986). Recently, however, transmission electron microscopy on small A1-Li-Cu precipitates have revealed that their electron diffraction patterns could be explained in terms of multiple twinning of a bcc phase with a large unit cell (Ball and Lloyd 1985). This experiment has called into question the putative stability of quasicrystalline A1-Li-Cu (Vecchio and Williams 1988). 3.1.2. Electronic structure Baxter et al. (1987) have examined the electrical resistivity of A1-Mg-Zn quasicrystals exploiting the fact that these alloys do not possess local moments and, therefore, the intrinsic quasicrystal resistivity could be explored. Single-phase icosahedral Mg3z(Al~-xZilx)49alloys were examined for x = 0.5 and 0.69. Their resistance and magnetoresistance behavior were well explained by application of quantum corrections to a model of conduction in disordered alloys. In particular, the low-temperature field-dependent resistivity was characterized by weak (defect-related) localization and enhanced electron-electron interactions. Most interesting was a strong dependence of the resistivity and the valence-electron susceptibility on composition. The Pauli susceptibility was observed to vary dramatically with small compositional changes, indicating structure in the density of states at the Fermi level. This compositional dependence could not be explained by a nearly free-electron model and was, therefore, taken to imply a more complicated structure to the D(E), i.e., a structure more peaked


473

and gapped like that observed in several calculations cited above. Room temperature resistivities of the two alloys were 59 and 90 Ixf~cm, respectively, a factor of 2-4 times lower than typical values observed in the QCs with local moments (e.g., A1-Mn-Si). Wong et al. (1987) have examined transport as well as superconducting properties of icosahedral (I) and Frank-Kasper (FK) phases of A15z.5Cu12.6 Mg3s. The icosahedral phase was reported to have a resistivity of 60 g~ cm at room temperature while that of the Frank-Kasper phase was ,,~37 gf~ cm. The I phase exhibited a relatively flat temperature dependence [p(4.2)= 58 gf~cm], while the FK phase had a small positive slope [p(4.2) = 23 g~ cm]. Both phases showed superconducting behavior at low temperatures. The superconducting transition temperature was found to be 0.81 K for the I phase and 0.73 K for the FK phase. From measurements of H~2, it was determined that D(Ev)= 0.52 state/eV atom for the I phase and 0.89 state/eV atom for the FK phase. The lower resistivities in these alloys as compared with A1-MnSi alloys were attributed to the absence of resonant d scattering. The higher resistivity of the I phase as compared in the crystalline FK phase as well as its field dependence were explained by localization theory. The D(EF) values derived for the I phase were consistent with a free-electron model, while those for the FK phase were nearly a factor of two larger (based on its significantly smaller normal state resistance). Inasmuch as the I phase resistivity in the normal state is strongly influenced by localization effects and defect scattering, it may not reflect an intrinsic resistivity. On the other hand, the crystalline FK phase has a D(Ev) nearly 50% of that of the freeelectron value and that of pure fcc A1 or bcc Mg. This is interesting in the light of the fact that the FK phase is constructed of precisely the same icosahedral units which are thought to exist in the I phase. Bruhwiler et al. (1988) have performed careful studies of the electronic structure of both the QC and FK phases of A1-Cu-Li and A1-Cu-Mg alloys. Alloys of composition A156CuloLi34 and A152.4Culz.6Mg3s were examined. Electronic structure parameters were determined from a combination of transport, heat capacity and soft X-ray measurements. Both from transport and X-ray spectroscopy, it was determined that the A1-Cu-Li density of states D(EF) was a factor of three less than that in A1-Cu-Mg alloys in either the I or the FK phase. The A1-Cu-Mg values are close to the free-electron value (see table 2). It was shown that, for both alloys, the calculated electronic properties were essentially similar between the I and FK phases. The authors point out that the properties of the I and FK phases remain alike because of essentially similar structure factors based on local icosahedral units. This is consistent with the notion that the local structure determines much of the detail in the electronic structure. Graebner and Chen (1987) have measured the specific heat for the cubic FrankKasper, icosahedral and amorphous phases of composition A12Mg3 Zn3. All three phases were reported to be superconducting with an T¢ of 0.32, 0.41 and 0.75K, respectively. It was concluded that the icosahedral phase resembled the FrankKasper phase in most respects and that its electronic density of states was very close to that predicted by a free-electron model (as determined from the linear specific heat term). Lattice softening was strong in the amorphous phase and weaker but

474


i ~

oo

r

~

~

I

~

I

0

+l+l+l+l

.u.l

I

I

I

I

I ~

~

l

V

I .,i~~

,-1 I

I

.2 ~o

¢}

.=

ta

o

.

6

~

.


475

significant in the I-phase. Thus, the renormalized electron-phonon coupling term 2 was observed to decrease with increasing order. Wagner et al. (1989) have studied the electronic properties of icosahedral alloys, Ga-Mg-Zn, A1-Cu-Fe and AI-Cu-V. The stable I phases of G a - M g - Z n and AICu-Fe show significantly lower values of D(EF) than expected from free-electron theory and smaller than observed in their metastable I phases. These factors are interpreted to suggest a type of Hume-Rothery stabilization due to reduction in D(EF) by a coincident peak in the QC structure factor. Icosahedral AI-Cu-V shows a D(EF) close to its free-electron value. The magnetic susceptibility of i-Al-Cu-Fe shows a strong departure from Curie behavior at low temperatures and a spin-glasslike peak near 1.6 K. General consensus now exists that decreased resistivities in the A1-Li-Cu and Mg[A1, Zr] class of quasicrystals, relative to the A1-Mn-Si class of materials, result mainly from the absence of s-d scattering. The electronic properties of these icosahedral systems are closely related to those of Frank-Kasper phases of similar composition. An appealing explanation for this similarity lies in the similar local packing units, and, therefore, structure factors, in these materials. Several of these alloys exhibit electronic state densities which do not differ appreciably from those predicted by free-electron theory. However, strong compositional variation in the density of states is not easily explained by a free-electron picture. Spectroscopic measurements to resolutions of ,-~0.6 eV have ruled out van Hove singularities.

3.2. Structure of Al-transition-metal quasicrystals The first discovered and most abundant class of quasiperiodic structures remains the A1-T-M icosahedral alloys IT--transition metal at 10-22at.%, M = metalloid Si or Ge at 0-8at.%]. Once it was established that AI-Mn and AI-Mn-Si were quasiperiodic with diffraction patterns indicating icosahedral symmetry (Shechtman et al. 1984, Bancel et al. 1985), it became a matter of much speculation and controversy as to exactly how to model the structure and how to decorate the quasilattice with the various atoms. Models considered included the three-dimensional Penrose tiling (3-D PT) (Elser 1985, Elser and Henley 1985, Levine and Steinhardt 1986, Henley 1986b), the modified ~-AI-Mn-Si structure (Guyot and Audier 1985, Audier and Guyot 1986), and the icosahedral glass (Shechtman and Blech 1985, Stephens and Goldman 1986). When modeled as a 3-D PT, the AI-Mn-Si QC alloys have a quasilattice constant (edge of either of the rhombohedra that make up the structure) of 4.6A. Their QC structure is more disordered than is that of i - P d - U - S i , Si additions reduce the disorder as judged by narrower diffraction peaks (Kofalt et al. 1986), and the AI-Mn pair correlations are much stronger than those of AI-A1 (Nanao et al. 1987, 1988). The competition between these three structural models can be followed in papers by Henley (1986a), Egami and Pooh (1988) and Janot and Dubois (1988a,b). For the A I - T - M (T -- Mn or Cr) family of QCs at least, the question of structure is no longer a matter of speculation. A series of neutron-diffraction experiments, making use of contrast variation due to the opposite scattering lengths of Mn and Cr (Dubois et al. 1986) has allowed the structure of A174Mn21Si6 to be deduced

476


(o)

(b)

Fig. 11. Decoration of Penrose bricks deduced by Janot and Dubois (1988a) from extensive scattering data on A1-Mn(Cr)-Si quasicrystals. Location of the atomic sites in (a) the prolate and (b) the oblate rhombohedra: [O, O] vertex sites occupiedmainly by Mn atoms; (D, II) A1 sites on faces;(~?) A1 sites on the triad axis of the prolate rhombohedra (from Janot et al. 1989a). without assumptions (de Boissieu et al. 1988, Janot et al. 1989a, Janot and Dubois 1988a,b). Partial pair correlation functions indicate that Mn atoms approach each other no closer than 4.5 A, while the A1-A1 pair correlations are similar to those of ~-A1MnSi. In six dimensions, the structure has a primitive CsCl-like space group symmetry which allows determination of the atomic density in three dimensions. The three-dimensional decoration of the 4.6A prolate and oblate Penrose icosahedra deduced from the neutron data (Janot et al. 1989a) are illustrated in fig. 11. Mn atoms occupy the vertices of the prolate rhombus with an average occupancy of 87%; one of these Mn sites has nearly spherical local environment symmetry (de Boissieu et al. 1988). On the oblate rhombus, Mn atoms rarely occupy adjacent vertices at the ends of the short body diagonals. A1 has three sites in the prolate rhombus: type I a 10% occupation of the vertices especially those at the ends of the short body diagonals; type II a 25% average occupation at distances of 2.57 or 6.78A along the triad axis; and type III an 81% occupation at 2.98 or 4.83A along the long face diagonals. No edge sites are occupied. Fragments of icosahedra of different sizes are found in the QC structure and some of them are occupied by either A1 or Mn atoms of different sizes (de Boissieu et al. 1988). This clearly rules out ~A1 M n - S i (where icosahedral sites are vacant) as a structural model for i-A1-MnSi QCs. With this decoration in mind, it can be shown that the Mn at the acute vertex has a reasonable probability of having nearly icosahedral symmetry. However, Mn clearly has at least one other environment (the obtuse vertex sites) which may create a different environment for magnetism. This multiplicity of Mn sites has ubiquitous effects on magnetic properties. Our understanding of the magnetism of QCs depends not only upon extending this sort of firmly established picture of atomic environments to other classes of QCs, but also on gaining an insight into the nature and extent of the defects in these materials.

3.3. Paramagnetic quasicrystals 3.3.1. AI- T Al-based QCs without a metalloid have narrow formation ranges. For T = Mn, the stoichiometric QC composition has 21.6 at.% Mn. Less Mn results in an appreciable


477

amount offcc A1 in the alloy (Dunlap and Dini 1985) and more Mn gives a decagonal phase (Machado et al. 1987b). The interpretation of magnetic behavior in A1-T QCs is invariably complicated by the presence of a second phase. Inoue et al. (1987) have reported a rapid increase in resistivity in A1-Mn and A1-Cr QC alloys with increasing T content. This has been explained by the disappearance of the fcc A1 phase with increasing T content. Pavuna et al. (1986) have reported an increasing resistivity upon increasing Mn content in A1-Mn alloys. Certain of the A1-T alloys, A1-Mn (Inoue et al. 1987) and A1-Co (Dunlap et al. 1986), exhibit Kondo-like resistance minima as a function of temperature. Cyrot and Cyrot-Lackmann (1986) have attributed large low temperature resistivities, comparable to those of metallic glasses, to magnetic scattering from virtual bound states in Mn or U containing QCs. A1-T QCs are all paramagnets and some show spin-glass freezing at low temperatures (Hauser et al. 1986). Further work on the icosahedral A18oMn2o phase and the decagonal (T-phase) A178Mn22 material (Machado et al. 1988) showed values of the transverse magnetic resistance to be comparable to those of other spin-glass systems. The longitudinal magnetoresistance was positive for the I phase and negative for the T phase. The electrical and magnetic properties of AI-T QCs are reviewed by Fukamichi and Goto (1989). The effective paramagnetic moments are derived by fitting the paramagnetic susceptibility to the form

Z = Zo + C / ( T - 0), C-

Npe2f

(4)

3kB '

where N is the concentration of the magnetic species, Peffis the effective paramagnetic moment in Bohr magnetons (#B) and kB is Boltzmann's constant. The effective paramagnetic moments determined from this equation and a linear fit to the susceptibility require an assumption about N, the concentration of the species responsible for the moment. If N is assumed to be the chemical concentration of a transition-metal (T) species, Peff will be in error if not all of the T atoms contribute equally to the moment. Fitting the field and temperature dependence of magnetization beyond the range linear in H/T with a Brillouin function allows independent determination of N and Perf"This approach has been taken by Machado et al. (1987a) on A18oMn2o QCs. They found that a moment of ll#B should be associated with a cluster of approximately 100 Mn atoms. Without this high-field data, their Curie constant is the same as that measured in this system by most other groups and, therefore, would give the same value, Peff"~ 1.2#B/Mn, as generally reported. Despite the additional parameter determined by including high-field data, this method cannot specify how the moment is distributed among the 100 atoms. These authors (Machado et al. 1987a) also measured the specific heat of this alloy (fig. 12) and found that only the full Brillouin-function-determined moment and concentration (11#B per 100 Mn atoms), and not Peff 1.2#B/Mn, gives a magnetic entropy ASm = NkBn(2S + 1) consistent with their specific heat data. Other specific =

478

R.C. O'HANDLEY ET AL. 1000 500 200

i

i

i iiii

I

L-AIsoMn2o

1oc 50

0.2

i

171111

j'

,~A T3

20 O lc 2

i

•~ e " Z

,,C// 0.5

1 2 Temperature (K)

5

10

Fig. 12. Heat capacity, Cp, in gJK -1 versus absolute temperature, T (in K) for a 35mg sample of icosahedral Also Mn2o with zero magnetic field: solid circles. The T 3 and T solid lines indicate the phonon and (upper limit) electronic contribution, respectively, while the broken line indicates their sum (Machado et al. 1987a).

heat and AC susceptibility data (Lasjaunias et al. 1987) support the model that most Mn atoms are not magnetic. The difficulty of interpreting data in this low-temperature regime near the onset of spin-glass behavior (bump just below 1 K, fig. 12) has been pointed out (Eibschutz et al. 1987). Berger and Prejean (1990) have completed a thorough study of the spin-glass behavior of i-A173Mn21Si6. They also find only a small fraction (~ 1%) of the Mn atoms present bear moments, and clusters of these atoms exhibit moments in excess of 7#B (see section 3.3.2.1). In light of these findings, we must regard with caution all values of Peefdetermined only by linear fits. This includes all values (other than the 11/~Bper 100 Mn and the 7.5#B mentioned above) reviewed in this chapter. The effective moment (linear fits) of All -xMnx QCs reported for x = 0.2 vary from 1.0#B to 1.3#~ per Mn and increase with increasing Mn content (Younquist et al. 1986, Goto et al. 1988). Hauser et al. (1986) have observed a nearly quadratic dependence of Poef on the Mn content in A1-Mn and A1-Mn-Si QCs. This is taken to suggest that Mn moment formation is due to M n - M n pair interactions. A problem with interpreting the variations in Mn moment with x is that as x varies, the composition of the QC phase does not change significantly from its strict stoiehiometric ratio A178.gMnzl.6 and second phases of varying composition occur that obscure any true trends. When data for amorphous and crystalline alloys are compared, the moments of the icosahedral phases are higher than those of the crystalline phases which also increase with increasing x. However, the M6ssbauer spectra of both crystalline and icosahedral A1Mn(Fe) alloys suggest equally low symmetry for the Fe sites (Swartzendruber et al. 1985). The stronger moment formation in i-A1Mn QCs is reflected in the strength of the magnetic interactions involved in the spinglass behavior. Berger et al. (1988a) find the spin-glass contribution to the specific heat at 1 to 2 K in i-Als6Mn14 and near 0.2K in amorphous A18sMn~s. The consistently negative values of 0 determined for A1-Mn QCs also suggest antiferromagnetic M n - M n interactions. These antiferromagnetic interactions, in combination with the disorder common to QCs, may be responsible for the spin-

M A G N E T I S M AND QUASICRYSTALS

479

glass behavior. The spin-glass freezing temperature Tg increases from 1 to 9 K as the Mn concentration increases from 14 to 22 at.% (Fukamichi et al. 1987). In A1-Fe, icosahedral QCs plus fcc A1 are found at x = 14at.% Fe (Dunlap et al. 1988a). Others report a decagonal phase at this composition (Zou et al. 1987). The only moment present in these A1-Fe QCs appears to be due to ~-Fe precipitates. Specific heat measurements on icosahedral A18oMn2o were compared with those for a crystalline hexagonal A14Mn phase, a hexagonal A17~Fe19Silo phase and a cubic A15oM12Si 7 phase by Maurer et al. (1987). They concluded that the DOS at Ev was a factor of three larger for the icosahedral phase and the hexagonal A14Mn phase as compared with the other crystalline phases and that of fcc aluminium. From this, they concluded similar local structures in the In and A14Mn phase were responsible for the enhanced DOS. This local structure was significantly different from that of fcc A1. It was further observed that increasingly Mn content in the In phase notably contributed to the specific heat. In this way, the Mn behaves like an impurity. It was further suggested that Mn was twelve-fold coordinated without Mn nearest neighbors. 3.3.2. A I - T - S i 3.3.2.1. AI-Mn-Si.

Si is found to broaden the range over which A1-T-based QCs can be formed (Chen and Chen 1986). Typical compositions have a Si content of 6% and Mn contents from 16 to 22%. While the structure of these materials has often been modeled as a distorted a-A1-Mn-Si phase (Guyot and Audier 1985, Audier and Guyot 1986), it is now clear that this model is not accurate. The structure and rhombohedral decoration deduced from careful neutron-diffraction studies without assumptions has been described above (section 3.2). Effective paramagnetic moments per Mn atom for these QCs are shown in fig. 13. Crystalline alloys of the same compositions show consistently lower effective moments (McHenry et al. 1988b). This difference has been attributed to several effects. (1) M n - M n neighbors do not exist in the crystalline phase. Disorder in the QCs would allow increased M n - M n pair formation with increasing Mn concentration (Hauser et al. 1986). 1.8 1.6

+

"~m 1# al

1.2 1.0

0.81

16

I

I

I

18 2~0 x (at% l'ln)

I

212

Fig. 13. Effective paramagnetic moment per Mn atom for icosahedral A1-Mn-Si. Data are from (+) Hauser et al. (1986), (©) McHenry et al. (1988a), (O)Eibschutz et al. (1988), (A) Bellisent et al. (1987) and (A) Edagawa et al. (1987).

480


(2) Icosahedral sites are not occupied in cz-A1-Mn-Si. Increased occupation by Mn of high-symmetry, nearly icosahedral sites in the QCs could lead to enhanced moments on Mn atoms at those sites (McHenry et al. 1986a) (section 2.1.3). Recent analysis of neutron scattering data from A1-Mn-Si QCs suggests that about 20% of Mn atoms occupy such sites (Nanao 1987). (3) The existence of two classes of Mn sites has been postulated in QCs (Eibschutz et al. 1987). These were originally suggested to be at the periphery of a Mackay icosahedroia: the nonmagnetic sites are involved in bonding between adjacent icosahedra and the magnetic ones are not (Eibschutz et al. 1987). The definitive structural results described above (section 3.2) preclude M n - M n nearest-neighbor pairs (hypothesis 1 above) in QCs at least up to 21 at.% Mn. The neutron scattering data (Janot et al. 1989a) also show that the modified Mackay icosahedron model (on which hypothesis 3 above was based) cannot be valid. It appears, then, that hypothesis 2 is presently a leading candidate to explain the larger paramagnetic Mn moments in the QC phases relative to the crystalline phase. Some specific heat measurements support this view, indicating higher values of D(EF) in QC phases (Maurer et al. 1987, Berger et al. 1988a), others do not (Machado et al. 1987a). It is likely that a distribution of sites is available to Mn; those with higher symmetry may be magnetic. This is not incompatible with hypothesis 3 if the connection with the Mackay structure is omitted. The two classes of Mn sites could be (a) nonmagnetic, bonding, low-symmetry sites and (b) magnetic, nonbonding, high-symmetry sites. Berger and Prejean (1990) analyzed their detailed linear and nonlinear susceptibility data for i-A173Mn21Si 6 and determined that only 1.3% of the Mn atoms nominally present bear moments. The moment-bearing Mn atoms are clustered in groups with average cluster moment of 7.5#B. This conclusion bears out a similar result found by Machado et al. (1987a) for A1-Mn QCs (section 3.3.1). The electric field gradient distributions have been carefully analyzed in several 57Fe-doped icosahedral and decagonal A1-Mn-Si QCs and compared with results for various related crystalline phases (Le Caer et al. 1987, Brand et al. 1990). A strong similarity in local order is indicated for the icosahedral phase and for the hexagonal f3-A1-Mn-Si phase. [When A1-Mn-Si alloys are rapidly solidified by gas atomization, the/3 phase appears in larger particles and the icosahedral phase in smaller particles (McHenry et al. 1988a). This suggests that there is a structural kinship between these two phases because the/3 phase nucleates and grows from the icosahedral phase when the quench rate is slower.] Le Caer et al. (1987) and Brand et al. (1988) also find no evidence for a two-site model in QCs at the level of Fe concentration they studied (Mn14Fe6). We will review below (section 3.3.2.2 to 3.3.2.4) abundant evidence for the distribution of Mn sites at higher levels of substitution of Cr, V or Fe for Mn. Again, for the A1-Mn-Si alloys, strong arguments for Mn virtual bound states have been made through consideration of transport and other measurements. Berger et al. (1988c) showed that the large electrical resistivities in A1-Mn-Si alloys were well accounted for within an extended Friedel-Anderson s-d model. A large excess specific heat term was shown to scale with Mn concentration and was taken to imply the existence of narrow-band resonant Mn states near EF. In complementary work,


481

Berger et al. (1988b) have explored canonical spin-glass behavior in A1-Mn-Si quasicrystals, demonstrating the existence of a cusp in the AC susceptibility with a frequency dependence similar to that of (Ag)Mn or (Cu)Mn. A1-Mn-Si QCs with 20 at.% Mn show spin-glass behavior at low temperatures (McHenry et al. 1988a), similar to that observed in A1-Mn QCs. Below the spinglass freezing temperature, the susceptibility is hysteretic, taking on different values for field-cooled and zero-field-cooled conditions (see fig. 14). Tg increases with Mn content as illustrated in fig. 15. Berger and Prejean (1990) established that the spinglass behavior in i-Alv3Mn2~Si6 is three dimensional and results from an almost equal fraction of ferromagnetic and antiferromagnetic interactions. We now consider the magnetic effects of V, Cr and Fe substitutions for Mn in A174Mn2o Si6 QCs.

3.3.2.2. Al-(Mn, V)-Si.

Eibschutz et al. (1988) showed that V may be substituted for Mn in i-A174Mnzo_xVxSi 6 up to 12at.%. The QC diffraction patterns are not significantly altered by these substitutions and very little residual fcc A1 second phase is present. The motivation for this study apparently was to test the hypothesis that two classes of Mn sites exist, a larger, magnetic site and a smaller, nonmagnetic site. Vanadium, being larger than Mn, is assumed to substitute preferentially in the larger Mn sites. The quasilattice constant, aR, was observed to increase from 4.595 to 4.660A as the amount of V increased from 0 to 12at.%. On the other hand, replacement of Mn by Fe (section 3.3.2.4) decreases ak. The susceptibilities of AI-(Mn,V)-Si QCs are described by eq. (4) quite well, giving ~'~

120

,o-'140[ "...fc

I

I

/". ~ 80

~I 0 0 ~ . 0

°

o 40

5

T (K)

10

o

i

°°°*

00

~

°

,,

o Q

50 100 150 200 250 T (K)

Fig. 14. Susceptibility for A|-Mn-Si showing evidence of spin-glass behavior (McHenry eta]. 1988b).

4-

2

16

'

18

'

20

'

22

x (of %Mn) Fig.15. Spin-glass freezing temperature T~ for icosahedra] A194_,MnxSi6. Data are from (+) Hauser eta]. (1986), (©) McHenry et a]. (1988b), and (Q) Bel]isent et al. (1987).

482

R.C. O ' H A N D L E Y ET AL.

0 values ranging from - 9 to - 3 K as the V content decreases from 0 to 12 at.% (Eibschutz et al. 1988). Using a clever, but simple and plausible method of analysis, Eibschutz et al. (1988) derived the x dependence of the effective paramagnetic moment per Mn p(x)= (-dpZef/dx) 1/z. p(x) decreases with decreasing x, vanishing near x = 12 at.%. The implication is that the Mn moments replaced by V are large initially, p(0) = 2.2#B/Mn, and decrease to p(12) = 0. The distribution of moment magnitudes P(p) was then obtained from

p=

;o

p'P(p') dp,

(5)

with p = 1.1#B averaged over all magnetic sites and 40% of the sites having p = 0. Figure 16 shows the average moment per Mn atom obtained in this way (Eibschutz et al. 1988). The kink marks the point at which, for increasing V content, two thirds of the moment-bearing Mn sites are occupied by nonmagnetic V atoms. Beyond that concentration, V apparently occupies the smaller, nonmagnetic sites and the alloy retains an effective moment due to the magnetic Mn atoms that were not replaced. These results provided the first experimental evidence that the distribution of Mn sites available in the (disordered) QC state is responsible for a distribution of effective Mn moments.

3.3.2.3. Al-(Mn, Cr)-Si.

Additional information concerning the distribution of magnetic sites in Al-based QCs has been provided by an investigation of the A 1 7 4 M n 2 o _ x C r x S i 6 series (McHenry et al. 1989a). This series is similar to the A1(Mn, V)-Si series discussed above since Mn is replaced by a larger transition metal. AI-(Mn, Cr)-Si alloys form single-phase, icosahedral QCs over the range of 0 ~<x ~ (mm/s)

AlsoMogFela

+0.274 +0.237

1.48 1.14

0.351 0.363

+0.005 -0.103

0.444 0.410

0.579 0.585

A17oTaxoFezo

Fe and A 1 - T a - F e spectra using the shell model (Czjzek 1982, Eibschutz et al. 1986, Stadnik and Stroink 1988). This model expands the quadrupole splitting, A, distribution as

P(A)(A/a)" e x p [ - A 2/(2o.2)],

(8)

where n and o- are fitting parameters. In order to account for the expected symmetry, the isomer shift, 5, and quadrupole splitting are correlated as 5(A) oc go + ~A,

(9)

where 50 and ~ also are obtained from the fits. These results will be considered below in the context of measurements on icosahedral A 1 - T a - F e . F o r the m o m e n t , it is interesting to note that the large value of n is suggestive of a structure with little disorder (Dunlap et al. 1989a). This is consistent, as well, with diffraction studies of this alloy (Hiraga et al. 1988, Ishimasa et al. 1985).

3.3.4.3. Al-Ta-Fe.

The existence of a single-phase icosahedral alloy with a c o m p o sition A17oTatoFe2o has been recently reported (Tsai et al. 1989). The temperature dependence of the magnetic susceptibility as reported by Srinivas et al. (1989) is illustrated in fig. 25. This shows behavior which is quantitatively the same as that for AlsoMo 9 F e l t . Parameters obtained from a fit to eq. (7) are given in table 4. These 12 ~_. 11 x

.~10 -~.

\

°°°*°'=oo.Q,~,

X B

'

'1 o' T

(K)

'3 o

Fig. 25. Magnetic susceptibility of icosahedral AlvoTatoFe2o obtained from SQUID magnetization measurements in an applied field of 10 kOe plotted as a function of temperature. Data are from Srinivas et al. (1989).

M A G N E T I S M A N D QUASICRYSTALS

491

results are similar to those in AI-Mo-Fe except that values of a, b and the Fe moment are significantly larger for the A1-Ta-Fe alloy. This may reflect the higher Fe content of the Ta-containing alloy. A room temperature 57Fe MSssbauer effect spectrum of icosahedral A1-Ta-Fe is illustrated in fig. 24. Parameters from a fit to the shell model [eqs. (8) and (9)] for this spectrum are given in table 5. The obvious difference between the A I - M o - F e and A1-Ta-Fe spectra lies in the asymmetry parameter e in the table. It is interesting to note that, in the case of A1-Ta-Fe, e is large and negative, meaning that the more positive velocity line is more intense. What is perhaps more significant are the values of n and tr given for A1-Mo-Fe and A1-Ta-Fe. For amorphous materials, n is assumed to be unity (Czjzek 1982). In well-ordered QCs, n has been found to be around 2. In a systematic investigation of the effects of disorder on the parameters n and a in single-phase icosahedral AI-(Cr, Fe)-Ge alloys, Srinivas et al. (1990) have suggested for quasicrystals that n approaching unity (from above) and a increasing indicate increasing atomic disorder. In the case of A1-Mo-Fe and A1-Ta-Fe, it is not possible to separate the effects of composition and order on the magnetic properties. However, an increase in the magnitude of the magnetic properties (Port, table 4) in the alloy which shows greater microscopic disorder (n, table 5) is certainly not inconsistent with the situation in crystalline and icosahedral A1-Mn-Si alloys (section 3.3.2). The data of tables 4 and 5 and the above comments suggest a correlation between the magnitude of the magnetic moment and the degree of disorder present in the alloy. Stadnik et al. (1989) have concluded that the degree of disorder is the only relevant parameter for magnetic moment formation in these alloys. This conclusion is consistent with the investigation of rapidly quenched and annealed A1-Cu-Fe quasicrystals presented by Fukamichi et al. (1988a). While the data presented here, as shown in fig. 26, certainly show a correlation between disorder and magnetic moment formation, there is also a clear correlation between the magnitude of the localized Fe moment and the amount of Fe in the alloys. Further systematic studies

0.2/*

I

,

o- (mm/s) 0.30 0.36 ,

,

,

,

0.6

0.4 "G u..

•~

3.2

0.6

:::k 0.4 0.2 0

I

I

10

15 x

I

20

(ai%Fe]

Fig. 26. Correlation between the parameter ~r from the shell model fit to 57Fe MSssbauer spectra and the localized Fe moment. Data are from Dunlap et al. (1991) and references therein.

492


are necessary to determine the relative importance of order, structure and composition on the resulting magnetic properties.

3.4. Ferromagnetic quasicrystals 3.4.1. Al-Mn-Si alloys Ferromagnetic and spin-glass behavior has been reported in amorphous A1-Mn-Si alloys (20at.% < Si < 30at.%) by Hauser et al. (1986) and Fukamichi et al. (1988b). These alloys contain a much larger percentage of Si than the paramagnetic QC A1Mn-Si alloys reviewed in section 3.3.2. Inoue et al. (1988) have shown that some of these melt-spun amorphous alloys could be annealed to form an icosahedral phase (see fig. 27). Dunlap et al. (1989b) have subsequently shown that these single phase ieosahedral A1-Mn-Si alloys exhibit ferromagnetism as well. A more thorough investigation of the A1-Mn-Si phase diagram by Srinivas and Dunlap (1989) has shown that ferromagnetic A1-Mn-Si quasicrystals can be prepared directly by melt spinning over a wide range of compositions (fig. 28). Magnetic measurements on two ferromagnetic A1-Mn-Si quasicrystals, Also Mn2o Siso and A15sMn2oSi25, have been reported by Dunlap et al. (1989b). Both

5

2O

I

I

/~0

I

I

6O 2 O (degrees)

I

80

Fig. 27. Cu Kc~ X-ray diffraction patterns of AlsoMn2oSiso, (a) as cast (amorphous), and (b) annealed at 648 K for 90 min (icosahedral). Data are from Dunlap et al. (1989a). Icosahedral indices are given according to the scheme given by Bancel et al. (1985).

At ~

Mn

'4

',0 si

Fig. 28. Phase diagram of the A1-Mn-Si system for greater than 20 at.% Si content. (Q) ferromagnetic quasicrystal as-quenched, (~) ferromagnetic quasicrystal prepared by annealing amorphous precursor, (O) amorphous, (A) mixed phase. All alloys were quenched onto a single Cu roller with a surface velocity of 60m s-1. Data are from Srinivas and Dunlap (1989).


493

of these alloys show essentially the same magnetic behavior. Figure 29 shows a typical low-field hysteresis loop for one of these alloys in the ferromagnetic regime. The coercivity is about 20 Oe, showing that these materials are not particularly hard magnets, but neither are they as soft as might be expected on the basis of theoretical predictions (section 2.5). Figure 30 shows the low-field magnetization curve (100 Oe) for A15oMn2o Si3o; for comparison, the figure also shows the 100 Oe magnetization curve of amorphous A15sMn2oSi2s. Table 6 compares the magnetic properties of icosahedral and amorphous A1-Mn-Si ferromagnets. Both alloys show similar Curie temperatures but have two important differences:

°11// flV

I

L

-0

i

I

600 H

i

1200 (Oe)

Fig. 29. Low-field hysteresis loop for icosahedral AlsoMn2oSiso at 10K. Data are from Dunlap et al. (1989a). 02 o°.

o

..~ =

"(a)

0.1

Z

•••e •o

tm io

o;

lOO 1so T(K)

Fig. 30. Magnetization curves measured in a field of 100Oe for (i) icosahedral A15oMn2oSiao and (a) amorphous A155Mn2oSi25 (Dunlap et al. 1989a). TABLE 6 Magnetic properties of icosahedral and amorphous A150Mn2o Si3o and A155Mn2o Si25 alloys; I = icosahedral, A = amorphous. Data are from Dunlap et al. (1989b). Alloy

Phase

A15oMn2oSiao

I A I A

AlssMn2oSi2s

Ms ( 100 Oe) (emu/g)

Tc (K)

Peff ( #B)

0.12 0.21 0.07 0.16

112 110 115 107

0.24 0.032 -

494


(1) the magnetization at 100 Oe for the amorphous alloy is somewhat greater than that for the icosahedral one; and (2) the icosahedral alloy shows a magnetization which has a slight upturn below about 15 K. This upturn is more apparent in larger applied fields, as illustrated in fig. 31 for i-AlavMn3oSi33 (Chatterjee et al. 1990). At the highest applied fields (H ~>5 kOe) the M - T behavior is almost Curie-like. At intermediate fields (100kOe ~ 100K, the following interesting features are apparent from the figure: (1) Both alloys show approximately the same Tc despite differences in composition and sizeable differences in the magnetization at low temperatures. This phenomenon has also been seen in ferromagnetic A1 M n - S i quasicrystals (McHenry et al. 1990). (2) The magnetization at low temperature is larger than that observed in icosahedral A1-Mn-Si ferromagnets, but Ms/Tc is comparable in magnitude in the two systems. (3) Both Ge based i-alloys show a concave upward behavior below about 200 K which is reminiscent of the upturn in the magnetization seen at low temperatures in i-A1-Mn-Si ferromagnets. McHenry et al. (1990) have measured the magnetization of the related quasicrystals A14oMn2s Fe3 CuT Ge25 and A14oMn25 Fe6 Cu4Ge25 down to ~ 5 K. Results for the latter alloy are shown in fig. 36; the former behaves the same, qualitatively. While the shape of the 100-400K portion of this curve is consistent with the data from A140Mn2sCuloGe25, the data below 100 K and the strong field dependence clearly 20

I

I

I

--

I

I

I

i

=

5

H--0.01T I

I

100

t

I

200

,

:500

400

Temperoture( K) Fig. 36. Temperature dependence of the magnetization in different applied fields for icosahedral AlaoMn25Fe6Cu4Ge25. Data are from McHenry et al. (1988b).

498


illustrate the complex behavior of this system. The addition of Fe has dramatically increased the magnetization relative to that of the alloys in fig. 35. The magnetization of 19emu/g corrresponds to a ferromagnetic moment per transition-metal atom of about 0.6#B. The addition of iron has also decreased Tc to about 400K. A very strong field dependence is observed in the magnetization over the entire temperature range and an anomalous low-temperature component to the magnetization appears below 100K in higher applied fields. Thus, this QC appears to have appreciable second phase with a magnetization that is more field dependent than the matrix. A departure of the zero-field-cooled magnetization from Curie-like behavior observed at low temperatures is associated with spin-glass ordering below about 15 K. The hysteretic behavior of the A1-Mn-Ge and A1-Mn-Cu-Ge alloys reported by Tsai eta L (1988) is illustrated in fig. 37. This figure reveals the difficulty in saturating these alloys, especially the A1-Mn-Ge, even in large applied fields, and shows their sizable coercive force. This latter characteristic is clearly at odds with the prediction of magnetic softness in magnetic QCs (McHenry et al. 1987, McHenry and O'Handley 1987) (section 2.5). Similarly, McHenry et al. (1990) have observed a coercive force of about 1.8 kOe at 4.2 K in A14oMn25Fe3CuTCu3Ge25. From the extrapolated saturation value of the magnetization (i.e., about 4 emu/g), the average ferromagnetic moment per Mn is determined to be ~0.12#B. Dunlap and Srinivas (1989) have recently reported 57Fe M6ssbauer effect studies of the ferromagnetic quasicrystal A14oMn2sFeaCuTGe25. Typical spectra obtained in this study are shown in fig. 38. Dunlap and Srinivas have shown that these spectra indicate an internal Fe hyperfine field of + 17 kOe. The hyperfine field distributions obtained from these spectra, using the fitting method of LeCaer and Dubois (1979), are shown in fig. 39. This figure shows a clear shift of the peak in P(H) towards higher field when an external field is applied and indicates the positive sign of the internal Fe field. Dunlap and Srinivas (1989) have shown, as well, that the temperature

(a)

0.2

i

(12

H

(k0e}

Fig. 37. Room temperature hysteresis for icosahedral (a) A152.sMn25 G%2.5, and (b) A14oMn25Cu~oGe25. Data are from Tsai et al. (1988).


2_ .-'~.,~ .~:,,..~.

.= -

.,.,.v.~. ~z

"""~'V.;:

.,"'~" " :" Ca)

~ ".'.. -

?

..

.~

;. g "~f"~" ,~.,~>.z.:. •, f Cb) \ -

E

i

"~"..'.,r,,'~.,

499

I

-1.0

(~

v

[minis)

+1.0

Fig. 38. Room temperature 57Fe M6ssbauer effect spectra of Al40 Mnz5 F% Cur Ge2s (a) without an external magnetic field, and (b) with an external magnetic field of 4.8 kOe. Data are from Dunlap and Srinivas (1989).

1 V

2_ 'E

J F-'--"

A

1]

(a)

I (b) t

I

0

[

i

10 H

(kOe)

2~0

~

30

Fig. 39. Room-temperature Fe hyperfine field distributions obtained from the M6ssbauer spectra of fig. 38, as described in the text. Data are from Dunlap and Srinivas (1989).

dependence of this hyperfine field is consistent with a value of Tc between 400 and 500 K. On the basis of the measured Fe hyperfine field, we estimate the average localized Fe magnetic moment to be 17 kOe/(150 kOe/#a) = 0.11#~. This value is similar to the value of the average Mn moment obtained in these materials on the basis of bulk magnetization studies. This is additional evidence that the weak ferromagnetic behavior, in conjuction with relatively high values of Tc, as seen in both the A1-Mn-Si and A1-Mn-Ge systems, is an intrinsic property of ferromagnetic A1-Mn-based quasicrystals. Comparisons have been made between icosahedral and amorphous phases of ferromagnetic A1-Mn-Si (section 3.4.1). No information concerning the magnetic properties of analogous crystalline alloys has been found in the literature. Some comparisons of the magnetic properties of the ferromagnetic A1-Mn-Si and A1-Mn-Ge quasicrystals with those of the crystalline equiatomic A1GeMn ( C u z S b structure) phases are noteworthy. Crystalline MnA1Ge shows a Tc of 484K, a ferromagnetic moment of 1.7#a/Mn and an effective moment from the paramagnetic susceptibility of 2.9#B/Mn (Shibata et al. 1972, Shinohara et al. 1981, Kamimura et

500


al. 1985). Although these crystalline materials show Curie temperatures similar to those of the icosahedral alloys, they show significantly larger saturation magnetizations (55 emu/g), and larger average Mn moments than the QCs. The amount of this crystalline phase necessary as an impurity to account for the magnetic properties of icosahedral A1-Mn-(Cu)-Ge (1 or 2%) would certainly not be observed in X-ray diffraction measurements (McHenry et al. 1989b). However, the amount needed to account for the magnetic properties of A1-Mn-Fe-Cu-Ge QCs certainly could not be missed by diffraction experiments. Electron microscopy (Tsai et al. 1988) has so far shown no evidence of crystalline A1MnGe precipitates. It is interesting to note that Fe substituted into crystalline ferromagnetic A1MnGe can occupy either the A1 or Mn sites. At neither site does Fe bear a moment (Shinohara et al. 1981). Also, other Mn-containing Cu2 Sb structures are antiferromagnetic [e.g., Mn2Si (Wilkinson et al. 1957)]. This illustrates the sensitivity of the sign of the M n - M n magnetic coupling to changes in chemical composition or MnMn distance. More careful comparison of magnetism in icosahedral A1-Mn-based materials with that of analogous crystalline compounds may be insightful, although it is important to consider the fact that quasicrystalline materials are intrinsically disordered. 3.4.3. A I - F e - C e alloys

Ferromagnetism has been reported in the icosahedral and decagonal QC phases of A165.3Fe27.3CeT.4 obtained by annealing the amorphous phase (Zhao et al. 1988). The magnetization curves show a strong paramagnetic component (4.5 x 10-5 emu/ g Oe) at 1.5 K superimposed on the weak spontaneous magnetization. The effective paramagnetic moment is reported to be 3.9#a/Fe for the icosahedral phase. The magnetization of the decagonal phase in H = 3 kOe, namely 2 emu/g, corresponds to a net ferromagnetic moment of 0.054#a/Fe. The spontaneous magnetization vanishes at Tc = 340 K. The M - H and M - T curves for these phases are shown in figs. 40 and 41. The weak spontaneous magnetization of the icosahedral phase is masked in fig. 40 by the strong paramagnetism in both the M - H (fig. 40) and M - T (fig. 41)

6 •

E 4 OA

z

x o

°•

_.'j*

x o

I •

l

i?

10

i

i

40 H (kOe)

i

60

Fig. 40. Magnetization versus applied field curves for Al-Ce-Fe alloys in the ((3) icosahedral, (O) decagonaland (x) amorphousphases at 1.5K. Data are from Zhao et al. (1988).


--~

501

(ca)

£ li

[',.,~

0[

0

.......

(b) ,

"~"-T-

100

"=',-'~

°-B: ~

200

----._

'"~ I I

300

T (K)

Fig. 41. Temperature dependence of the magnetization of AI-Ce-Fe in the (a) decagonal, (b) icosahedral and (c) amorphous phases. Data are from Zhao et al. (1988).

curve. In both curves, the decagonal QC phase shows a behavior more typical of ferromagnetism. Zhao (1989) reports other nearly equiatomic A1-Fe R (R = rare earth) QCs which have saturation magnetizations from 40 to 50 emu/g. 4. Quasierystals not based on AI

4.1. Ti-Ni based quasicrystals Kuo and coworkers (Zhang et at. 1985, Zhang and Kuo 1986) first reported the presence of small grains of a decagonal quasicrystalline phase in Ti2_xVxNi alloys. Part of the interest in this system stems from two factors: first, that it is based entirely on transition metals, and second that the fcc structure of crystalline TizNi (Yurko et al. 1959) contains two interpenetrating icosahedra with central sites occupied by Ni atoms. Given the importance attached by theoretical considerations (sections 2.1.1 and 2.1.3) to transition metals in high-symmetry sites, the occupation of such sites in this crystalline phase and their nonoccupation in ~-A1-Mn-Si, the crystalline analog of A1 Mn-Si QCs was significant at the time ~-A1MnSi was a possible structural model for A1-Mn-Si QCs. It no longer is (de Boissieu et al. 1988). Chatterjee and O'Handley (1989) were able to fabricate single icosahedral phase QCs having large grains in the Tis6Ni28 Si16 system. Magnetic susceptibility shows Curie-like behavior at low temperature with an effective paramagnetic moment of only 0.05#B/Ni. The structure of this new class of QCs (Dunlap et al. 1988c, 1989b) appears to be quite different from that typical of other QCs (sections 3.2 and 3.3.4). In the TiNiSi QCs, the intensity of the [110000] peak is 4 to 5 times that of [100000]. In A1 M n Si, the [100000] peak is more intense than the [110000]. Structure factor calculations (Ishihara and Shingu 1986) for different decorations of the prolate and oblate rhombohedra of three-dimensional Penrose lattice show that the observed dominance of the [110000] reflection can only be accounted for in such a lattice by a decoration with atoms at both the vertices and edges of the rhombohedra (Dunlap et al. 1988c). This is in contrast to the three-dimensional real space structure determined for A1-MnSi (Janot et al. 1989a) which has vertex, face- and body-centered sites but no edge sites (fig. 11).

502

R . C . O ' H A N D L E Y ET AL.

Substitution of Fe for Ni in Ti56Ni28_xFexSiz6 QCs improved the ease of icosahedral phase formation. Magnetic measurements on these materials gave the following results. For the first time in a QC, Fe exhibited a local moment of order 0.2#B (X = 15) (Dunlap et al. 1988b). Magnetization measurements for alloys with x up to about 8 at.% Fe (Christie et al. 1990) reveal anomalous behavior of the susceptibility as shown in fig. 42. This figure indicates Curie-like behavior for x = 5 at low temperatures and an increasing, possibly Pauli paramagnetic behavior, at high temperatures. For higher Fe concentrations (x = 10), the Curie behavior dominates the temperature dependence of Z. There is, however, a large residual value of Zo. Since the temperature dependence of the Pauli contribution to the susceptibility is fairly sensitive to the density of states at the Fermi energy, it is not surprising that the substitution of one transition metal for another can, in cases where Pauli paramagnetism is observed, have substantial effects on the temperature dependence of Z (White 1970). M6ssbauer effect spectroscopy showed no detectable quadrupole splitting (0___0.05ram/s) at the Fe sites in Ti-(Ni, Fe)-Si QCs (Dunlap et al. 1989b). In contrast, A1-Mn-Si QCs show a mean quadrupole splitting of order 0.4mm/s. Clearly, the Fe sites in Ti-(Ni, Fe)-Si QCs see a crystalline electric field of considerably higher symmetry than the Fe sites in A1-Mn-Si QCs. Because there are no sites of cubic symmetry in a three-dimensional Penrose lattice, it appears likely that Fe occupies sites of nearly icosahedral symmetry in Ti-(Ni, Fe)-Si. Figure 43 compares the M6ssbauer spectra for several related Ti-(Ni, Fe)-Si phases. The M6ssbauer spectrum of Ti2Nio.85 Feo.15 (which has the fcc Ti2Ni structure) shows a nonzero electric quadrupole splitting as expected for this structure. The addition of Si stabilizes the bcc TiNi phase in Ti56Ni2s.sFe2.sSi16 and this crystalline phase shows no quadrupole splitting as would be expected for the nearly cubic environment of Fe in a bcc structure. Amorphous Ti-(Ni, Fe)-Si shows a quadrupole splitting comparable to that of fcc Ti(Ni, Fe). It is instructive to consider the magnetic results on i-Ti-(Ni, Fe)-Si in light of the structure of these materials, particularly the implication of vertex and edge site occupation on the acute Penrose bricks. The implication of the low quadrupole splitting is that Fe (and Ni) occupy the acute vertices of the prolate rhombohedron, one of which may be at an icosahedral site. In this respect, the structure of i-Ti-(Ni, Fe)-Si may resemble that determined by neutron scattering on i-A1-Mn-Si (Janot

3.6 x=5

2 3.2 *....

x=lO * * o

.

~ 213

T (K) Fig. 42. Magnetic susceptibility of Ti56Ni23 Fe 5 Si16 and Ti56NilsFeloSi 6 measured in an applied field of 1 T. Data are from Christie et al. (1990).

M A G N E T I S M AND QUASICRYSTALS

503

(') '\ , [ t'

t

8

L

I

I

-1.0

I

V

I

I

L

I

0 +1.0 {mm/s)

Fig. 43.57Fe M6ssbauer-effect spectra obtained at room temperature for (a) crystalline Ti2Nio.85Fe0.1s, (b) crystalline Tis6Nizs.s Fe2.5 Si16, (c) icosahedral Ti~6Ni25.sFe2. s Six6 , (d) icosahedral Tis6Ni23 Fe5 Si16, (e) icosahedral Ti56Ni2o.sFev.sSi16, and (f) amorphous Tis6Ni25.sFe2.sSi16. The full lines represent computer fits to two doublets for (a) and to one singlet for (b)-(e) and one doublet for (f). Data are from Dunlap et al. (1989b).

et al. 1989a), where a high probability of Mn at the apices of the acute rhombohedron is deduced for that structure. However, the prolate rhombohedron in A1-Mn-Si is face and body occupied, whereas for Ti-(Ni, Fe)-Si it appears to be edge occupied.

4.2. Other quasicrystals Quasicrystals have also been made in a variety of alloy classes not yet discussed here. These include Pd6oUzoSi (Poon et al. 1985), Ni-Zr (Jiang et al. 1985), TizFe (Dong et al. 1986), and GaMg2.1Zn3.8 (Ohashi and Spaepen 1987) which are icosahedral, (V or Cr)-Ni-Si (Wang et al. 1987) and Mn4Si (Cao et al. 1989) which are octagonal, and (TiV)2 Ni (Fung et al. 1986), Ni-Cr (lshimasa et al. 1985) and T - N i Si (T = V, Cr, or Mn) (Wang et al. 1987) which are decagonal. For most of these, no magnetic properties have been reported. The magnetic susceptibility of i-PdUSi is very well described by eq. (4) with Pelf = 2.3#B/U atom, 0 = - 1 0 K and Xo = 0.22 x 10-3 emu/mol. Consideration of the magnitude of the contributions to Xo suggests that the I phase has a lower density of states at EF than the amorphous or crystalline counterparts (Pooh et al. 1985, Bretcher 1987). The AC susceptibility shows a peak at 5.5 K which is not suppressed by a DC field (Wong and Poon 1986). It is suggested to be linked to the onset of an antiferromagnetic state. The low temperature specific heat shows a large electronic term, 7 = 165mJ/ mol U K 2, 37% greater than that of the amorphous phase (Wosnitza et al. 1988).

504


5. Conclusions and outlook

We have seen that Al-based quasicrystals show magnetic behavior that ranges from diamagnetic (A1-Cu-Fe) to ferromagnetic (A1-Ce-Fe, A1-Mn-Si, AI-Mn-Ge and related alloys). Paramagnetic and spin-glass behavior is observed in many Cu- Mnor Fe-containing alloys. The strength of the magnetic interactions is closely correlated to the degree of disorder in the alloy and appears to be governed by a distribution of transition-metal environments. The possible bimodality of this site distribution has been the subject of controversy and appears still to be an open question. The only nonlinear determinations of the effective paramagnetic moment concentration in QCs are based on a fit to the magnetization data beyond the regime linear in H/T (Machado et al. 1987a) or on detailed linear and nonlinear susceptibility measurements at low temperature (Berger and Prejean 1990). The former indicates a moment of 11#~ per cluster of 100 Mn atoms and the latter suggests only 1.3% of the Mn bear moments and they are grouped in clusters having a moment of 7.5#B. These results are clearly at odds with the results of linear fits (1.2#B/Mn in A1-MnSi QCs). Only the former results are compatible with specific heat measurements. Despite this glaring deficiency in the linear data, we have reviewed it in order to reveal trends in p~ff with composition and structure. Plausible fits to the Peel versus x data in Al-(Mnzo_xTx)-Si QCs strongly suggest a distribution, largely bimodal, of moments: larger (smaller) moments appear on Mn atoms in larger (smaller) sites. Thus, to speak of magnetic species concentration as equivalent to Mn concentration is probably wrong. The concentration of magnetic moments is much less than the Mn (or other moment-bearing T species) concentration. Weak ferromagnetism has been found in A1-Ce-Fe and high metalloid, high Mn content in A1-Mn-Si and A1 Mn-Ge quasicrystals. The substitution of Ge for Si in paramagnetic quasicrystals enhances the ability of Cr and Mn to form a localized moment. In the case of ferromagnetic quasicrystals, substitution of Ge for Si increases the Curie temperature and the saturation magnetization. With saturation magnetizations in some A 1 - M n - F e - C u - G e quasicrystals approaching 20 emu/g the possibility that their ferromagnetism is due to an undetected crystalline precipitate seems unlikely. These ferromagnetic QCs typically show paramagnetic or spin-glass behavior combined with the ferromagnetic ordering. This is manifested by anomalies in the low-temperature magnetization and differences between the field-cooled and zerofield-cooled behavior. It is possible that some of the behavior described as ferromagnetism in certain QCs (e.g., A155Mn2o Si25) is in fact concentrated spin-glass or mixed magnetic behavior with a time-dependent remanence that decays to zero only after long times for Tg < T < Tc, and in experimental times near Tg. That lower Mn content QCs (e.g., A174Mn20 Si6) exhibit dilute spin-glass behavior is well documented in the literature. The term dilute is not inappropriate because, as mentioned above, although the Mn concentration may be 20at.%, only a small fraction of these Mn atoms appear to bear moments. The compositional trend in measured Tgs (fig. 15) is consistent with compositional scaling theories

M A G N E T I S M A N D QUASICRYSTALS

505

for spin glasses (Sherrington and Kirkpatrick 1975). It may also be described by a more general formalism (Sellmyer and Naris 1985), if it is accepted that the mean exchange interaction Jo increases with increasing Mn content (fig. 44). Thus, the relative magnitude of the exchange fluctuations 6 AJ/J o decreases with increasing Mn content. Further, increases in Mn content and possible QC structural stabilization with increasing Si (Ge) content (e.g., A137Mn3oSi33) decreases 6 even more, moving the alloys into the mixed ferromagnetic spin-glass regime. This accounts for the timedependence, anomalous Arrott plots and large high-field susceptibility of some of the so-called ferromagnetic QCs (section 3.4.1). It is important to establish whether the fluctuations responsible for the spin-glass behavior are a necessary concomitant of perfect quasiperiodicity or whether they are associated with the disorder in all the QCs studied so far. To this end, it will be important to look for signs of spin-glass behavior in stable QCs such as A1-Cu-Fe (Burkof 1989). In this alloy, it is possible to anneal-out many of the defects without loss of the quasiperiodicity. It has been five years since quasicrystals were discovered. During that time, and since mid-1988 in particular, the diverse and unusual magnetic properties have become known from extensive experimental work. Also, a number of theoretical considerations of the effects of QC order on magnetism have appeared. Experimental and theoretical efforts in this area have, however, made separate progress without significant interaction. For example, a clear comparison of measured and predicted state densities has not been made and is certainly an area in which future work could be highly informative. There is a great opportunity to explore the phase diagrams and critical behavior of QCs exhibiting mixed magnetic and reentrant spin-glass behavior. The major question here is the origin of the random exchange interactions. Coercivities are another case in point. Predictions of magnetic softness have not been realized; ferromagnetic QCs are frequently very hard magnetically. Are the coercivities strongly time dependent? Measured Ms values of, at most, a few emu/g and mediocre coercivities, until recently, seemed to suggest little hope for commercial utilization of magnetic QCs. Now, QC alloys with Ms values approaching those of =

!

"~T.~ M I SG

i

S" Fig. 44. Sellmyer-Nafis phase diagram (Sellmyer and Naris 1985) for r a n d o m exchange systems, t = kB T/ Jo, ~ = A J / J o , F = ferromagnetic, P = paramagnetic, SG = spin-glass and M = mixed magnetic phase fields. Some of the QCs reviewed here are located on the 6 axis.

506


ferrites, modestly high Tc values and coercivities approaching 2 kOe, certainly encourage further research in this area. Most recently, reports of Fe-rich QCs, Fe85Cu15 (Shang and Liu 1989), seem to offer hope for continued growth and interest in magnetic quasicrystals. Acknowledgements The authors gratefully acknowledge the hospitality of Los Alamos National Laboratory for a period in 1989 which this chapter was begun. The work at MIT was supported initially by a grant from the National Science Foundation (DMR 8318829) and is continued under U.S. Army Research Office contract DAAL-03-87-K-0099. Work at Dalhousie University was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada (operating grant OGP0005604) and a NSERC Cooperative Research and Development grant (CRD0039103) in conjunction with Alcan International Limited. The technical assistance of Robin Lippincott on the manuscript, the references and the figures, is deeply appreciated. References Aharony, A., and E. Pytte, 1980, Phys. Rev. Lett. 45, 1583. Alben, R.A., J.I. Budnick and G.S. Cargill III, 1978a, in: Metallic Glasses, eds J.J. Gilman and H.J. Leamy (ASM, Metals Park) p. 304. Alben, R.A., J.J. Becker and M.C. Chi, 1978b, J. Appl. Phys. 49, 1653. Artman, J.O., 1990, personal communication. Audier, M., and P. Guyot, 1986, Philos. Mag. B 53, L43. Bagayoko, D.N., N. Brener, D. Kanhere and J. Callaway, 1987, Phys. Rev. B 36, 9263. Ball, M., and D.J. Lloyd, 1985, Scr. Metall. 19, 1065. Bancel, P.A., and P.A. Heiney, 1986, Phys. Rev. 33, 7917. Bancel, P.A., P.A. Heiney, P.W. Stephens, A.I. Goldman and P.M. Horn, 1985, Phys. Rev. Lett. 54, 2422. Baxter, D.V., R. Richter and J.O. Str6m-Olsen, 1987, Phys. Rev. B 35, 4819. Bellisent, R., F. Hippert, P. Monod and F. Vigneron, 1987, Phys. Rev. B 36, 5540. Bendersky, L., 1985, Phys. Rev. Lett. 55, 1461. Berger, C., and J.J. Prejean, 1990, Phys. Rev. Lett. 64, 1769. Berger, C., K. Hasselbach, J.C. Lasjaunias, C. Panlsen and P. Germi, 1988a, J. Less-Common Metals 145, 565. Berger, C., J.C. Lasjaunias, J.L. Tholence, D.

Pavuna and P. Germi, 1988b, Phys. Rev. B 37, 6525. Berger, C., D. Pavuna, F. Cyrot-Lackmann and M. Cyrot, 1988c, Mater. Sci. Eng. 99, 353. Bernal, J.D., 1965, Liquids: Structure Properties, Solid Interactions (Elsevier, New York). Brand, R.A., G. Le Caer and J.M. Dubois, 1988, Suppl. Trans. JIM 29, 471. Brand, R.A., G. Le Caer and J.M. Dubois, 1990, Hyperfine Interact. 55, 903. Bretcher, H., 1987, Z. Phys. 68, 313. Briant, C.E., B.R.C. Theobald, J.W. White, L.K. Bell and D.M.P. Mingos, 1981, J. Chem. Soc. Chem. Comm. 5, 201. Briant, C.L., and J.J. Burton, 1978, Phys. Status Solidi 85, 393. Bruhwiler, P.A., J.L. Wagner, B.D. Biggs, Y. Shen, K.M. Wong, S.E. Schnatterly and S.J. Pooh, 1988, Phys. Rev. B 37, 6529. Budai, J.D., and M.J. Aziz, 1986, Phys. Rev. B 33, 2876. Burkhof, S.E., 1989, private communication. Callen, E., Y.J. Liu and J.R. Cullen, 1977, Phys. Rev. 16, 263. Cao, W., H.Q. Ye and K.H. Kuo, 1989, submitted for publication in Phys. Status Solidi. Cassada, W.A., G.J. Shiflet and S.J. POoh, 1986, Phys. Rev. Lett. 56, 2276. Casula, F., W. Andreoni and K. Machke, 1986, J. Phys. C 19, 5155.

MAGNETISM AND QUASICRYSTALS Chatterjee, R., and R.C. O'Handley, 1989, Phys. Rev. B 39, 8128. Chatterjee, R., R.A. Dunlap, V. Srinivas and R.C. O'Handley, 1990, Phys. Rev. B 42, 2337. Chattopadhyay, K., S. Ranganathan, G.N.S. Subbanna and N. Thangaraj, 1985, Scr. Metall. 19, 767. Chen, C.H., and H.S. Chen, 1986, Phys. Rev. B 33, 2814. Choy, T.C., 1985, Phys. Rev. Lett. 55, 2915. Christie, I.A., R.A. Dunlap and M.E. McHenry, 1990, J. Appl. Phys. 67, 5885. Coey, J.M.D., 1978, J. Appl. Phys. 49, 1646. Coey, J.M.D., J. Chappert, J.P. Rebouillat and T.S. Wang, 1976, Phys. Rev. Lett. 36, 1061. Cyrot, M., and F. Cyrot-Lackmann, 1986, unpublished. Czjzek, G., 1982, Phys. Rev. B 25, 4908. de Boissieu, M., J. Pannetier, Ch. Janot and J.M. Dubois, 1988, J. Non-Cryst. Solids 106, 211. Demuynck, J., M.M. Rohmer, A. Strich and A. Veillard, 1981, J. Chem. Phys. 75, 3443. Dong, C., Z.K. Hei, L.B. Wang, Q.H. Song, Y.K. Wu and K.H. Kuo, 1986, Scr. Metall. 20, 1155. Doria, M.M., and I.I. Satija, 1988, Phys. Rev. Lett. 60, 444. Dubois, J.M., Ch. Janot and J. Pannetier, 1986, Phys. Lett. A 115, 177. Dubost, B., J.M. Lang, M. Tanaka, P. Sainfort and M. Audier, 1986, Nature 324, 48. Dunlap, R.A., and K. Dini, 1985, Can. J. Phys. 63, 1267. Dunlap, R.A., and K. Dini, 1986, J. Phys. F 16, 11. Dunlap, R.A., and V. Srinivas, 1989, Phys. Rev. B 40, 704. Dunlap, R.A., G. Stroink, K. Dini and D.F. Jones, 1986, J. Phys. F 16, 1247. Dunlap, R.A., D.J. Lloyd, I.A. Christie, G. Stroink and Z.M. Stadnik, 1988a, J. Phys. F 18, 1329. Dunlap, R.A., M.E. McHenry, R.C. O'Handley, D. Bahadur and V. Srinivas, 1988b, J. Appl. Phys. 64, 5956. Dunlap, R.A., R.C. O'Handley, M.E. McHenry and R. Chatterjee, 1988c, Phys. Rev. B 37, 8484. Dunlap, R.A., M.E. McHenry, V. Srinivas, D. Bahadur and R.C. O'Handley, 1989a, Phys. Rev. B 39, 4808. Dunlap, R.A., M.E. McHenry, V. Srinivas, D. Bahadur and R.C. O'Handley, 1989b, Phys. Rev. B 39, 1942. Dunlap, R.A., R.C. O'Handley, M.E. McHenry

507

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chapter 6 MAGNETISM OF HYDRIDES

G. WlESINGER and G. HILSCHER Institute for Experimental Physics, TU Vienna A-1040 Vienna, Austria

Handbook of Magnetic Materials, Vol. 6 Edited by K. H. J. Buschow © Elsevier Science Publishers B.V., 1991 511

CONTENTS 1.

Intr oduct:'on

2.

Formation

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3.

E l e c t r o n i c !0rol:erties

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534

Binary actinide hydrides

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5.2.1.

ThHx

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.

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535

5.2.2.

PaI-t~

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535

5.2.3.

UHx

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535

5.2.4.

NpHx

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536

5.2.5.

PuHx

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5.3.

Binary transition-metal

54.

Ternary rare-earth-transition-melal 5.4.1.

5.4.2.

h3drides .

Hydrides of Mn compcunds 5.4.1.1.

General feattres

5.4.1.2.

R6 M n 2 3

5.4.1.3.

RMn 2 .

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536

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536 .

537

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537

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537

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539

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540

Hydrides of Fe compounc's 5.4.2.1.

General feattres

5.4,2.2.

RFe12 .

5.4.2.3.

R2Fel7

5,4.2.4.

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541

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541

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541

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542

R2 F e 1 4 B .

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543

512

MAGNETISM 5.4.2.5.

RFe5

OF HYDRIDES

513

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

544

5.4.2.6. R6 Ee23 . . . . . . . . . . . . . . . . . . . . . . . 5.4.2.7. R F e 3 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2.8. R F e 2 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2.9. R F e . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2.10. R 2 F e , R 3 F e . . . . . . . . . . . . . . . . . . . . . 5.4.2.11. R v F e 3 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3. H y d r i c ' e s of C o c o n : p o u n d s . . . . . . . . . . . . . . . . . . . 5.4.3.1. G e r e r a l f e a t u r e s . . . . . . . . . . . . . . . . . . . . 5.4.3.2. R / C o 1 4 B . . . . . . . . . . . . . . . . . . . . . . . 5.4.3.3. g C o 5 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3.4. R 2 C o v . . . . . . . . . . . . . . . . . . . . . . . 5.4.3.5. R C o 3 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3.6. R C o 2 , R T C o 3 . . . . . . . . . . . . . . . . . . . . . . 5.4.3.7. U C o , U 6 C o 5.44. Hydrides of Ni compcunds . . . . . . . . . . . . . . . . . . . 5.4.4.1. G e r e r a l f~atures . . . . . . . . . . . . . . . . . . . . 5.4.4.2. R N i 5 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4.3. R 2 N i 7, R N i 3 . . . . . . . . . . . . . . . . . . . . . 5.4.4.4. R a N i . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4.5. R T N i 3 . . . . . . . . . . . . . . . . . . . . . . . . 5.4.5. H y d r i & s o f m i s c e l l a n e o u s c o m p e t n d s . . . . . . . . . . . . . . . 5.4.5.1. R a r e - e a r t h a n d ~ctinide c o m p o u n d s . . . . . . . . . . . . . 5.4.5.2. P u r e a n d o x y g e n - s t a b i l i z e d Ti a n d Z r c o m p o u n d s . . . . . . . . 5.5. H y d r i d e s c f a m o r p h o u s alloys . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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548 549 550 553 554 554 554 554 554 554 558 559 560 560 561 561 561 562 562 563 563 563 566 567 570

1. Introduction

Intermetallic compounds of 3d metals (particularly Mn, Fe, Co and Ni) with rareearth elements exhibit a large variety of interesting physical properties. The magnetic properties of these intermetallics [-for reviews see, e.g., Wallace (1973) Buschow (1977a, 1980a) and Kirchmayr and Poldy (1979)] are a matter of interest for two main reasons. Firstly, their study helps to elucidate some of the fundamental principles of magnetism (RKKY interaction, crystal-field effects, valence instabilities, magnetoelastic properties, coexistence of superconductivity and magnetic order). Secondly, they are of technical interest, because several compounds (RCos, R2Co17, NdzFelgB ) were found to be a suitable basis for high-performance permanent magnets. More recently, the unique soft-magnetic properties made amorphous metal-metalloid alloys to a further class of materials which are of considerable importance with regard to industrial application. Since the discovery of LaNi5 as a hydrogen storage material roughly two decades ago, a vast number of intermetallic compounds and alloys has been involved in studies of the hydrogen-induced changes of their physical properties. A large variety of techniques has been applied in order to elucidate the mechanism of hydrogen uptake which is particularly complex in intermetallic compounds. They can roughly be divided into surface-sensitive methods (photoemission and related spectroscopies, transmission electron microscopy, conversion electron M6ssbauer spectroscopy and to some extent susceptibility measurements, N M R and ESR) and surface-insensitive experiments, where only the bulk properties can be studied (magnetic measurements, neutron- and X-ray diffraction, X-ray absorption, transmission M6ssbauer spectroscopy). Despite the complex hydrogen-absorption mechanism, some general statements concerning the influence of hydrogen upon the physical properties can be made. Hydrogen uptake commonly leads to a considerable lattice expansion. Although the absorption of hydrogen can lead to a volume increase of up to 30%, the overall crystal structure frequently is retained. The hydrogen-induced rise in volume is to a large extent the essential reason for the altered magnetic properties in the hydrides. A larger volume implies narrower bands which, on the other hand, may reduce a hybridization having perhaps been present in the host compound. When a transition metal (TM) is alloyed to a rare earth or a related metal (R), the R-3d exchange interaction (3d-5d overlap) leads to a significant reduction of the TM moment. The strong hydrogen affinity of the R metals brings about a decrease of the 3d-5d overlap 514

MAGNETISM OF HYDRIDES

515

in the hydrides. Thus, the absorption of hydrogen commonly cancels this moment depression to a certain degree. This partial restoration of the 3d moment is interpreted as a hydrogen-induced screening effect. The predominant part of published results connected with magnetism considers binary R hydrides (R = rare-earth element) and hydrides of binary compounds of the general formula RyTMz, R being a rare-earth element, which may be replaced by elements such as Sc, Y, Zr, Ti; and TM standing for a transition metal. Particularly Mn, Fe, Co and Ni compounds have been examined with regard to hydrogenabsorption properties. Consequently, after some theoretical considerations, this chapter will deal with the experimental results regarding binary rare-earth hydrides, followed by a short treatment of transition-metal hydrides. The main part covers ternary hydrides along the element order mentioned above, the final part containing hydrides of less-common compounds and alloys (e.g., GdRh2, oxygen stabilized TiTM compounds, amorphous alloys). Experimental data are only to some extent mentioned in the text. They have been summarized in this chapter in several tables according to the transition element present in the compound. In order to limit the number of references to a reasonable number, attention is focused to the literature cited subsequently to 1980, except those papers which contain physical quantities given in the tables. For the remaining former literature, the reader is referred to the comprehensive review articles by Buschow et al. (1982a), Buschow (1984a) and Wiesinger and Hilscher (1988a).

2. Formation of stable hydrides In order to predict the formation of metal-hydrogen systems, the heat of formation has to be evaluated. Up to now, only a few first-principle calculations have been performed. However, empirical and semiempirical models have been proposed for the heat of formation and heat of solution of metal hydrides. For a recent review, we refer to chapter 6 of Hydrogen in Intermetallic Compounds I (Griessen and Riesterer 1988). The cellular model of Miedema et al. (1976) and, more recently, the band-structure model of Griessen and Driessen (Griessen and Driessen 1984a,b, Griessen et al. 1984) have successfully been applied in metal-hydride research. While the former model is already known fairly well and thus does not need to be introduced separately, the latter one shall be described briefly, particularly because the electronic band structure is involved and thus the connection with magnetism is obvious. Empirical linear relations are proposed between the standard heat of formation AH and characteristic band-structure energy parameters of the parent elements in order to predict AH of the ternary hydrides. In the case of binary metal hydrides, the standard heat of formation is correlated with the difference between the Fermi energy and the energy of the centre of the lowest s-like conduction band of the host metal. In the case of ternary metal hydrides, the energy difference for intermetallics of two d-band metals has been evaluated using the model of Cyrot and CyrotLackmann (1976). The exact density of states (DOS) of an alloy is approximated by a 'simple' DOS, where the individual contributions of the elements are acting in an additive way (coherent potential approximation). There are various steps involved

516

G. WIESINGER and G. HILSCHER

in the scaling of the DOS function of each metal. In the first step, the widths of the d bands of both metals are set equal to their weighted average and the (DOS) curves are brought to a common width. In the second step, the Fermi energies are equilibrated. The agreement of the calculated heat of formation values with the experiment was found to be remarkably good. In most of the cases, the band-structure model yields better results than the Miedema model, which furthermore has the disadvantage of involving more fit parameters.

3. Electronic properties The knowledge of the electronic properties (band structure, DOS) considerably helps in understanding the magnetic properties of a material. In the last few years, the number of papers dealing with band structure calculations has increased considerably (Gupta 1989). Moreover, the accuracy of the DOS and the Fermi-energy calculations has grown substantially. Decomposition of the DOS into site and angular momentum components are now available for many metal hydrides. Charge transfer calculations, however, are still at their beginning. The kind of the electronic charge transfer upon hydrogenation is an essential point for interpreting the hydrogen-induced change of the magnetic properties. In order to explain the magnetization data of rare-earth-transition-metal hydrides, a few earlier works favoured a hydrogen-transition-metal charge transfer in connection with the rigid-band model (see, e.g., Wallace 1978, 1982). A similar interpretation has been given more recently with regard to Mn, Fe and Ni hydrides (see, e.g., Antonov et al. 1989). However, theory [-energy band and DOS calculations, see, e.g., Vargas and Christensen (1987), Gupta (1982, 1987, 1989)] and experiment [M6ssbauer studies performed on R nuclei and X(U)PS investigations, see, e.g., Cohen et al. (1980), Schlapbach (1982), Schapbach et al. (1984), H6chst et al. (1985), Osterwalder et al. (1985)] proved the indefensibility of this position. Details will be found below in the common part of this chapter. There are a number of experimental methods in order to compare theory and experiment in the field of the electronic properties. The Pauli contribution of the magnetic susceptibility and the electronic specific heat coefficient ~ are proportional to N(EF). Resistivity measurements yield valuable results for binary hydrides (see section 5.1), for hydrides of intermetallic compounds this method is rarely applied because of experimental difficulties (contacting brittle samples or disintegration of the specimens into powder). Spectroscopic techniques such as electron and X-ray photoemission belong to the most powerful methods to study the electronic structure. A valence-band photoelectron spectrum resembles a one-electron DOS curve. Within some approximations, photoelectron spectra yield directly position and width of the occupied bands, charge transfer is indicated by XPS core level and M6ssbauer isomer shifts. In valence fluctuation systems, X-ray absorption experiments are particularly valuable. The X-ray absorption near-edge structure (XANES) contains information about the partial DOS and becomes an increasingly important technique. For the most recent comprehensive review covering experimental as well as theoretical work


517

on hydrides, we refer to chapter 5 of Hydrogen in Intermetallic Compounds I (Gupta and Schlapbach 1988).

4. Basic aspects of magnetism Metallic magnetism covers a wide range of phenomena, which are intimately correlated with both the electronic structure and the metallurgy of a given metal or compound. Particularly the latter appears to be an important factor when considering the formation and properties of intermetallic compounds and binary (ternary) hydrides. Frequently, the studies of hydrides of intermetallic compounds have led to a deeper insight into the fundamental properties of the parent system. For quite a long time, 3d magnetism has been a controversial topic, where still some problems are not completely settled. The reason for this controversy is the absence of a general agreement upon the microscopic nature of the magnetic state above and below the Curie temperature. Two opposite standpoints have, so far, been used to explain the magnetic order as a function of temperature. In the Heisenberg model, magnetism is described in terms of localized moments and the magnetization vanishes at Tc because of disorder in the local moments due to thermal fluctuations. Nevertheless, their absolute value remains almost independent of temperature. In the Stoner-Wohlfarth itinerant-electron model, the magnetic moment is determined by the number of unpaired electrons in the exchange-split spin-up and spindown bands. Within this model, the thermal excitations of electron-hole pairs reduce the exchange splitting and thus favour the paramagnetic state. Consequently, the magnetization disappears only if the absolute value of the magnetic moment goes to zero, which only happens if the exchange splitting is zero too. This model sufficiently describes magnetism in metals at 0 K. Unfortunately, it predicts Curie temperatures which are 5-10 times larger than those observed experimentally. The controversy has been settled recently in favour of the itinerant-electron model. In an improved theory (spin-polarized band theory), a magnetic polarization exists, the direction of which may vary from one unit cell to the other. Thus, the global magnetization vanishes at Tc not because the magnetic moments are zero, but because they point in random directions (Gyorffy et al. 1985, Staunton et al. 1985). A great deal of progress was made in the theory of fluctuating moments in itinerant systems (Moriya 1987, Lonzarich 1987, Mohn and Wohlfarth 1987), which is a similar approach to solving the old problem of magnetism at elevated temperatures by taking account of the parallel and transversal components of the local fluctuating moments. Noting that the fluctuating moments must increase as the static magnetization decreases, it became clear that the Stoner model involving only single-particle excitations of itinerant electrons is insufficient for most systems and that collective excitations are also inevitably present to different degrees, depending on the temperature and the position in the co, q plane. At higher temperatures, Murata and Doniach (1972) made clear that spin fluctuations persist side by side with single-particle excitations, but it is difficult to describe these theoretically for realistic metals. A very much simpler and new approach to the problem has been developed recently by Wagner and Wohlfarth (1986) and Mohn and Wohlfarth (1987). This retains the

518


Stoner model in its equivalent expression as a Landau theory of phase transitions, but takes account of the influence of the parallel and transversal local fluctuating moments by appropriately renormalizing the Landau coefficients of the free-energy expansion. With this approach and the use of band-structure calculations, including correlation effects, rather good agreement is found with experimental Curie temperatures of Fe, Co, Ni and other intermetallic compounds. Furthermore, this formalism lead in a simple way to the pressure dependence of the Curie temperature and the magnetovolume effects as well as to a realistic description of the magnetic contribution to the heat capacity (Mohn et al. 1987, Mohn and Hilscher 1989). Contrary to the magnetism of the 3d-metals, the magnetic properties of the rareearth elements (R) are unambiguously described in terms of the RKKY theory; because of the localized nature of the 4f electrons no overlap exists between 4f wave functions on different lattice sites. Thus, the magnetic coupling can only proceed indirectly via the spatially nonuniform polarization of the conduction electrons. The pure 4f-4f interaction and its behaviour upon the absorption of hydrogen can be studied directly not only in binary rare-earth hydrides, but also in ternary hydrides with a zero transition-metal moment. As a first apgroximation, one would expect that hydrogen-induced changes in the magnetic properties of the latter can be explained in analogy with the binary hydrides, i.e., in terms of the anionic model. There, the conduction electron concentration is lowered after hydrogen uptake which in turn reduces the RKKY interaction. The rare earths form binary hydrides with the stoichiometries x = 2 and x = 3. In the case of x approaching 3, metallic conductivity disappears, which has been attributed by Switendick (1978) to the formation of a low-lying s-band with the capacity to hold six valence electrons. This in fact equals the number of electrons supplied to the conduction band by one R and three H atoms. Since this low-lying bonding band is completely filled up with electrons, in RH3 conduction electrons are no longer present, prohibiting the transmission of the RKKY interaction. This accounts for the suppression of the magnetic interactions, which indeed is generally observed experimentally. However, as will be seen later, details of the physical properties of the rare-earth hydrides in the a-phase and of the broad homogeneity range of the R-dihydrides are only partly solved and several exceptions from the simple approach can be found. In R-3d-intermetallics and their hydrides, where both R and the 3d element carry a magnetic moment, we can distinguish between three main types of magnetic interactions which are quite different in nature: that (i) between the localized 4f moments; (ii) between the more itinerant 3d moments; and (iii) between 3d and 4f moments. Generally, it is observed that these interactions decrease in the following sequence: 3d-3d > 4f-3d > 4f-4f. In contrast to the binary 4f hydrides, for ternary R-3d hydrides no similar straightforward arguments can be used about the hydrogen-induced change of the magnetic order. The only statement being generally valid is that upon hydrogen absorption the magnetic order of Co and Ni compounds is considerably weakened which is not observed in the case of Fe compounds. As will be described in detail below, hydrogen absorption usually weakens the


519

magnetic coupling between the 4f and the 3d moments and can lead to substantial changes of the 3d transition-metal moment in either way. As mentioned earlier, hydrogen in the lattice reduces the 4f-3d exchange interaction. This is explained by a reduced overlap of the 3d-electron wave functions with the 5d-like ones due the narrower bands as a consequence of the hydrogen-induced increase in volume. Furthermore, concentration fluctuations of H atoms over a few atomic distances may frequently occur, leading to a difference in electron concentration between one site and another and, therefore, to a varying coupling strength. Additionally, a disturbance of the lattice periodicity takes place in the hydrides, reducing the mean free path of the conduction electrons (see section 5.1). This leads to a damping of the RKKY conduction electron polarization which in turn decreases the magnetic coupling strength. If the magnetic order in R-intermetallics is dominated by the 4f moments, the concept of an R - H charge transfer in analogy with the binary rare-earth hydrides has proved to be a reasonable explanation for the hydrogen-induced changes in magnetism (see the data containing an isomer shift obtained from Mrssbauer studies on rare-earth nuclei). In the case where 3d magnetism is dominant in the R-3d compounds, no general rule can be given. Commonly, hydrogen absorption leads to a loss in the 3d moment in Ni- and Co-based intermetallics, but to an enhancement of the Fe moment. For Mn-intermetallics, both changes from para- to ferromagnetism and vice versa are obtained. In Fe-containing intermetallic hydrides, the 3d states are localized to a greater extent compared to the parent compound. This leads to an enhancement of the molecular field which, on the other hand, is opposed by the influence of the grown Fe-Fe distance, tending to reduce it. As is observed experimentally, the former is apparently the dominating one, yielding an increased or at least an unchanged molecular field constant nRFe upon hydrogenation. When discussing the hydrogen-induced change of the magnetic properties, one is, among other things, faced with the problem of finding confidential moment data. Frequently, one has to rely on magnetization measurements, which may lead to wrong results in those cases where, from experimental reasons (lack of a high-field facility), only incomplete saturation has been achieved. As will be seen below, particularly in the case of ternary hydrides, magnetic saturation is difficult to obtain. An alternative way is offered by Mrssbauer measurements carried out in zero applied field. However, the problem of correlating the hyperfine field unambiguously with the magnetic moment (particularly in the case of the hydrides) still remains. Only in a few cases, one can refer to reliable data from neutron-diffraction experiments. For a detailed summary of the experimental data obtained up to now in the field, we refer to chapter 4 in Hydrogen in Intermetallic Compounds I (Yvon and Fischer 1988). 5. Review of experimental and theoretical results

5.1. Binary rare-earth hydrides 5.1.1. s-rare-earth hydrides Hydrogen is readily absorbed by the rare earth (R) and forms solid solutions (~phases) at high temperatures. The solubility limits at a certain temperature generally

520

G. WIESINGERand G. HILSCHER

increase with the atomic number. Vajda and Daou (1984) established that the heaviest trivalent lanthanides, Ho, Er, Tm and Lu, and the closely related elements Sc and Y (all of them have the hcp structure) retain hydrogen in solution down to 0 K without any evidence of an ~-13 phase transition but with a resistivity anomaly in the range between 150 and 180K. This anomaly was attributed to short-range ordering of the interstitial H atoms. In the case of c~-LuHx, it has been identified by neutron scattering as the creation of linear chains of H - H pairs on tetrahedral sites along the c axis surrounding a metal atom (Blaschko et al. 1985). Contrary to the heaviest rare earths, hydrogen in solution appears to be unstable in the lighter R elements at a certain temperature (decreasing from 700 to 400 K for La to Dy, respectively) and precipitates into the 13-phase (dihydride). ~-HoHx, cz-ErH~ and uTmH~ yield a hydrogen interstitial solubility limit of 3, 7 and 11 at.%, respectively (Daou and Vajda 1988), which was previously believed to be lower. Hydrogen in solution reduces the antiferromagnetic ordering temperature TN of Ho (133 K) at a rate of about 2 K/at.% H (D), which is in agreement with the results obtained for the two other magnetic R-hydrogen systems, ~-ErH~ and ~TmH~ (Daou et al. 1987). The effect of hydrogen absorption upon the magnetic properties in ~-ErHx has been studied by resistivity (Daou et al. 1980, Vajda et al. 1987b), magnetic (Vajda et al. 1983, Ito et al. 1984, Vajda and Daou 1984, Burger et al. 1986b, Burger 1987) and specific heat measurements (Schmitzer et al. 1987). Er is well known to exhibit three different magnetic structures: below the N6el temperature TN of 85 K there is a sinusoidally modulated magnetization along the c axis, while the basal-plane magnetization remains zero. The basal-plane component starts to order in a helicoidal structure at TH= 51 K and spiral (conical) ferromagnetism is stable below Tc = 19.5 K [for a review, see Coqblin (1977)]. The above-mentioned measurements show that TN and TH decrease, while Tc and Tcl (at which a transition to an incommensurate structure of 15 layers occurs) increase with H or D content (see fig. la,b). The rise of Tc is interpreted by Burger et al. (1986b, 1987) in terms of a hydrogen-induced dilation of the c axis as a consequence of the interplay between the uniaxial anisotropy and the magnetoelastic energy, and the coupling between the axial and basal-plane magnetization. The increase in the electronic specific heat with rising H content (up to 1.5 at.%), indicates a growing density of states at EF for Er in the cz-phase (at least at low concentrations), which leads to the suggestion that the decrease of TN, TIj and the spin disorder resistivity Pspd are due to a reduction in the exchange interaction, in agreement with magnetic measurements. The thermal variation of the resistivity and the specific heat in the ferromagnetic cone-structure regime (below Tc) gives evidence for the existence of a gap-like behaviour in the spin wave spectrum, which is reduced with the addition of hydrogen in solution. From this variation of the exchange-anisotropy gap and the nuclear specific heat, Schmitzer et al. (1987) and Vajda et al. (1987b) draw the same conclusion as above, namely that the exchange field is reduced with rising hydrogen content in u-ErHx. Contrary to ~-ErH~, for cz-TmH~ both TN (57.5 K) and the order-order transition at Tc (39.5 K) decrease with rising H content down to 45.5 and 29 K, respectively, for x = 0.1 (Vajda and Daou 1984). This different behaviour is suggested to arise


521

Hydrogen in solid solution in erbium

25001(a)//o[l

I

1000 500 o

~ 2~

sb

r (K)

~..~'+"%,. L 7~

Fig. 1. (a) Variation of the magnetizationwith temperature for pure Er (x = 0) and ErH0.035. A field of H = 0.02T is applied parallel to the c axis [(O) x = 0, (+) x = 0.035] (Burger et al. 1986b). from the specific magnetic structures, which are, in the case of Tm, sinusoidally modulated antiferromagnetic below TN and gradually squares up to yield below Tc = 39 K an antiphase ferromagnet with three spins up and four spins down and has, therefore, no basal-plane component, in contrast to Er below Tc. The fall of TN and Tc in ~-TmHx is governed also by the reduction of the indirect exchange interaction. In Tm, there is no interaction present between the short-range ordered H - H pairs with the uniaxially aligned moments. On the other hand, in ~-ErHx a strong interaction between the H - H pairs and the conical structure appears to change the magnetoelastic energy, giving rise to a Tc enhancement in Er with H in solution. In fig. 2a,b, a global view of the temperature dependence of the electrical resistivity of an ~-TmH~ single crystal parallel to the b and c axis is presented, showing a significant different p(T) behaviour between the two crystal orientations with x. While the b-axis oriented crystal exhibits a nearly linear increase of the residual resistivity, p~, with x (fig. 2a), the apparent increase of p~ (p parallel to the c axis) is much larger and nonlinear. In fact, the resistivity decrease due to ferrimagnetic ordering is strongly suppressed by hydrogen in solution, disappearing completely for x > 0.05, which is attributed to the evolution of magnetic superzones, a phenomenon already observed to a smaller degree in single crystals of ~-ErH~ (Vajda et al. 1987b). The insert of fig. 2a shows a substantial rise of the magnetic contribution to the resistivity Pmag(r) with x. The analysis of these data in terms of a sum of a power function and an exponential expression for the anisotropy gap A, pbag(T ) = AT" + B T 2 e x p ( - A / k r ) ,

522

G. W I E S I N G E R and G. H I L S C H E R

(b)

o

(22,

__,,,,

,

0.00

,

i

I0,00

20.00

i

30.00

i

i

40.00 Temp [K]

i

50,00

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

,

q

50.00

,

70.00

Fig. 1. (b) Heat capacity of ~-ErHx with various hydrogen concentrations: (©) x = 0; ( ~ ) x = 0.01; ([~) x = 0.03 and (m) ErDo.o3 (Schmitzer et al. 1987).

shows that both n and A decrease with rising x. Specific heat measurements show a similar trend (Daou et al. 1988b), namely that an anisotropy gap occurs in the spin wave spectrum, and is reduced with growing amount of hydrogen and goes hand in hand with the development of a complex magnetic structure. Magnetization measurements of monocrystalline 0~-TmHxindicate that hydrogen gives rise to the following main effects: (i) a decrease of the antiferro- and ferrimagnetic (along the c axis) transition temperatures due to modifications of the electronic structure; (ii) a hardening of the ferrimagnetic M(H) relation along the c axis due to an increase in the coercivity or the pinning of the domain walls; (iii) a decrease of the anisotropy between the c axis and the basal-plane magnetization (Daou et al. 1981, 1990). Of the magnetically unordered elements, Sc, Y and Lu, the H system of the latter has been investigated thoroughly by specific heat and susceptibility measurements (Stierman and Gschneidner Jr 1984). These authors state that Lu is a spin fluctuation system, where the fluctuations are quickly degraded by impurities and by hydrogen in solid solution. Both the susceptibility Z and the electronic specific heat coefficient show a similar variation as a function of H-composition, yielding a peak at 3 and


523

(a) TmH x//b

100 ,o

o

~o 6070

I..'" "

•

"

" " " " °'°~'~'~ii~ -~'J"~

• .;-"iii'.'. °:-'40 ""

"" "'""'" • •°

30

• • ,,

20 ,, 1 0 II

• ."

,"

•

t

." .. ." •

""

I

o ,° • ." ° ." • .

.-"

• I

50

....

.,,~,,..°° o°O°'~ ......o" •

~.,...~ 18.5

"

,.,,,,,,,~"

18.3L~--,-,~*,"."

"

0

.,..,'" "

J1 5~ 1.31 2 I

"

~io'~ 30.6 :

10.6

,,,,,,,

"~,-."•'"•:•~ 10.4 ..~ . . . . . . .........'... i I I I I I I I 4 6I 8 1OK

100

~

150

200

T(K)

..

(b)

0.10

~

40

o.

217

0

I

I

100 T (K)

I

I

200

Fig. 2. (a) Temperature dependence of the resistivity parallel to the b axis for various ~-TmHx crystals with the x values labelled; the insert shows the magnified low-temperature region. The arrows indicate the high-temperature anomaly above 150 K as well as the variation of the N6el temperature TN. (b) The same as (a) for single crystals with an c axis orientation. Both figures after Daou et al. (1988b).

1.5 at.% H, respectively. This difference is attributed to hydrogen tunneling, giving rise to a linear contribution to the heat capacity. Correcting for this brings into good agreement the concentration dependence of both ~ and X with a peak at about 3 at.% H. In this context, it is worth to note that also in ~-ErH~ and presumably in ~-

524


TmHx an increase of the electronic specific heat with x is observed. However, in ~TmHx the increase of 7 with growing x is not established for x > 0.02, since in this regime the magnetic contribution to the heat capacity could not unambiguously be resolved, since a not yet determined magnetic structure occurs below 4 K (Daou et al. 1988b). Susceptibility measurements of ~-ScH~ by Volkenshtein et al. (1983) indicate that spin paramagnetism is reduced by a factor of two for x = 0.36. This can be associated (neglecting a possible change of the Stoner enhancement factor) with a decrease in the density of states at EF, whereby EF passes through a maximum of the N(E) curve down to lower energies. This trend of the m-phase is also observed in the dihydride. According to band-structure calculations, susceptibility measurements and the spinlattice relaxation time, the DOS at EF in comparison with that of parent Sc is reduced by a factor of 3.5, 3 and 4.5, respectively.

5.1.2. Rare-earth di- and trihydrides The rare earths commonly form dihydrides and trihydrides. The dihydrides exhibit a broad homogeneity range and crystallize, except for Eu and Yb, in the CaF/ structure. The CaF/ structure forms a fcc unit cell, where in the ideal case all tetrahedral (T) sites are occupied. On increasing the hydrogen content, the octahedral (O) sites become gradually filled up with hydrogen atoms to form the BiF3 structure. Dihydrides of Eu and Yb are of the orthorhombic (Pnma) structure. The trihydrides exhibit the hcp structure except for La and Ce where the cubic structure is sustained. While the trihydrides are ionic semiconductors, the dihydrides are metallic with low hydrogen content and semiconductors with high concentration of hydrogen (Libowitz 1972). In reality, the 'pure' dihydride is frequently substoichiometric. The occupation of the octahedral (O) sites already starts sometimes for x = 1.8, depending on the material purity; in particular the oxygen content is of importance, and also the sample shape (foils, powder, etc.) used for hydrogen loading. It seems that the larger the purity of the parent material, the closer is the approach to the ideal stoichiometry of the dihydride. In the case of a heavy rare earth with a purity of 99.9% and 99.99%, the stoichiometry of the dihydride is usually 1.90 < x < 1.95 and 1.96 < x < 1.98, respectively. The absorption of hydrogen affects the magnetic properties of the rare earths indirectly via a reduction of the number of conduction electrons and a volume expansion. Both effects lead to a drastic decrease of RKKY indirect exchange interaction between the localized 4f electrons mediated by the conduction electrons. Consequently, the magnetic ordering temperatures are much lower than in the parent metals (e.g., Tc= 291K for Gd, TN = 20K for GdH1.93 ). On raising the H content above the pure dihydride, it is obvious that a random and/or ordered occupation of the octahedral sites with H significantly influences the crystalline electric field (CEF). This plays an important role in the change of the magnetic properties of those compounds located in the intermediate range between the di- and trihydrides. The dihydride acts as a monovalent metal (one conduction electron per atom), the trihydride as an insulator or a semimetal. Whereas the electronic structure and the magnetic properties of stoichiometric dihydrides and trihydrides seem to be rather


525

well understood, considerable confusion exists in the intermediate composition range (-0.15 to -0.05 < x < 1 of REH2+x). To elucidate the transition between these two extreme situations, this regime became, therefore, of growing interest during the last few years. Simplifying the matter, one may expect a continuous decrease of the conduction electron density with rising x, implying that each H atom depopulates the conduction band by one electron through the formation of a low-energy metalH band. However, this simple model is complicated by several structural transitions: attractive H - H interactions lead to a phase segregation with the formation of a dilute metallic phase (x = 0.1-0.2) and a concentrated nearly insulating phase or ? phase (x = 0.8-0.9). This seems to be the case in the heavy rare earths (R = Gd to Lu), where no homogeneous dihydride exists for x > 0.25. In the lightest rare earths (La, Ce and possibly Pr), such segregations are not observed and mainly orderdisorder transitions occur within the H-sublattice, presumably due to more repulsive H - H interactions (Burger et al. 1988). From electronic band-structure calculations, it is known that a charge transfer occurs from the metal atoms to the hydrogen atoms in the tetrahedral sites, whereas the hydrogen atoms at the octahedral sites can be considered as essentially neutral (Misemer and Harmon 1982, Fujimori et al. 1980). Although the theoretical values of the charges transferred are still a matter of debate, the occurrence of charge transfer is supported by experimental XPS data on the metal core-level shifts obtained on hydrogenation (Schlapbach 1982, Osterwalder 1985, Gupta and Schlapbach 1988). Negative charges at the tetrahedral sites yield crystal-field ground states that have been confirmed experimentally by neutron scattering, M6ssbauer spectroscopy, susceptibility and specific heat measurements. This favours the so-called anionic or hydridic model for the formation of binary rare-earh hydrides which, however, has to be regarded with some caution. The limits of this model have been assessed by Gupta and Burger (1980) by means of a site and angular momentum analysis of the DOS. These authors were able to show that there exists a considerable hybridization of the low-lying hydrogen-metal bands. For further discussions of band-structure calculations on RH2 and R H 3 we refer to Gupta and Schlapbach (1988). Their results support a metal to semiconductor transition, whereby the explanation concerning the origin and nature of the gap and its opening particularly in the intermediate concentration range is still not resolved. The rare-earth dihydrides order antiferromagnetically with ordering temperatures below 20 K, except for CeH2+x, NdHz +x and EuHz+x which exhibit ferromagnetic order. In view of their orthorhombic structure (Pnma), dihydrides of Eu and Yb are also an exception among their cubic neighbours. The magnetic structure of the RD1.95 for the light rare earth (R = Ce, Pr or Sin) and GdD1.95 has been resolved by neutron diffraction and appears to be rather similar: for Sm and Gd dideuterides ferromagnetic coupling occurs within the (111) plane, which couple antiferromagnetically with the adjacent sheets (MnO-type structure), while for Ce and Pr an additional modulation within the (111) plane is observed into the [1T0] and [112] direction, respectively (Arons and Schweizer 1982, Arons and Cable 1985). Thus, NdH1.95 is the only ferromagnet in the antiferromagnetic series of the R deuterides with the cubic C a F 2 or BiF3 structure and seems, therefore, to be an unresolved exception.

526

G. W I E S I N G E R and G. H I L S C H E R

The RDz compounds in which R is a heavy rare-earth element (R = Tb, Dy or Ho) exhibit modulated magnetic structures (see fig. 3) where the modulation period 4ao~/ll along [113] is commensurate with the crystallographic lattice (Shaked et al. 1984). This corresponds to a ferromagnetic coupling of the magnetic moments within the (113) planes and an antiferromagnetic alignment between those planes. The direction of the spin axis is [001] for Tb and Dy but [863] for HoDz. The magnetic structure of ErD2 contains both a commensurate component (belonging to the magnetic lattice, 4ao) and an additional incommensurate component which could not yet be resolved. The ordering temperatures and the magnetic structure of the single-phase dihydrides with the respective x values according to various authors are collected in table 1. The orthorhombic dihydrides of Eu and Yb are not included. From this table, it is obvious that those elements situated on the boundaries of the 4f series exhibit the more complicated antiferromagnetic structure, while Nd which is ferromagnetically ordered is rather exceptional in this type of compound. The transition temperatures reported for the pure dihydrides agree fairly well with each other, although the hydrogen content given for the pure dihydride varies significantly in particular cases. This indicates - as discussed above - that the purity of the starting material is of crucial importance since impurities presumably occupy the tetrahedral lattice sites which prevents the formation of the strictly stioehiometric dihydride RH2. This suggestion deduced from the comparison of the transition temperatures and magnetic phase diagrams (table 1, see also fig. 4) seems to be in contradiction with the statement of Arons et al. (1987c) that a stoichiometric dihydride with all tetrahedral sites occupied by H atoms does not exist, since the occupation of the octahedral sites starts already at RHt.g5 with 2.5% vacancies on the tetrahedral lattice sites. Already a slight increase of absorbed hydrogen leads to a loss of long-range magnetic order and shows sometimes spin-glass-like behaviour at low temperatures. In this context, it should be noted that the nature of the magnetic transition of hyperstoichiometric dihydrides at low temperatures depends sensitively on the cooling rate. From a resistivity anomaly at about 150 K, which is different for quenched and slowly cooled samples (103K/min and 0.3K/min), Vajda et al. (1985, 1989a) deduced that in the latter case short-range ordering occurs within the octahedral H

.[113]

(a)

/[113]

(b)

Fig. 3. Magnetic structure of T b D 2 and H o D 2 according to Shaked et al. (1984).


527

TABLE 1 Magnetic properties of cubic single-phase dihydrides RH2 +x. R Ce Pr Nd Sm Gd Tb

Dy Ho Er

Transition temperature (K) 6.2 3.3 3.5 6.8 9.6

9.6 21 17.2 18.5 18.0 3.5 5.0 4.5 6.5 2.15 2.13

Type of magnetic order

AF AF AF F AF AF AF AF AF AF AF AF AF AF AF AF

MnO type modulated along the [110] axis MnO type modulated along the [112] axis

MnO type MnO type Commensurate modulated along [113], spin axis along [001] Commensurate modulated along r i l l ] , spin axis along [001] Commensurate modulated along [113], spin axis along [-863] Commensurate and incommensurate components no magnetic order down to 2 K

Tm

* References: [1] Arons et al. (1987c). [2] Arons et al. (1987a). [-3] Arons and Cable (1985). [-4] Vajda et al. (1989a). [5] Senoussi et al. (1987). [6] Arons and Schweizer (1982). [7] Vajda et al. (1989b).

[8] [9] [10] [11] [12] [13]

x

Ref.*

-0.05 -0.05 -O.03 0.0 -0.15 -0.12 -0.7 -~0.0 -0.5 -0.08 =0.0 -0.0 20.0 -~0.0 -~0.0 -0.1 -~0.0 0.0

[1] [-2, 3] [4] [5] [6] [7] [6] I-8] [9] [4] [8] [10] [8] [-10] [-8] [-11] [12] [13]

Shaked et al. (1984). Arons et al. (1982). Daou et al. (1988a). Oprychal and Bieganski (1976). Kubota and Wallace (1963b). Burger et al. (1986a).

Cell2÷ x ()O

o

Para 0

0

//

/

/

/ I

0.0

I

I

I

0.5

'II I

I

i'

AF I

I

1.0

X ~

Fig. 4. Magnetic phase diagram of Cell 2 +x determined by (©) susceptibility measurements (Arons et al. 1987a, Abeln 1987). Additional transitions are observed by (0) resistivity measurements (Vajda and Daou 1989, Vajda et al. 1990). The hydrogen stoichiometry of the latter data is shifted by x = -0.05 for comparison with the susceptibility data.

528


sublattice. This significantly affects the magnetic transition, presumably as a result of a modified crystal-field scheme due to local symmetry distortions. Valuable information about the behaviour of hydrogen in binary hydrides has first been obtained from the analysis of the susceptibility by Wallace and Mader (1968) and from the Schottky anomaly in the low-temperature specific heat (Bieganski 1972, Bieganski and Stalinski 1970, 1979). Further information is found in references given by Arons (1982). The energy level scheme which has been derived clearly favours the anionic model. Inelastic neutron scattering and M6ssbauer spectroscopy are further techniques which have been applied in order to determine the crystal-field level scheme in binary RHz hydrides (Knorr and Fender 1977, Knorr et al. 1978, Arons 1982, Arons et al. 1987b, Shenoy et al. 1976). From these results, the anionic state of the hydrogen ions has been corroborated also. In the heavy rare-earth dihydrides, the analysis of the paramagnetic spin-disorder resistivity in terms of crystalline-field effects gives furthermore reasonable agreement with the generally considered anionic H - model (Daou et al. 1988a). The rare-earth trihydrides (except for CeHz.75_3) do not show magnetic ordering down to liquid-helium temperature (Wallace 1978, Birrer et al. 1989). This is consistent with the assumption of anionic hydrogen has a completely depopulated conduction band, giving rise to the semiconducting or insulating behaviour of those hydrides. In the following, we present the main results since 1980, in particular concerning the intermediate range between the di- and trihydrides. For previous data of the magnetic properties of those hydrides we refer to the comprehensive compilation by Arons (1982) and the reviews by Libowitz and Maeland (1979) and Wallace (1978, 1979). Cerium and its compounds exhibit an exceptional behaviour in the series of the rare earth. The ambivalent character of the one 4f electron, behaving either atomic like as in 7-Ce or less-localized and stronger-hybridized as in ~-Ce, gives rise to fascinating magnetic and electronic properties as, e.g., mixed valency, Kondo and heavy fermion behaviour (Fisk et al. 1988). Figure 4 shows that the magnetic order changes from antiferromagnetism in the slightly hydrogen-deficient dihydride CED1.95 via no magnetic order at about x = 0.05 (for T > 1.3 K) to ferromagnetism for 0.1 < x < 0.75 and again to antiferromagnetism at x > 0.8 (Arons et al. 1987a). Additional magnetic transitions have been observed in CEH1.95 by heat capacity measurements (Abeln 1987) and by resistivity measurements at various x values, 0 < x < 0.4 (Vajda et al. 1990). These additional transitions, whose nature is not yet resolved, are also presented in the phase diagram proposed by Abeln (1987) and Arons et al. (1987a) (fig. 4). Good agreement between the two data sets of Abeln (1987), Vajda and Daou (1989) and Vajda et al. (1990) is obtained, if the hydrogen stoichiometry of the respective samples are shifted by 0.05at.% relative to each other. This means that the substoichiometric dihydride CEH1.95 of Abeln (1987) corresponds to CeH2.oo of Vajda and Daou (1989). The antiferromagnetic structure of CED1.95 and CeD2.91 is presented in fig. 5. The obvious difference between these magnetic structures is the additional antiferromagnetic modulation along the [110] direction with a period of 5ao for CED1.95. The magnetic 5.1.2.1. CeHe+ x.


529

t

•

(a) ,

",,

I¢

'\

II"

oI--~ ",,, ~"--v

.1

"

(b)

j

(

--

7

aft --~

A --z ~

,-

f

Fig. 5. Magnetic structure of (a) CED1.95 and (b) CeDz.91 (after Abeln 1987). The antiferromagnetic coupling between (111) planes is additionally modulated along the [li0] direction for CeD1.9s.

moment determined by neutron diffraction (Schefer et al. 1984) in the ferromagnetic range (1.1#B at 1.3 K for x = 0.29) as well as in the antiferromagnetic CED2.96 (0.61#B at 1.3K) is by far smaller than that expected for a free Ce 3+ ion (2.14#B). These moments lie just between the calculated moments of 1.56#B and 0.71 #B corresponding to a/"8 and F? ground state, respectively. From high-field measurements, up to 30 T, on a single crystal also a rather low saturation moment of 0.9#B has been derived, which hardly changes with hydrogen content (Arons et al. 1984). Except for the ferromagnetic CeDz.46 compound, the moment attains 1.03#B. The reduced moment may be attributed to crystal-field effects since the overall crystal-field splitting was determined from susceptibility measurements by Osterwalder et al. (1983) to be 285 K (assuming the /"8 quartet to be the ground state). This finding is corroborated by inelastic neutron scattering and susceptibility measurements, according to which the F7 doublet is situated 20 meV above the Fs ground state (Abeln 1987). The four-fold degenerate/"8 ground state of CEH1.95 will be split into two doublets, separated by 12 K, as the hydrogen content is increased up to Cell2, but remains almost unchanged for higher hydrogen contents. Abeln (1987) deduced this from inelastic neutron scattering and from a pronounced Schottky anomaly occurring in the heat capacity of Cell 2 at about 5 K. Furthermore, no magnetic order could be detected in Cell2 down to below 1 K where the susceptibility becomes fiat. These findings, together with a rather high electronic heat capacity (Y = 179 mJ/molK z) strongly suggests that CeH2 is a Kondo system with a nonmagnetic ground state. Resistivity measurements (Vajda et al. 1990) confirm the above suggestion, since an incoherent and a coherent Kondo lattice behaviour has been observed above and below 20 K, respectively. The magnetic phase diagram in fig. 4 shows a narrow paramagnetic range separating the intermediate ferromagnetic- and the antiferromagnetic range for x > 0.8. In this context, it is worth noticing that Kaldis et al. (1987) reported on a miscibility gap for 0.56 < x < 0.64 between the tetragonally distorted and the cubic structure at room temperature. However, for Cell2.8, a two phase region (cubic and tetragonal) occurs below 238 K while above this temperature only the cubic phase appears to be stable. Schlapbach et al. (1986) excluded from photoemission experiments a metal

530


to semiconductor transition. They suggested a metal to semiconductor transition occurring at the surface, where upon cooling below 70 K hydrogen is removed from the more weakly bound octahedral-like surface hydrogen sites and is dissolved in the bulk. The electronic specific heat coefficient 7 of CEH2.65 is rather large (110 mJ/mol K z) and strongly enhanced (by a factor of 10) compared with the elemental 7-Ce, or the corresponding La compound with the similar electronic structure (LaH2.65~ < 0.04mJ/molK z) (Schlapbach et al. 1987). However, the absolute value of 7 is rather low in comparison with other Ce- and U-based heavy fermion compounds. Although the valency in Ce hydrides (3 +) is hardly changed (Gupta and Schlapbach 1988), the high 7 value of both compounds (Cell2 and the CEH2.65 ) indicates 4f hybridization with the conduction band. Thus, Ce hydrides have a tendency towards heavy fermion compounds.

5.1.2.2. PrHz+x. Below TN= 3.3K, PrD1.95 orders antiferromagnetically (MnO type, see above) with an ordered moment of 1.5#B/Pr atom (Arons et al. 1987c), while PrH2.25 is a weak Van Vleck paramagnet down to 2 K [Wallace and Mader (1968), and references given by Arons (1982)]. From the analysis of susceptibility measurements of PrH2 +x in terms of crystal-field effects, Wallace and Mader (1968) proposed the anionic model for hydrogen in these types of compounds which has later been supported by specific heat measurements (Bieganski 1973). Both experimental results are satisfactorily described by the F5 ground state caused by the crystal-field splitting of the degenerate 3H, ground state of Pr 3+ due to the surrounding of negatively charged hydrogen ions. This assumption is furthermore confirmed by inelastic and polarized neutron scattering (Knott and Fender 1977, Knorr et al. 1978, Arons et al. 1987a). The antiferromagnetic transition and the resistivity minimum at about 28 K was tentatively attributed by Vajda et al. (1989a) to Kondo scattering or to crystal-field effects if the first excited state F1 (nonmagnetic) is close to the ground state. Burger et al. (1990) explained the resistivity minimum in terms of spin-disorder resistivity taking the presence of crystal-field effects into account where the nonmagnetic first excited state (FI) is situated very close above the magnetic Fs ground state. For x > 0.0, the noncubic symmetry of the crystal field, induced by the supplementary H ions, may split the degenerate ground state Fs, causing suppression of both the magnetic order and the resistivity minimum. For samples with x > 0.2, neither susceptibility (Wallace and Mader 1968) nor resistivity measurements down to 1.5 K manifest magnetic order. According to the specific heat measurements (Drulis and Bieganski 1979), the ground state for PrH2.57 is a nonmagnetic singlet which appears to be in line with the nearly temperature independent Van Vleck susceptibility at low temperatures. The transition from antiferromagnetism to Van Vleck paramagnetism was explained by Arons et al. (1987b) in terms of a degeneracy of the magnetic F 5 and the singlet F1 states. However, this needs a change of the cubic crystal field parameter x [in the notation of Lea et al. (1962)] from x > 0.54 to x < 0.54 although the additional hydrogen atoms on octahedral sites should be considered as essentially


531

neutral. In view of the significant resistance anomaly at 150 K, it seems likely that noncubic ordering of the octahedral hydrogens modifies the local symmetry of the crystal field. While for PrD 2 the crystal field experienced by the majority of Pr ions is cubic, Knorr et al. (1978) demonstrated by a careful analysis of their neutron data that in PrDz.5 the distribution of the octahedral hydrogen interstitials occurs not at random but rather in a mer-XA3 configuration leading to an orthorhombic crystal field at the Pr site. With this orthorhombic crystal-field symmetry, they could explain their neutron and susceptibility data of PrD2.5 satisfactorily. Furthermore, it is stated that Pr does not undergo a valence change from PrH2 to PrH2.5. Besides the pronounced resistivity anomaly at 150 K commonly found in these superstoichiometric samples, a further anomaly occurs in the hydrogen-richest compound x = 0.76 at about 220-250 K with indication for a first-order transition (similar to Ce and La) (Burger et al. 1988, Vajda et al. 1989a). The strongly x-dependent structural transformations affects the magnetic transitions at low temperatures via a modification of the local crystal-field symmetry. For high x-values, the analysis of the phonon and the residual resistivity by Burger et al. (1988) implies that the carrier density decreases strongly, and thus that the system approaches the metal-insulator transition. 5.1.2.3. NdHe+ ~. NdH 2 has been reported by Kubota and Wallace (1963a) to order ferromagnetically at 9.15 K with a moment of 1.36#a, while Carlin et al. (1982) found Tc = 5.6 K and a saturation moment of 1.9#B. The latter ordering temperature is in good agreement with specific heat measurements of Bieganski et al. (1975b) and N M R investigations (Kopp and Schreiber 1967). Both indicate magnetic ordering at 6.2K. Senoussi et al. (1987) performed systematic hysteresis measurements on NdH2 +x up to x = 0.7 which indicate, for x = 0, ferromagnetic behaviour below 6.8 K with a coercivity of 150 Oe and a spontaneous moment of 1.06/aB. For increasing H content, the spontaneous moment is drastically reduced. Moreover, thermomagnetic irreversibilities observed by zero-field-cooled (ZFC) and field-cooled (FC) M versus T measurements point to freezing effects and spin-glass behaviour. However, a clearcut spin-glass behaviour is rather unlikely for the stoichiometric dihydride since, in their specific heat measurements, Bieganski et al. (1975b) obtained a pronounced sharp peak at 6.2 K. Both the considerably reduced moment (relative to the free Nd 3 + value 3.37#B) and the freezing phenomena (growing with rising hydrogen content) may arise from a complex interplay between the RKKY interactions and the magnetic anisotropy. In particular the random uniaxial anisotropy, which could be induced by the crystal field and the local fluctuations of the hydrogen concentration on the octahedral interstitials, together with the reduced conduction-electron concentration are suggested to suppress long-range magnetic order for x > 0.

For the antiferromagnetic transitions in SmH2+x, good agreement is obtained from susceptibility and resistivity measurements (Arons and Schweizer 1982, Vajda et al. 1989a). However, the H stoichiometries of the corresponding samples differ significantly: the pure dihydride is referred to as SmH1.85

5.1.2.4. Smile+ x.

532


and as SmH1.98 by the above authors, respectively. With rising H content, TN is shifted from 9.6 K to lower temperatures [to 5.5 K for x = 0.08 (Arons 1982) and to 8 K for x = 0.16 (Vajda et al. 1989a)]. In the resistivity curve, the antiferromagnetic transition is observed as a sharp transition for x < 0.1 which becomes smoother at higher x values and disappears at x = 0.26. Furthermore, a resistivity minimum occurs just above TN, remaining observable up to x = 0.26. The p(T) minimum was tentatively attributed to incommensurate magnetic order or to corresponding critical fluctuations (Vajda et al. 1989b). The magnetic structure is of the M n O type and changes to an incommensurate structure, as found for GdH2 +x (Arons et al. 1987a). Vajda et al. (1989a) stated that not only the concentration of octahedral H atoms, but also their configuration is of importance for the shape of the transition. The reason for this is that quenching from room temperature introduces local disorder due to the presence of isolated H atoms on octahedral sites which can be recovered above about 150 K where a resistivity anomaly occurs.

5.1.2.5. EuH2+x. EuHz is a ferromagnetic semiconductor with Tc = 18.3K, 0 = 23.13K, Ms = 7.1/~B and peff= 7.94#B (Bischof et al. 1983). The semiconducting behaviour of the divalent dihydride is in accord with the anionic model.

5.1.2.6. GdH2+x. The antiferromagnetic MnO-type structure in GdD1.93 (with TN = 20K) changes into an incommensurate helical structure with the axis along [111] and TN = 15.5 K (Arons and Schweizer 1982, Arons 1982). The excess hydrogen (x) located on octahedral interstitials has a tendency to order below room temperature in short-range and long-range ordered structures which influences the type of magnetic order. Based on resistivity measurements, Vajda et al. (1990, 1991) proposed a structural and magnetic phase diagram for 0 ~<x ~ 0.2 are metallic and are reported to be of the fcc structure (Drulis et al. 1988, Bfichler et al. 1989). Susceptibility measurements of YbHz.41, shown in fig. 6, indicate, together with specific heat measurements, the presence of a Kondo scattering mechanism and/or an intermediate valent behaviour: the effective moment of 3.82#B/ Yb is smaller than expected for a Yb 3+ ion (4.45#B), the susceptibility deviates from 5.1.2.12. YbH2+x.

534


48

I-t II

40 ~

oE F r

o

E

32

l× ;

F

|x,~' x

/ 0

%

o

#~

1

,

" .x,

/

," I

I 4

I

I 8

.,

4/ ~ . ~~

"',

424"

I

I T/ 12

T {,I

16 9 1 ~ _ . ~ ~

E

160 f ' " .~(X,'e'

:eft = 3"82

80

x x x x x xx x x Xxxxxxxxxx XxXXxxxxx'xXxxxx Xxxxxxxxxxxxxx>o,~xx~,~x ~,Xxxxxxxz'

/

0

24°T

i 0

I 80

i

I 160

i

I 240 T (K)

i

0 ~-

Fig. 6. Susceptibility of YbH2.41 as a function of temperature (Drulis et al. 1988).

the Curie-Weiss law and levels off below 4 K (fig. 6) and the heat capacity shows a pronounced upturn at low temperatures with a high C/T value of 589 mJ/mol K -z at 2.48 K (Drulis et al. 1988). Finally, the photoelectron spectra according to Biichler et al. (1989) clearly show a valence transition from the divalent YbHz with a 4 f 14 configuration to a mixed valent behaviour in YbH2.6 with a 4f13/4f 14 configuration.

5.2. Binary actinide hydrides The early actinide hydrides exhibit fascinating properties. In particular the structural properties may be classified as being unique in the periodic table. Complex phases form for the ThHx and UHx systems that are not observed for other metals. In the PaH~ system, simple bcc, cubic C15 Laves and A15 phases occur depending on temperature and composition. Rare-earth-like hydrides with the C a F 2 structure are found beyond uranium for the NpH~ and PuH~ systems with a trivalent metallic state. For a general review on the properties of actinide hydrogen systems, we refer to Ward (1985a). The magnetic and electronic properties of the actinides and their intermetallics are largely determined by the partly filled 5f shell [for details and references, we refer to the review by Sechovsk) and Havela (1988)]. Concerning the localization of the 5f electrons, the actinides may be placed between the d transition metals and the rareearth elements. The 5f electrons in the actinides are less localized than the 4f electrons in the corresponding rare-earth series, but the 5f-5f overlap decreases on going from the early to the late actinides. The fact that the degree of 5f localization is determined by the 5f-5f overlap is documented in the well-known Hill plot which correlates the simplest ground states (superconductivity, paramagnetism or magnetic order) with the actinide-actinide distances. Superconductivity occurs in the early actinides (Th,


535

Pa and U) while spin-fluctuation effects are found in Np and Pu. For the transplutonium elements, the 5f electrons become more localized and thus, starting from Am, the series becomes rare-earth-like. As the hydrogen absorption generally expands the lattice and reduces the 5f-5f overlap, a more localized behaviour is expected and indeed observed in the hydrides than in the parent metals. Th4I-I~5 is a superconductor with a rather high transition temperature (8 K). Magnetism occurs in the U and Pa hydrides, but disappears in the NpHx system and reappears in the Pu hydrides. The 5f electrons finally become fully localized for the transplutonium elements and the heat of formation approaches that of typical rare-earths hydrides (Ward 1985a). The following actinide hydrogen systems are expected to exhibit properties similar to those of the rare earth. Unfortunately, very few experiments have been performed because of the intense radioactivity of the transplutonium elements.

5.2.1. ThHx ThH2 with the face-centred tetragonal structure is isostructural with the dihydrides of Ti, Zr and Hf, but exhibits an appreciably larger lattice constant. The higher hydride Th4H15 is superconducting below 8 K and crystallizes in a complex bcc structure containing 16 atoms per unit cell (Satterthwaite and Toepke 1970, Ward 1985a,b). No evidence for superconductivity could be found for ThH 2 down to 1 K, although the parent metal is superconducting below 1.37 K. The reappearance of superconductivity in Th4H15 initiated band-structure calculations, inelastic neutron scattering experiments and heat capacity measurements (Winter and Ries 1976, Dietrich et al. 1977, Miller et al. 1976). From specific heat measurements with and without external field Miller et al. (1976) concluded that Th4H15 is a bulk type-II superconductor whose properties are in fair agreement with the BCS theory. The electronic specific heat coefficient (7 = 8.07 mJ/mol K 2), the Debye temperature (0 = 211 K) and the electron-phonon enhancement factor (2 = 0.84) of Th4H15 is by 87%, 29.5% and 58% larger than in the parent metal. According to valence band spectra (Waever et al. 1977), the increase of the 7 value is not caused by an enhanced density of states at the Fermi energy. No significant increase of the phonon enhancement factor is derived from band-structure calculations by Winter and Ries (1976). According to their calculation, they predicted a Tc enhancement if Th is substituted by elements with a lower valency. This, however, is not in agreement with the experimental results which show a depression of Tc (Oesterreicher et al. 1977). 5.2.2. PaHx No magnetic order was detected by susceptibility measurements above 4 K in the C15 Laves phase and the A15 phase. The effective paramagnetic moment is 0.84#B and 0.98#B, respectively (Ward et al. 1984). 5.2.3. UHx Usually, the [~-UH3 phase occurs which crystallizes in the A15 structure, while the ~-UH3 phase is difficult to prepare and contains frequently a mixture of ~- and 13phases (Ward 1985b). Both crystal structures belong to the Pm3n group. There are many magnetic and N M R measurements of the [3-hydride and few of the m-hydride,

536


which are reviewed by Ward (1985a). Both order ferromagnetically. The paramagnetic Curie temperature of ~-UH3 is between 174 and 178 K. According to specific heat, neutron diffraction and magnetic measurements, Tc of [3-UHa is in the range between 170 and 181 K. Due to the lack of saturation, the data of the spontaneous moment exhibit a considerable scatter (0.87#B--l.18#B), while the neutron diffraction result of Shull and Wilkinson (1955) gives a moment of 1.39#B. This is obviously a consequence of a rather high magnetocrystalline anisotropy, which is also reflected in the heat capacity: Fernandes et al. (1985) analysed the specific heat data of Flotow and Osborne (1967) in terms of spin wave contributions and found good agreement with the experimental data if an energy gap of about 80 K is taken into account. The appearance of an energy gap in the ferromagnetic spin wave spectrum is a strong indication for a high magnetocrystalline anisotropy. The electronic specific heat coefficient of 13-UH3 (7 = 28.7 mJ/mol K 2) is nearly by a factor of three larger than that of U metal. By analogy with Ce hydrides, this 7 enhancement may presumably arise from a f-d correlation effect as in heavy fermion systems rather than from a simple increase of the density of states at the Fermi energy. 5.2.4. NpH~

Neptunium forms, analogous to the rare-earth hydrogen systems, a cubic dihydride (CaF2 structure) and a hexagonal trihydride. The susceptibility of NpHx (x = 2.04, 2.67, 3.0) exhibits only a weak temperature dependence which is nearly constant below 200 K (Aldred et al. 1979). A crystal-field calculation based on the Np a+ (5f 4) ground state yields good agreement with the experimental data. 5.2.5. P u l l x

Magnetic order occurs in the PuHx system for all x values (1.99 < x < 3.0) and changes from antiferromagnetic order in Pull1.99 (TN-- 30K) to ferromagnetism (Aldred et al. 1979, Ward 1985a). Instead of antiferromagnetism in the powdered dihydride, ferromagnetic order was reported for a bulk sample with x = 1.93 [Tc = 45 K; Willis et al. (1985)]. The Curie temperatures increase with the hydrogen content up to 101 K for the hexagonal trihydride, while the spontaneous moments decrease from 0.57#B for x = 1.93 to 0.353#B for x = 3.0. By analogy to the Np system, Aldred et al. (1979) suggested from susceptibility measurements a Pu 3+ (5f 5) ground state. With the same crystal-field parameters as for NpH2, the magnetic ground state consists mainly of the J = ~ manifold with 3 % admixture of J = 7. Thus, the expected ordered moment (1.0#B) is significantly higher than the experimental value (< 0.57#B). The ordered moment determined from neutron diffraction equals 0.8 T- 0.3#R for the three deuterium concentrations investigated (x = 2.25, 2.33 and 2.65) (Bartscher et al. 1985). The significant difference between the neutron and magnetization data of the magnetic moment is presumably due to a large magnetocrystalline anisotropy. 5.3. Binary transition-metal hydrides

The work on these systems until 1977 is covered by the review of Wallace (1978), where predominantly studies on the systems Ti-H and P d - H are treated. All d


537

transition metals which were found to form stable hydrides are paramagnetic. In most of the cases, hydrogen uptake leads to a reduction of the susceptibility, which is attributed to a hydrogen-induced decline in the density of states. Limitations for the application of the rigid-band model in order to explain the susceptibility behaviour were found, which is due to the two-phase nature of the T M - H systems. Particularly for these systems, an appreciable number of theoretical studies on the electronic properties have been carried out, the early work of which having been reviewed by Switendick (1978). Aspects of both simple pictures, the proton model (electrons added at the Fermi level) and the anion model (low-lying states associated with electronic charge in the vicinity of the hydrogen) are found. Later on, the application of pressures in the GPa range lead to the preparation of further transition-metal hydrides [Cr-H (Ponyatovskii et al. 1982), M n - H (Antonov et al. 1980b, Fukai et al. 1989), F e - H (Antonov et al. 1981, 1989), Co-H, and N i - H (Antonov et al. 1980a, 1983, Hanson and Bauer 1988)]. Upon hydrogen uptake, the magnetic order is generally reduced. Antonov and co-workers interpreted their magnetization results within the framework of the rigid-band model, considering hydrogen as a donor of a fractional quantity of electrons to a common band. As, however, Vargas and Christensen (1987) and Vargas and Pisanty (1989) deduced from their linear muffin-tin orbital calculation for several transition-metal hydrides, the rigid-band approximation is not valid in the case of these transition-metal hydrides. The presence of hydrogen in the metal matrix strongly modifies the electronic structure, leading to new states far below the d band of the host and to an increase of the density of states at the Fermi level. Both facts have been verified experimentally by photoemission (see, e.g., Riesterer et al. 1985), soft X-ray emission (Fukai et al. 1976) and specific heat measurements, respectively (see, e.g., Wolf and Baranowski 1971). Valuable information in this respect may further be obtained from 1H-NMR Knight shift studies (Schmidt and Weiss 1989).

5.4. Ternary rare-earth-transmission-metal hydrides Different from section 5.1, here the symbol R means not only a rare-earth element but also elements such as Ti, Zr, Hf.

5.4.1. Hydrides of Mn compounds 5.4.1.1. Generalfeatures. Particular for Mn-containing ternary hydrides, no general prediction can be made of the changes in magnetic properties upon hydrogen uptake (table 2). Onset and complete loss of magnetic order after hydrogen absorption are found, as well as a substantial reduction of Tc and the magnetization. Moreover, spin-glass behaviour is frequently obtained for Mn-rich ternary hydrides which most probably has to be related to the presence of Mn segregations detected by means of XPS (Schlapbach 1982). The reason for these heterogeneous results lies in the specific sensitivity of the magnetic properties of Mn compounds upon interatomic distances. Particularly Buschow and Sherwood (1977) pointed to the importance of a critical M n - M n distance for the occurrence of magnetic order. However, in order to explain

538

G. WIESINGER and G. HILSCHER TABLE 2 Magnetic properties of R - M n compounds and their hydrides.

Compound

Structure

Space group

Tc (K)

#s (#B/f.u.)

#Mn (#B/Mn)

Y6Mn23

Yh 6 Mn23 Th 6 Mn23 Th6 Mn23 Th6 Mnz3

Fm3m Fm3m Fm3m Fm3m

486, 498 563 700 -

13.2, 13.8 -

0.4

Y6 Mn23 H9 Y6 Mn/3 H2o Y6 Mnz3 H2s Nd6 Mn23 Nd6 Mn23 Hx

Th6 Mn23 Th6 Mnz3

Fm3m Fm3m

438 220

4.8 20.8

[7] [7]

Sm6Mn23 Sm6 Mn23 Hx

Th6 Mn23 Th6 Mn23

Fm3m Fm3m

450 230

3.0 15.3

[7] [7]

Gd6 Mn23 Gd6 Mn23 H22

Th6 Mn23 Th6 Mn23

Fm3m Fm3m

461 140, 180

49 14.2

[2] [2, 8, 9]

Tb6Mn23 Tb6 Mn23 H/3

ThrMn23 Th6 Mn23

Fm3m Fm3m

455 220

49 17.2

[10] [ 10]

Dy6Mn23 Dy6Mn/3H23

ThrMn/3 Th6Mn23

Fm3m Fm3m

443,435

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