Landbolt-Börnstein Numerical Data and Functional Relationshps in Science and Technology Volume 19 Magnetic Properties of Metals Subvolume a 3d, 4d and 5d Elements, Alloys and Compounds

LANDOLT-BORNSTEIN Numerical Data and Functional Relationships in Scienceand Technology

N&v Series Editors in Chief: K.-H. Hellwege - 0. Madelung

Group III : Crystaland Solid StatePhysics

Volume 19 Magnetic Propertiesof Metals Subvolumea 3d, 4d and 5d Elements, Alloys and Compounds K. Adachi * D. Bonnenberg * J.J.M. Franse R. Gersdorf . K. A. Hempel K. Kanematsu - S.Misawa * M. Shiga M. B. Stearns * H. l?J.Wijn

Editor: H. P J.Wijn

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo

ISBN 3-540-15904-5 Springer-Vcrlag Berlin Heidelberg New York ISBN o-387-15904-5 Springer-Verlag New York Heidclbcrg Berlin

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This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under $54 of the German Copyright Law, where copies are made for other than private use, a fee is payable to “Verwertungsgesellschaft Wart”, Munich. 0 by Springer-Verlag Berlin Heidelberg 1986 Printed in Germany The use of registered names, trademarks, etc. in this publication does not imply, even in the absence ofa specific statement, that such names arc exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting. printing and bookbinding: Briihlschc Universititsdruckerei, 2163/3020-5432 10

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Editor H. P. J. Wijn Institut IIir Werkstoffe der Elektrotechnik der Rheinisch-Westfalischen Technischen Hochschule Aachen, Templergraben 55, D-5100 Aachen

Contributors K. Adachi Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464, Japan D. Bonnenberg Institut ftir Werkstoffe der Elektrotechnik der Rheinisch-Westfalischen Technischen Hochschule Aachen, Templergraben 55, D-5100 Aachen J. J. M. Franse Natuurkundig Laboratorium Amsterdam, Nederland

der Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE

R. Gersdorf Natuurkundig Laboratorium Amsterdam, Nederland

der Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE

K. A. Hempel Institut fir Werkstoffe der Elektrotechnik der Rheinisch-Westfalischen Technischen Hochschule Aachen, Templergraben 55, D-5100 Aachen K. Kanematsu Department of Physics, Nihon University, Kanda-Surugadai, Chiyoda-ku, Tokyo 101, Japan S. Misawa Department of Physics, Nihon University, Kanda-Surugadai, Chiyoda-ku, Tokyo 101, Japan M. Shiga Department of Metal Science and Technology, Kyoto University, Sakyo-ku, Kyoto 606, Japan M. B. Stearns Department of Physics, Arizona State University, Tempe, Arizona, 85287, USA H. P. J. Wijn Institut fI.ir Werkstoffe der Elektrotechnik der Rheinisch-Westfalischen Technischen Hochschule Aachen, Templergraben 55, D-5100 Aachen

Vorwort Metalle, Legierungen und Verbindungen, die such andere Elemente des Periodensystems enthalten (eine Inhaltsiibersicht fur den ganzen Band III/19 befindet sich auf der Innenseite des vorderen Buchdeckels). Da jedoch selbst geringe Mengen solcher Elemente einen grol3en EinfluD auf die Eigenschaften der Substanzen haben kiinnen, erschien esverniinftig, im jetzigen Teilband such d-Ubergangselemente und Legierungen mit kleinen, aber genau delinierten Zusatzen anderer Elemente aufzunehmen. Die Definition von ,,gering“ ist natiirlich weitgehend willkiirlich und hangt von der jeweiligen Legierung ab. In der Forschung und in der Literatur auf dem Gebiet des Magnetismus findet ein allmahlicher Ubergang im Gebrauch von cgs/emu-Einheiten zu SI-Einheiten statt. Es wurde jedoch davon abgesehen, alle Daten in den Einheiten eines einzigen Systems darzustellen, wie vorteilhaft dies such immer von einem systematischen Standpunkt aus betrachtet gewesenware. Stattdessen ist dem System von Einheiten, das die Autoren der zitierten Arbeiten urspriinglich benutzten, meistens der Vorzug gegeben. Damit treten cgs/emu-Einheiten bei weitem am hauligsten auf. Dem Benutzer des Bandes wird selbstverstandlich auf mehreren Wegen geholfen die Daten in das Systemvon Einheiten zu iibertragen, das ihm am gelaufigsten ist, so z. B. durch eine Liste der Delinitionen, Einheiten und Umrechnungsfaktoren fur die am htiufigsten auftretenden magnetischen Gr6Den. Besonderer Dank gebiihrt den Autoren fur die angenehme Zusammenarbeit, der LandoltBornstein-Redaktion, hier insbesondere Dr. W. Finger und Frau G. Burfeindt, fur die grol3e Hilfe beim Bewlltigen der redaktionellen Arbeit, sowie dem Springer-Verlag fur die Sorgfalt bei der Veroffentlichung dieses Bandes. Wie alle anderen Bande des Landolt-Bbrnstein wurde such dieser Band ohne finanzielle Hilfe von anderer Seite veriiffentlicht. Der Herausgeber

Aachen, September 1986

Preface Since the appearance in 1962of Landolt-Bernstein (6th Edition), Volume II, part 9, dealing with the magnetic properties of a wide variety of substances, the number of alloys and compounds with interesting magnetic properties has enormously increased. The preparation of these substancesaimed, in the first place, at a better understanding of the magnetic behaviour of the already well-known substances, but it also accelerated the industrial development of new magnetic materials with optimized properties for various applications. Progress in electronics as well as the development of new measuring techniques has also led to an enormous extension of the knowledge of intrinsic magnetic properties. Since 1970several volumes of the Landolt-Bornstein New Serieshave been devoted to, or at least contain data about, the magnetic properties of some special groups of substances.The present Volume 19 of Group III (Crystal and Solid-State Physics) will deal with the magnetic properties of metals, alloys and metallic compounds which contain at least one transition element. It was not attempted, however, to be very critical about the metallic character of the substances discussed. Where appropriate, semiconductors and even insulators have been included. Regarding the properties to be listed, not only data on magnetic properties but also on those nonmagnetic properties have been included which, to some extent, depend on the magnetic state of the metallic system. The literature that appeared until about one year before the publication of each subvolume has been covered.

VIII

Preface

The amount of information available has become so substantial that a larger number of subvolumes is neededto cover the reliable data on magnetic properties of metals. The data arc not arranged according to specific magnetic properties, but rather follow the lines of the various groups of magnetic substances.It appeared during the organization of the work that in this way the largest coherence within the contents could bc obtained. This was also reflected in the experience that in this way competent authors could be found who, in their contributions to this volume, covered important groups of metals, instead of a single, narrowly defined magnetic property. The first subvolumcs will deal with the intrinsic magnetic properties of metals, i.e. data on those magnetic properties are represented in tables and figures which depend only on the chemical composition and on the crystal structure of the metal. Data on properties that, in addition. depend on the preparation of the samples used in the mcasurcments, as is for instance the case for thin films and for amorphous alloys, will be given in the last subvolumc. A clean-cut division is of course illusory for at least two reasons. In the first place the properties of metals and alloys can be depend on the chemical purity and on the physical quality of the crystal. And moreover, in alloys the ordering of the various atoms in the crystal lattice may in some casesinfluence the magnetic properties. This first subvolumc, 111/19a,deals with the magnetic propcrtics of metals and alloys of the 3d. 4d, and 5d transition elements. Subsequent subvolumes will treat metals, alloys and compounds that also contain other elements of the periodic table (see the survey of contents for the Volume 19 on the inside front cover). However, since small amounts of such elements can have a large influence on the properties of the solvent, it appeared reasonable to include in the present subvolumc d transition metals and alloys that contain very small. but well-defined additions of other elements. The definition of “small” is of course rather arbitrary and may depend on the alloy under discussion. In the field of magnetism, there is a gradual transition from the use of cgs/emu units to SI units. It was. however, not intended to represent all data in the units of one system, regardless of how nice this would have been from a systematic point of view. Instead, mostly preferencewas given to the system of units that was originally used by the authors whose work is quoted. Thus cgs/emu units occur most frequently. Of course the user of the tables and figures is helped in several ways to convert the data to the units which he is most familiar with, see, e.g., the list of definitions, units and conversion factors for the magnetic quantities occurring most frequently. Many thanks are due to the authors for the agreeable cooperation, the Landolt-Biirnstein editorial office in Darmstadt, especially Dr. W. Finger and Frau G. Burfeindt, for the great help with the editorial work, and to the Springer-Verlag for the carefulness with respect to the publication of this volume. Like all other volumes of Landolt-Bernstein, this volume is published without outside financial support. Aachen, September 1986

The Editor

List of symbols Symbol

Unit

Quantity

Introduced in subsect.

A A AU-) AU-)

erg crnm3 A-2 Gcm3g-’ Oe-“2 MHzG-’

1.1.2.10 1.1.2.11 1.1.2.4 1.1.2.8

85 91 34 59

Ai A;

Oe-’

exchange stiffness constant area of extremal Fermi surface cross section magnetization expansion coefficient of H”’ term ratio of NMR frequency and spontaneous magnetization linear saturation magnetostriction coefficient forced linear saturation magnetostriction coefficient lattice parameter magnetization expansion coefficient of T” term electrical conductivity expansion coefficient bulk modulus magnetic induction applied magnetic flux density residual flux density rf field maximum energy product lattice parameter susceptibility expansion coefficient susceptibility expansion coefficient magnetoelastic coupling constant Curie constant per unit mass

1.1.2.6 1.1.2.6

48 49

1.1.2.9 1.3.8

73 513

a a, Oij B B B awl 4

A K-”

&h,, b bII b, bi c,

GOe A Oem2 K-2 dyn cmm2 cm3 Kg-’ m3K kg- ’ cm3K mol- ’ m3K mol-’ calK-’ mJK-’ A

cm c,. c,. C

bar G. T T T

c C

cij D Dn D(EA d E E

ms-’ Mbar eVA2 A-’ Mbar

J, erg ev, RY

E.3

ergcmm3

EF ES

eV meV

e

e2clQ

mms-’

F F(rl. El

(eV)- l

Page

XIX 1.1.2.8

59

1.3.4 1.3.2 1.1.2.6 1.1.2.3

506 494 48 30

1.1.2.9 1.1.2.9

72 73

1.1.2.5

41

1.1.2.9

72

1.3.1 1.1.2.9

491 73

Curie constant per mole heat capacity at constant pressure/volume lattice parameter concentration velocity of light elastic constant spin wave stiffness constant spin wave stiffness expansion coefficient electronic density of states at the Fermi energy inverse distance of nearest-neighbor plane Young modulus energy free energy per unit volume of magnetocrystalline anisotropy Fermi energy spin wave energy electron charge electric quadrupole splitting Stoner (Landau) enhancement factor spectral weight function

List of symbols

Symbol

Unit

F(Q) ?

G G Ghkl

MG Mbar A-’

9 9’

91

mms-’ mms-’

2

Oe, Am-’

90

H aPPl H.4 HC

H eff H hyp H hyp,eff H core H ext & H orb

2 Am-’ Oe Oe Oe Oe Oe Oe Oe Oe

Quantity

Introduced in subsect.

magnetic form factor of the unit cell magnetic crystal structure amplitude magnetic form factor dHvA frequency shear modulus free energy reciprocal lattice vector for hkl reflection spectroscopic splitting factor magnetomechanical ratio ground state splitting excited state splitting free energy expansion coefficient magnetic field applied magnetic field anisotropy field coercive field effective magnetic field magnetic hyperfine field effective magnetic hyperfine field Is, 2s and 3s core electron contribution to Hhyp external field contribution to Hhyp 4s electron contribution to H,,, unquenched orbital moment contribution

1.1.2.7 1.1.2.7

52 52

1.1.2.11

91

1.3.4 1.1.2.7

506 52

1.1.2.8 1.1.2.8 1.3.4

61 61 506 XIX

1.1.2.9 1.1.2.8

72 58

1.1.2.8 1.1.2.8 1.1.2.8 1.1.2.8

58 58 58 58

1.1.2.6 1.1.2.6

48 49

1.1.2.3

30

1.3.6 1.3.6 1.3.6 1.3.6 1.1.2.5

508 508 508 508 41

1.1.2.10 1.1.2.12 1.1.2.6

85 113 48

1.1.2.12

113

1.1.2.13

118

to

H hi res hi’ I I IS J

Oe

J K K Kl K orb

meV Mbar

Oe-’ mms-’

KS K Ku KS KR K&i

k’ k, k k b L L 1

Al/l M

ergcmw3 erg cmm3 erg crnm2

XIII

Page

Hhyp

resonance magnetic field magnetostriction coefficient forced magnetostriction coefficient nuclear spin quantum number exchange interaction constant isomer shift total angular momentum quantum number of atom exchange integral bulk modulus Knight shift d spin contribution to Knight shift d orbital contribution to Knight shift s contact contribution to Knight shift magnetocrystalline anisotropy constant uniaxial anisotropy constant surface anisotropy constant Kerr rotation coefficient expansion coefficient of 1, wavevector Fermi wavevector light extinction coefficient modulus of Jacobian elliptic function Boltzmann constant Widemann-Franz ratio film thickness interatomic distance thermal expansivity ion mass

List of symbols

XIV

Symbol

Unit

Quantity

hi

G

magnetization

Am-‘, T G Am-‘, T

spontaneous (saturation) magnetization

PB

nt m*

h’ hT hTA II

g-l, kg-’

n n Ii 40

states eV atom spin

P P P P P

kbar

Pelf

PB

PB

PB PB PB

Pi Plot PhdPd

PB

Porb

PB

Pspin Ei :Q

PB PB

PB ;I:

kHz mms-’ pVK-’

ii

QO q 4 4( R R R RO

A-’ A n RcmG-’ m3C’

Fourier transform of unit cell magnetization dynamic component of magnetization component of the magnetization in direction of the magnetic field at position x electron mass effective electron mass number of atoms per unit mass demagnetizing factor Avogadro constant shell parameter number of electrons per atom refractive index complex index of refraction

Introduced in subsect.

Page

XIX

1.1.2.7 1.1.2.10 1.1.2.7

52 85 52

1.1.2.12 1.1.2.12

113 113

1.1.2.5

41

1.1.2.6

48

1.1.2.3

30

1.1.2.3

30

1.1.1.3

7

1.1.1.3

6

density of states at energy E probability distribution expansion parameter of magnetocrystalline anisotropy expansion parameter of R, pressure atomic magnetic moment in paramagnetic phase atomic magnetic moment in paramagnetic phase, derived from Curie-Weiss law average magnetic moment (average) magnetic moment per atom (average)conduction electron magnetic moment per atom magnetic moment of impurity atom average localized magnetic moment per atom (average)magnetic moment of atom M orbital magnetic moment per atom spin magnetic moment per atom spin density wavevector wavevector of momentum transfer electric quadrupole splitting quadrupole shift thermoelectric power gyroelectric parameter amplitude of gyroelectric parameter phase of gyroelectric parameter wavevector expansion parameter of 1, atomic radius; distance electrical resistance reflectivity of light roll reduction ordinary (normal) Hall coefficient

1.1.2.8 1.1.2.13 1.2.1.2.12 1.2.1.2.12 1.2.1.2.12

61 118 269 271 271

1.1.2.6

48

1.1.2.13

118 XIX

xv

List of symbols

Symbol

Unit

Quantity

Introduced in subsect.

Page

QcrnG-l m3 C-l A

extraordinary (spontaneous, anomalous) Hall coefficient shell radius expansion parameter of 1, atomic long-range order parameter spin quantum number of atom spin density wave amplitude of n-th spin density wave harmonic neutron scattering function expansion parameter of magnetocrystalline anisotropy shape magnetostriction volume magnetostriction expansion parameter of 1, temperature temperature related to maximum in x annealing temperature ferromagnetic Curie temperature commensurate-incommensurate transition temperature spin glass freezing temperature Kondo temperature martensitic transition temperature melting point temperature Neel temperature superconducting transition temperature; transition temperature between two types of magnetic order spin flip transition temperature spin reorientation temperature tetragonal phase transition temperature transition temperature nuclear longitudinal (spin-lattice) relaxation time nuclear transverse (spin-spin) relaxation time nuclear relaxation times T,, T2 at position x in the domain wall time annealing time expansion parameter of 1, volume volume per atom molar volume velocity concentration Cartesian coordinates atomic number spin wave specific heat coeffkient linear thermal expansion coefficient ultrasonic attenuation coefficient Kerr effect direction cosine of angle between magnetization and crystallographic axis lattice specific heat coefficient

1.1.2.13

118 XIX

1.1.2.6

48

1.1.1.3 1.1.1.3 1.1.2.9 1.1.2.5

6 6 73 41

1.3.7 1.3.7 1.1.2.6

512 512 48

1.3.2

494

PB PB

K, “C K K K K K K K K, “C K K K K K K s s s S s

cm3 A3 cm3 ems-l

mJmol-’ Ke5j2 K-’ rad mJmol-’ Km4

1.1.2.8

59

1.1.2.6

48

1.1.2.13

118

1.1.2.12 1.1.2.5

113 41

1.1.2.13

118

XVI Symbol

List of symbols

Unit

Quantity

Introduced in subsect.

A2

coefficient in spin wave dispersion relation direction cosine of the direction in which the change in length due to magnctostriction is measured expansion coefficient of 1, expansion coefficient of magnetic susceptibility expansion coefficient of magnetic susceptibility magnon lincwidth of spin fluctuations electronic specific heat coefftcicnt gyromagnetic ratio fraction of 3d electrons in E, state amplitude of periodic lattice distortion exchange splitting band gap incommensurability parameter of spin density wave transverse (equatorial) Kerr effect critical exponent of r enhancement factor relating magnetic hyperfine field to spontaneous magnetization enhancement factor E at position x in the domain wall thermal expansivity strain dielectric tensor real part of dielectric tensor element imaginary part of dielectric tensor element ellipticity of light reflected in polar Kerr effect paramagnetic Curie temperature Debye temperature angle angle between magnetization and wavevector q of spin wave nuclear specific heat coeflicicnt light absorption index compressibility inverse correlation range of spin fluctuations photon wavelength thermal expansion thermal conductivity electron-phonon interaction constant Landau-Lifshitz damping parameter linear saturation magnetostriction forced linear magnetostriction expansion coefficient of i, expansion coefficients of %, volume magnetostriction fluctuation term in x(q, 8) Poisson ratio permeability of free space Bohr magneton nuclear Bohr magneton ground state nuclear magnetic moment frequency

1.1.2.9 1.1.2.6

72 48

1.1.2.6 1.3.4 1.3.2 1.1.2.9 1.1.2.13

48 506 493 73 118

1.1.2.11 1.1.2.11 1.1.1.3

92 92 8

1.1.2.12 1.1.2.9 1.1.2.8

113 73 58

1.1.2.8

58

1.1.2.12

113

1.1.2.3

30

1.1.2.9

72

1.1.2.13

118

1.1.2.9

73

1.3.1 1.1.2.10 1.1.2.6 1.1.2.6 1.1.2.6 1.1.2.6

491 85 48 48 48 50

1.1.2.3

30

1.1.2.8

61

0e-2 K-2 meV mJmol-’ Ke2 kHzG-’ A eV eV

K K rad. deg mJmol-‘K bar-’ A-’ w Wcm-‘K-l s-1

Oe-’

s-1

Page

List of symbols Symbol

Unit

Quantity

s-1

NMR frequency expansion coefficient of G density resistivity element of resistivity tensor Hall resistivity magnetoresistance tensile stress magnetic moment per unit mass

gcmm3 pR cm pQ cm @cm @cm kbar Gcm3 g-’ Am2 kg-’ Vsmkg-l Gcm3 mol-’ Am2 mol - 1 Vsmmol-’ Gcm3g-l Gcm3g-’ Gcm3g-’ R-l cm-’ R-‘cm-’ 0-l cm-l R-‘cm-’

S S

rad, deg eV cm3g-’ m3 kg-’ cm3mol- 1 m3 mol-l cm3cmm3 m3 mm3 cm3g-’ cm3mol-’ cm3g-l cm3g-’ cm3g-’ cm3mol-’

cm3mol-’ cm3mol-’

XVII

Introduced in subsect.

Page

1.3.4

506

1.3.8 1.1.2.13

513 118 XIX

magnetic moment per mole remanence spontaneous (saturation) magnetic moment per unit mass magnetic moment per unit mass for magnetic field in hkl direction electrical conductivity element of electrical conductivity tensor real part of electrical conductivity tensor element imaginary part of electrical conductivity tensor element reduced temperature pulse length average time between collisions angle work function magnetic mass susceptibility

XIX

1.1.2.4

34

1.1.2.12 1.3.8

113 513

1.1.2.11

91

1.1.2.11

94 XIX

magnetic molar susceptibility

XIX

magnetic volume susceptibility

XIX

high-field magnetic susceptibility low-field magnetic susceptibility initial magnetic susceptibility spin susceptibility of noninteracting electrons diamagnetic susceptibility of core electrons diamagnetic susceptibility orbital magnetic susceptibility d-orbital magnetic susceptibility spin-orbit interaction contribution to magnetic susceptibility orbital magnetic susceptibility Pauli spin susceptibility s, p, d spin susceptibility spin susceptibility ac susceptibility wavevector-dependent magnetic susceptibility wavevector- and frequency-dependent magnetic susceptibility

1.1.2.4

34

1.3.2

493

1.1.2.4 1.3.2 1.3.2

40 493 493

1.1.2.4 1.3.2 1.3.2

40 493 493

1.1.2.9 1.1.2.3

73 30

XVIII

List of symbols

Symbol

Unit

Quantity

4’ 4’

rad. deg

angle spin antisymmetric part of quasiparticle interaction function Landau parameter angular frequency cyclotron frequency spin wave dispersion relation volume magnetostriction spontaneous (saturation) volume magnctostriction forced volume magnetostriction

s-1 s-1 s-1

&!I,@H

Oe-’

Introduced in subsect.

Page

1.3.1 1.3.1

491 491

1.1.2.11 1.1.2.9 1.1.2.6

91 12 48

1.1.2.6

52

Definitions, units and conversionfactors In the SI. units are given for both defining relations of the magnetization, B = u,,(H + M) and B = poH+ M, respectively. u0=4rt. IO-‘Vs A-’ m- ‘, A: molar mass,e: mass density. Quantity

cgsjemu

SI

B

G=(ergcm-3)1/2 1Gs Oe = (ergcme3)*‘* IOes

T=Vsm-* 10-4T Am-’ 103/4rrAm- ’

H M

B=H+4nM G 1GG

P 5

5,

Ro.R,

P=MI' Gcm3 1 Gcm3s o= M/Q Gcm3g-’ lGcm’g-‘G a,,,=cA Gcm3mol-’ 1 Gcm3mol-‘2

B=p,(H+M)

B=p,H+M

Am-’ IO3Am-’

T 4~. 10-4T

P=MV Am* 10m3Am*

P=MV Vsm 47r.lO-l’Vsm u= M/Q Vsm kg-’ 4n.10-7Vsmkg-’ o,=aA Vsmmol-’ 4rr~10-‘“Vsmmol-1

~==M/Q

Am* kg- ’ 1 Am* kg-’ o,,,=aA Am* mol - ’ 10-3Am2mol-1

P=)IH

P=xH

cm3 lcm3; xv = x/v cm3crne3 1cm3cmw3& xg= x,-/e cm3g-r lcm3g-‘s Xltl=XgA cm3mol- ’ 1 cm3mol-’

m3 4n. 10m6m3 X”=XIV m3mm3 4nm3me3 xp= xv/e m3 kg-’ 4n.10-3m3kg-1 Xm=XpA m3 mol-’ 4rt~10-6m3mol-1

4~. 10e6 m3 X”=%lV m3 mw3 47rm3mm3 xp= XVI@ m3 kg- ’ 4x~10-3m3kgg1 Xlll=%gA m3mol-’ 47r~10-6m3mol-1

Q,,= R,Bf4nR,M, RcmG-’ IRcmG-‘g

ell = ROB+ P~R,M, m3C-’ 100m3C1

e,,=RoB+fW, m3C-’ 100m3Cr

P=%PoH m3

List of abbreviations AF AFo AF, AF, ARPES bee CAF CPA cw cw dCEP dhcp dHvA DM DOS EDC F FC fee FI FID FMR GM hcp KK KS L LA LEED LIAF LSDW MAG ME MSM NBS NMR P PAC PP If RKKY RRR RSM RT SAS sCEP SDW SE SG SRARPES

antiferromagnetic commensurate spin density wave state transverse incommensurate spin density wave state longitudinal incommensurate spin density wave state angle-resolved photoemission spectroscopy body-centered cubic commensurate spin density wave state coherent potential approximation Curie-Weiss-type paramagnetism continuous wave d conduction electron polarization double hexagonal close-packed de Haas-van Alphen diffraction method density of states energy distribution curves ferromagnetic field-cooled face-centeredcubic ferrimagnetic free induction decay ferromagnetic resonance giant magnetic moment hexagonal close-packed Kramers-Kroenig analysis Kohn-Sham potential Lifshitz point longitudinal acoustic low-energy electron diffraction longitudinal incommensurate spin density wave state longitudinal spin density wave magnetization Miissbauer effect moving-sample magnetometer National Bureau of Standards, nuclear magnetic resonance paramagnetic perturbed angular correlation technique Pauli-type paramagnetism radio frequency Rudermann-Kittel-Kasuya-Yosida residual resistance ratio rotating-sample magnetometer room temperature small-angle scattering s conduction electron polarization spin density wave spin echo spin glass spin-resolved, angle-resolved photoemission spectra

xx SRMO SWR SXPS TAS TE TIAF

TQ

TRM TSDW UPS vBH XPS

ZFC

List of abbreviations short-range magnetic order spin-wave resonance soft X-ray photoelectron spectroscopy triple axis spectroscopy thermal expansion transverse incommensurate spin density wave state magnetic torque measurement method thermoremanent magetization transverse spin density wave ultraviolet photoemission spectroscopy von Barth-Hedin exchange correlation potential X-ray photoelectron spectroscopy zero-field cooled

Ref. p. 221

1.1.1.1 Ti

1

1 Magnetic properties of 3d, 4d, and 5d elements, alloys and compounds 1.1 3d elements 1.1.1 Ti, V, Cr, Mn Survey Metal

Property

Fig.

Table

Ti

I$-) xm(T) (C/T> (T2> x&T)

1, 2, 4, 5, 7, 8 3 6

1

v Cr

a-Mn

9

SDW m magn. phase diagram xg(T) TN(x,14 (Ala) (4 04 latent heat (x) W/l) CT> elastic properties

10, 12-16, 19 11, 23 17, 18, 30 20-22 23-27, 29 19 28

magn. structure x,( T> e4,,,)

35 3638 39

T,(P, xl Knight shift (T)

4&42 43

icAT)

36, 38, 44 36,45 36 46,47

x,(T) L(T)

3 4 5

31 32-34

PMn

p-Mn y-Mn 6-Mn Mn-H

2

7 8

1.1.1.1 Ti Titanium metal is a Pauli paramagnet; no localized magnetic moments have been observed.Since Ti becomes superconducting below 0.4 K, probably no magnetic ordering occurs. The crystallographic structure of a-Ti, the most stable phase at room temperature, is hexagonal; in single crystals the magnetic susceptibility is therefore a function of the angle between the direction of the magnetic field and the c axis. Next to a-Ti, there are two other phases of Ti known: P-Ti, with a body-centered cubic crystallographic structure, which is stable above 1155K [56 M 11,and o-Ti, with a hexagonal crystallographic structure, stable only under high pressure, but metastable at pressure zero [74 D 11. The susceptibilities of all phases of Ti are given in Figs. 1...5 and Table 1. For the low-temperature specific heat properties, seeTable 2 and Fig. 6. Dilute alloys of titanium with aluminum have been investigated by [71 C 11,seeFig. 7, and, for completeness, also Fig. 8.

Frame, Gersdorf

2

[Ref. p. 22

1.1.1.1 Ti Table 1. Room temperature values of the magnetic masssusceptibility ,+ of cold-rolled commercial grade cr-Ti. for three directions of the magnetic field [77A 11. Measuring direction

Xe[10-6cm3g-‘]

Rolling direction Perpendicular to sheet Perpendicular to rolling

3.04 3.32 3.12

3.8 -105

I

Cm3 a-Ti

+rl

2.6 0

200

100

single cryslo

-xov 300

J , LOO

K

IO

I-

Fig. 1. Tempcraturc depcndcnccof the magnctic mass susceptibility xp of various polycrystallinc a-Ti specimcns,and of a single crystal of cc-Ti[7OC I]. Sample

Impurity in wt%

02

N2

TS HP ID

0.086 0.037 0.040

Crystal

0.0063

0.01I 0.004 0.037 0.003 Cr = 0.0078 Zr=0.002 A1=0.0015

Cl,

Mg

Sn

Fc

0.01 0.00I 0.01 0.009 (Fe, Cr. Ni) all < 0.001

Frame, Gersdorf

0.003

1.1.1.1 Ti

Ref. p. 221

1.50 10-6 :m3 s

I

60 40-6 cm3 ia

3.02 w6 -cm3 9

1.112

2.94

.34

2.90

.30

.& 2.86 I 2.82

U8

I

I

48

I_ G

,951 w ,950

I

141

2.78

.949

2.14

.948 DI

2.70

,947

4.683 8, 4.682

946

40 I 32 E

3

16

8

I 0

,945

I

I

I

I

200

400

600 T-

800

I

h

1000 K 12

Fig. 3. Temperature dependence of the crystalline anisotropy of the magnetic molar susceptibility. Ax, = xl1 -x1 of Ti, Zr, and Hf [74 V 11.

4.681 I u 4.680

3

-

4.679 4.678 4.677 0

50

100

150

200

250 K 3;oo

TFig. 2. Temperature dependence of the magnetic mass susceptibility xs of a single crystal of pure a-Ti compared with the temperature dependences of the lattice parameters a and c [67 E 11. The susceptibility of Ti is seen to be practically temperature-independent up to about 70K. The low-temperature upturn is accountable to a trace of dissolved Mn [71 C 11, see also [72V 11.

5.5 ;lOm" Ti -cm3 9

,-

--.--

?L-!L-I

4.5 t

2.75 2.50 0

50

100

150

200

250 K 300

a TFig. 4. Temperature dependence of the magnetic susceptibility xp ofpolycrystalline samples of a- and (a) Impurity content of the samples: C and 0: . 10m2at%; Al: < 1. 10m3at%; S, N, Cu, Fe, V, ~3. 10e4at%; other elements: < 1. 10m5at% [74D 13.

mass w-Ti. 5 1 Mn: each

2.51 0

500

1000

1500

K

2000

b) shows xn vs. T for an exteL=perature range: the different lines represent data of different authors.

Franse, Gersdorf

4

1.1.1.1 Ti

[Ref. p.

22

5.5 1O-6 Tj -cm3 g-

I

1.5

2? Fig. 5. Tcmpcraturc dcpcndcncc of the magnetic mass susceptibility lE. for two samples. I and 2. of polycrystallinc r-Ti and P-Ti [65 K I. 69 K I], Typical impurity content: Sample I: 0.001 wt%C: 0.00-7n?%Nz; 0.002 \vt?b 02; 0.005 \vt% Al: 0.002 vvt% Fc. Sample 2: 0.001 \vt?6 C: O.O02\vt% O>; 80 K). This is explained by assuming that a Cr, Fe or Co atom in a surrounding of p-Mn has a local magnetic moment ofabout 1 pe. Ni atoms in p-Mn behave differently, [74 M I] and Figs. 38 and 44. -7

100

300 K

, fbMn'-lot%i3d

0

1

50

1

I

, /"

8

12

16 .1F3K-' 20

Fig. 44. Change of the magnetic mass susceptibility, Azr:= xa(alloy)-X&P-Mn), for alloys of p-Mn containing 1at% of other 3d elements, vs. inverse temperature. Dashedlint: Curie law correspondingto perf= I .73pn per solute atom [74 M I].

l/T -

Franse, Gersdorf

Ref. p. 221

1.1.1.4 Mn

21

y-Mn y-Mn is another allotropic modification of manganese,this phase is only stable between 1368K and 1406K. y-Mn can be stabilized at low temperatures by alloying manganesewith small amounts of C, Fe, Ni, Cu or Pd, and quenching the alloy from high temperatures. At high temperatures, y-Mn has a face-centeredcubic crystalline structure. The Mn-rich alloys in the y-phase at low temperature, however, are antiferromagnetic and have a substantial tetragonal deformation of the crystal lattice in the direction of the sublattice magnetization, which is along [OOl]; the ratio of axes, c/a, is 0.945 [71 E 11. At low temperatures, the magnetic moment of the Mn atoms in y-Mn is 2.1...2.3 un, and the Neel point is about 500K [71 E 11. The magnetic susceptibility as a function of temperature is given in Figs. 36 and 45.

IL .lOP cm3 9 I IO s

8

Fig. 45. Temperature dependenceof the magnetic mass susceptibility xeof y-Fe-Mn alloys, stabilized with 5 at% of Cu [71 E 11.

6

0

100

200

300 T-

400

500 K 600

6-Mn The fourth allotropic phase ofmanganese, S-Mn, is stable between 1406K and the melting point is at 1517K; it has a body-centered cubic crystallographic structure. Its magnetic susceptibility at high temperatures has been measured, seeFig. 36; no other magnetic data are available. Mn-hydrides The hydrides and deuterides of manganese have a hexagonal close-packed crystallographic structure; it appearsthat MnH 0.94is slightly ferromagnetic, with a Curie point near room temperature, [78 B l] and Figs. 46 and 47. 2.0 Gcm3 9 1.5

2.0 Gcm3 9 1.5

I 1.0 b

t b 1.0

0.5

0 0

50

100

150

200

250 K 300

T-

Fig. 46. Temperature dependenceof the mass magnetization u of MnH 0.94in an applied magneticflux density of 5T (open circles), the same for a-Mn (solid circles) [78 B l] Landolt-BOrnstein New Series 111/19a

0.25

0.50

x-

0.75

1.00

Fig. 47. Dependenceof the massmagnetization of Mn hydrides (open circles) and Mn deuterides(solid circles) on, respectively,the hydrogen and deuterium content x. Applied magneticflux density 5 T, temperature82K. For a-Mn prepared by decomposition of MnH,.,,, seehalf black point [78 B 11.

Franse, Gersdorf

22

References for 1.1.1 1

1.1.1.5 References for 1.1.1 52M 1 53K I 55R 1 56M I 5SLl 61 B 1 6201 62s I 62Tl 62T2 62 W 1 63B I 64K I 64 hl 1 64M2 64Wl 65A 1 65Kl 65M I 66K 1 66Pl 67El 68s 1 68U 1 69Kl 69K2 69s 1 7OCl 7OSl 7OY 1 7OY2 7OY3 71Cl 71 E 1 71Hl 71Kl

McGuire. T.R.. Kriessman, C.J.: Phys. Rev. 85 (1952) 452. Kriessman. C.J.: Rev. Mod. Phys. 25 (1953) 122. Rostoker. W., Yamamoto, A.: Trans. Am. Sot. Met. 47 (1955) 1002. McQuillan. A.D., McQuillan. M.K.:Titanium, London: Butterworth Scient. Publ. 1956. Lingelbach. R.: Z. Phys. Chem. N.F. 14 (1958) 1. Burger, J.P., Taylor, M.A.: Phys. Rev. Lett. 6 (1961) 185. Overhauser, A.W.: Phys. Rev. 128 (1962) 1437. Shirane, G., Takei, W.J.: J. Phys. Sot. Jpn. 17, B III (1962) 35. Taniguchi. S., Tebble, RX, Williams, D.E.G.: Proc. R. Sot. London A 265 (1962) 502. Taylor. M.A.: J. Less-Common Met. 4 (1962) 476. Wilkinson, M.K., Wollan, E.O., Koehlcr, W.C., Cable, J.W.: Phys. Rev. 127 (1962) 2080. Bolef. D.I.. Klerk, J. de: Phys. Rev. 129 (1963) 1063. Komura. S., Kunitomi. N.: J. Phys. Sot. Jpn. 20 (1964) 103. Montalvo. R.A.. Marcus, J.A.: Phys. Lett. 8 (1964) 151. Munday, B.C.. Pepper, A.R., Street, R.: Brit. J. Appl. Phys. 15 (1964) 611. Weiss. W.D., Kohlhaas, R.: Z. Naturforsch. A 19 (1964) 1631. Arrot, A., Werner, S.A., Kendrick, H.: Phys. Rev. Lett. 14 (1965) 1022. Kohlhaas, R., Weiss, W.D.: Z. Naturforsch. A 20 (1965) 1227. Mitsui. T., Tomizuta, CT.: Phys. Rev. 137 (1965) 564. Koehler. WC., Moon. R.M., Trego, A.L., Mackintosh, A.R.: Phys. Rev. 151 (1966) 405. Pepper, A.R.. Street, R.: Proc. Phys. Sot. 87 (1966) 971. Ebneter, A.E.: Thesis. Air Force Inst. of Techn., Wright-Patterson Air Force Base,Ohio USA 1967. Street. R., Munday, B.C., Window, B., Williams, I.R.: J. Appl. Phys. 39 (1968) 1050. Umcbayashi. H., Shirane, G., Frazcr, B.C., Daniels, W.B.: J. Phys. Sot. Jpn. 24 (1968) 368. Kohlhaas, R., Weiss. W.D.: Z. Angew. Phys. 28 (1969) 16. Kohlhaas. R., Weiss. W.D.: Z. Naturforsch. A24 (1969) 287. Steinitz. M.O., Schwartz, L.H., Marcus, J.A., Fawcett, E., Reed, W.A.: Phys. Rev. Lett. 23 (1969)979. Callings. E.W., Ho, J.C.: Phys. Rev. B2 (1970) 235. Steller. B.: Physica Scripta 2 (1970) 53. Yamada, T.: J. Phys. Sot. Jpn. 28 (1970) 596. Yamada. T., Kunitomi. N., Nakai. Y.: J. Phys. Sot. Jpn. 28 (1970) 615. Yamada, T., Tazawa. S.: J. Phys. Sot. Jpn. 28 (1970) 609. Callings. E.W., Gehlen, P.C.: J. Phys. F 1 (1971) 908. Endoh. Y., Ishikawa. Y.: J. Phys. Sot. Jpn. 30 (1971) 1614. Huguenin. R., Pclls. G.P., Baldock, D.N.: J. Phys. F 1, (1971) 281. Kostina, T.I., Shafigullina. G.A., Kozlova, T.N., Kuznetsov, V.I.: Phys. Met. Metallogr. (USSR) 32 (1) (1971) 203. 71Pl Palmer, S.B.. Lee. E.W.: Philos. Mag. 24 (1971) 311. Whittaker. K.C., Dziwornooh, P.A.: J. Low Temp. Phys. 5 (1971) 447. 71Wl 71 W2 Whittaker, K.C., Dziwornooh, P.A., Riggs, R.J.: J. Low Temp. Phys. 5 (1971) 461. Zavadskii, E.A., Morozov, E.M.: Sov. Phys. Solid State 13 (1971) 1263. 7121 72V 1 Volkenshtein. N.V., Galoshina, E.V., Romanov, E.P., Shchegolikhina, NJ.: Sov. Phys. JETP 34 (1972) 802. 72Y 1 Yamagata. H., Asayama, K.: J. Phys. Sot. Jpn. 33 (1972) 400. 73Al Arajs. S.. Rao, K.V., Astriim, H.U., De Young, T.F.: Physica Scripta 8 (1973) 109. 73K 1 Kondorskii. E.I., Karstens, G.E., Kostina, T.I., Shafigullina, G.A., Ekonomova, L.N.: Proc. Int. Conf. Magnetism ICM-73 (Moscow) I(1) (1973) 310. Nagasawa. H., Uchinami, M.: Phys. Lett. 42A (1973) 463. 73Nl 73 w 1 Williams jr.. W., Stanford, J.L.: Phys. Rev. B7 (1973) 3244. Degyareva, V.F., Kamirov, Yu.S., Rabin’kim, A.G.: Sov. Phys. Solid State 15 (1974) 2293. 74Dl 74M 1 Mekata. M.. Nakahashi, Y., Yamaoka, T.: J. Phys. Sot. Jpn. 37 (1974) 1509. 74M2 Mdri, N.: J. Phys. Sot. Jpn. 37 (1974) 1285. 74Tl Tsunota. Y., Mori, M., Kunimoto, N., Teraoka, Y., Kanamori, J.: Solid State Commun. 15 (1974)287. 74v 1 Volkenshtein. M.V., Galoshina, E.V., Panikovskaya, T.N.: Sov. Phys. JETP 40 (1975) 730. 75Bl Benediktsson. G., Astr6m, H.U., Rao, K.V.: J. Phys. F 5 (1975) 1966. 76Fl Fawcett, E.. Gricssen. R., Stanley, D.J.: J. Low Temp. Phys. 25 (1976) 771. Frame, Gersdorf

Referencesfor 1.1.1 IlAl llA2 18Bl 78Gl 79Kl 1921 80Kl 80Rl 8OVl 8OWl 8OW2 81Bl 81B2 81B3 81Fl 81Gl 8111 81Ll 81Ml 81M2 81Wl 81W2 82Bl 82Ll 82Sl

Landolt-Bornstein New Series IWl9a

23

Adamesku, R.A., Mityushov, E.A.: Phys. Met. Metallogr. (USSR) 43 (4) (1977) 70. Alikhanov, R.A., Zuy, V.N., Karstens, G.E., Smirnov, L.S.: Phys. Met. Metallogr. (USSR) 44 (3) (1977) 178. Belash, LT., Ponomarev, B.K., Tissen, V.G., Afonikova, N.S., Shekhtman, V.Sh., Ponyatovskii, E.G.: Sov. Phys. Solid State 20 (1978) 244. Golovkin, V.S., Bykov, V.N., Levdik, V.A.: Sov. Phys. Solid State 20 (1978) 651. Katahara, K.W., Nimalendran, M., Manghnani, M.H., Fisher, E.S.: J. Phys. F9 (1979) 2167. Ziebeck, K.R.A., Booth, J.G.: J. Phys. F9 (1979) 2423. Koning, L. de, Alberts, H.L., Burger, S.J.: Phys. Status Solidi A62 (1980) 371. Ruesink, D.W., Fawcett, E., Griessen, R., Perz, J.M., Templeton, I.M., Venema, W.J.: Int. Conf. on Phys. of Transition Metals 1980 (Leeds), p. 335. Venema, W.J., Griessen, R., Ruesink, W.: J. Phys. FlO (1980) 2841. Walker, M.B.: Phys. Rev. B22 (1980) 1338. Williams, I.S., Street, R.: J. Phys. FlO (1980) 2551. Barak, Z., Fawcett, E., Feder, D., Lorinck, G., Walker, M.B.: J. Phys. Fll (1981) 915. Barak, Z., Walker, M.B.: J. Phys. F 11 (1981) 947. Booth, J.G., Ziebeck, K.R.A.: J. Appl. Phys. 52 (1981) 2107. Fincher jr., CR., Shirane, G., Werner, S.A.: Phys. Rev. B24 (1981) 1312. Geerken, B.M., Griessen, R., Dijk, C. van, Fawcett, E.: Proc. Intern. Conf. Physics of Transition Metals, Leeds 1980, 1981,p. 343. Iida, S., Tsunoda, Y., Nakai, Y., Kunimoto, N.: J. Phys. Sot. Jpn. 50 (1981) 2587. Lahteenkorva, E.E., Lenkkeri, J.T.: J. Phys. F 11 (1981) 767. Murayama, S., Nagasawa, H.: J. Phys. Sot. Jpn. 50 (1981) 1189. Murayama, S., Nagasawa, H.: J. Phys. Sot. Jpn. 50 (1981) 1523. Williams, I.S., Street, R.: Philos. Mag. B43 (1981) 893. Williams, I.S., Street, R.: Philos. Mag. B43 (1981) 955. Benediktsson, G., Astrom, H.U.: Phys. Ser. (Sweden) 25 (1982) 671. Littlewood, P.B., Rice, T.M.: Phys. Rev. Lett. 48 (1982) 44. Siegmann, H.C.: J. Appl. Phys. 53 (1982) 2018.

Franse, Gersdorf

24

1.1.2.1 Fe, Co, Ni: introduction

[Ref. p. 134

1.1.2 Fe, Co, Ni 1.1.2.1 Introduction In the last two decadesprogresshas been made in the solution of the understanding of the origin and behavior of magnetism in the metallic 3d elements. These advances have been achieved by the replacement of the earlier thermodynamic approaches to magnetism with a microscopic understanding in which the magnetic behavior is related to the underlying electronic interactions within and between the atoms. This has been achieved becausea number of new and improved experimental techniques becameavailable along with the development of highspeedcomputers used for both complex data acquisition and analysis and for band structure calculations. Often in the past the interpretation of magnetic data was made in terms of a purely localized or itinerant model. We now know that these two extreme models are oversimplifications of the real situation and that the d valence electrons have both features.As a result, the type of behavior that is obtained is strongly dependent on the experiment performed. Experiments that probe the regions close to the nucleus such as nuclear magnetic resonance.neutron scattering. etc., are sensitive to the more local, atomic-like character of the electrons while other techniques such as specific heat, transport properties, dc Haas-van Alphen effectthat probe mainly the tails of the wave functions are sensitive to the nonlocal or itinerant character. Some of the significant techniques developed and achievements made in the recent years are: I. Neutron scattering techniques allowed the measurementsof the form factors, magnetization distributions and magnon dispersion relations. 2. The development of Miissbaucr and pulsed nuclear magnetic resonancespectroscopiesmade possible the determination of the shape of the s and d conduction-electron polarizations, which showed that the mechanism responsible for the origin of ferromagnetism in 3d metallic ferromagnets is the alignment of the “quasi-local” d moments by the polarized itinerant d electrons rather than by the s valence electrons as was the favored mechanism in the early 1960s. 3. Improvements in de Haas-van Alphen measurementslead to the determination of the Fermi surfacesof these complex metals. 4. The development of angle-resolved photoemission spectroscopy allowed the direct measurement of the excited-state exchange splittings and band structures. 5. The availability of high-speed computers made the complex calculations of the ferromagnetic band structures routine so that the effects of different approximations and potentials could easily be investigated. The transition elementsare ofgreat technological importance precisely becauseof the complex and versatile character of their outer electrons. This compilation will concentrate on presenting the current experimental data. It will discuss theory only in so far as it enhances the description of the data or when it is so symbiotic to the data, as in the case of band structure. that it is necessaryfor a sensible presentation of the data. There are numerous theoretical calculations aimed at describing particular experimental results; no attempt will be made to review theseor the present state of the agreement between the theoretical details and experiment. Data on alloys of Fe, Co and Ni are included in this compilation when they predominately provide information about the host.

1.1.2.2 Phase diagrams, lattice constants and elastic moduli At atmospheric pressure Fe undergoes the following transitions [670 I, 74D 11:

bee a

a fee

1665K

bee-liquid.

Earlier measurements[62 J l] found that the room-temperature phase transformation to a hexagonal close packed (hcp) structure occurred at 130kbar and the triple point at 775 K and 110kbar. More recent [71 G l] measurementshave found it to occur at 107(8)kbar with the triple point at about 750 K and 90 kbar. The theory of the phase diagram for Fe has been discussed by Grimvall [76G 11. At high temperature Co is fee and at low temperature it is hcp. The transformation is sluggish so that both forms coexist from room temperature to 450°C. The stable structure of Ni is fee.It has been claimed to have beenprepared in the hcp form by several workers [74D 11. It has also been prepared in the bee structure [74D 11.

Stearns

Ref. p. 1341

1.1.2.2 Fe, Co, Ni: phase diagrams, lattice constants

25

Table 1. Lattice constants, interatomic distances, atomic volumes and thermal expansion coefficients of Fe, Co, and Ni [74D 11. T

Phase

P

“C

i

ri

x

13

~1,bee ct, bee Y, fee Y, fee 6, bee a, bee E, hcp

2.86638(190) 2.9044 3.6467 3.6869 2.9315 2.805 2.468l)

3.956

2.482(8) 2.515(S) 2.579(12) 2.607(12) 2.5388(g) 2.429(S) 2.468(6) 2.408(6) 2.507(6) 2.497(6) 2.506(12) 2.492(12) 2.495(6) 2.484(6)

11.78 12.25 12.12 12.53 12.60 10.43

bar

Fe

20 910 910 1390 1390 23 23

1 1 1 1 1 130.103 130.103

co

20

1

a, hcp

2.5070(3)

4.0698(9)

Ni

20 20 20

1 1 1

P, fee fee hcp

3.5445(4) 3.5241(7) 2.495(12)

4.048(43)

20

1

bee

2.775(14)

-

2.403(8)

E lo-‘jK-’ 11.7; Fig. 3a

11.03 11.08

Figs. 3a, 4a

11.13 10.94(1)

12.5; Fig. 3a

10.91(16) 10.68(16)

‘) For pressure dependence,see Fig. 2.

.

6 calculated

P-

P-

Fig. la. Pressure-temperaturephasediagram for pure Fe [71G1].1:[62K1],2:[60C1],3:[63C1],4:[62J1],5: [65B1],6: [65B2], 7,8: [69M2],9: [71Gl].

Landolt-BBmstein New Series 111/19a

Fig. lb. Pressure-temperaturephase diagram for Co [63 K 11.hcp: a-Co and fee: P-Co. Other notation used to designate hcp and fee phases is E-CO and y-Co, respectively.

Stearns

[Ref. p. 134

1.1.2.2 Fe, Co, Ni: lattice constants

26

3.62, ii I

I

I

I

I

I

INifcc

I/

/I I

3.56 cc 3.56

I 3.59

1 3.52 D

3.57 I cl

2.91 a

2.91 a

2.92

2.92

2.86r D

a

I 60'3

300

I 900

I I 1200 "C 1530

Fig. 3a. Temperature dependcncc of the lattice constants of Fc, Co, and Ni above room temperature [67 K 23. 0

50

100

150

200 P-

250

300

kbor LOO

Fig. 2. Pressure dependence of the room-temperature values of the lattice constants and axial ratios of hcxagonal Fe: open circles [64C I]; solid circles [66 M I].

18

12 .1rj-5

16

AK.1

6 I

c,

3

3 0 -2OG b

0

200

400

600 I-

800 1000 12oo"cl~oo

Fig. 3b. Temperature derivative of the lattice constant, dn’dT. for Fe and B-Co [67 K 21.

Fig. 3c. Thermal expansion coefficient of Ni vs. tempcraturc (solid line) and the calculated (dashed lint) paramagnetic values [77 K 33. Curve 1: [65 W 13, 2: [68 C 11, 3: [64T I]. 4: [38 R I]. 5: [63 K 21.

0 C

200

400

600 T-

800

1000

1200 K 1400

Ref. p. 1341

1.1.2.2 Fe, Co, Ni: lattice constants

d

15.5II 605

610

615

620

625

630

635

27

640

645 K 650

Fig. 3d. Thermal coefficient near the Curie temperature of Ni. Data I: [77 K 3],2: [71 M I].

8 .lO-3 6 I : z

4 2

I

1.625 1.630

4.06 5 1.620 1.615

b a

0

100

200

300

400

500

600 K :

7-

Fig. 4a. Thermal expansion curves ofhcp Co. The dashed curves (3: [810 11) are obtained by fitting the bulk thermal expansion curve (I: [65 W 11)to the experimental points (2: [67 M 11). Land&-Bbmstein New Series IIV19a

1.610 0

100

200

300

400

500 K 600

T-

Fig. 4b. Plot of available c/a data for hcp Co with the predicted temperature dependence from a single-ion model of the anisotropy [84P I]. Curve 1: [48 E 11, 2: [36M1],3:[67M1],4:[36N1],5:[5401],6:[27Sl], 7: [5OT I], 8: [31 W 11, open circles: private communication of P. Goddard.

Stearns

[Ref. p. 134

1.1.2.2 Fe, Co, Ni: elastic constants

2s

Table 2. Room-temperature

values of the elasticity moduli of polycrystalline

Ref.

K

E

Fe, Co, and Ni.

G

P

Ref.

0.823 0.799 0.834

0.291 0.310 0.304

67Al 67Al 67Al

Mbar

Mbar Fe

1.681

61Rl

co

1.914

64Gl

Ni

1.836

60A 1

2.08 2.089 2.197

Table 3. Elastic stiffness constants of Fe and Ni as derived from ultrasound measurements on single crystals. c’=(c,, -c,,)/2. T “C

Cl1

C’

c44

Ref.

0.483 0.139 0.504

1.170 0.993 1.235

72Dl 72Dl 60A 1

Mbar Fe

25

880 Ni

RT

2.322 1.505 2.508

1.20I Mbor

a-Fe

0.95I 0.50,

I

/

1

I I

I

2.: I

2.0

z 1.9

I

Mbor/\l I

1.8

I

I

I

1 (

0.G

1.7 1.6

0.10

1.5 153

a

300

150

600

750 "C 900

Fis. 5a. Temperature depcndencc of the longitudinal elastic constant c, L of r-Fc as dcrivcd from ultrasonic measursmcnts. The expcrimcntal data points of [72 D l] are all within the drawn cuwcs. Also included arc the data points of (open circles) [66 L 11, (solid circles) [6S L 11.

\

0.35

I-

1 1% 0.30 I

L-i

Fig. Sb. Tempcraturc depcndencc of measured shear elastic constants c’=(c,,-c12)/2 and c44 of a-Fc as derived from ultrasonic mcasurcmcnts. The cxpcrimcntal data points of [72 D I] arc all within the drawn curves. Solid circles [6S L I].

o.loI 0

b

150

300

450

T-

600

750 "C

Ref. p. 1341

1.1.2.2 Fe, Co, Ni: elastic constants 1.3:IMbar 2. 1.3(I-

,-

l-

1.15

l.l[ lj 2 i-

0.5c

O.L7 I t 0.44

O.Ll 0.3F 3.4 Mbor 3.3

3.2 I u' 3.1

3.0

2.E 100

200

300

$00 T-

500

600

700 K 800

Fig. 6. Temperature variation of the elastic moduli of Ni ultrasonically measured at 10 kOe applied magnetic field. The vertical dashed line marks the Curie temperature

WAU

(a>c44, 0~1c’=h-~~~~/2~

cc>cL=hI+clz

+ 2c4,)/2. The dashed curve represents the extrapolation to low temperatures of the high-temperature data. Land&Bbmstein New Series 111/19a

29

1.1.2.3 Fe, Co, Ni:

30

[Ref. p. 134

paramagnetic properties

1.1.2.3 Paramagnetic properties The paramagnetic behavior is studied through the susceptibility above the Curie temperature. A localized magnetic moment follows the Curie-Weiss law given by dT)=

NP:U 3k,o

C, - T-O

Here p is the maximum value of the free-atom’s localized magnetic moment in direction of the applied magnetic field. J denotes the angular momentum quantum number of the atom, 9 the spectroscopicsplitting factor, and pa the Bohr magneton. N is the number of atoms per unit massand 0 the paramagnetic Curie temperature. The magnetic moment associatedwith itinerant electrons has an enhanced susceptibility and the general expression is given bj x(4.4 = %0(%4/C1 - I%,(%4 + 4%41 (2) where x0(4.(!I)is the wavevector- and frequency-dcpcndent susceptibility for a noninteracting systemofelectrons, I is an exchange -interaction constant, and I.(q.Q) is a fluctuation term which has been extensively discussedby Moriya et al. [73 M 3, 79 M 21. In general the itinerant part of the magnetic moment is more polarizable in an applied field than the local part so that the moment obtained by applying eq. (I) in the paramagnetic region results in the paramagnetic moment being larger than the moment obtained from magnetization measurementsin the ferromagnetic region. The susceptibility has been determined by magnetization measurements and neutron scattering, the magnetization measurementscorresponding to Q =O. From a plot of l/x vs. T obtained from magnetization measurementsthe paramagnctic Curie temperature @is obtained from the intercept with the temperature axis, the Curie constant C, and thus pcrris obtained from the slope.

Table 1. Paramagnctic properties of Fc, Co, and Ni. AT is the temperature interval for which the parameters of the Curie-Weiss law are determined. pa, denotes the magnetic moment per atom in the ferromagnetic phase extrapolated to T=OK. The ratio p/p,, gives an indication of the degree of localization or itineracy of the electrons forming the moment. A completely localized moment would have a value of one and a completely itinerant moment a large value > 10;e.g.Fe,,, ,Cr0.49has a ratioof 17.6(Tc=9K)and Ni0,43Pt0,57aratio of 17.2 ( Tc= 23 K) [78 W 11.Thus the moments of Fe, Co, and Ni are seento have a high degreeof localized character. Fig. a-Fe p-co Ni ‘) Liquid-Ni

la, b.d 3a 3b. c 3c

0 K + 1093(3) 1403...1428 654.1

c, 10m3cm3 K/g

AT

Peff

K

PB

22.0 20.8 5.546 8.55 16.7

1100...1180 1430...1710 740...970 1528...1728 1728...1928

3.13 3.15 1.613

PIP,,

Ref.

1.01 1.28 1.375

60A2 38Sl 63A2 73B2 73B2

‘) Ni does not obey a Curie-Weiss law; at temperatures above 970 K an additional temperature-dependent contribution 1, is found, seeFig. 4.

31

1.1.2.3 Fe, Co, Ni: paramagnetic properties

Ref. p. 1341 5 .lOC 9 iiT 4

I 3 G 2

1

0 750 a

850

950

1050

1150 “C 1250

T-

1100 b

Fig. la. Temperature dependence of the inverse paramagnetic mass susceptibility of Fe [60 A2]. I: [ 11W 11, 2: [17Tl], 3: [34P 11, 4: [38S I], 5: [56Nl], 6: [60A2].

A heating Q cooling I 1300 1500 “C 1700 T-

Fig. lb. Temperature dependence of the inverse paramagnetic mass susceptibility of Fe [56 N 11: 1: Liquid is supercooled, but &phase is not supercooled. 2: Both liquid and &phase are supercooled. 3: Liquid is supercooled to y-region.

4.10-l cm3 9 2

5.0 .in4

;;mc:=rri

! --.

1400 1500 1600 1700 1800 1900 2000K 2100 C

I

o Hopp~ = 181Oe 272

\

I2

Fig. lc. Temperature dependence of the inverse paramagnetic mass susceptibility of solid and liquid Fe [72 B 41.

1o-3 6, ir’t7 1 d

2

4

6

RIO

z

K 40

T-7, -

Fig. Id. Temperature dependence of the magnetic mass susceptibility of Fe above the ferromagnetic Curie temperature, Tc= 1044.1K. The straight line represents the relationship xp = K( T - 7”)” with n = - 1.33 [64A 21. Symbols indicate different applied magnetic fields. Landalt-Bbmstein New Series lll/l9a

Stearns

[Ref. p. 134

1.1.2.3 Fe, Co, Ni: paramagnetic properties

32

lo-',

cm3 9 6 4

2.5 .l FL UT!

2.0 2

I x”

10-2 8 6

4

“I 1103

1300 I-

1200

a

0 cooling I 1500 “C 1600 Vi00

2.10-3 1

4

2

b

Fig. 2a. Temperature dependence of the inverse paramagnetic mass susceptibility of fee Co [56N 11.

r-r,

6

Ni r, 0

cm3

d

12 10 I 8 -i! 6

0 5 0

a

.^

.^^^

10

K

20

Fig. 2b. Temperature dependence of the magnetic mass susceptibility of fee Co above the ferromagnetic Curie temperature, T,= 1388.2K, in an applied magnetic field H npp,= 181Oe. Straight lines represent tits to the data of the form xg = K( T- T,)” for various n [65 C 21.

16

.c

8

-

1100 1200 1300 1LOO 1500K 1600 I-

Fig. 3a. Tempcraturc dcpcndcncc of the inverse paramagnetic mass susceptibility of Ni. Samples 1 and 2: [63 A2],3: [I I W I], 4: [38 S 2], 5: [44 F I].

Stearns

\

2

33

1.1.2.3 Fe, Co, Ni: paramagnetic properties

Ref. p. 1341

\

,

I

n HoppI=45.3 Oe . 12.5 . 90.6 181.2 D 18 ,104 s cm3 17 I $16

8,10-'1 b

2

6

4

6

IO

K

1500

20

1600

1700

c

T-Tc -

Fig. 3b. Temperature dependence of the magnetic mass susceptibility of Ni above the ferromagnetic Curie temperature, Tc = 626.2 K, as measured for various applied magnetic fields I&.,,,. Straight lines represent fits to the data of the form xp =K( T- Tc” for various n [65A 11.

a

1100

1200

1300

1400

1500 K 1600

Fig. 4. The temperature-dependent susceptibility ofNi can be described with a Curie-Weiss law with an additional temperature-dependent susceptibility xa [63 A2].

Landolt-BOrnstein New Series lll/l9a

1900 K 2000

Fig. 3c. Temperature dependence ofthe inverse paramagnetic mass susceptibility of Ni near its melting point [73 B2].

1.0 40-6 cm3 Ti-

t IYIOO

1800 T-

Stearns

34

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

[Ref. p. 134

1.1.2.4 Spontaneous magnetization, magnetic moments and high-field susceptibility bee Fe, hcp Co, fee Co and fee Ni The room-temperature magnetic phasesof Fe, Co, and Ni are ferromagnetic. The spontaneous magnetization data. oJT), quoted in the literature are obtained by extrapolating the magnetization a(7; H) to zero internal field. The general expression for the temperature and magnetic field dependenceof the magnetization per unit mass is given b) a(T.H)=~~(T)+A(T)H’IZ+X,,,(T)H,

(1)

where H is the internal field equal to the applied magnetic field minus the demagnetizing field. The second term on the r.h.s.ofthe equation is due to the effectof the magnetic field on the spin waves and xHF(T) is a susceptibility term that must be included at high fields. This term is attributed to various small contributions such as orbital and spin susceptibility of the 3d and 4s electrons [82P 11. fee Fe There has been extensive controversy about the magnetic properties of the feephaseof Fe (y-Fe) with several diverse results reported in the literature. From thermodynamic considerations on Fe it was suggested[63 W 1, 63 K 21 that y-Fe has two possible magnetic moment states depending on the lattice constant; a low-moment state at smaller lattice constants and a high-moment state at larger lattice constants. Band calculations indeed show that the magnetic moment of feeFe should undergo a rather rapid transition from a lower-moment state to a higher-moment state for a small variation in lattice constant, seeFig. 8. The rapid transition is manifestation of the flat (localized) E, bands being very near and intertwined with the Fermi level [78 M l] as seen in a band structure calculation of the paramagnetic state (seesubsect. 1.1.2.11on band structure). Conditions are thus favorable for small changesin the lattice constant to shift the E, bands through the Fermi level and thus causea rapid variation in the magnetic moment. Since feeFe is stable only at high temperatures two separatelines of study have developed. One concerns the nature of the magnetic properties of y-Fe which has been stabilized by various means at room and lower temperatures and the other is the state of y-Fe in the high-tempcraturc region. Neutron scattering measurements at 1320K have found y-Fe (a= 3.658A) to be paramagnetic with a magnetic moment of 0.9(1)~, [83 B 21. However. this moment may bc lessthan the actual magnetic moment since the characteristic interaction time of the neutrons was comparable to or slightly less than the spin-flipping time of the magnetic moment (see subsect.1.1.2.8). The low-temperature work has involved considerable controversy. This has usually arisen due to the difficulty of preparing samplesthat arc free from bee Fe which, if present, appears as a high-spin ferromagnetic state with a high transition temperature. In recent years many of the discrepancieshave been resolved by using measurement techniques such as Miissbaucr spectroscopy and neutron diffraction which are capable of correlating the structural properties with the ferromagnetic and antiferromagnetic phases as opposed to techniques which measure more macroscopic properties, such as LEED, X-ray diffraction and magnetization measurements. Since y-Fe is unstable at low temperatures it has been studied as coherent precipitates (~200...10OOA) in a Cu matrix and as pseudomorphic epitaxial thin films on a Cu substrate, seeTable 6. hcp Fe Miissbauer effect measurements down to 0.030K in the pressure range from atmospheric pressure to 21.5GPa detected no measurable hyperline field for the E-phase.This shows that the hcp phasehas no magnetic ordering down to 0.030K in this pressurerange [82 C 1,72 W 11.Massbauer effect measurementsin an applied magnetic field found that at 50 kOe, upon scaling from the 3d free-ion moment, the induced magnetic moment is ~0.08 pn. the susceptibility is 93. 10-4cm3/mol and the effective hyperfine field at the “Fe nucleus is H,,jp =030 Hap,+[82T 33. Seealso Fig. 5 in subsect. 1.1.2.8.

Stearns

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

Ref. p. 1341

35

Table 1. The spontaneous magnetization crsand the high-field susceptibility ~nr, at various temperatures obtained by computer fit of the curves of Figs. la..e with the equation in subsect. 1.1.2.4.1. Applied field direction is indicated. For Fe and Ni no anisotropy in cs or xHF was found. See also Table 3 Fe and Ni [83P l-J, Co [83 P 21.

Fe [loo]

co [OOOl]

CO[ioiol

Ni [111]

T K

0s Gcm3g-’

XHF

4.21 24.79 51.06 75.34 100.51 131.55 165.81 197.45 226.34 254.53 286.41 4.21 24.79 55.31 75.28 100.46 131.31 165.30 197.01 225.69 254.67 286.61 4.21 24.79 55.36 75.28 100.51 131.31 165.50 196.81 225.74 254.67 286.66 4.21 25.00 50.08 75.15 100.51 131.08 165.49 196.71 225.74 254.82 286.66

222.671 222.596 222.367 222.071 221.825 221.443 220.937 220.346 219.736 219.049 218.210 163.82 163.79 163.68 163.54 163.50 163.44 163.39 163.29 162.99 162.93 162.62 163.00 162.98 162.70 162.65 162.64 162.58 162.46 162.40 162.26 162.08 161.86 58.872 58.810 58.698 58.550 58.349 58.063 57.671 57.223 56.724 56.121 55.370

3.60 3.66 3.70 3.81 3.84 3.79 3.76 3.70 3.81 3.90 3.95

10e6 cm3 g-r

a

1.59 1.64 1.58 1.52 1.48 1.37 1.21 1.11 1.13 1.18 1.12 For Figs. lb and c, see next page.

Land&Bdmstein New Series III/l9a

Fig. 1. Magnetization as a function of the magnetic field, at different temperatures below room temperature, of single crystals of Fe, Co, and Ni [83P 11. (a) Fe. The magnetic field is applied along, respectively, the [ 1001,[ 11l] and [ 1lo] directions [83 P 11.The measured change in flux was produced by moving the sample from one pick-up coil to a precisely matched pickup coil in series opposition in a highly uniform magnetic field. The calibration to absolute values was obtained from the measurements of Danan et al. [68 D l] on Ni as the standard of reference [83P 11. The data was accurately fit by eq. (1). It was observed that all the isotherms of magnetization curves had a continuous and welldefined, although small, curvature. Thus the usual procedure ofusing an averaged straight line to determine a,(T) is not valid for data of this quality.

Stearns

[Ref. p. 134

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

36

60.0 Gcm3 9 59.5

5B.U

I+F

I

I 57.5

A225.75

b

I 1

163.35

I b 163X 56.5 16325 560

0

50

100

150

200 kOe 250

H-

C

Fig. lc. Ni. The magnetic field is applied along. respcctivcly, the [ill], [IOO] and [I IO] directions [83P 11.

16!25

Fig. lb. Co. The magnetic field is applied along, rcspcctivcly, the c axis and the [loo] direction in the basal plant [83P I]. b

HTable 2. Spontaneous magnetization a, and magnetic moment per atom, p,,, extrapolated to 0 K for Fe, Co, and Ni. In case of single crystals the direction of magnetization is indicated. 0s

Fe

Cl001 Co, hcp [0001-J [0001-J

poio]i

co, fee Ni

IIll

PSI

Gcm3g-’

PB

221.71 (8) 222.67 1 162.55 163.76 162.95 166.1 58.57(3) 58.872

2.216(l) 2.226 1.715 1.728 1.719 1.751 0.6155(3) 0.619

Stearns

Ref

68Dl 83 P 1 51M2 83P 1 83P 1 55Cl 68Dl 83Pl

1.1.2.4 Fe, Co, Ni: spontaneous

Ref. p. 1341

31

magnetization

Table 3. Survey of the spontaneous magnetization of Fe, Co, and Ni [82P 11. Direction of magnetization is indicated. See also Table 1. T

Fe [loo] co [OOOl] Ni [111]

0s

e

n/i,

7.93 7.87 9.0 8.9 8.97

1766 1717 1475 1447 528

8.91

493

K

Gcm3g-’

gcmm3

4.2 286.41 4.21 286.61 4.21 286.66

222.671 218.210 163.862 162.624 58.872 55.370

4nM,

G

G 22189 21580 18532 18 188 6636 6200

0.8

Fig. 2a. Reduced spontaneous magnetization a,( T)/o,(O) of [loo] bee Fe vs. reduced temperature T/T,. 1: [71C1],2:[82P2],3:[81H3].Thedataof[7lCl]was obtained by measuring the force on prolate ellipsoids in a field gradient while that of [81 H 31 was extracted from measurements of the ac susceptibility of iron whiskers. The data of [Sl H3] has been normalized to that of [71 C l] at room temperature and corrected for the lattice expansion to give B, in [Gcm3/g]. The reduced magnetization curve has been empirically fitted to a function [S 1 H 31: cT,(T) = CT,(O) (1 - z)B/(l - /3r + A?‘2 - W’Z) ,

_I 0.6 ” d \ kY 0.4

I

(2)

where /?=0.368, A=O.1098 and C=O.129.

0

I

0.2

a

I

I

0.4

I

0.6

0.8

IO

0.4 0.6 r/r, -

0.8

1.0

T/T, -

1.0

0.8

I - 0.6 0 \6” G 0.4

0.2

0 b

c!

r/r, -

Fig. 2b. Reduced spontaneous magnetization of Co vs. reduced temperature. I: fee [71 C 11, 2: [OOOl] hcp [SZP 11. Land&-Bbmstein New Series III/I%

0.2

Fig. 2c. Reduced spontaneous magnetization of [l 1l] Ni vs. reduced temperature. 1: [71 C 11, 2: [82P 11, 3: [69 K 11.

Stearns

[Ref. p. 134

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

38 15.0 jc& 9 12.5

10.0

I 1.5 b

2.5

1035

1OLO

1015

1050

1055

1060

1065 K 10

I-

Fig. 3. Magnetization of Fe for various applied magnetic fields in the neighborhood of the ferromagnetic Curie temperature [64 A23.

15.: Gem' 9 12.5

1oc

500 Oe

I b 1.5

LOO

I 300 z 2 200

5s

2.E 100 c 1389

a

0 1385

1390

1395

1

1400 K l&O5

I-

1388

K 13

b ‘:

Fig. 4a. Magnetization offcc Co sphere in various applied maenetic fields in the neighborhood of the ferromagnetic Cuhc temperature [65 C I].

Fig. 4b. T, offcc Co as a function ofapplied magnetic field. Tc is the Curie tempcraturc derived from the magnetization curve in an applied field, see Fig. 4a. as the temperature at which CTstarts to decrease [65 C I].

Stearns

Ref. p. 1341

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

39

8

I b

6

100

620

625

630

635

K

0 640

b

T-

a

Fig. 5a. Magnetization of Ni in various applied magnetic fields in the neighborhood of the ferromagnetic Curie temperature [65A 11.

622

623

62L

625 T; -

626

627 K 628

Fig. 5b. T&as a function of applied magnetic field for two Ni spheres A and B with, respectively, 1Oppm Fe and 0.01 wt% Fe. Td is the Curie temperature derived from the magnetization curve in an applied field as the temperature at which 0 starts to decrease [65A 11.

Table 4. Curie temperature and pressure dependence of the Curie temperature of Fe, Co, and Ni. Metal

T, K

Fe, bee

1044(2) 1044 1045(3) 44 ‘)

Fe, fee co, fee

Ni, fee

1388(2) 1398 1390.0 624.0(3) 627 631(2) 627(l)

Ref.

O.OO(3); Fig. 6

0.5 ‘); Fig. 9 O.OO(5)

0.36(2); Fig. 7

64A2 72Ll 71Cl 79Ll 65Cl 72Ll 71Cl 61Ml 72Ll 71 c 1 65Al

800 I h 700 600

‘1 TN. “) W’ildp),=o.

300 0

IO

20

30

40

50

60 kbor70

PFig. 6. Curie temperature (solid line and circles) and cl-y phase boundary (broken line) of pure Fe as a function of pressure. (In the insert are shown three different series of measurement for the shift of Curie temperature. The temperature scale has been enlarged 10 times). Magnetic determination ofthe a-y phase upon heating and cooling [72L 11. Land&Bdmstein New Series 111/19a

Stearns

1.1.2.4 Fe, Co, Ni: spontaneous magnetization

40

[Ref. p. 134

3.2

2x I y" Q 25

0

50

75 P-

125 kbar150

100

1.6

Fig. 7. Shift of the Curie tempcraturc for Ni as a function of pressure measured with opposed Bridgman anvils [74B I]. The results obtained by [72L I] in a belt apparatus are shown for comparison (dashed curve). 70, K

I

I

I

atbcc) -

Fig. 8. Calculated and measured magnetic moments per Fe atom for fee (curves 2...4) and bee (curve I) Fe as a function of the lattice constant. The lattice constants of room temperature bee Fe and fee Cu are indicated by arrows on the abscissas. The experimental moments are shown by asterisk for bee Fe and by circles for fee Fe, obtained from neutron scattering 5 [83 B 21, 6 [62A I] and Mossbauer effect 7 [63 G l] measurements obtained by scaling Hhyp to the a-Fe moment. Calculated curves I and 2 [83 B 1],3 [Sl K I], 4 [77A I].

60

10 0

A

I

10

20 P-

30 kbar 40

Fig. 9. Pressure dependence of the Necl tempcraturc of y-Fe in Cu [79L I]. dTs:,ldp=0.5K kbar-‘. Different symbols indicate different runs. Table 5. High-field susceptibility xHF and relative anisotropy of the magnetization at 4.2 K for Fe, Co, and Ni. Applied field strength up to 50 kOe. Also estimations of Pauli susceptibility xs and orbital contribution to the susceptibility, xL, are given [72 R 11. Direction of applied fields is indicated. For xHF, see also Table 1. Fe XHF

[lo+

co

cm3 mol- ‘1

xs [10-6cm3mol-‘] xL [10-6cm3mol-1] (0 111- 01ooh b 110 -~,ooY~, (~1*1--~11oY~s (a,,,-~,cM,,c

266(2) 305(9) [loo] 231(15) 69...98 110...142 - 7.8. lo-’ - 3.5.10-s - 4.3.10-s -

265(2)

21...40 ~2240 w450.10-5

Ni

Ref.

113(l) [111] 116(l) [llO] 118(l) [loo] llO(7) [ill] 129(10) 40...55 77...82 18.10-5 13.10-5 5.10-5 -

72R2 72R2 72R1 69Fl 69s 1 72R2 72R2 72R2 72R2 72R2 72R2

1.1.2.5 Fe, Co, Ni: magnetocrystalline

Ref. p. 1341

41

anisotropy

Table 6. Magnetic properties of fee Fe. P: paramagnetic, F: ferromagnetic, AF: antiferromagnetic, RT: room temperature. Sample y-Fe, bulk at 1320K precipitates in Cu-matrix: a=3.59...3.61 A particle size: x25OA x7ooA

Magnetic state

pFe

P

0.9(1)6)

TN K

PB

AF, P at RT AF

55(3) 67(2) 67 g4) 46

0.75 6OA epitaxial films on Cu: electrolytic [110] y-Fe, 3OA ‘) [ill] y-Fe, 6.*.80A

F at RT F at RT

four layers separated by Cu (ill), (110) or (100) layers, lg...25 A ‘) 2, 3, “) “) 6,

H hw

kOe

x24(6) x 23(6)

:::8(13) 3,

Measuring method

Ref.

polarized neutron scattering

83B2

Mijssbauer sp. Mijssbauer sp. neutron diff. neutron diff. Miissbauer sp. ‘)

63G1 63Gl 7OJl 62Al 79 L 1

FMR “) magnetization “)

71Wl 7662, 77Kl

Mijssbauer sp.

77K2, 83Hl

AF, P at RT 20...40

Large fraction of a-Fe appears also in the spectrum. Presenceof a-Fe can not be excluded. Independent of thickness. Estimated, see [70 J 11. K,=-2.0.104ergcm-3. May be less than the actual moment.

1.1.2.5 Magnetocrystalline

anisotropy constants

The anisotropy constants K,, K,, . . . are defined for cubic lattices such as Fe and Ni by expressing the free energy of the crystal anisotropy per unit volume by E,=Ko+K,S+K2P+K3S2+K4SP+...

(1)

with s = u;u; + c7.g;+ c&;

and P = ct2c12u2 1 2 3r

where cli, clj, elkare the direction cosines of the angle between the magnetization vector and the crystallographic axes. For hexagonal lattices, such as Co, it is more convenient to use the definition

where 4 is the angle between the magnetization and the c axis, and 0 is the angle in the basal plane. The measurementsare usually made on single-crystal spheresin a field large enough to remove the domain walls (called technical saturation). It is usually assumed that all the work done in changing the direction of magnetization is used to overcome the crystal anisotropy. The most common techniques used to measure this work are: 1. Measurements of the torque required to change the direction of the saturation field (TQ). 2. Measurements of the magnetization in different crystallographic directions with a moving (MSM) or a rotating (RSM) sample magnetometer. Land&Bbmstein New Series 111/19a

Stearns

1.1.2.5 Fe, Co, Ni: magnetocrystalline

Ref. p. 1341

41

anisotropy

Table 6. Magnetic properties of fee Fe. P: paramagnetic, F: ferromagnetic, AF: antiferromagnetic, RT: room temperature. Sample y-Fe, bulk at 1320K precipitates in Cu-matrix: a=3.59...3.61 A particle size: x25OA x7ooA

Magnetic state

pFe

P

0.9(1)6)

TN K

PB

AF, P at RT AF

55(3) 67(2) 67 g4) 46

0.75 6OA epitaxial films on Cu: electrolytic [110] y-Fe, 3OA ‘) [ill] y-Fe, 6.*.80A

F at RT F at RT

four layers separated by Cu (ill), (110) or (100) layers, lg...25 A ‘) 2, 3, “) “) 6,

H hw

kOe

x24(6) x 23(6)

:::8(13) 3,

Measuring method

Ref.

polarized neutron scattering

83B2

Mijssbauer sp. Mijssbauer sp. neutron diff. neutron diff. Miissbauer sp. ‘)

63G1 63Gl 7OJl 62Al 79 L 1

FMR “) magnetization “)

71Wl 7662, 77Kl

Mijssbauer sp.

77K2, 83Hl

AF, P at RT 20...40

Large fraction of a-Fe appears also in the spectrum. Presenceof a-Fe can not be excluded. Independent of thickness. Estimated, see [70 J 11. K,=-2.0.104ergcm-3. May be less than the actual moment.

1.1.2.5 Magnetocrystalline

anisotropy constants

The anisotropy constants K,, K,, . . . are defined for cubic lattices such as Fe and Ni by expressing the free energy of the crystal anisotropy per unit volume by E,=Ko+K,S+K2P+K3S2+K4SP+...

(1)

with s = u;u; + c7.g;+ c&;

and P = ct2c12u2 1 2 3r

where cli, clj, elkare the direction cosines of the angle between the magnetization vector and the crystallographic axes. For hexagonal lattices, such as Co, it is more convenient to use the definition

where 4 is the angle between the magnetization and the c axis, and 0 is the angle in the basal plane. The measurementsare usually made on single-crystal spheresin a field large enough to remove the domain walls (called technical saturation). It is usually assumed that all the work done in changing the direction of magnetization is used to overcome the crystal anisotropy. The most common techniques used to measure this work are: 1. Measurements of the torque required to change the direction of the saturation field (TQ). 2. Measurements of the magnetization in different crystallographic directions with a moving (MSM) or a rotating (RSM) sample magnetometer. Land&Bbmstein New Series 111/19a

Stearns

1.1.2.5 Fe, Co, Ni: magnetocrystalline anisotropy

42

[Ref. p. 134

3. Ferromagnetic resonance experiments (FMR). The anisotropy constants depend weakly on the applied field at high fields (> 5.. .lO kOe) and vary greatly in some temperature ranges. Due to this it is necessaryto specify how the data was treated in order to obtain the anisotropy constants. Comparisons with anisotropy constants obtained from various band structure calculations are discussedin [78 G I. 71 F 1] as well as in a number of papers listed in [SOW 11. Table 1. Magnetocrystalline anisotropy constants of Fe, as derived from magnetization (M,, M,,) and torque (TQ) measurements.M,: analysis, above technical saturation, of the magnetization perpendicular to the applied field vs. direction of Harp, in the plane indicated. M ,i: analysis, below saturation, of the magnetization parallel to the applied field. direction as indicated, vs. H,,,,. Method

T

K,

K2

K

K3

Ref.

0.22 -0.64

82T4 82T4 82T4

lo5 ergcme3 4.2

M,; [111]

4.70 5.35 5.64

1.90

MI; [1101 20

TQ

5.20

-0.158

77

M, (110)

2.41

TQ TQ ‘1 TQ 2,

4.48 5.31 5.56 5.15 5.15 5.02

TQ TQ TQ Xnc7

4.81 4.75 4.50 4.71

M, (110)

MI, iIll M,, Cl111

273

1.94

0.202 0.25 -0.62 0.711

1.79 -0.154

0.012

-0.012 ZO.195

w -0.13

68Gl 82T4 82T4 82T4 68K 1 66Kl 73 El 68Gl 66Kl 81H3

‘) K, vs. H at constant T, extrapolated to zero field. 2, T vs. H at constant K,, extrapolated to zero field. 3, ac susceptibility measurementson whiskers. 6 405 -erg

cm3 0.E a5

Fe cm3 0 + ox

I g’

erg

s" ?O
C62S21.

Fig. 3. Magnetization distribution in the interstitial region of the Fe unit cell, obtained by averaging over a cube size of0.5 8. The numbers correspond to the magnetization in [kG]. Negative magnetization was found to occur in a series of interlocking rings throughout the Fe lattice [66 s 31.

Landolt-Biirnstein New Series IWl9a

Stearns

55

56

1.1.2.7 Fe, Co, Ni: Form factors, magnetic moment distribution

[Ref. p. 134

0.81 co hcp 0.7 p 0.6

o hcp Co fee

l

COD.92 ho0

0.5

I 0.1

t 0.3 0.2 0 0’ 04

0.i

---

fJ73K

-

300 K 0.5

0.6 ti-’ 0.7

sin 0 /A -

0 -0.1 0.2

0.6

0.6

0.8

H’

Fig. 5. Form factor offcc Co at 600 “C (dots)compared tf the form factor at room temperature (crosses) [63 M 1: Curves rcprcsent smooth interpolations. Wavevector c momentum transfer: Q = 47tsin O/I..

1.0

Fig. 4. Measured magnetic form factor of hexagonal Co (open circles) [64 M I] and fee Co--8 at%Fe (solid circles) [59N I]. Wavevector of momentum transfer: Q = 471sin O/L. The solid line emphasizes the almost sphcrical symmetry of the hexagonal form factor. The form factor for Co showed no dependence on temperature between 78 and 300K.

(0.0)

co.gfl

0.9

Ni

E f

0.8 1

0.7

/

B &

1

. measured o calculated

1

l *

0.5

I

-A

I

Fig. 6. Projection of magnetic moment density on has; plane of hcp Co. Lower right diagram shows projecte position of atoms in orthorhombic unit cell. Dashed line’ indicate portion of cell shown in density map [64 M I]

0.5 R ;

0.L ZN 0:

0.3

%

0.2

9: 6% e” FiR

0.1

90 5

0 -0.1 I 0

0.2

0.L

I

I

0.6

0.8

I

1.0 Yi’ Iu

Fig. 7. Comparison of the measured (solid circles) ant calculated (open circles) free atom magnetic form factors o Ni. Wavevector ofmomentum transfer: Q =4n sin8/7,.Thc measured magnetic form factor was determined from the first 27 Bragg reflections. The model used in the calculatec form factor consisted of a uniform negative spin contri bution of -0.019 pa/A3,aspincontribution obtained fron unrestricted Hartrcc-Fock calculations for Ni + + [60 W 1 61 W 43, an orbital part and a core contribution [66 M 21 The inelastic magnetic form factor in the [ 1001directior was found to be the same as that ofthe elastic form facto] [8l S I].

sin 0 /1 -

Stearns

Ref. p. 1341

57

1.1.2.7 Fe, Co, Ni: Form factors, magnetic moment distribution

a 7-

Ni nucleus

Ni nucleus

Ill01

w

-

0 -0.0085#

-0.0085

-0.0085

I

-;s

-0.0085

b a T-

Ni nucleus

Fig. 8. Contour maps of the magnetic moment density in Ni obtained by Fourier inversion of the data for (a) the (100) plane and (b) the (110) plane. The numbers labelling the contours give the magnetization in [ur,/A3], [66 M 21.

0

100

200

300

400

500

600 K 700

Fig. 9. Temperature dependence of the T,, and E, subband magnetizations per atom in Ni as derived from the temperature dependence ofthe 333 and 511 reflections in a polarized neutron scattering experiment [81 C2].

Land&-Bdmstein New Series IIl/19a

Stearns

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation

58

time

[Ref. p. 134

1.1.2.8 Hyperfine fields, isomer shifts and relaxation time The hypcrfinc magnetic fields have been mainly determined using three techniques: nuclear magnetic resonance (NMR), Massbauer effect spectroscopy (ME) for Fe and variations of the perturbed angular correlation technique. A number of books and review articles are written on the subject [64 W 1,65 F I,71 F 1, 74V 11.Only results from NMR and Miissbauer effect measurementswill be discussed here. Magnetic hyperfine field Hhrp NMR experiments measure the hyperlinc fields by observing the Zeeman splitting of the ground state of nuclei having nuclear magnetic moments, i.e. of nuclei with angular moment quantum number I+O. The resonance linewidths of ferromagnetic materials are naturally relatively large, of the order of 0.5 kOe. These widths are attributed to anisotropy fields and defects.Spin-echo and modulated continuous wave (cw) NMR techniques are used to study these materials. The Miissbauer effect measuresthe magnetic hyperline fields and electric quadrupole fields from the Zeeman splittings of the ground and excited states of the nuclear transitions. These splittings are obtained by varying the relative velocity of the source and absorber [62P l] and are given in the practical unit [mms-‘1. Miissbauer effect measurementscan not be made on Co. 61Ni, having a 67.4keV y-ray, is a possible but poor ME nucleus, “Fe an excellent one. The hyperfine field Hhypis made up from several contributions which can be represented by f&p = Hcorc+ Has+ Hart,+ Ha, .

(1)

H coreis due to the Fermi contact interaction of the spin-polarized Is, 2s, and 3s core electrons. H,, is the contact term arising from the spin polarization of the 4s conduction electrons which is due to exchange and hybridization interactions with the d spin moment. Herbis the field contribution from the dipolar interactions from any unquenched orbital momentum on the central atom. H,,, is due to external influences such as applied fields. demagnetizing tields and Lorentz fields. This contribution is zero in cubic Fe, Co or Ni when there are no applied or demagnetizing fields, such as in domain walls for NMR experiments or in thin films magnetized in the plane of the films for Miissbauer effect measurements. Enhancement factor E An applied rf field causesthe electron moments to oscillate, the much smaller nuclear moments will then follow the motion of the electron moments. The rf fields at the nuclei in the domains thus undergo an enhancement by a factor of E, .c.= fh,,,IM, ,

(2)

which is about 200 for Fe and 150for Co and Ni [6OP 11.The rf fields at nuclei in domain walls undergo further enhancement depending on the position of the nuclei in the wall. The finite angles between electron spins in the domain walls causethe magnetic moments of wall nuclei to be turned through larger angles than the moments of domain nuclei. Furthermore the walls have been shown to be pinned around their periphery and to oscillate in a drumhead-like fashion [67 S 11.Due to the angle between electron spins being greatest at the center of the wall, the enhancement E is greatest at the wall center, E,,,and in Fe decreasesas: E(X)= E,,sechx

(3)

to the domain value at the edgesof the wall, where x is in units of the wall width. The enhancement at the wall center is a factor of 30...100 over that in the domains [67 S 11.The wall enhancement factors are dependent on the purity and heat treatment ofthe material since theseaffect the domain wall areas[71 S 33.The drumhead wall motion model [67 S 1] has been extended to include a finite excitation bandwidth and a finite spectral distribution of resonance frequencies [79 B 21. Because of the larger enhancement in the walls spin-echo measurementson Fe, Co, and Ni usually measure domain wall nuclei. Isomer shift The valence state of the atoms can be obtained from the isomer shifts, i.e. the shifts in the position of the center of the Miissbauer pattern which are dependent on the charge density at the nucleus [67I 1, 74V 1). Stearns

Ref. p. 1341

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation

time

59

Relaxation times 7” and T, The nuclear longitudinal (spin-lattice), T,, and transverse (spin-spin), T,, relaxation times are measuredwith the spin-echo technique. There are a number of relaxation mechanismspresent in the transition metals. They are the contact interaction with s electrons [5OK 11,dipolar and orbital interaction with non-s electrons [63 0 11, core polarization [64 Y 11;spin-spin interaction via virtual magnons [SSS 1,58 N 1,59 S l] and spin interaction with domain walls [61 W l] and bulk magnons [69 S 23. Care must be taken in measuring relaxation times so that the rffield applied is small enough so that it doesnot move the wall to a different part of the sample,and thus to different nuclei, during the course of the measurement. Becauseof the variation of enhancement factor with position in the domain walls the nuclear spins undergo a complex rotation distribution. It is also been shown that the domain walls vibrate like drumheads [71 S 31. Thus the shapes of the relaxation curves differ widely from exponential behavior and are strongly dependent on the product of the rf field B, and the pulse length r which determine the turning angle, 8=ysB,z, of the nuclear spins, y being the gyromagnetic ratio of the nuclei. It has been shown that for Fe the relaxation rates vary with positions in the walls as: -=- 1 W4

1 T,LOZ

sech’x

(4)

and are thus largest at the center of the walls [69 S 21. To, and To2are the longitudinal and transverse relaxation times at the center of the wall and x is measured in units of the wall thickness. It is clear from Fig. 13a that meaningful longitudinal relaxation times can not be obtained by assuming an exponential decay but that the details of the excitation and motion of the spins must be considered. Also the relaxation rates have been found to be somewhat dependent on the purity and heat treatment of the sample.Due to these complications in the domain walls the literature unfortunately contains a wide variety of ill-defined relaxation times for Fe, Co, and Ni with few details of the operating conditions or analysis procedures used in obtaining the relaxation times. Many of theseresults are thus of questionable value as can be seenfrom the wide range of measured relaxation times listed in Table 5. The behavior of the spins in the domains is much simpler and the results for such spins should be more reliable. The transverse relaxation time is obtained by measuring the echo height of a pair of pulses separated by a variable time. In caseswhere the relaxation times are comparable to the nuclear lifetime the Mossbauer effect can also give information about the relaxation times. Fe, Ni For Fe and Ni the spin-echo technique has a resolution which is about a factor of 10 greater than that of the Mijssbauer effect technique. The temperature dependence of the hyperfine field is found to be slightly different from that of the magnetization [61 B 21. A proportionality factor A(T) has been defined by v(T) =4Wf,(T)

>

(5)

where v(T) is the measured hyperfine field resonance frequency and M,(T) is the spontaneous magnetization. co Many complex effectsare seenin Co spin-echo experiments which do not occur for Fe and Ni. These are due to a number ofproperties of Co such asthe large nuclear moment and the 100% isotopic abundance of sgCowhich allows nuclear spin-spin (Suhl-Nakamura) interactions to be important in contrast with dilute isotopic materials, the large anisotropy fields in the hcp phase and the two possible phases of Co at low temperatures. The anisotropy field in hcp Co causesthe hyperfine fields of the domain wall nuclei to vary with position in the wall. This results in the NMR spectrum of hcp Co being very broad. Other unusual effectsseenin Co are single pulse echoes [72 S l] and enhancement of a modulation field on the spin-echo envelope [77 S 11. Due to all these complexities the hyperfine field values quoted in the literature for Co are often not well defined.

Landolt-Bbmstein New Series III/I%

Stearns

60

[Ref. p. 134

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time Table la. NMR frequencies and magnetic hyperfinc fields of Fe, Co, and Ni. Metal

T

Nucleus position

K

Fe, bee

Co, hcp

wall center wall edge

co, fee Ni

4.2

46.64

RT

45.43

4.2 RT 4.2 RT 4.2 RT 4.2 RT

Hhsn

KHz

Ref.

kOe

-339(l) ‘) - 339.0(3) -330 - 330.4(3) - 225.7‘) -218 -217.7 2 -212 -215 3, -211 - 75(l) - 69(l)

228 220.5 219.9 x214.5 217.23, 213.1 28.46 26.04

61 B2 71 Vl 61Bl 71Vl 72Kl 72Kl 72K1 72Kl 6OPl 6OPl 63Sl 63Sl

‘) An upper limit for the anisotropy for a single crystal is 1OOOe[SO0 11. +8W)kOe [72K 11. ‘1 H hjp.IIc-Hhyp.lc= ‘) Extrapolated from high-temperature values. Table 1b. Temperature dependence of the NMR frequency for 57Fe in iron [61 B I].

T

T K

LHz

K

KHz

77 193 297 351 397 438 490 543

46.52 46.09 45.43 44.99 44.55 44.09 43.42 42.58

607 683 693 701 719 730 756 785

41.45 39.73 39.39 39.32 38.68 38.39 37.72 36.79

Table 2. Measured, by a technique which combines Miissbauer and internal conversion electron spectroscopy [74 S 2, 84 B 11, and calculated individual ns shell contributions to the hyperfine magnetic field of Fe metal in [kOe]. Fe band structure calculations are quoted for both the exchange correlation potential of von Barth-Hedin (vBH) and a Kohn-Sham (KS) local-exchange potential. Shell

Contribution to Hhrp[kOe] Measured

Calculated 1s 2s 3s 4s total

[68 w l] - 14 -739

-409

[75 D 1) -623 + 243 + 33 +210 -347

vBH [77C l] - 21 -388

KS [77C 13 - 67 -451

[74S2] - 1640(390) +517(240)

-213

-343

‘1

‘) The measured total field is - 339 kOe which includes about 25 kOe of orbital field. So the sum of the contributions from the ns electrons is about -365 kOe. Clearly there is a large unresolved discrepancy between the calculated and measured 2s values.

Ref. p. 1341

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

61

Table 3. Room-temperature parameters used for correction of hyperfine frequency and spontaneous magnetization to constant volume. Note that (i%/ap),/ v is opposite in sign for Fe from that for Co and Ni. Calculations [79 J l] confirm that this behavior of the hyperfine magnetic fields with pressure is reasonable. 1 av - v ( aP > T . 10Y4kbar- 1

Metal

Fe co Ni

i av v aP T -(->

Ref.

1

Ref.

MS

. 10m4kbar-l

- 5.92 - 5.28 - 5.4

49Bl 49Bl 60 Al

aM (

aP 9

Ref. T

. 10m4kbar-’

-1.66(l) 6.13 (fee) 9.2(l)

61B2 6051 79Rl

-2.83(25) -2.18 (hcp) -2.9

Table 4. Mijssbauer effect parameters for 57Fe (I= l/2) in practical units. 90: ground state splitting PO: ground-state nuclear magnetic moment excited state splitting in nuclear Bohr magnetons u,, 91: H hyp: hyperfme field dQ: quadrupole shift K: Knight shift Property

Unit

90

mms-’ mms-’ mms-’

CiQ PO

H hyp

he

T=4.3 K

T=298K

4.0117(10) 2.2931(10) 0.0088(25) 0.09024(7)

+ +

+

-339.0(3)

3.9098(g) 2.2342(g) 0.0023(15)

-330.4(3)

Ref. 71Vl 71Vl 71Vl 65Ll 71Vl

0.0078(10)

K’)

‘) Measured in an applied field up to 20 kOe.

Table 5. Paramagnetic phase d electron contribution to hyperfine field, H,,,,,(d), ferromagnetic phase hypertine field Hhyp,R divided by the respective magnetic moments per atom,p and pa,,orbital contribution to the Knight shift, Korb, and orbital susceptibility xv”, corrected to constant volume and OK, for Co and Ni [SOS 11. Hhyp,,(d)/P kOehB Co solid liquid Ni

-121(7) - 128(7) - 140(8) -113(5)‘)

h&Pat

Korb B

- 127 -128

%

XV” .10-3cm3mol-1

1.5(2) 2.1(2) 1.84(20)

0.14(4) 0.18(5) 0.18(5)

‘) Not corrected to constant volume, the correction is about +3 kOe [78 S 11.

Landolt-Bornstein New Series 111/19a

Stearns

61Kl 64Kl 60K2

[Ref. p. 134

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time 24c MHz 2oc 16C I * 12c

200

600

100

800

K

0

1000

T-

200

400

600

800

1000

1200 K 1L'

T-

b

30 w: 24 18 I a 12 6

0

100

200

C

300 I-

LOO

500

600 K 7

Fig. lax:. NMR frequency Y vs. temperature in the ferromagnetic state of(a) “Fe in bee Fe metal, I: [SOS I], 2:[61Bl];(b)5gCoinfccCometal,1:[80S1],2:[60Kl], 3:[63LI];(c)61NiinNimetal,l:[80S1],2:[70Rl];cw mcasurcmcnts in natural Ni, 3: [63 S 11.

230 MHz

100

200

300

LOO

500

600

700

d Fig. Id. Temperature dependence ofthe “Co wall center and wall edge NMR frcquencics in hcp Co. The dashed curve rcprcscnts the data in the feephase [72 K I], set also [63 F 11. Stearns

K

63

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

Ref. p. 1341 t 1.0 ;; J, 0.9 s Gy 0.8 0 II : 0.7 -2 0.6

0.96

I ;; 0.92 11 " -3 =; 0.88

0.80 0

0.2

0.4

0.6 r/r,

0.8

-

Fig. 2. (a) The solid curve is the measured reduced spontaneous magnetization as a function of reduced temperature for Fe (see Fig. 2a in subsect. 1.1.2.4). The circles are the measured reduced hyperfine field tiequencies vs. reduced temperature as measured by Budnick et al. [61 B I]. Both of these measurements are made at constant pressure. (b). Reduced proportionality constant A/A( T = 0) as defined in eq. (5) vs. reduced temperature; the solid line is for the hyperfine field and magnetization data corrected to constant volume [61 B2]; circles are for the uncorrected constant-pressure data shown in (a). The decrease in A/A(T=O) is about 5% lower, than MJA4,(T=O) at T/!&x0.8. It is not surprising that the magnetization and hyperfine field temperature dependences are not identical since they are sensitive to and depending on the detailed electronic band structure and their variation with temperature is expected to differ in a number of ways [71 S 2,72 B 23.

Land&-Bdmsfein New Series 111/19a

0

0.2

0.6

0.4

I 0.8

1.0

r/r, -

Fig. 3. Reduced hyperfine field frequency v and magnetization as a function of reduced temperature as derived from NMR measurements for Ni. (a) at constant pressure, I: [80 S 1],2: [63 S 1],3: [26 W 1],4: [69 K l], and (b) corrected to constant volume. The difference between the reduced magnetization and hyperfine field decreases from a maximum of about 6% to about 3% after correcting to constant volume [80 S 11.

Stearns

[Ref. p. 134

1.1.2.8 Fe, Co, Ni: hypcrfine fields, isomer shifts, relaxation time

64

0

20

40

60

a

80

100

120kbar140

P-

O

10

20

45.5

30

40 kOe

50

Howl -

Kc

Fig. 5. Relative hypertine field Hhgp/Ha.pp,at the “Fe nucleus in E-Fe as a function of the applied field. Data were taken at pressure of 15.0 and 21.5 GPa [82T 33.

45.1 -1400 45.0 -1200 44.9 0

b

10

20

30

40

50

60 kbor70

-1000

P-

Fig. 4. Room-temperature variation of the magnetic hypcrfinc ficld of Fe with pressure as dcrivcd from (a) relative M&batter effect mcasurcmcnts. diffcrcnt symbols referring to different pressure runs [68 M I], see also [6S S I]. and (b) NMR frequency measurements [63 L 21. Triangles indicate pressure calibration by linear interpolation of the data represented by circles.

-800 -600 z s-400 I -200 0 kOe

200

-200 kOe 0 0

0.5

1.0

1.5

2.0

2.5 pB 3.0

Fig. 6. Hypcrtine field at nuclei of atoms dissolved in Fe, Co, and Ni lattices, plotted against the host magnetic moments. The signs of the fields are not always given in the original literature see [65S 11, where also various other dissolved atoms are considered.

Stearns

Landolr-Rornmin NW Scricr 111/19a

Ref. p. 1341

Fig. 7. Si atoms act as near perfect magnetic holes in the Fe lattice so that it was possible to obtain the change in the hyperfine fields of Fe atoms caused by the alloying of Si. Fe,Si contains atoms with three widely seperated hyperfine fields: Fe(D) with 8 nearest neighbor (nn) Fe(A) atoms; Fe(A) with 4 nn Fe(D) and 4 nn Si Si atoms; and the Si atoms themselves. This allows a determination of hyperfine field contributions due to at least the first six neighbor shells of an Fe atom. The NMR frequency variations as a fnnction of Si content for Fe-Si ordered alloys for the first six neighbor shells are indicated by ANnn, N= 1..~6. The shifts indicated by the vertical arrows labeled ANnn are the hyperfine field contributions due to an Fe atom in the Nth shell. The notation is: &, where m is the number ofFe@) atoms in the Inn shell and n the number of Fe atoms in the 4nn shell to a Fe(A) atom, all the other shells out to the 8nn contain Fe atoms; D,, where m is the number ofFe atoms in the 2nn shell, all the other shells out to the 5nn contain Fe atoms; Si:, where m is the number of Fe(D) atoms in the 3nn shell and n is the number of Fe atoms in the 6nn shell, all the other atoms out to the 9nn shell are Fe atoms. Since the hyperfine field of Fe is negative (points in the opposite direction) with respect to the magnetization, an increase in the frequency due to a neighboring Fe atom corresponds to a negative polarization of the s conduction electrons [71 S 11. The results of these measurements have led to the conclusion that conduction electron polarization of the s electrons can not be responsible for the exchange interaction between the Fe atoms. Polarization by a sufficiently small number of itinerant d electrons, leading to d conduction electron polarization can lead to a positive exchange interaction. Similar reasonings hold for Co and Ni [71 S 2, 66S1,74S1,76Sl].

50lMHz

Fe-Si

o3 =

7.5 0

0.5

1.0

02 -

4 Do Pr

46

42

I e 38

34

30

26 17

I

I

I

19

21

23

SI -

-2.5

1.5

2.0

2.5

3.0

Fig. 8. Frequency shift (Av)~caused by adding an Fe atom into the Nth shell over the number present in Fe,Si vs. shell radius r. A positive shift corresponds to a more negative Hhyp. This can be attributed to a negative s conduction electron polarization contribution caused by the added Fe atom. This polarization is directly proportional to the measured shift. Where error bars are not shown the error is less than the size of the symbols [71S 11.

Landok-Bbmstein New Series 111/19a

65

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

Stearns

I

25 at%

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

66 0

[Ref. p. 134

0.045

mm 5

mm 0,;30

-0.03

0.015 0

-0.12 0

-0.015

25

50

1

75

100 kbar 1

P-

?ig. 9a. Change of the isomer shin with pressure for bee %.rclativc tozcro-pressurcisomcr shift.diffcrcnt symbols ndicating dilfcrent pressure runs [68 M I], xc also 168S I]. In [67 121 many data arc given ofthc isomer shift If 5’F~ in transition metals under prcssurc.

t I -0.0301 $ -0.075 -0.090 -0.105 -0.120 -0135

-01sn 0

b

IO

20

30

40 P-

50

60

kbor 80

Fig. 9b. Prcssurc dcpcndencc ofthc isomer shill ofy-Fe in copper at room temperature and 79 K. Velocity scale is rclativc to iron at room temperature [79 L I]. Symbols rclatc to diffcrcnt prcssurc runs.

210 kHz

193

I 170 Q n

153

13s 0

\ 100

200

300 I-

400

500 K 600

Fig. IO. Temperature dependence of the electric quadrupole splitting dQ and anisotropy in the hyperfine field of the wall edge nuclei. In the hcp phase of 59Co dQ=172(5) kHz at 290K and 207(5)kHz at 4.2K. The temperature variation of this splitting is similar to that of the ratio c/a. The anisotropy in the hyperfinc field at 4.2 K was measured to be +8.0(l)kOe. It arises from dipolar and orbital fields with the orbital field being about twice as large as the dipolar field [72 K I].

Stearns

Ref. p. 1341

1.1.2.8 Fe, Co, Ni: hyperfine fields, isomer shifts, relaxation time

67

1250 , kHz 59co 1000 hcp ' 1 t $ ?

I

I

6

I

750

2 500 w + ; 250 0 230 MHz 220

Fig. 11. High-held Knight shift of 5gCo in ferromagnetic single-crystal hcp Co at 4.2 K. Circles and squares refer to different spherical samples. Curve 1: observed NMR frequency v vs. applied magnetic field, v= ve -yeffHappJ2n. Curve2: difference between the resonance frequency expected for yerf=y5’ and the observed NMR frequency vs. applied field. ysg/2n = l.O054(20)kHz/Oe. Note that for H .,,, 250K normal coiductivity theory [55A 1, 59 R I] was used. while for Ts250 K nonlocal conductivity theory [65 H I] was used. Fig. 5. Angular dependence of the external resonance magnetic field (V=71.52 GHz) for two thin disks of single crystal hcp Co in which (1) the plane is parallel to the [OoOl] axis (points on curve I) and (2) the plane is perpendicular to the [OOOI] axis (points on curve 2). In case 1. ~3denotes the angle between the easy axis of the crystal and the direction of H; in case 2, w denotes the angle between an arbitrary direction in the sample plane and direction of H. The finI curves are the calculated angular dependences [64F I]. Open and solid circles refer to different samples.

500

600

K

700

26 kOe 2.

I *

f 16

Stearns

12

8 0

n

2

rod

Ref. p. 1341

1.1.2.10 Fe, Co, Ni: g factors, ferromagnetic resonance

Fig. 6. Measured and calculated (fnll lines) angular dependence of the FMR field at various temperatures of a disc-shaped single crystal of hcp Co at 36.97GHz. The angle v is the angle between the magnetizing field and the [OOOI] axis, both in the disc plane. Tin c”C] : I) 20,2), 250, 3) 275, 4) 300, 5) 325, 6) 350, 7) 375, 8) 400. At all temperatures the value obtained for the g factor was 2.02 which is significantly different from other measured values of 2.18 [73 0 11.

7.0 kOe

Ni

kOe 9.5

9s I L a? 8.F:

8.0

Fig. 7. Temperature variation of the observed FMR field for a cylindrical single crystal of Ni in (a) the [loo] and [l 1I] directions at 23.3 GHz and (b) the [IOO] direction at 3 1.8GHz. The full line was obtained using eq. (1) with g = 2.21. The different symbols stand for results of different heating cycles. The lower-temperature data is good to EZ10% [69B 11. Landolt-Bbmstein New Series IWl9a

89

90

1.1.2.10 Fe, Co, Ni: g factors, ferromagnetic resonance

II

0.2 b 0

50

100

150

200 7-

250

300

1.50 kOe 1.25

0.25

I

50

I

100

I

I

150 T--

200

I

I

350 "C 400

Fig. 8. Variation ofthe observed FMR peak-to-peak linewidth with temperature of a cylindrical single crystal of Ni for (a) the [IOO] and [l I I] directions at 23.3 GHz and (b) the [ 1001direction at 3 I .8 GHz. The full curve was calculatedwith%=2.3~10ss-‘andg=2.21 [69Bl].The different symbols stand for results of different heating cycles.

0

[Ref. p. 134

I

250 K 300

Fig. 9. Temperature variation of FMR peak-to-peak lincwidth in single crystal cylinders of Ni at 22 GHz. The symbols represent diffcrcnt samples with resistivity ratios varying between 60...170 [74 B I].

Ref. p. 1343

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

91

1.1.2.11 Fermi surfaces, band structures, exchange energies and electron spin polarizations Introduction In the last decade the band structures of Fe, Co, and Ni have undergone extensive study by a variety of experimental techniques as well as numerous band calculations (seee.g. A.P. Cracknell in Landolt-Bornstein, New Series,Group III, vol. 13c.).One of the problems that arises in comparing the experimental data and the calculations is that the band structure calculations are of the ground state of the systemwhereasthe experiments, of necessity,always perturb the system.This difficulty is well known in studies of atomic energy levels where an emitted electron emergeswith less energy than its ground state binding energy becausethe remaining electrons becomemore tightly bound due to decreasedscreening of the nucleus. The usual rationalization of this difficulty in solid state studies is to argue that the Fermi level remains unchanged and the energy levels near it also undergo negligible shifts upon perturbing the systemand thus the measurementsgive a reasonable,accurate picture of the ground state and can be compared to band structure calculations. This type of rationalization obviously depends on the time and energy scalesof the measurements.At extremely small times such that the readjustment of the electron cloud has not yet occurred the usual concept of the Fermi level is not applicable. Measurements that occur over long times (> 10-i’ s)and involve small energy excitations such asde Haas-van Alphen measurements perturb the systemleast and thus most closelv measurethe ground state.Although even in thesemeasurementsa dependence of the spin-orbit splittings on the applied magnetic field directio;has often been seen. Measuring methods a) de Haas-van Alphen (dHvA) measurements The dHvA oscillations are periodic in the inverse of the magnetic induction B-i with the frequency f given by (1) where A is an extremal area of cross section of the Fermi surface in a plane normal to B. Thus the Fermi surface can be obtained by measuring the dHvA frequencies as a function of the applied magnetic field direction. b) Magnetoresistance The magnetoresistance is the relative change of the electric resistivity in a high magnetic field defined by: Aeleo = (e(B) - eo>leo

(2)

where Q,,is the resistivity in zero field. It gives information about the presenceof open orbits and the connectivity of the Fermi surfacewhen the effect of collisions on the motion of the carriers is negligible compared to the effect of the magnetic field [64 F 21.This requires pure single crystal samplesand low temperatures in high fields such that w,z < 1,where o,( = eB/m*c) is the cyclotron frequency, z is the averagecollision time and m* is the effective massof the electrons or holes. The variations of the magnetoresistancewith magnetic field can be related to the orbits of the carriers on the Fermi surface. The power dependence of the magnetoresistance on the field, Aeleo = bB:

(3)

gives further information about the Fermi surfaces.If the magnetoresistance is large and n = 2 (unsaturated), the metal is compensated (has an equal number of electrons and holes) and open orbits are indicated by sharp minima in the magnetoresistance. If the magnetoresistance is low and saturation occurs (n < 1) for most field directions, the metal is uncompensated and open orbits are indicated by sharp maxima in the magnetoresistance. For data on magnetoresistance, seesubsect. 1.1.2.13. c) Photoemission Photoemission experiments do not measure the initial ground state energies but the difference in energy between the initial ground state and the final ionized state. A classic discussion of the interpretation of measured energy levels was given by Parratt [59 P 11.Due to the emission of an electron there is decreasedshielding of the nucleus in the final excited state. This causesthe valence electron statesto be more tightly bound so that, except for the electrons at the Fermi level which are pinned, the electrons are emitted with less energy than they would Land&Bbmstein New Series 111/19a

Stearns

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

92

[Ref. p. 134

have if they came from the unperturbed ground state energy. The measured energy levels thus are shifted up relative to the initial ground state energies.This effect may be small for some valence states and increaseswith distance from the Fermi level. set Fig. 1.

Fig. 1.Schematicshifts in the measuredenergylevelsdue to perturbing the energy levels by the photocmission process.Heavy lines depict the unperturbed ground state

ground state. t: majority spin, 1: minority spin

Wovevector -

Table 1. Measured dHvA frequencies A Fermi wavevectors k,, number of itinerant d electrons per atom assuming free electron behavior, n(d,), polarization and the paramagnetic Fermi wavevector kt!’ for the spherelike Fermi surfaces of Fe [73 B 11. Spin up: majority spin, spin down: minority spin. Property

Crystal plane

Spin

I CMGI ‘)

up down up down up down

kf l3+71 II Polarization [%] k;” [271/o]

(100)

(111)

(110)

436 71 0.51 0.24 0.28 0.030 80 0.42

370 52 0.495 0.18 0.25 0.012 90 0.40

349 58 0.43 0.19 0.17 0.014 85 0.35

r) Accuracy + 1%. Table 2. Measured room-temperature values A, and calculated values A, [77C l] of the exchange splitting for Fe.

AC Symmetry

eV

point

Crystal surface

Ref.

eV 1.5(2) 2.08(10) 2

1.3 1.8

P, I-;, 1-’ 25

(111) (110)

80El 82Tl 83Fl

4

(100)

Table 3. Measured exchange splitting A, for Fe at high temperatures (T,= 1043K). T

4

K

eV

973 983 886

1.2 1.8 1.7

Symmetry point

MJM,(T=O)

A,/Am(RT)

Ref.

P4

0.60 0.56 0.73

0.80 0.90 0.85

80El 81H2 83H2, 83Rl

T;,(T2,)

l-25

Ref. p. 1341

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

93

Table 4. Slope (df/dp)/f of the change in the dHvA frequency with pressure of single crystal Ni. 7: majority spin, -1:minority spin. The subscripts of the field direction symbols refer to the f vs. p plots in Fig. 19. Part of Fermi surface:

Spin-up neck t

Field direction:

c1111,

Clq3

f$[lO-‘kbar]

8.0(12)

6.6(25)

Spin-down ellipsoid 4 [llllb

6.6(25) 6(l)

Ref.

c1m

WOI,

lS(8)

-0.8(8) 1.2(3)

77Vl 75A2

Table 5. Measured room-temperature exchange splitting A,,,and band gaps 6, for Ni as obtained from angle-resolved photoemission spectroscopy. Spin-resolved photoemission experiments on (110) surface of Ni gave the same splittings [83 R 11, The region of k-spaceX,(S,) is comprised of considerable hybridization between d and sp states, thus leading to a smaller exchange splitting. t: majority spin. Symmetry point

Crystal surface

u34)

(110)

‘)

X&34)

(110)

US4)

(110)

r-m,) near L3(Ax) near L&J near L [ii21 near L [l lo] l/2 (W-X)

(110) (111) (111) (111) (100) (100)

A, eV

Ref.

4n eV

0.17 0.17 0.18(2) 0.33 0.31(3) 0.30 0.33(2) 0.26(5) 0.28(5)

o.l5’0,:;5(L,t)

o.lO-‘;::s(X,t)

80H2 81H1,81H2 83Rl 81H2 79Hl 82Ml 80Gl 80E2 80E2

‘) The measuredband splittings are consistently smaller than those given by tirstprinciple one-electron band calculations using the local-density approximation which yield values in the range of 0.4.. .0.6eV [77 W 11.The measuredd band widths are also narrower than those obtained from these calculated band structures. How much thesediscrepancies are due to inadequacies in the local-density approximation or how much is due to the excited-state effectsinherent in photoemission experiments is not known and very difficult to determine.

Table 6. Measured excited-statesexchange energiesper spin,Jg,and calculated ground state exchange energies.Jp for the sameregions of k-spaceas the quoted measuredvalues for Fe, Co, and Ni. KS: Kohn-Sham potential, vBH: von Barth-Hedin potential. J in [eV].

JE ‘) Jdd c

Fe (r,‘J

Ref.

1.00(5) 0.85 (vBH) 1.1 (KS)

77Cl 77Cl

co m

Ref.

Ni 04

Ref.

75Bl

0.63(5) 0.92 (vBH) 1.27 (KS)

77Wl 77Wl

0.8(2) 0.88 (KS)

‘) Obtained from the measured exchange splitting A, divided by the total spin, Jid = AJp,, in un. Landok-Bbmstein New Series llVl9a

Stearns

94

1.1.2.11 Fe, Co, Ni: Fermi surfaces, band structures, spin polarizations

[Ref. p. 134

Table 7. Spin polarizations, in [%I, of Fe, Co, and Ni as derived from various experiments. Ato: photon energy, @: work function. Method

Fe

co

Ni

Photoemission

34(l)

17(2)

‘) *I Tunneling between polycrystalline film and superconductor

26.6 30 0.44(2) 0.45 3)

17.5 20 0.34(4) -

3(2) 5(3) g(3) 5.6 6 0.11 0.103)

?%i-@ eV 2 5 16 > 10 :.: 0.X 025 0.26 0: 5

035

0

100

2OG

300

LOO

500

600 K 700

I-

Fig. 205. Temperature depcndencc ofthc elastic constant r’=(cI, -c12)/2 as determined from neutron scattering measurements of the [l IO] acoustic shear modes of the phonon spectrum of the invar crystal Fc,,,,Ni,,,, [77E I]. The solid line represents the ultrasonic measurcmcnts of [73 H 11. For more details on diffcrcnccs betlvccn elastic constants derived from dispersion relations for acoustic phonon modes and ultrasonic mcasurcmcnts. xc [79 E 2. 79 E I] and also [83 K 33, where the phonon states of alloys arc tabulated.

0

5

10

15

20

25 kOe

HopplFig. 206. Field depcndencc of the sound velocities t’ at various temperatures for a single crystal of Fc 0.634%366C76 H Il. c,=(c,,+c,,+2c4,)/2=QI:: c = c44 = p:,

whcrc u, is the longitudinal sound velocity and c,r and c,~ refer to the velocities ofshcar waves polarized in the [ IOO]

and [I IO] direction, [60A 11.

Bonnenberg, Hempel, Wijn

respectiveI;

[76 H 11, see also

Ref. p. 2741

1.2.1.2.10 Fe-Co-Ni: thermal expansion 1.2.1.2.10 Thermomagnetic properties, thermal expansion coefficient, specific heat, Debye temperature, thermal conductivity

8.9 9 cm3

8.6 8.5

I cl0

8.4 8.3

8.2 8.1 8.0

Fig. 207a. Density Qand the linear thermal expansion coefficient LXfor Fe-Co alloys. Solid circles: [Sl B 11, open circles: [29 W I], triangles: [41 E 11.For Fig. 207b, see next page.

7.3 7.8 IO a

20

30

40

50 co -

60

70

80 co

18 t 16

8

Fig. 208. For caption and Fig. (b), see next page. a Landok-BBmstein New Series 111/19a

0 Fe

IO

20

30

40

Bonnenberg, Hempel, Wijn

50 NI -

60

70

80

90wt%100 Ni

1.2.1.2.10 Fe-Co-Ni: thermal expansion

246

0 b

300

200

[Ref. p. 274

“C !

I-

IFig. 207b. Thermal expansion of polycrystallinc Fe-Co ialloys. The arrows indicate the phase transition. The ,ja+cd lines apply to samples cooled from about 400°C I[S-l I I].

Fig. 208. (a) Linear thermal expansion coetkient tl at various tcmpcratures for Fe-Ni alloys [Sl B fl. (b. c) Temperature dependence of the linear thermal expansion coefficient c(for fee Fe, -XNi, alloys above room temperaturc(b)x~0.5(c)x~0.5[7lT2],secalso[70T1,73Z1, 17C1,28Cl].

Bonnenberg,

Hempel,

Wijn

Ref. p. 2741

1.2.1.2.10 Fe-Co-Ni: thermal expansion

247

-2 -: 25

a

50

75

100 T-

125

150

175

200 K 225

Fig. 209a. Temperature dependence of the linear thermal expansion coefficient tl of the invar alloy Fe,.,,Ni,,,, below room temperature. The solid line is according to a calculation using the itinerant electron model with contributions from lattice vibrations, spin waves and single particle excitations [79 0 11. Crosses: [65 W 21, circles: [67Z I], triangles and dashed line: [71 S 11.

-0.8

I -1.2 b

-2.41

b

0

I IO

I

20

I 30

I K 40

Fig. 209b. Low-temperature linear thermal expansion coefficient CIfor a polycrystalline invar alloy sample of approximate composition Fe,,,,Ni,,,,. I: [67 Z 11, 2: [65 W 2],3: annealed, measured without magnetic field (square) and in a magnetic field (circles) of 21.6 kOe [71 S 1],4: cold worked and measured in a magnetic field (crosses) of 21.6kOe [71 S 11. Landolt-Bijrnstein New Series 111/19a

Bonnenberg, Hempel, Wijn

1.2.1.2.10 Fe-Co-Ni: thermal expansion

248

1J

[Ref. p. 274

I

I.

I*

6

2 0 -2 -4 4 2 0 I -2 84

-1

0.369 [llOl 0.408 I1001

2

--I

-2

5u

0

I

I

I

100

150 I-

200

b

-2 4

I 250 K 300

Fig. 2lOb. Linear thermal expansion cocfkicnt z for three invar alloy Fe, -,Ni, single crystals. Measured parallel to the [IOO] direction in the (001) plane. For the alloy x =0.369 also mcasurcmcnts parallel to the [I IO] direction have been made [78 K I].

2 0 -2 6

2

3 m' K-1 2

rl

I 1

4

-2 50

a

100

150

200

250 K 300

8 0

J-

Fig. 2lOa. Temperature dcpcndcncc ofthc linear thermal expansion cocflicient r for various Fe-Ni invar alloys below room temperature [83 R I].

-1 -2 0

50

C

100

150 T-

200

250 K 300

Fig. 210~. Linear thermal expansion coefficient a as a function of tempcraturc for the invar alloy Fe,,,,Ni,,,, after diffcrcnt heat trcatmcnts: qucnchcd in oil from 1000°C (solid circles), additionally annealed for 9 h at 314°C (triangles) and for 75 h at 525°C (open circles). rcspcctivcly [72 M I].

Bonnenberg, Hempel, Wijn

249

1.2.1.2.10 Fe-Co-Ni: thermal expansion

Ref. p. 2741

15.0,

21 .'a-4

xm4

18

I

I

I

I

I

I

Ni0.33H,

k0.67

c A

12.5 .

15

. 0 a

10.0 I 12

.

.

.

&*

Yl a

A

: a9

6

3 0 -180

-150

-120

d

-90 T-

-60

-30

-180

"C 0

-150

-120

Fig. 210d. Temperature dependence ofthe linear thermal expansion Al/l for hydrogenated Feo,zsNio,,5 alloys. The thermal expansion coefficient is given by the gradient of the curves [83 H 11.

-90

-60

-30

"C 0

T-

e

Fig. 210e. Temperature dependence of the linear thermal expansion AZ/1as in Fig. 210d, but now for Fe,,,,Ni,,,,H, [83 H 11.

15 10-6 K-1 IO I 8 5

0 0

f

0.05

0.10

015

x-

Fig. 210f. Hydrogen concentration dependence of linear thermal expansion coefficient CIfor Fe,,,,Ni,,,, alloys in the temperature range on - 150 to 0 “C [83 H 11.

Fig. 211. Low-temperature value of the linear thermal expansion coefficient ccof an Fe,,,,,Ni,,,,s invar alloy single crystal as a function of roll reduction R for the case of(OO1)[ 1lo] rolling, measured parallel (open circles) and perpendicular (solid circles) to roll reduction. For the difference Act between both expansion coefficients as a function of R, see Fig. 162b [77 K 11.

Landolt-Bbmstein New Series lll/l9a

x-

g

Fig. 210g. Hydrogen concentration dependence of the linear thermal expansion coefficient c(as in Fig. 21Of,but now for Fe,,,,Ni,,,, alloys [83 H I].

0

IO

Bonnenberg, Hempel, Wijn

20

30 R-

40

50 %

60

1.2.1.2.10 Fe-Co-Ni: specific heat

2.50

[Ref. p. 274

0.50 col gK 045

O.LO

c 0.30

0.25

0.20

0.15

0.10 600

700

800

900

1000

1100

1200 K 1:

Fig. 212.Spcciticheat C, vs. tcmpcraturc T for the alloy Fe,,,Co,,,. Different symbols refer to diffcrcnt runs [7402]. I cal~4.187 J. The lower lint rcprcscnts the lattice and conduction electron contribution to C,

Table 28. The low-temperature spccitic heat of fee FeNi alloys as the sum of three terms: C,=~T+/?T3+aT3’*, electronic, lattice, and spin wave contributions, respectively [68 D 11, see also [74 C 43. at% Ni 100

95.7 90.3 86.2 81.1 68.7 59.2 55.1 50.1 45.0

Y mJmol-‘K-*

P mJmol-‘K-4

c( mJmol-LK-5/2

7.039(16)')

0.0179(7) 0.0186(12) 0.0184(13) 0.0189(17) 0.0167(10) 0.0175(8) 0.0187(6) 0.0194(9) 0.0226(g) 0.0257(20) 0.0278(12)

O.Oll(13) 0.026(22) 0.043(22) 0.074(29) 0.083(17) 0.072(14) 0.115(12) 0.165(17) 0.045(14) 0.149(35) 0.235(21)

7.028(27)‘) 6.411(26) 5.58l(35) 4.957(20) 4.418(16) 3.899(14) 3.986(20) 4.028(16) 4.429(40) 4.929(24)

‘) Values from [65 D 11.

Bonnenberg, Hempel, Wijn

251

1.2.1.2.10 Fe-Co-Ni: specific heat

Ref. p. 2741 0.25

Fig. 213. Spin wave specific heat coefficient c(offcc Fe-Ni alloys as derived from various measurements. Triangles: specific heat measurements [68 D 11,open circles: specific heat measurements of [68 D l] combined with ultrasonic measurements of the elastic constants [68 B2], solid circles and line: neutron scattering measurements [64H 11. Cross: disordered FeNi, [70 K 21.

mr& 0.20

0.15

I 0.10 8

-0.05 0 Ni

0.1

0.2

0.4

0.3 x-

0.5

0.7

0.6 -^

s.u mJ mol K2

ordered

-cc))-I-

--

--

CD= 2.286.10-2T3t3.301 T 3.0 0

2

6

4

8

12

IO T2 -

14

16

18 K2 20

Fig. 214. Low-temperature specific heat capacity C, of ordered and disordered FeNi, [70 K 21.

Fig. 215. For caption, see p. 253.

8

0

a Fig. 215a. Land&Bbmstein New Series III/I%

200

600

400 T-

800 K

IC

0

b Fig. 215b.

Bonnenberg, Hempel, Wijn

200

400

600 T-

800

K II

252

1.2.1.2.10 Fe-Co-Ni: specific heat

[Ref. p. 274 -l

12 Cii

mz’ K 10

I Fed%.:77 I

I

12 COI molK

HI P

10

8

8

I cl6

I ,6

4

4

2

2

0

200

400

600

800

200

K 1000

400

600

800

I

I

600

800

K 1030

T-

I-----

C

Fig. 21.5~-f.

1;

Ii COI mol K

CUl

mzl K

Fe0.508 Ni0.492

I

I

l[

0 e

200

400

600 I-

800

K 1000

200 f0

Bonnenberg, Hempel, Wijn

400 T-

K 1000

253

1.2.1.2.10 Fe-Co-Ni: specific heat

Ref. p. 2741

IO col mol K 8

200

600

400

800

K IC

0

200

400

800

600

K 1000

T-

h

T-

Fig. 215g-j.

IC col molK

I

FeO.662 Ni0.338 81

8

I

%I Fe0.708,i0@

I

r

cv

I

I

/

1

61

I4

u

I

i

200

600

400 T-

800

K 1000

0

200

400

j

Fig. 215a-j. Specific heat C of fee Fe-Ni alloys at high temperature. Sample annealed at 1000 “C for 25 h and cooled in the furnace. C,: derived from C, by substrating the contribution of thermal expansion, C,,: specific heat contribution from lattice vibrations, as calculated from Debye temperatures obtained from measurements of the elastic moduli, C,,: contribution from conduction electrons, supposed to be proportional to the temperature, also at higher temperatures, Cv, and Cv,: contributions from magnetic and atomic ordering, respectively [73T2]. lcal~4.1875.

Landolf-Bijrnstein New Series 111/19n

Bonnenberg, Hempel, Wijn

600 T-

800

K 1000

[Ref. p. 274

1.2.1.2.10 Fe-Co-Ni: specific heat

254

40 mJ K.* Cotom

i

JGT7-1 I

20

unFertoinly in,CvJ

2E

I

10

6

O -10

2i -20 2G

-30 ( 2000

0

Cl.1

Fe

Fig. 216. Specific heat ofdisordered FeNi, as a function of temperature. Experimental curve C, from [73 K 31. C, is derived from C, using a dilatation correction. The lattice specific heat C,., is derived from a Dcbye tempcraturc of 38-l K. C,., is the electronic specific heat. T,=872.6K is Curie temperature of the disordered alloy and Trd = 773 K is the order-disorder transition temperature [82 B I]. For specific heats ofFcNi, samples with various degree of order. see [73 K 33.

0

so

100

150 I-

200

250 K 300

0.2

0.3

0.4

0.5

0.6

0.7

X-

Fig. 217. Increment of the electronic specific heat coeflicicnt Ay per C atom in Fc,Ni, -,C, alloys [74C 23.

Fig. 218. Debye temperature 0, ofFe, -,Ni, invar alloys as derived from measurements ofintegrated intensities of X-rays at various temperatures. T, = 92 K is the temperature where the martensitic transformation starts [79 M 11.

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.10 Fe-Co-Ni: specific heat

255

Fig. 219a. Debye temperature On of Fe,-.Ni, alloys as derived from low-temperature elastic constants. The dash-dotted curve refers to the paramagnetic state by extrapolating the elastic constants from above the Curie temperature [75 H 11.1: [75 H 1],2: [68 B 2],3: [6OA 11, 4: cl-Fe [61 R 11. Dashed line: calculated from elastic constant data extrapolated to low temperature. For 0, derived from low-temperature specific heat measurements, see [68 D l] : Ni [at%]

@DCKI

Ni [at%]

@niw

100

477.4(62)

68.7

470.9(101)

59.2 55.1

470.6(50) 464.4(72)

441.4(52)

50.1 45.0

412.2(59)

95.7

473.2(111)

90.3

469.1(141)

86.2

488.2(98) 480.6(73)

81.1

423.0(110)

500 K 460

0.6

I,420 0

a

0.8

1.0 Ni

x-

Fe

380 v 3LO 30

40

50

70

60

80

400°C 90 wt%loo

b Ni Ni Fig. 219b. Debye temperature On of Fe-Ni alloys as derived from elastic constant at various temperatures [71 T 11. 2.5 mW cmK

40 mW cmK

4 -mW cmK

w . oc .O Ir! 0 -b Tl .O .0O

20

2

1

I ‘!

0.7 I 0.8 0.6 x'

; x 6 5

0.5

4

0.4

3

0.3

2

0.2

0.5 0.1

1 1

01 1.0

1.5

2.0

2.5

3.0

3.5

4.0

L.5 K 5.0

TFig. 220. Decrease of the low-temnerature thermal conductivity II of an Fe,,,Ni,,, alloy in various magnetic fields [70 Y 11. Landolt-Biirncfein New Series 111/19a

2

3 T-

4

5 6 7 EKIO

Fig. 221. Low-temperature total thermal conductivity x of two Fe-Ni alloys, as well as the supposed magnon part of the thermal conductivity, x,, both in absence of a magnetic field [70 Y 11.

Bonnenberg, Hempel, Wijn

1.2.1.2.10 Fe-Co-Ni: specific heat

256

[Ref. p. 274

25 molKL

mJ molK2 7.0

\ \

/

6.5

6.0 I x 5.5

5.0

1.8Ol 0.3

0.4

0.5

0.7

0.6

0.8

4.5 I Ni

0.9

X-

Fig. 222. Electronic and lattice specific heat constants, 1 and /?, rcspcctivcly, for Co, -,Ni, alloys as dcrivcd from low-tempcraturc (1.2.‘.8 K) specific heat mcasurcmcnts [74C4]. see also [59 W I].

I

400

16 >:I

D 0

A

14

0

co

- 300

0.2

0.4

x-

0.6

0.8

1.0 Ni

Fig. 223. Electronic specific heat constant y and Debyc tempcraturc 0, for Co,-,Ni, alloys [68 H I]. lcal&4.187J.

Bonnenberg,

Hempel,

Wijn

Ref. p. 2741

1.2.1.2.11 Galvanomagnetic

properties

26, p.Qcm 1

257

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

I

I

I

I

18

20

22 co -

24

I

Fe-Co

20

I Qr 18

0 16

2 30

IQn 0

IO

0 Fe

16 b

0

26 wt% ;

Fig. 224b. Electrical resistivity of Fe-Co alloys at room temperature [75 F 11.

0 2 0 2 0

Okdl 0

-200

a

T-

800 1000 "C Ii

Fig. 224a. Temperature dependence of the electrical resistivity Q for Fe-Co alloys [39 S 21.

UI

0

c Fe

20

40

co-

60

80 wt% 1’

co

Fig. 224~. Resistivity of the Fe-Co alloys, at various temperatures [74V 11.

Land&Bbrnstein New Series lll/l9a

Bonnenberg, Hempel, Wijn

258

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefiicient, thermoelectric power

4s .?i-2

Fe-Co

[Ref. p. 274

I = -195°C

3.f

i 3.2

I sr”

2.6

60

40

2.4

20

-195°C

0

-20 0

c

20

Fe

60

40

co -

80 wt% 100 co

Fig. 225~. Concentration depcndcncc of the anomalous Hall constant R, for Fe--Co alloys at various temperatunes [74V I].

0.E

0.4

C

1

-0.i a

1

20

FE

60

Fig. 225a. Longitudinal magnctorcsistancc. i.e. the rclative change of the electrical rcsistivity, AQ ,/Q. as a conscqucncc of an applied ficld of I.5 kOc for Fc Co allow at various tempcraturcs [39 S 2).

80 wt%

co -

co

80

I d

63

40

20

0 -20 -200

-100

0

100

200

300

400

0 500 "C 601

Fig. 225b. Tcmpcraturc depcndcncc of anomalous Hall constant R, for Fc Co alloys [74V I].

b

Bonnenberg, Hempel, Wijn

I.andolr.Rornrlcin Neu Scricr III ‘19:s

Ref. p. 2741

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

n

rc-‘y’

259

29.87wt%Ni

Fe-Ni

11 p!h

IL

-F-

j

19.56

I 13 Qr

12

IO

7

-!73 -200 a

II

200

I

I

400 7-

600

I

800 “C IC

b

0 -273 -200

0

200

KIO

600

800 “C I[

7-

Fig. 226. Temperature dependence of the electrical resistivity Q for FeNi alloys. (a) 0...30wt% Ni, (b) 35 . ..lOO wt% Ni. The arrows on the curves indicate the temperature sequence of the measuring points. The vertical arrows denote the Debye temperature On as derived from the specific heat. The vertical scale is equal for all compositions and is given by the length ofthebarindexed40@2cm[39S3,60K1,71T1].

1.F pQcm

1.C I Q 0.5

Fig. 227. Electrical resistivity Q at 4.2K vs. Fe concentration in Fe,Ni,-, alloys. The straight line derived trom a least-squares fit is given by @=0,03(2)+33(1)x, p in @cm [71 S 21. Landolt-BBmstein New Series Ill/~%

0 NI

Bonnenberg, Hempel, Wijn

0.01

0.02

0.03

x-

O.OL

0

[Ref. p. 274

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

260

I quenched from1400K 2 equilibrium at 767 755 3 735 4 713 5

6

1000

1200 K 1L

Fig. 228. Electrical rcsistivity Q vs. tempcraturc T for FeNi, alloys after various heat trcatmcnts leading to rarious degrees of atomic ordering [73 K 31. See also [82 0 21. Krd: order-disorder transition tempcraturc.

0

10

20

30

LO

50

60

70 K 80

I-

Fig. 230. Tcmpcraturc dcpcndcncc of the rclativc change of the electrical rcsistivity for small incrcmcnts of the magnetic field. (Aplp,)‘A,H at high values of the magnetic licld strength H. i.e. in the range ofthc pnraproccss for Fe Ni invar alloys. 40 denotes the rcsistivity in zero magnetic licld [59 K I].

5

0

10

20

30

40 I-

50

60

70 K 80

Fig. 229. Temperature dependence of the relative change of the electrical rcsistivity under hydrostatic pressure p, (A?/+)/Ap, for an invar alloy Fe,,,,Ni,,,,. where o0 is the rcslstlvity under ambient pressure [59 K I].

0 Ni

0.1

0.2

0.3 0.1 x-

0.5

0.6

0.7

0.8

Fig. 23 1. lncrcmcnt of the residual (i.e. low temperature) rcsistivity per atom percent c of C. A.o,lc, for (Fe,Nil -,) C, alloys [74 C 23.

Bonnenberg, Hempel, Wijn

I.andolr.Bornrrcin Nea Scrim III ‘19n

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

Ref. p. 2741 110

261

I

pQcm Fe-Ni-Ti

0

u-o AT

100 0

3 4.75 at%Ti

60

30

34

38

42

46 wt%

50

0

50

100

NI -

Fig. 232. Influence of Ti additions on the roomtemperature electrical resistivity Q of Fe-Ni invar alloys [73K2].

150 200 T-

250

300 K 350

Fig. 233. Temperature dependence of the longitudinal magnetoresistance (A@/@) ,,, measured in a magnetic field of 20 kOe for various orientations of the crystal axis of an invar alloy [78 V 11. %65%35

1.6 %

8

1.2

6 ‘= G ch

I =

I

0

I

I

IO

20

I

I

I

30 Fe -

40

I

Landolt-Bdmstein New Series I11/19a

F 2 0.4

2

0

0

50 wt”/o

Fig. 234. Spontaneous resistance anisotropy (Q,,- el)/Q for fee Fe-Ni alloys as defined by the value of the difference ofthe resistance ofa sample magnetized parallel or perpendicular to the measuring current relative to the average of their values [74 C 31. Open circles: T=20K [59 E 11, solid circles: 4.2 K [74C 31.

For Fig. 235, see next page.

4s

0.8

-0.4 0 Fe

F 1M I d+AFpIANi I I I I 20 40

60 NI -

80 wt% lOi Ni

Fig. 236. Longitudinal magnetoresistance as a consequence of an applied field of 1.5kOe for FeNi alloys at various temperatures [39 S 11. F: ferrite, M: martensite, A: austenite. Dashed curves: cooling.

Bonnenberg, Hempel, Wijn

262

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

1.2 %

‘;,y Fe-Ni 0.; fee

0.8

0.5

-

0

[Ref. p. 274

Hopp, = 1.5kOe 35wl%Ri

-_)

40

0

? 0

0.1

1 0

0

0.8

1 0.1

0 I = 2 5

I 0 204 ,a G -4

z- 1

0 0.2

0

0

1

0.2

0

0

1

0.2

C

0

1

0.2

0

0

1 0

-0.4 I -203

I 200

I 0

a

I 400 I-

I 600

I 800 “C

1;

b

IIIII

0

200

400

600

800 “C

T-

Fig 235. Longitudinal magnetoresistance vs. temperature for (a) hcc Fc-Ni and @) fee Fe-Ni alloys [39 S I]. Arrows indicate hystcrcsis. 0.3 1=20K

I = G T2

0.2 o Ni -Fe Ni-Co A Ni-Cu -A Ni-Fe-k l

0.i

0

41 ) ;’ II d Ni 0.5

1.0 PO:-

0 uCob 1 Ps

2.0

Fip. 237. Longitudinal magnetoresistancc (AQ/Q,,),, at 20K as a function of the mean magnetic moment per atom. &,, for various 3d-element alloys [Sl S 1, 575 1, 64C I].

Ni

Fe -

Fig. 238. Normal Hall coefficient R, vs. Fe concentration in Fc-Ni alloys at various temperatures [7OC I]. lm3C-‘nIO-2R cmG-‘.

Bonnenberg, Hempel, Wijn

Ref. p. 2741 0 .lO"

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

263

N i _ Fe 2000III4000

I ?2

1600

-‘!b

1.2 p&m

3200

800

t 2400 z .s s K 1600~

400

800

I 1200

1.8

P-

Fig. 239. Anomalous Hall angle Q,JQ vs. the resistivity Q for Fe-Ni alloys with small concentration in the range from 0.5 up to 5at% Fe. T=4.2K. Open circles: [75 D I], solid circle: [74 J 11. can: en = R,B + eaH.

CT

0

0

-400 -200

200

0

a

400

“C

-800 600

T-

Fig. 240a. Temperature dependence of the spontaneous Hall coefficient R, for Fe-Ni alloys. The scale on the right-hand side applies to 55wt% Fe [64K I]. lm3C-1~10-ZQcmG-1.

5

0

b

4.07 3.09 . 2.44 P I.08

I t -4+. 40

80

120

160

200

240

d

280 K 320

T-

-0 0.89

Fig. 240b. Low-temperature values of the spontaneous Hall coefficients R, of Fe-Ni alloys [65S 11. 1m3C-‘~10-Z~cmG-1.

0 a -v o

-6

1 1

I I

I

F-h\\ Y\\\

u\ I\ \

1~1if

0.43 0.35 0.07 NiII

-7

Fig. 240~. Temperature dependence of the spontaneous Hall coefficient R, for small Fe concentrations in Fe-Ni alloys NQ): annealed at 105O”C, 1 h [65H I]. 1m3 C-l& 10-2ficmG-‘. The original literature gives the absolute values of R,. Landolt-BBrnsfein New Series lll/l9a

-8 c

t

-91 0 C

Bonnenberg, Hempel, Wijn

50

100

150 T-

200

250 K :

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

264

[Ref. p. 274

-0x

=a

I oe

b

c

-0.8

\ 4

1 I 15ot% Ni 0

I 0 . -0.5

--a-

-1.2 0

50

150 I-

100

d

-1.6

-2.0 200

80

250 K 300

160 I-

e

Fi_e.240d. Normal Hall coetlicicnt R, vs. temperature for small Fe concentrations in FeNi alloys [65H I]. NiI(II): annealed at 1200“C (1050 “C) for 2 h (I h). then cooled at a rate of S”C!min. The original literature gives the absolute values of R, [65 H I].

2LO

-0.E -0,s 0.5

1.0

1.5

2.0

320

Fig. 240~. Low-temperature values of the normal Hall coefftcicnts R, of Fe-Ni alloys [65S I]. n: effective number of electrons per atom, n = - l/R,Ne, where N is the number of atoms per m3 and e is the electron charge 1m3C-‘a 10-ZRcmG-‘.

-0.E

0 Ni

K

2.5 3.0 Fe,Co,Cu -

3.5

L.0

4.5

ot%

Fig. 241. Normal Hall coctlicicnt R, for alloys ofNi with Fe.Co,andCu[65Hl].lm3C-r&IO-*ficmG-’.Thc original litcraturc gives the absolute values of R,.

Bonnenberg, Hempel, Wijn

5.5

Ref. p. 2741

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

265

Fe,-, Ni, Fel-x Ni,

0

100

200

300

a

400

500

100

600 K 71

200

300

400

500

600 K

T-

I-

Fig. 242a. Temperature dependence of the anomalous Hall resistivity can extrapolated from saturation region to zero field for Fe,-,Ni, invar alloys. The vertical arrows indicate the Curie temperatures. The vertical scale is equal for all compositions and is given by the length of the vertical bar showing a scale of 0.5 @I cm. The reference levels for the ordinate are given by the figures attached to horizontal arrows [76 S 11.

Fig. 242b. Temperature dependence of the spontaneous Hall coefficient R, in Fe,-,Ni, invar alloys. The vertical scale is equal for all compositions and is given by the length of the bar showing a scale of 50.10-lo m3 C-‘. The reference level for the ordinate is given by the figure attached to horizontal arrows [76 S 11. 1m3C-‘~10-2~cmG-‘.

0 a

20

40

60 7-

80

0

K 100

2

4

6

b

Fig. 243. Temperature variation of the thermoelectric power Q of Fe-Ni and Co-Ni alloys [70F 11. (a) T=O...lOOK, (b) T=0...15K.

Landolt-Bbmstein New Series IWl9a

Bonnenberg, Hempel, Wijn

8

T-

10

12

14 K 16

1.2.1.2.11 Fe-Co-Ni: resistivity, Hall coefficient, thermoelectric power

266

-0.5 0

0.1 0.2

0.3 0.1 0.5

0.6 0.7

Iii XM Fig. 24-l. Thcrmoclcctric power Q at I K for Fc,-,Ni, alloys and tcmary FqNi, - ,C, alloys [74 C 21. G

-2

0

Ni-Co

0.8

0

200

300

LOO

500 K 600

IFig. 245. Thermoelectric power Q of a monocrystallinc. slowly cooled sample of the invar alloy Fe,,,,Ni,,,, as a function of tcmncraturc for various crvstal directions . [78Vl]. L

I

c.2

100

[Ref. p. 274

-0.3

0.4 0.6 pQcn 1.0 $= -04 4Fig. 246n. Anomalous Hall angle P,,,/Q vs. the rcsistivity -0.5 e for Ni-Co alloys with small concentration in the range from 0.5 up to 5at% Co. e depends linearly on the Co -0.6 concentration. Solid circle: [74 J I]. open circles: [75 D I]. a

- 0.8 0

50

b

100

150

200

250 K 300

I-

Fig. 246b. Temperature dcpcndencc of the normal Hall cocffkicnt R, of Ni--Co alloys [65 H I]. I m3C-‘~10-20cmG-‘. For NiII,scccaption to Fig. 240d.

. 1.01 -1 0 C

50

100

150

200

Fig. 246~. Temperature dcpcndence of the spontaneous Hall coefficient R, of Ni -Co alloys [65H I]. lm3C-‘a10-252cmG-‘.ForNiII,scecaption toFig. 250 K 300 240d

I-

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.12 Fe-Co-Ni:

267

Kerr effect, optical constants

1.2.1.2.12 Magneto-optical

properties

Table 29. Polar Kerr rotation angle ak for normal incident polarized light on Fe-Co and Fe-Ni alloy surfaces, seealso Fig. 247.aK= K&f, is the rotation angle between plane of polarization of incident light and major axis of the elliptically polarized reflected light. The minus sign meansthat the rotation is opposite to the circular current producing the magnetization. (s): saturated, (u): unsaturated. Composition

Fe-25 wt% Ni

5300 5670 5890

Fe-27 wt % Ni

5890

Fe0.67Ni0.33

5300 5670 5200 5740

Fe0.67COO.33

Fe-36 wt% Ni, Invar

H

EK

41tK,

kOe ‘)

min

10m4min G-r

23.3 6) 16.8(u) 14.9(u) 16.3(u) 14.4(u) 19.13(s) (4 19.8(s) 14.51(s) 13.30(s)

-27.64 - 29.94 - 15.92 - 14.32 - 17.29 - 16.45 - 15.05 - 22.55 - 13.86‘) - 13.65 - 13.66

- 11.9 x - 9.5

17Bl 18Ml 12Ll

z - 12.5

12Ll

- 13.7

17Bl 18Ml 12Fl 12Ll

- 12.9 - 20.2

‘) Ellipticity of the reflected light ak = -0.44.10 - 3. J .lO"A

6

5

--36' 4

6

5

l 2 OAV.7 I 7 .1rl'4s-'

8

Y-

Fig. 247.Polar Kerr rotation anglec~kfor normal incident polarized light on Fe-Co and Fe-Ni alloy surfacesas dependenton the frequencyof the light [62 L 1,p. l-1941. Curve I: [18M 1],2: [17B 1],3: [12L 11. Landolt-Bdmstein New Series 111/l%

Bonnenberg, Hempel, Wijn

Ref.

268

1.2.1.2.12 Fe-Co-Ni:

[Ref. p. 274

Kerr effect, optical constants

Table 30. Room-temperature magnetization, Kerr rotation at a wavelength of 633OA of Fe, -Co, alloys in a not completely magnetically saturated state of the alloy. Saturated values estimated to be less than 10% higher than the values shown [83E 11. Alloy

0 Gcm3g-’

Fe Fe,Co FeCo FeCo, co

213 234 230 200 156

% deg

I%;/4 10-3degG-1cm-3g

-0.41 -0.41 -0.54 - 0.48 -0.35

1.9 1.8 2.3 2.4 2.2

I

Fe -36wt%Ni

Fig. 248.Frcqucncy dcpcndcnccof the cllipticity Edof the polar Kerr effectof an Fe-36~1% Ni invar alloy [62 L I. 5

6

7 .lO“ s-1

8

12Fl].

iI ,_

6

I-

I-

0

-0.4

-2

0.L

0.8 pm 1.0

0.6 A-

0.6

0.8 pm 1.O

-0.E

b!

L-

Fig. 249.Equatorial Kerr effect(M, parallel to the surface of the specimen and pcrpcndicular to the plant of incidence of the light). 6=1/l,. the relative change of intensity ofrctlcctcd light polarized parallel to the plant of incidcncc. as dcpcndcnt on wavclcngth and on angle of incidcncc 0 ofthc light [73 B 21.(a) Fe,(b) Fe-45 wt% Ni, (c) Fe-EOwt% Ni. (d) Ni.

Bonnenberg, Hemp& Wijn

0.8 pm

0.6 A-

1.0

Ref. p. 2741

1.2.1.2.12 Fe-Co-Ni: Kerr effect, optical constants

269

60 .10-i 50

-40 -50

-50 0

Fe

20

40

60 Ni-

80wt%100 Ni

0 Fe

20

40

60 Ni -

80wt%100 Ni

Fig. 250. Components of the magneto-optical parameter Q = Q, -iQ, as dependent on the composition of Fe-Ni alloys for several wavelengths ofthe light, as derived from the equatorial Kerr effect. Q = is&,, (H in z direction). [73 B 21. Curve I: 6700 A, 2: 6000 A, 3: 5400 A, 4: 4700 & 5: 4400 A.

05'

1

8

0'

-05'

Fig. 251. Longitudinal Kerr rotation angles (M, parallel to surface of the specimen and plane of incident light) a, and tlP for light polarized normal or in the plane of incidence, respectively, as dependent on the angle of incidence f3for Fe,,,Ni,,, . The wavelength ofthe light is a parameter. Room-temperature measurements [68 J 1, see also 66 T 11.The sign of the Kerr angle is chosen positive when the rotation and the direction of the reflected beam form a right-handed screw. Landolt-BBmstein New Series 111/19a

-1 0'

-1 5'

-20' 0"

Bonnenberg, Hempel, Wijn

15"

30"

45"

60"

75"

90"

1.2.1.2.12 Fe-Co-Ni: Kerr effect, optical constants

270 I

I

Fe-Ni

I

[Ref. p. 274

5.

t

CT 14 3 2 J’ r

1 I 70 NI -

I 63

I 50

I 80

I I 90 wt % 100 Ni

Fig. 25%. Longitudinal Kerr rotation angle tl, (for incident angle 0 =45’)vs.composition and wavclcngth for fee Fe -Ni alloys r68 J I]. The data for Ni arc due to [61S7].

-

-

0 40 50 60 70 80 90VAO/c103 Ni Ni b Fig. 252b. Kerr rotation (xP(for incident aqle 0 =4Y) vs. composition and wavelength for fee Fe -Ni alloys [68 J I]. The data for Ni arc due to [64 S 23.

-

0

I

*lo-‘ Fe-Ni -1

I

IEot%Ni

70 75 81 84 90 95 Ni

-6 0.25

0.50 0.75 1.00 1.25 1.50 1.75 2.00$25 1.-

FYg. 253a. Wavelength dependence of the longitudinal ma_rncto-optical Kerr rotation in the visible and near infrared regions for Fe-Ni alloys mcasurcd with s polarized light at the incident angle of 60”. The 1000A films are evaporated on a glass substrate at 200 “C in a vacuum of 2. IO-‘Torr (2.7. 10e5 mbnr) and annenlcd for about 2h [69YI].

-7 0.25

I

0.50 0.75 1.00 1.25 1.50 1.75 2.ooplr;z.25

Lb Fig. 253b. Wavclcngth dependence of the longitudinal magneto-optical Kerr rotation as in Fig. 2.53a,but nou for p polarized light and an incident angle of7Y [69Y I].

Bonnenberg, Hempel, Wijn

Ref. p. 2741

1.2.1.2.12 Fe-Co-Ni: Kerr effect, optical constants

271

Fe- Ni

.lO” 14

a= 5000 A 12 IO 8

t I

-2 --•--

-41 0”

I

I

I

Fe-BOwt% Ni

I

I

IO”

20”

I

I

30” 40” Q-

6

r

I

I

I

50”

60”

70”

80”

Fig. 254. Longitudinal Kerr rotation for light polarized in the plane ofincidence, as dependent on angle of incidence, 0, of light, and the composition of Fe-Ni alloys evaporated films. Wavelength of the light 5OOOA [76 M 31. Solid circles and dashed line: [68 J 11. 0 0

2i .,o-?

IO”

20”

30”

40”

50”

60”

70”

80”

Fig. 255. Kerr ellipticity sKfor Fe-Ni films as a hmction of the angle of incidence 0. Longitudinal arrangement, light wavelength 5000& polarized in the plane of incidence [76 M 31.

I

Fe-Ni

2c

Fe-Ni’

I

4J-N

0.6

IE

14 I 0” 12

IO

8

0 n=40508, . 4590 5030 6 -v . 5490 A 5980 4 1 50

I

60

70 NI -

80

90 wt% 100 Ni

Fig. 256. Amplitude Q, of the magneto-optical parameter Q =is.&,, (H in z direction), vs. wavelength and composition for fee FeNi alloys, as derived from longitudinal Kerr-effect [68 J 11. Q = Q, expiq. Landolt-Bbmstein New Series lll/l9a

40

50

60

70 Ni -

80

90 wt% 100 Ni

Fig. 257. Phase factor of the longitudinal magnetooptical parameter, q, as a function of composition and wavelength for fee Fe-Ni alloys [68 J 11. Q=Q,expiq = isx,,/.s,, (H in z direction).

Bonnenberg, Hempel, Wijn

[Ref. p. 274

1.2.1.2.12 Fe-Co-Ni: Kerr effect, optical constants

272

IIIrFq--j-

20’ r

0”

t -20’ b

LO50 v 5550 I 3’ -film tit7

0

-Ci

20

40

60

80 wt% 100

NI -

o SOwt%Ni 1.6

Fig. 258. Phase factor (I of the longitudinal magnctooptical parameter Q = Q. expiq = ic,)./c,, (H in z direction) as a function of composition for Fe-Ni alloys [76 M 33. Circles: [76 hl33. squares: [12 F I], upward triangles: [63 R 11, crosses and open circles [68 J 11. lozcngc and downward triangles: [63 T I].

l

80

v 70 . 60 1.4I 4000

I 1500

5d30

I 5500 1 E

Fig. 2.59.Rcfractivc index n,(n = nO(1-ix)) vs. wavelength and composition for fee Fc-Ni alloys [68 J I].

1.9 1.8 1.7

I

x

1.6

1.5

1.4 4[

L500

5000 1-

5500 1 6000

Fig. 260. Imaginary part of rcfractivc index. x(n=n, .( I -ix)), as a function of wavclcngth and composition for fee FeNi alloys [68 J I].

Bonnenherg,

0 Fe

20

40

60 NI -

80 VA% 100 Li

Fig. 261. Rcfractivc index II = nO(1-ix)vs. composition of Fc-Ni alloys, measured at 5OOOA. Circles: [76M 33. triangles: [68 J I], squares: [63 R I], lozenges [06 I I].

Hempel,

Wijn

I.andol~-Rornwin Ncu

Sericq

111’19n

Ref. p. 2741

273

1.2.1.2.13 Fe-Co-Ni: ferromagnetic resonance 1.2.1.2.13 Ferromagnetic resonanceproperties

Fig. 262. Landau-Lifshitz damping parameter L for different FeNi alloys as derived from ferromagnetic resonance linewidth data obtained at frequencies of 19.5 and 26 GHz on (100) disks of bulk single crystals [76 B 11. For single crystal of Co,,,,Ni,.,,, 1=2.18. 10-8s-1 [75W 11.

10.0 w* s-1

I

Fel+ Ni, 1.5 mg s-1 5.0

1.5

~t 5.0

I c-”

2.5 2

2.5 0 0.25 Fig. 263. Landau-Lifshitz damping parameter 1 for Fe75 wt% Ni as dependent on the state of ordering [76 B 11, see also [74 B 11. For the case of small dopes with MO or Cu, see [74P 11.

Landolt-B6mstein New Series lll/l9a

0.35

0.45

0.55 x-

0.65

0.75

0 0.85

Fig. 264. Room-temperature value ofthe Landau-Lifshitz damping parameter L for fee Fe, -,Ni, alloys as derived from ferromagnetic resonance experiments at a frequency of 6.375GHz on annealed and quenched samples, and relaxation frequency l/T, after Bloch-Bloembergen [73P 11.

Bonnenberg, Hempel, Wijn

274

Refcrcnccs for 1.2.1

1.2.1.3 References for 1.2.1 1897G 1 Guillaume, SE.: CR. Acad. Sci. 125 (1897). Nagaoka. H.. Honda. K.: Philos. Msg. 4 (1902) 45. OSH 1 Honda. K.. Shimizu, S.: Philos. Msg. 10 (1905) 548. 0611 Ingersoll. L.R.: Philos. Mag. 11 (1906) 41. Pancbianco. G.: Rend. Accad. Sci. Fis. Mat. Sot. Naz. Sci. Napoli 16 (1910) 21b. lOP1 12F 1 Foote. P.D.: Phys. Rev. 34 (1912) 96. 12Ll Loria. S.: Ann. Physik 38 (1912) 889. 17Bl Barker. S.G.: Proc. Phys. Sot. (London) 29 (1917) 1. 17c 1 Chcvenard. M.P.: Rev. Met. Paris 14 (1917) 610. 18M 1 Martin. P.: Ann. Physik 55 (1918) 561. 20G 1 Guillaume. SE.: Proc. Phys. Sot. (London) 32 (1920) 374. 25P 1 Pcschard. M.: Rev. Met. Paris 8 (1925) 490. 25P2 Pcschard. M.: Rev. Met. Paris 8 (1925) 581. 27K I Kase. T.: Sci. Rept. Tohoku Univ. 16 (1927) 491. 28C1 Chevenard. P.: Rev. Met. Paris 10 (1928) 14. 28E 1 Eimen. G.W.: J. Franklin Inst. 206 (1928) 317. 29E 1 Ehnen. G.W.: J. Franklin Inst. 207 (1929) 583. 29M 1 Masumoto. H.: Sci. Rept. Tohoku Univ. 18 (1929) 195. 29Wl Weiss, P., Forrer, R.: Ann. Phys. Paris 12 (1929) 279. 31 M 1 Masiyama. Y.: Sci. Rept. Tohoku Univ. 20 (1931) 574. 3’Sl Sadron. C.: Ann. Phys. Paris 17 (1932) 371. 35K I Kornetzi, M.: Z. Phys. 98 (1935) 371. 36Fl Fallot. M.: Ann. Phys. Paris 6 (1936) 305. Shih. J.W.: Phys. Rev. 50 (1936) 376. 36Sl 37El Ebert. H., KuBmann, A.: Phys. Z. 38 (1937) 437. 37M 1 McKeehan. L.W.: Phys. Rev. 51 (1937) 136. 3701 Owen. E.A.. Yates. E.L. et al.: Proc. Phys. Sot. (London) 49 1937) 17. 3702 Own. E.A.. Yates. E.L. et al.: Proc. Phys. Sot. (London) 49 1937) 178. 3703 Owen. E.A., Yates. E.L. et al.: Proc. Phys. Sot. (London) 49 (’1937)307. Snoek. J.L.: Physica IV 9 (1937) 853. 37s1 Shirakawa. Y.: Sci. Rept. Tohoku Univ. 27 (1938) 485. 39Sl Shirakawa. Y.: Sci. Rept. Tohoku Univ. 27 (1938) 532. 3932 Sucksmith. W.: Proc. R. Sot. London Ser. A 171 (1939) 525. 39s3 39Tl Tarasov, L.P.: Phys. Rev. 56 (1939) 1245. 41 E 1 Ellis, W.C., Grciner. E.S.: Trans. Am. Sot. Met. 29 (1941) 415. Ovvcn. L.A., Sully, A.H.: Philos. Mag. 31 (1941) 314. 4101 Rathenau, G.W., Snack. J.L.: Physica VIII 6 (1941) 555. 41R1 43F 1 Fallot. M.: Metaux Corrosion-Ind. 18 (1943) 214. Barnett. S.J.: Phys. Rev. 66 (1944) 224. 44Bl Fallot, M.: J. Phys. Radium VIII 5 (1944) 153. 44Fl 49G 1 Goldman. J.E.: Phys. Rev. 76 (1949) 471. Taylor, A.: J. Inst. Metals 77 (1950) 585. 50Tl Bozorth. R.M.: Ferromagnetism, Toronto, New York, London: D. van Nostrand Comp. Inc. 1951. 51 Bl Lement. B.S., Averbach. B.L., Cohen, M.: Trans. ASME 43 (1951) 1072. 51Ll Smit. J.: Physica 16 (1951) 612. 51Sl Tsuji. T.: J. Phys. Sot. Jpn. 13 (1958) 1310. 51Tl 51Wl Went. J.J.: Physica 17 (1951) 98. 52B 1 Barnett. S.J.,Kenny, G.S.: Phys. Rev. 87 (1952) 723. 52K 1 Kondorskii, E.J., Fedotov, J.N.: Izv. Akad. Nauk. SSSR 16 (1952) 432. 52u 1 Urquhart. H.M.A., Goldman, J.E.: Phys. Rev. 87 (1952) 210. 53B 1 Bozorth, R.M., Walker, J.G.: Phys. Rev. 89 (1953) 624. Bozorth. R.M.: Rev. Mod. Phys. 25 (1953) 42. 53B2 Galpcrin, D., Larin. C., Schischkow, A.: Doklady Akad. Nauk. USSR 89 (1953) 419. 53Gl 53 w 1 Wakelin. R.J.. Yates. E.L.: Proc. Phys. Sot. (London) Sect. B66 (1953) 221. 53Y 1 Yamamoto. M., Misyasawa, R.: Sci. Rept. Tohoku Univ. A 5 (1953) 113. 54B 1 Bozorth. R.M.: Phys. Rev. 96 (1954) 311.

02Nl

Bonnenberg,

Hempel,

Wijn

References for 1.2.1 54Pl 54Tl SC1 55Ml 55Sl 5582 56Cl 56Nl 56Sl 57Cl 57C2 5751 57Nl 58Al 58Fl 58Gl 58Hl 58Yl 59Al 59El 59Hl 59Kl 59Wl 60Al 6OCl 60Kl 60Tl 6OWl 61Jl 61 K 1 61 M 1 6101 61Pl 61Rl 62Cl 62C2 62Gl 62Kl 62K2 62Ll 62Sl 6282 62Tl 63Cl 63C2 63C3 63C4 6351 63Pl 63Rl 63Tl 63T2 63Wl 64Al 64Cl 64C2 64El

275

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Hempel,

Wijn

References for 1.2.1 69Nl 69Rl 69Sl 69S2 69S3 6934 69Yl 70Al 70Bl 7OCl 7OC2 70Dl 70Fl 70Gl 70Hl 70Kl 70K2 70Ml 70Tl 70T2 7OWl 7OYl 71Al 7lA2 71Bl 71El 71Hl 71H2 71Kl 71Pl 71Sl 71S2 71s3 71s4 71Tl 71T2 71T3 71Wl 71Yl 72Bl 72Cl 72Dl 72Hl 72H2 72H3 72H4 72Ll 72Ml 72M2 72M3 72Nl 72Rl 72R2 72Sl 72Tl 72T2

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12T3 73B I 73B2

Tino, Y., Arai, J.: J. Phys. Sot. Jpn. 32 (1972) 941. Brian, M.M.: C.R. Acad. Sci. Paris 277 (1973) B-695. Burlakova. R.F., Edel’man, I.S.: Phys. Met. Metallogr. (USSR) 35 (1973)200 (Fiz. Met. Metalloved. 35 (1973) 1101). 73c1 Cable J.W., Wollan. E.O.: Phys. Rev. B7 (1973) 2005. 73D 1 Dubinin. SF., Sidorov, S.K., Teploukhov, S.G., Arkhipov, V.E.: JETP Lett. 18 (1973) 324. 73Hl Hausch. G., Warlimont. H.: Acta Metal!. 21 (1973) 401. 73H2 Hayase. M., Shiga. M., Nakamura. Y.: J. Phys. Sot. Jpn. 34 (1973) 925. 73K 1 Kalinin. V.M., Beskachko, V.P.: Phys. Met. Metallogr. (USSR) 36 (1973) 65. 73K2 Kalinin. V.M., Danilov, M.A., Komarova, L.K., Tscytlin, A.M.: Phys. Met. Metallogr. (USSR) 36 (1973) 15. 73K3 Kollie. T.G., Brooks, C.R.: Phys. Status Solidi (a) 19 (1973) 545. 73M 1 Maedo, T., Yamauchi. H., Watanabe. H.: J. Phys. Sot. Jpn. 35 (1973) 1635. 73 M 2 Menshikov, A.Z., Yurchikov, E.E.: Sov. Phys. JETP 36 (1973) 100. 13 h4 3 Mook. H.A., Lynn, J.W., Nicklow, R.M.: Phys. Rev. Lett. 30 (1973) 556. 730 1 Ozone, T., Morita. H., Hiroyoshi, H., Saito, H.: J. Phys. Sot. Jpn. 35 (1973) 298. 73 P 1 Pokatilov, V.S., Puzei, I.M.: Sov. Phys. JETP 36 (1973) 108. 13R 1 Rechenberg, H., Billard, L., Chamberod, A., Natta, M.: J. Phys. Chem. Solids 34 (1973) 1251. 73v 1 Voroshilov, V.P., Zaktlarov, A.I., Kalinin, V.M., Vralov, A.S.: Fiz. Met. Metalloved. 35 (1973) 953. 73 w 1 Wakiyama. T.: AIP Conf. Proc. Mag. Magn. Mater. 2 (1973) 921. 73 w 2 Window, B.: J. Appl. Phys. 44 (1973) 2853. 732 1 Zakharov, AI., Men’shikov, A.Z., Uralov, AS.: Phys. Met. Metallogr. (USSR) 36 (1973) 170. Bastian. D., Biller, E., Chamberod, A.: Solid State Commun. 14 (1974) 73. 74Bl 74c 1 Cable. J.W., Chield. H.R.: Phys. Rev. B 10 (1974) 4607. Cadeville. M.C., Caudron, R., Costa, P., Lerner, C.: J. Phys. F 4 (1974) L 87. 74C2 Campbell. LA.: J. Phys. F4 (1974) L 181. 74c3 Caudron, R., Meunier. J.-J., Costa, P.: Solid State Commun. 14 (1974) 975. 74c4 Crowe!!. J.M.. Walker, J.C.: J. Mag. Magn. Mater. 2 (1974) 427. 74c5 74D1 Dubovka. G.T.: Phys. Status Solidi (a) 24 (1974) 375. Edwards, L.R., Bartel. L.C.: Phys. Rev. B 10 (1974) 2044. 74El Jaou!. 0.: Thesis Univ. de Paris-Slid Centre d’Orsay 1974. 745 1 74K 1 Kalinin. V.M.. Beskachko, V.P., Khomenko, O.A.: Phys. Met. Metallogr. (USSR) 37 (1974) 184. Litvinsey, V.V., Torba. G.F., Ushakov, A.I., Didovich, Yu.N., Rusov, G.I.: Fiz. Tverd. Tela 16 (1974) 74Ll 3135. 14 hl 1 Mori. N., Ukai. T., Kono, S.: J. Phys. Sot. Jpn. 37 (1974) 1278. Menzinger. F., Sacchetti, F., Leoni, F.: II Nuovo Cimento 20B (1974) 1. 74M2 74M3 Miwa. H.: Progress of Theor. Phys. 52 (1974) 1. 74Nl Nishi. M.. Nakai. Y., Kunitomi, N.: J. Phys. Sot. Jpn. 37 (1974) 570. Ono, F., Chikazumi, S.: J. Phys. Sot. Jpn. 37 (1974) 631. 7401 Orehotsky, J., Schrader, K.: J. Phys. F4 (1974) 196. 7402 Onozuka. T., Yamaguchi. S., Hirabayashi, M., Wakiyama, T.: J. Phys. Sot. Jpn. 37 (1974) 687. 7403 Puzey. M., Pokatilov, VS.: Phys. Met. Metallogr. (USSR) 37 (1974) 174. 74P1 74R 1 Rode. U.Ye.. Krynetskaya, I.B.: Phys. Met. Metallogr. (USSR) 38 (1974) 183. 14R2 Rogozyanov, A.Ya.. Lyashchenko, G.: Phys. Met. Metallogr. (USSR) 37 (1974) 87. 74s1 Sandier, L.M., Popov, V.P., Gratsianov, Yu.A.: Phys. Met. Metallogr. (USSR) 37 (1974) 76. Sandier. CM.. Popov, U.P., Naglyuk, Ya.V.: Phys. Met. Metallogr. (USSR) 37 (1974) 187. 7432 Shiga. C., Kimura, M., Fujita, F.E.: J. Jpn. Inst. Met. 38 (1974) 1037. 7483 1434 Shiga. M.. Maeda. Y., Nakamura, Y.: J. Phys. Sot. Jpn. 37 (1974) 363. Sikorska. B., Dobrzyhski. L., Maniawski, F.: Acta Phys. PO!. A45 (1974) 431. 74S5 Tino, Y., Arai, J.: J. Phys. Sot. Jpn. 36 (1974) 669. 74Tl Vasil’eva, R.P., Cheremushkina, A.V., Yazliyav, S., Kadyrov, Ya.: Fiz. Met. Metalloved. 38 (1974) 55. 74Vl 74 w 1 Window, B.: J. Phys. F4 (1974) 329. 15B 1 Billard. L.. Chamberod, A.: Solid State Commun. 17 (1975) 113. 75Dl Dorleijn. J.W.F., Miedema, A.R.: Phys. Lett. A55 (1975) 118. 75F 1 Foster, K., Thornburg. D.R.: AIP Mag. Magn. Mater. New York 24 (1975) 709. 75Gl Gonser. U., Nasu, S., Keune, W., Weis, 0.: Solid State Commun. 17 (1975) 233. 75H 1 Hausch. G.: Phys. Status Solidi (a) 30 (1975) K 57. 75H2 Hennion. M., Hennion, B., Castets, A., Tochctti, D.: Solid State Commun. 17 (1975) 899.

Bonnenberg, Hempel, Wijn

Referencesfor 1.2.1 75Kl 75Ml 75M2 75M3 75M4 75Rl 75Wl 75W2 76Bl 76B2 76El 76Hl 76H2 76Jl 76Kl 76Ml 76M2 76M3 76M4 76Pl 76Sl 76Tl 77Bl 77Cl 77Dl 77D2 77El 77Hl 77H2 7751 77Kl 77K2 77Ml 77M2 77M3 77M4 77Sl 77Tl 77T2 77Yl 78Al 78Bl 78B2 78Cl 78Hl 78Kl 78K2 78Sl 78Tl 78T2 78T3 78Vl 78Wl

279

Kalinin, V.M.: Phys. Met. Metallogr. (USSR) 39 (1975) 201. Makarov, V.A., Puzei, I.M., Sakharova, T.V., Gutovskii, LG.: Sov. Phys. JETP 40 (1975) 382. Menshikov, A.Z., Kazantsev, V.A., Kuzmin, N.N., Sidorov, S.K.: J. Mag. Magn. Mater. 1 (1975) 91. Mokhov, B.N., Goman’kov, V.I.: JETP Lett. 21 (1975) 276. Makarov, V.A., Puzey, I.M., Sakarova, T.V.: Phys. Status Solidi (a) 30 (1975) K21. Riedinger, R., Nauciel-Bloch, M.: J. Phys. F5 (1975) 732. Wu, C.Y., Quach, H.T., Yelon, A.: AIP Conf. Proc. Mag. Magn. Mater. 29 (1975) 681. Wakiyama, T., Chin, G.Y., Robbins, M., Sherwood, R.C., Bernardini, J.E.: AIP Conf. Proc. 29 (1975) 560. Bastian, D., Biller, E.: Phys. Status Solidi (a) 35 (1976) 113. Bastian, D., Biller, E.: Phys. Status Solidi (a) 35 (1976) 465. Edwards, D.M., Hill, D.J.: J. Phys. F6 (1976) 607. Hausch, G.: J. Phys. F6 (1976) 1015. Hennion, M., Hennion, B., Nauciel-Bloch, M., Riedinger, R.: J. Phys. F6 (1976) L 303. Jo, T., Miwa, H.: J. Phys. Sot. Jpn. 40 (1976) Kohgi, M., Ishikawa, Y., Wakabayashi, N.: Solid State Commun. 18 (1976) 509. Maeda, I., Yamauchi, H., Watanabe, H.: J. Phys. Sot. Jpn. 40 (1976) 1559. Mikke, K., Jankowska, J., Modrzejewski, A.: J. Phys. F 6 (1976) 631. Muyahara, T., Takahashi, M.: Jpn. J. Appl. Phys. 15 (1976) 291. Muraoka, Y., Shiga, M., Yasuoka, H., Nakamura, Y.: J. Phys. Sot. Jpn. 40 (1976) 414. Ponyatovskii, E.G., Antonov, V.E., Belash, I.T.: Sov. Phys. Solid State 18 (1976) 2131. Soumura, T.: J. Phys. Sot. Jpn. 40 (1976) 435. Takahashi, S., Ishikawa, Y.: Phys. Status Solidi (a) 33 (1976) K 141. Bessmertnyi, A.M., Mushailov, E.S., Pyn’ko, V.G., Suvorov, A.V.: Sov. Phys. Solid State 19 (11977) 1473. Cullis, I.G., Heath, M.: Solid State Commun. 23 (1977) 891. Drijver, J.W., Woude van der, F., Radelaar, S.: Phys. Rev. B 16 (1977) 985. Drijver, J.W., Woude van der, F., Radelaar, S.: Phys. Rev. B 16 (1977) 995. Endoh, Y., Noda, Y., Ishikawa, Y.: Solid State Commun. 23 (1977) 951. Hatta, S., Hayakawa, M., Chikazumi, S.: J. Phys. Sot. Jpn. 43 (1977) 451. Hesse,J., Mtiller, J.B.: Solid State Commun. 22 (1977) 637. Jo, T.: Physica 86-88B (1977) 747. Kagawa, H., Chikazumi, S.: J. Phys. Sot. Jpn. 43 (1977) 1097. Kanamori, J., Akai, H., Hamada, N., Miwa, H.: Physica 91 B (1977) 153. Makarov, V.A., Puzey, I.M., Sakharova, T.V.: Phys. Met. Metallogr. (USSR) 44 (1977) 64. Menshikov, A.Z., Shestakov, V.A.: Phys. Met. Metallogr. (USSR) 43 (1977) 38. Mikke, K., Jankowska, J., Modrzejewski, A., Frikkee, E.: Physica 86-88 B (1977) 345. Mizia, J., Kajzar, F.: Phys. Status Solidi (b) 80 (1977) K 75. Singer, V.V., Radovskiy, I.Z.: Russ. Metall. 1 (1977) 65. Takahashi, S.: Phys. Status Solidi (a) 42 (1977) 201. Takahashi, S.: Phys. Status Solidi (a) 42 (1977) 529. Yamada, O., Ono, F., Nakai, I.: Physica 91 B (1977) 298. Antonov, V.E., Belash, LT., Degtyareva, V.F., Ponomarev, B.K., Ponyatovkii, E.G., Tissen, V.G.: Sov. Phys. Solid State 20 (1978) 1548. Bansal, C.: Phys. Status Solidi (a) 48 (1978) K 119. Billard, L., Villemain, P., Chamberod, A.: J. Phys. C: Solid State Phys. 11 (1978) 2815. Campbell, C.C.M., Schaf, J., Zawislak, F.C.: J. Mag. Magn. Mater. 8 (1978) 112. Hamada, N., Miwa, H.: Progress of Theor. Phys. 59 (1978) 1045. Kim, C.-D., Matsui, M., Chikazumi, S.: J. Phys. Sot. Jpn. 44 (1978) 1152. Kitaoka, Y., Ueno, K., Asayama, K.: J. Phys. Sot. Jpn. 44 (1978) 142. Shirakawa, Y., Tanji, Y.: Phys. and Appl. of Invar Alloys. Honda Mem. SeriesMat. Science3 (1978) 137. Takahashi, M., Kono, T.: Jpn. J. of Appl. Phys. 17 (1978) 361. Takahashi, M., Kadowaki, S.,Wakiyama, T., Anayama, T., Takahashi, M.: J. Phys. Sot. Jpn. 44 (1978) 825. Takahashi, S.: Phys. Status Solidi (a) 45 (1978) 133. Vasil’eva, R.P., Puzei, I.M., Akgaev, A.: Sov. Phys. J. 21 (1978) 383. Wakiyama, T., Brooks, H.A., Gyorgy, E.M., Bachmann, K.J., Brasen, D.: J. Appl. Phys. 49(1978) 4158.

Landolt-BOrnstein New Series 111/19a

Bonnenberg, Hempel, Wijn

2ao 79B 1 79c I 79C2 79Dl 79E 1 79E2 79Gl 79 G 2 79H 1 79H2 79 H 3 7911 7912 7913 79K 1 79M 1 79 M 2 79N 1 790 1 7902 79 0 3 79Rl 79Sl 79s2 7933 79s4 79Tl 79Y 1 79Y2 79 Y 3 80A 1 80Dl 80D2 80D3 80H 1 8011 8OLl 80Ml 80M2 80Nl 8OSl 80Tl SOT2 80T3 80T4 8OYl 81Hl 81 H2 81Kl 8101 8102 8103 8104 81 W 1

Referencesfor 1.2.1 Bansal. C., Chandra. G.: J. Phys. Coil. C 2, 40 (1979) C2-202. Chnmberod. A.. Laugicr. J.. Pcnissan. J.M.: J. Mag. Magn. Mater 10 (I 979) 139. Chikazumi. S.: J. Mag. Magn. Mater. 10 (1979) 113. Deen van, J.K.. Woude van der, F.: Phys. Rev. B20 (1979) 296. Endoh. Y.: J. Mag. Magn. Mater. 10 (1979) 177. Endoh. Y., Noda, Y.: J. Phys. Sot. Jpn. 46 (1979) 806. Goman’kov, V.L., Mokhov, B.N., Nogin, N.I.: Russ. Metall. 4 (1979) 97. Gonser, U., Nasu, S., Kappes, W.: J. Msg. Magn. Mater. 10 (1979) 244. Hamada. N.: J. Phys. Sot. Jpn. 47 (1979) 797. Hamada. N.: J. Phys. Sot. Jpn. 46 (1979) 1759. Hesse.J., Wiechmann. B.?Miiller, J.B.: J. Mag. Magn. Mater. 10 (1979)252. Inone. J., Yamada. H., Shimizu, M.: J. Phys. Sot. Jpn. 46 (1979) 1496. Ishikawa. Y., Onodera. S., Tajima. K.: J. Mag. Magn. Mater. 10 (1979) 183. Ito. Y., Akimitsu. J.. Matsui, M., Chikazumi, S.: J. Mag. Magn. Mater. 10 (1979) 194. Komura. S., Takeda. T.: J. Mag. Magn. Mater. 10 (1979) 191. Matsui. M.. Adachi. K.: J. Mag. Magn. Mater. 10 (1979) 152. Miwa. H.: J. Mag. Magn. Mater. 10 (1979) 223. Narayanasamy, A.. Nagarajan. T., Muthukumarasamy, P., Radhakrishnan, T.S.: J. Phys. F9 (1979) 2261. Ono, F.: J. Phys. Sot. Jpn. 47 (1979) 84. Ono, F.: J. Phys. Sot. Jpn. 47 (1979) 1480. Oomi, G., Mori, N.: J. Mag. Magn. Mater. 10 (1979) 170. Rode, V.E.: Phys. Status Solidi (a) 56 (1979) 407. Sandler. I.M.. Popov, V.P., Nagljluk, Ya.V.: Phys. Status Solidi (a) 55 (1979) 271. Shiozaki. Y., Nakai. Y., Kunitomi, N.: J. Phys. Sot. Jpn. 46 (1979) 59. Skvortsov, 1.1.:Phys. Met. Metallogr. (USSR) 45 (1979) 178. Sohmura. T., Fujita. F.E.: J. Mag. Magn. Mater. 10 (1979) 255. Takahashi. M.. Kadowaki. S.,Wakiyama, T., Anayama, A., Takahashi, M.: J. Phys. Sot. Jpn. 47 (1979) 1110. Yamada. H., Inouc. J., Shimizu, M.: J. Phys. Sot. Jpn. 47 (1979) 103. Yamada. H., Inoue. J., Shimizu, M.: J. Mag. Magn. Mater. 10 (1979) 241. Yamada, O., Nakai. I., Fujiwara, H., Ono, F.: J. Msg. Magn. Mater. 10 (1979) 155. Antonov, V.E., Belash. I.T., Pnomarev, B.K., Ponyatovskii, E.G., Thiessen, V.G.: Phys. Status Solidi (a) 57 (1980) 75. Decn van. J.K., Woude van der, F.: J. Phys. 41 (1980) C l-367. Dubovka. G.T.: Phys. Status Solidi (a) 59 (1980) K 35. Dubinin. S.F., Teplouchov, S.G., Sidorov, S.K., Izyumov, Yu.A., Syromyatnikov, V.N.: Phys. Status Solidi (a) 61 (1980) 159. Hennion. B.. Hennion. M.: J. Phys. F 10 (1980) 2289. Ishikawa. Y., Tajima. K., Noda, Y., Wakabayashi, N.: J. Phys. Sot. Jpn. 48 (1980) 1097. Morin-L6pez, J.L., Falicov, L.M.: J. Phys. C: Solid State Phys. 13 (1980) 1715. Morita. H., Hiriyoshi. H., Fujimori, H., Nakagawa, Y.: J. Mag. Magn. Mater. 15-18 (1980) 1197. Masumoto, H., Takahashi, M., Nakayama, T.: Trans. Jpn. Inst. Met. 21 (1980) 515. Nakai, I., Ono, F., Yamada, 0.: J. Phys. Sot. Jpn. 48 (1980) 1105. Shimizu, M.: J. Mag. Magn. Mater. 19 (1980) 219. Takahashi. S.: Phys. Lett. 78A (1980) 485. Takahashi. S.: Phys. Status Solidi (a) 59 (1980) K 135. Takahashi, M., Kadowaki, S.: J. Phys. Sot. Jpn. 48 (1980) 1391. Tino, Y., Nakaya, Y.: J. Phys. Sot. Jpn. 49 (1980) 2198. Yamada, O., Pauthenet, R., Picoche, J.-C.: C.R. Acad. Sci. Paris, t 291 (1980) SCr.B-223. Harada. S., Sohmura, T., Fujita, F.E.: J. Phys. Sot. Jpn. 50 (1981) 2909. Hayashi. K., Mori, N.: Solid State Commun. 38 (1981) 1057. Kakehashi. Y.: J. Phys. Sot. Jpn. 50 (1981) 2236. Ono. F.: J. Phys. Sot. Jpn. 50 (1981) 2231. Onodera, S.. Ishikawa, Y., Tajima, K.: J. Phys. Sot. Jpn. 50 (1981) 1513. Oomi. G.. Mori, N.: J. Phys. Sot. Jpn. 50 (1981) 2917. Oomi, G.. Mori, N.: J. Phys. Sot. Jpn. 50 (1981) 2924. Wagner. D., Wohlfarth. E.P.: J. Phys. F 11 (1981) 2417.

Bonnenberg, Hempel, Wijn

References for 1.2.1 81Yl 8121 82Bl 82Cl 82Hl 82Kl 8201 8202 82Wl 83Dl 83El 83Fl 83Hl 83H2 8311 83Kl 83K2 83K3 83Ml 83M2 83Nl 83N2 83N3 83Pl 83P2 83Rl 83Tl 83T2 83Yl 8411 84Kl 84Pl 84Vl 84Yl 8511

Land&-B6mstein New Series lll/l9a

281

Yamada, O., Nakai, I.: J. Phys. Sot. Jpn. 50 (1981) 823. Zolotarevskiy, I.V., Snezhnoy, V.L., Georgiyeva, I.Ya., Matyushenko, L.A.: Phys. Met. 51(1981) 191. Brooks, C.R., Meschter, P.J., Kollie, T.G.: Phys. Status Solidi (a) 73 (1982) 189. Cable, J.W., Brundage, W.E.: J. Appl. Phys. 53 (1982) 8085. Ho, K.-Y.: J. Appl. Phys. 53 (1982) 7831. Kakehashi, Y.: J. Phys. Sot. Jpn. 51 (1982) 3183. Ono, F., Yamada, 0.: Solid State Commun. 43 (1982) 873. Orehotsky, J., Sousa, J.B., Pinheiro, M.F.: J. Appl. Phys. 53 (1982)7939 Weissman, J., Levin, L.: J. Mag. Magn. Mater. 27 (1982) 347. Davies, M., Heath, M.: J. Mag. Magn. Mater. 31-34 (1983) 661. Eugen van, P.G.: Thesis, Delft 1983. Fujika, S.: J. Mag. Magn. Mater. 31-34 (1983) 101. Harada, S.: J. Phys. Sot. Jpn. 52 (1983) 1306. Hatafuku, H., Takahashi, S., Sasaki, T., Ichinohe, H.: J. Mag. Magn. Mater. 31-34 (1983) 847. Iida, S., Nakai, Y., Kunitomi, N.: J. Mag. Magn. Mater. 31-34 (1983) 129. Kakahashi, Y.: J. Mag. Magn. Mater. 31-34 (1983) 53. Kakehashi, Y.: J. Mag. Magn. Mater. 37 (1983) 189. Kress, W., in: Landolt-Bornstein, NS, (Hellwege, K.-H., Olsen, J.L., eds.), Berlin, Heidelberg, New York: Springer, vol. 111/13b(1983) 259. Mori, N., Ukai, T., Oktsuka, S.: J. Mag. Magn. Mater. 31 (1983) 43. Morita, H., Tanji, Y., Hiriyoshi, H., Nakagawa, Y.: J. Mag. Magn. Mater. 31-34 (1983) 107. Nakai, I., Yamada, 0.: J. Mag. Magn. Mater. 31-34 (1983) 103. Nakai, I.: J. Phys. Sot. Jpn. 52 (1983) 1781. Nakai, I., Ono, F., Yamada, 0.: J. Phys. Sot. Jpn. 52 (1983) 1791. Pauthenet, R., Maruyama, H.: J. Mag. Magn. Mater. 31-34 (1983) 835. Pierron-Bohnesn, V., Cadeville, M.C., Gautier, F.: J. Phys. F 13 (1983) 1689. Rode, V.E., Olszewski, J., Plevako, T.A., Kavalerov, V.G.: J. Mag. Magn. Mater. 31-34 (1983) 99. Takahashi, S.: J. Mag. Magn. Mater. 31-34 (1983) 817. Tanaka, T., Takahashi, M., Kadowaki, S., Wakiyama, T., Watanabe, D., Takahashi, M.: J. Mag. Magn. Mater. 31-34 (1983) 843. Yamada, O., Ono, F., Nakai, I., Maruyama, H., Ohta, K., Suzuki, M.: J. Mag. Magn. Mater. 31-34 (1983) 105. Ishio, S., Takahashi, M.: J. Mag. Magn. Mater. 46 (1984) 142. Koike, K., Hayakawa, K.: Jpn. J. Appl. Phys. 23 (1984) L 85. Preston, S., Johnson, G.: J. Mag. Magn. Mater. 43 (1984) 227. Victora, R.H., Falicov, L.M.: Phys. Rev. B30 (1984) 259. Yamada, O., Du Tremolet De Lacheisserie, E.: J. Phys. Sot. Jpn. 53 (1984) 729. Ishio, S., Takahashi, M.: J. Mag. Magn. Mater. 50 (1985) 271.

Bonnenberg, Hempel, Wijn

1.2.2 Alloys between Ti, V, Cr, Mn

282

[Ref. p. 480

1.2.2 Alloys between Ti, V, Cr or Mn 1.2.2.0 General remarks In this subsection magnetic properties of binary alloys between Ti, V, Cr or Mn are representedwhile in the following one, subsection 1.2.3,binary alloys of Ti, V, Cr or Mn and Fe, Co, or Ni are dealt with. The latter subsection also includes magnetic data on V-Cr-Mn and the pseudo-binary alloys ofTi, V, Cr or Mn and Fe, Co or Ni in which one the 3d transition metals is partially substituted by a third 3d metal. The data is compiled in figures and tables. Referenceshave been made to the main papers that appeared before 1975.For the time from 1975to 1983,about 80% of the relevant papers cited in the Chemical Abstracts have been selectedfor quoting important and reliable properties of the alloys under discussion. For each alloy system a chronological listing of relevant referencesprecedesthe representation of the data. These lists also include rcfcrcnces to papers not cited subsequently in the figures and tables. The complete list of referencesis provided at the end of subsection 1.2.3. The arrangement of the alloys is in the order of increasing atomic numbers of their constituent elements.Each of the following subsections is devoted to a particular binary alloy between Ti, V, Cr or Mn. For details, see Survey 1. Since figures and tables for a given material may contain also data of other alloys for comparison, information on a particular alloy may be found in the other subsections as well. The retrieval of such scattered information is facilitated by Survey 2 which provides all the figures and tables in which, for a given alloy and property. data is represented.

Survey 2. For each binary alloy between Ti, V, Cr or Mn the figures and tables are listed in which data on the properties specified is provided. Referenceis given not only to subsect. 1.2.2(Figs. 1...58 and Tables 1...12) but also to subsect.1.2.3(Figs. 59...427 and Tables 13...88). Numbers in roman and italic refer to figures and tables, respectively. Allo)

Phase diagram. lattice constants

Susceptibility, paramagnetic properties

V-Ti

1

2...4

I 311,312

11 I 3, 13, 14, 101, 102

Cr-Ti Cr-V

Mn-Ti Mn-V

25,311

Mn-Cr ‘)

35,41,311

Magnetization, average magnetic moment

Atomic magnetic moments, g-factor, spin structure

15...17

20

2, 9, 74

2,3, 74

19, 21, 47, 49, 264, 266 2, 3, 9, 10, 74

Magnetic transformation temperatures

12

6

3, 26...29 7 36,..39, 41, 101, 162, 224

‘) Young’s modulus: Fig. 39.

166, 227 6, 7 15, 40, 42, 43, 162, 166, 227 2, 6, 8, II, 12, 39, 74

30,31 20, 42.. .45 2

19, 21, 46...49, 264, 266 2, 9...12, 74

Ref. p. 4801

1.2.2 Alloys between Ti, V, Cr, Mn

283

Survey 1. The subsections devoted to the binary alloys between Ti, V, Cr or Mn are given, as well as information on atomic ordering and crystallographic phases considered. dil: dilute alloy, diso: disordered alloy, (3: 1): Cu,Au-type superlattice, (1: 1): CuAu-type super-lattice,(l/l): CsCl-type compound, (cr):o-phase, (L): Laves phase.

Ti V Cr

Mn

Ti

V

1.2.2.1 diso 1.2.2.2 dil diso (L) 1.2.2.4

1.2.2.3 dil diso

(4,(L)

High-field susceptibility

NMR, Mijssbauer effect

5, 8, 9

1.2.2.5 dil diso O/l)

Spin waves, exchange

Cr

Mn

1.2.2.6 dil diso, a-Mn bee, y-Mn

Magnetic anisotropy, magnetostriction

-

Specific heat, thermal expansion

Alloy

5...7, 10 5

V-Ti Cr-Ti

5, 8, 18, 22, 23

5, 10, 17, 24

4

5 Mn-Ti Mn-V

5, 32...34, 179 50

Landolt-Bbrnstein New Series 111/19a

5, 51.e.56, 179, 318 II

Cr-V

57, 58 5

Mn-Cr ‘)

284

[Ref. p. 480

1.2.2.1 V-Ti

“C

kl

V-Ti

1

1

( 600

\

200

II-

dhcp)’

sod ’ 0

I

I

10

a Ti

\

I

‘1 0

5

\ \

15 ot%

20

v-

0 b Ti

4

8

J 12 at% 16

v-

Fig. 1. (a) Equilibrium phase diagram for V-Ti alloys [QAI]. (b) Noncquilibrium phase diagram for V-Ti quenched from the elevated-tcmpcraturc, bee phase to the temperature indicated on the scale [53 D 1, 75C23. M, and M, indicate the start and the end of the martcnsitic transition. respectively.

3.0 .lG-'

1.95 xl 4 cm3 mol

Cm! TiT" .,

I

/

1

Ti- lSat%V

I

2.4

1.85

I

r:

2s

v a-Ti

6

1.80

1.8 1.5 0 a 11

20

40

60 v-

80 ot% 100 V

Fig. 2a. Room-tempcraturc magnetic molar susceptibility xrn for V-Ti alloys qucnchcd from about 1000“C into iced brine [75 C 23.

1 b

IO

102 h

10:

4 -

Fig. 2b. Variation of the room-temperature magnetic molar susceptibility I,,, for Ti-15 at% V as a consequence of annealing the alloy for various times t, at 300 “C (open symbols). Solid circles: various samples quenched from about 1000“C into iced brine [75 C 23.

Adachi

Ref. p. 4801

285

1.2.2.1 V-Ti

V-Mn

\ 10-3 c

104

1 4 -

10

3.0

IO3 h IO4

IO2

Fig. 2c. Variation of the room-temperature magnetic molar susceptibility x,, for Ti-19at%V [75C2]. Open symbols: aging results for four samples. Solid circles: various samples quenched from about 1000°C into iced brine. Solid square: P-Ti [72 C 11.

’

2.5

\40

2.0 0 V

5

. \I

v-co I V-Ni

IO 15 Impurity -

20 at%

25

Fig. 3. Magnetic molar susceptibility x,,, at 20 K for solid solutions of 3d elements in V [63 C 31.

.--I V-Ti

I

1

1

,k---PTi

1.4

;; 1.3 0 R Ix 1.2 -& 1.1 1.0 0.9

Fig. 4. Temperature dependence of the relative magnetic susceptibility for V-Ti alloys [62T 11. The broken line represents data of McQuillan and Evans (1960) for Ti. Landolf-BCi’msfein New Series 111/19a

Adachi

1.2.2.1 V-Ti

286

‘i 3d alloys ‘r

[Ref. p. 480

- 60 w

col

molK2 50 0 - 40 0 *b S5Plrl 5’v 0.

0 0

>

-

Y

x

-30 I x - 20

- 10 25

4

V 5

Cr 6

0 Mn 0

1

I 20

10

I 30

I 40

I 50

I I 60 K2 70

12-

t-l-

Fig. 5. Nuclear spin-lattice relaxation time 7” (expressed as its product with temperature T) for paramagnetic V-Ti. Cr-V and Mn-V alloys and antiferromagnetic Mn-Cr alloys. Also given is the electronic spccitic heat coeflicient 7 [73T I]. “Mn in (open circles) Mn-Cr [73T I] and (solid circles) Mn-V [7l M I]. “V in (crosses) hln-V [71 M I] and (triangles) V-Ti [64 M 3, 64 K 21 and Cr-V [64 B I]. Solid line: y [60 C 3,62 C I]. n: average number of 4s and 3d electrons per atom.

Fig. 6. Specific heat divided by temperature, C,/T, vs. the square of temperature, T*, for bee V-Ti alloys [62 C I].

I

I

-4.0

4.5

l-l’ Ti Fig. 7. Electronic specific heat coefticient y for bee V-Ti alloys [62 C I].

I

I

16

5.0 n-

5.5

0 6.0

Fig. 8. Nuclear spin-lattice relaxation time Tr for ‘IV in V-3d transition metal alloys and the density of states at the Fermi surface IV(&), as dependent on the average number of4s and 3d electrons per atom, n, [64 M 33; the experimental data for Cr-V alloys are from [64 B I].

Adachi

Ref. p. 4801

1.2.2.2 Cr-Ti

287 x in Ti Fe~.,Co,-

0.7 % V-Ti Cd

K*mol

0

20

Ti

LO

60

80 at%

v-

IO

100 V

Fig. 9. Knight shift K for 51V in bee V-Ti alloys at room temperature [62 V 21.

0

I V

5

1 Cr 6

I Mn 7

I Fe 8

I co 9

n-

Fig. 10. Electronic specific heat coefficient y of 3d transition metal alloys vs. the average valence electron (4s 3d) concentration per atom, n, [68 B 11. x corresponds to compositionin TiFe, $0,. Dashed line: bee Ti-V, V-Cr, Cr-Fe and Fe-Co alloys, solid line: Fe-Co-Ti and CoNi-Ti alloys [62 S 2, 60 C 2, 62 C 11.

1.2.2.2 Cr-Ti References:68 A 2, 71 C 2. 3.35 @ ‘i$ cm3 Y 9

e

Cr-Ti

330.3 K

5.8

K I

I 3.25

z

x” 3.20 3.15

3.20

3.10

3.15 t 0, 3.10H

0 a Cr 125 K

I

/

270.4 I e 221.4

e 5.6

3.30 D” -cm3 9

e 5.1 efr*

3.05

0.2

0.1, Ti -

0.6

181.3 0.8 at% 1.0

t 120 z 115

3.00 (((111112.95 0 50 100

150

200

250

300 K 350

b

T-

Fig. 11. Magnetic mass susceptibility xs vs. temperature for Cr-Ti alloys [71 C 21.

Landolt-Bornctein New Series 111/19a

Cr

Ti -

Fig. 12. Neel temperature TN(a) and spin-flip temperature T,, (b) vs. composition for Cr-Ti alloys. Cr : TN= 311 K [71 C2].

Ada&i

Ref. p. 4801

1.2.2.2 Cr-Ti

287 x in Ti Fe~.,Co,-

0.7 % V-Ti Cd

K*mol

0

20

Ti

LO

60

80 at%

v-

IO

100 V

Fig. 9. Knight shift K for 51V in bee V-Ti alloys at room temperature [62 V 21.

0

I V

5

1 Cr 6

I Mn 7

I Fe 8

I co 9

n-

Fig. 10. Electronic specific heat coefficient y of 3d transition metal alloys vs. the average valence electron (4s 3d) concentration per atom, n, [68 B 11. x corresponds to compositionin TiFe, $0,. Dashed line: bee Ti-V, V-Cr, Cr-Fe and Fe-Co alloys, solid line: Fe-Co-Ti and CoNi-Ti alloys [62 S 2, 60 C 2, 62 C 11.

1.2.2.2 Cr-Ti References:68 A 2, 71 C 2. 3.35 @ ‘i$ cm3 Y 9

e

Cr-Ti

330.3 K

5.8

K I

I 3.25

z

x” 3.20 3.15

3.20

3.10

3.15 t 0, 3.10H

0 a Cr 125 K

I

/

270.4 I e 221.4

e 5.6

3.30 D” -cm3 9

e 5.1 efr*

3.05

0.2

0.1, Ti -

0.6

181.3 0.8 at% 1.0

t 120 z 115

3.00 (((111112.95 0 50 100

150

200

250

300 K 350

b

T-

Fig. 11. Magnetic mass susceptibility xs vs. temperature for Cr-Ti alloys [71 C 21.

Landolt-Bornctein New Series 111/19a

Cr

Ti -

Fig. 12. Neel temperature TN(a) and spin-flip temperature T,, (b) vs. composition for Cr-Ti alloys. Cr : TN= 311 K [71 C2].

Ada&i

Table 1. Crystal and magnetic properties of Lavcs phase compounds. P: Pauli paramagnetism, F: ferromagnctism, AF: antiferromagnctism, x,,,: susceptibility per mole, Tc and TN:Curie and N&cl temperatures, respectively, pco: magnetic moment per Co atom, H,,,: hypcrfine magnetic field for 57Feobtained from Miissbaucr effect measurements. NiTi, and CoTi, were reported to have a cubic Laves structure [63 n I, p. 1461 but the magnetic properties are unknown. Crystal ‘) structure

a ‘)

c ‘)

A Ni,Sc co,sc Fe,Sc Mn,Sc Co,Ti co 2.13Ti0.87 Fe,Ti

MgCu, MgCuz MgNi, WW MD, MgNi, MS&

Cr,Ti ‘) [63n 1, p. 146).

xmW)

G

10-4cm3mol-’

K

6.926 6.921 4.972 5.033 6.706 4.729 4.779

16.278 8.278 15.41 7.761

P [69C l] P [69C I] F [64N I] P [70B2] AF [66A 1, 68N l] F [66A 1, 68N 13 AF [64W3]

0.76 6.95

6.493

-

P [68A2]

5.16 4.17

44

TN

pco

F,yp,F,W

PB

kOe

K)

202 [64N l] 43 0.12 273 97.3 [64Nl]

Remarks

NMR [66B2] NMR [66 B 21

InT,-,Fe,+,,AFforxO r68 N 21 resistivityC69 I 1, 71 I 1, 721 11, thermal expansion [66 G 11, specific heat [67 w l]

Ref. p. 4801

289

1.2.2.3 Cr-V

1.2.2.3 Cr-V References: 58 L 1,60 C 1,61 V 1,62 C 1,62 T 2,62 V 2,64 B 1,64 K 2,64 M 3,65 H 1,65 K 1,65 M 1,66 B 1, ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3.2 w4 cm3 mol 2.8

1.6 I

0 1.2 0 V

20

40

60

80 at% 100 Cr

Cr-

Fig. 13.Magnetic molar susceptibility x,,, at 20 K for Cr-V alloys prepared from V and Cr originating from various sources [60 C 11. Crosses: x,,, at 100 K [58 L 11.

600,

I

I

I

I

I

I

I

I

50

100

150

200

I

I

250 K 300

Fig. 14. Magnetic mass susceptibility xs vs. temperature for Cb.95Vo.05 and (Cro.9~Vo.o~)o.99Coo.o~ alloys [77A2].

I

250 I 200 h'

I 3001 I

2001

A

I

\\I

150

\ I

100

100II

ii*0

dew

50

i;),

1 s*o \

0 -v

1.0 at%

0.5

Mn-

fr

Fig. 15. Magnetic phase diagram of Cr-V and Cr-Mn alloys [65 H 11, see also [66 B 11. To: transition temperature from incommensurate to commensurate structure (see Fig. 19), T,,: spin flip transition temperature horn longitudinal (L) to transverse (f) spin density wave (SDW) state, 6 = 0: commensurate phase, 6 $0: incommensurate phase, P : paramagnetic, AF: antiferromagnetic. Landolt-BHnstein New Series lll/l9a

0

3

v---b

Fig. 16. Neel temperature TN deduced from electrical resistivity minima for Cr-V alloys. Open circle: [64 K 21, solid circles: [62 T 21.

Adachi

[Ref. p. 480

1.2.2.3 Cr-V

290 400 K

3.0 mJ molK2

33C

2.5

I_2Of

1OC

c Cr

v-

Gg. 17.Neel temperature TNofCr-V alloys, defined as the cmperature where the rcsistivity shows a minimum. Also ,hown is the linear specific heat coefficient y [80T 21.

Fig. 18.NMRspin-echo spectra for 5’V in the spin density wave state of Cr-V alloys, obtained at 10 MHz and I .4 K [75 K 1-J.

I 0.8

g 0.6 9 (?*=m)

AF 0.4

0.2 0

a Cr

Fig. 19.Spin structure ofCr and Cr-based alloys: TSDW: transverse spin density wave (incommensurate). LSDW: longitudinal spin density wave (incommensurate), AF: ordinary antifcrromag.nctic structure (commensurate), I.: wavelerqth of SDW (/.=2x!@, cf. caption to Fig. 21.

1

2

3 4 Impurity -

5 at%

6

Fig. 20. Maximum magnetic moment per atom for Cr alloys at 77 K containing V, Mn, Fe, Co and Ni impurities C68El-J.

291

1.2.2.3 Cr-V

Ref. p. 4801

Table 2. Neel temperature TN, average magnetic moment per atom, J?,and wavevector Q of the spin density waves in Cr-V and Cr-Mn alloys at 77K [67 K 11.

1.00

v 0.99

Mn

at % Cr’) Cr-V

0.98 I co

Cr-Mn

L 0.97

0.45 1.00 -

0.70 1.85

TN

p

K

PB

QaPn

310 0.40(2) 0.9518 268(5) 0.36(3) 0.9431(25) 220(5) 0.28(3) 0.9300(25) 440(5) 545(5)

‘) [62Wl]. 0.96

0.95

0.94

3

2

1

c!

It at%

5

Impurity -

Fig. 21.Variation of 1- 6 for Cr alloys containing V, Mn, Fe, Co and Ni impurities at TN(dashedcurve) and at 0 K (solid curve) [68E 11. The satellite of the magnetic reflection appearsat 5 (1k 6,0,0), etc.The wavelengthof a

the SDW is A=~Tc//~,seeFig. 19.

Table 3. Spin density wave properties of Cr-V alloys in comparison with Cr: spin density wavevector Q, wavelength of antiferromagnetic modulation, 1, and average (rms) magnetic moment per atom, p. V at%

Cr 0.45 1 1.9

QaPn

PB

78K

197K

78K

197K

OK

0.9519 0.9431 0.93

0.9554 0.9480

20.8 ‘) 17.6(8) 13.2

22.4(8) 19.2(8)

0.40(2)“) 0.36(3)

‘) [62S3]. ‘) [62 W 11. 3, Room temperature.

Landolt-Bbmstein New Series lWl9a

Ref.

P

ala

Adachi

78K 0.35(3) 0.28(3)

197K 0.26(3) n

siteIII

7= UK

T = 42 K site IY

r\

1 at% Fe

I

20

30

40

50

60

70 MHz

IO

5

15

Y-

180

I

I

25

30 MHz

/

I

t I

20 Y-----c

r sitelI

50

site Ill I + = s

40

P

P

* 30 fl 20 a e Mn

5

III

15 Fe,Ru -

Fig. 174. (a.. .d) Line shapes of NMR spin-echo spectra of 55Mn in a-Mn-Fe alloys at 4.2K on the four different crystallographic sites (I...IV) of Mn [74K 11. For their definition, see Fig. 46. See also Table Il. (e) Magnetic hyperfine field Hhyp of 55Mn at 4.2K for the crystallographic sites I, II and III derived from sublattice NMR spectra for a-Mn-Fe and wMn-Ru alloys [74 K 11.

Landolt-BBmstein New Series 111/19a

Adachi

cc-Mn-Ru 0 a-Mn-Fe I I 20 25 at% 30

l

[Ref. p. 480

1.2.3.4 Fe-Mn

p-Mn-Fe I I

I

Fe -

&r

Fig. 175. Average hypcrfinc field f7,,, at site I for “Fc in P-hln-Fe alloys [77 N I]. T=4.2 K: Fig. 176. Magnetic hypcrfinc field Hhgp derived from “Mn Miissbaucr expcrimcnts, as dependent on impurity concentration for b-Mn alloys with Fe, Co and Ni impurities. The quantity An, is the impurity concentration, multiplied by the difference in the number of 3d electrons between the impurity atom and Mn [74K2]. T= 1.4K.

240 MHz

53 r

kCle

220

ul -

200

I a 30 f

-

2 20 10

0

50

100

150

200

250

300

1\ 350 K 400

I-

180 1 c 5 160 s lb0 120 100

Fig. 177.Temperature depcndcncc ofthc magnetic hypcrtine fields Hhjp as derived from Miissbaucr resonance experiments on “Fe in hcp and fee Fe-Mn alloys [7lO I,

80 0

68121.

100

200

300

LOO 500 I-

600

Fig. 178.Temperature dependence ofthe NMR v, in zero applied magnetic field for Fe o.996Mno.oo4. vJ4.2 K)= 239.42 MHz Hhyp=225.5(5)kOe at “Mn in Fe,.,,,Mn,,,,,

Adachi

700 K I390

frequency “Mn in [74 K 33. [64K I].

371

1.2.3.4 Fe-Mn

Ref. p. 4801

0

y

Fe-Mn

zI -0.1 c; 2

-0.2 ,’

/

/' /. 0 ,/

-0.3 0.2 I -mm s

-----_

0

2% 0.1 c, Q E3

0 0 Fe

20 at% 30

10 Mn -

Fig. 180.Electric quadrupole shift dQ and isomershift IS, relative to bee Fe, for “Fe in hcp and feeFe-Mn alloys [710 11.Seealso Table 42. 3 at% 2

1 0 -Impurity-

1

2

3

4 at% 5

Fig. 179.Shift Av ofthe NMRfrequency for 55Mn at site I asdependenton impurity concentration of a-Mn alloys at 4.2K [74K 11.

Table 42. Magnetic properties of hcp and fee Fe-Mn alloys [710 11. Isomer shift IS, relative to bee Fe, quadrupole shift dQ and hyperfine magnetic field H,,,,r for 57Fe, extrapolated to OK. p: average sublattice magnetic moment per atom, TN: NCel temperatur, x,. . magnetic molar susceptibility at RT. Mn at%

Lattice structure

TN K

17.8 25.9 28.6 25.9 28.6

hcp hcp hcp fee fee

230 230 230 400 420

P PB

0.25 2.0 ‘)

Xm 1Om6cm3mol-l

KJ5’W kOe

dQ

556 528 734 930

1613) 16(3) 16(3) 38(3) 41(3)‘1

0.12 0.13 0.15 0.0

‘) [6711].

Landolt-BOrnstein New Series 111/19a

Adachi

mms-’

IS mms-’ - 0.05 -0.05 -0.01 -0.03

[Ref. p. 480

1.2.3.4 Fe-Mn

372

Table 43. Average magnetic hyperfine fields I?,,, derived from Miissbauer spectra for “Fe and “‘Sn in P-Fe-Mn-Sn alloys at 4.2 K [77 N 11. R,,,(57Fe)

X

A,,,(’ ’ gSn)

kOe Fe,Mn,-,

0.02 0.05 0.10 0.15 0.20

s" 100

p

YP

AL

A

75 50 10

a

A

Mn

20 co -

30 ot% 40

20

300~% 10

35 kOe 3c T= L.2K

I

30

60 90 1' -

120

150 MHz180

Fig. 236. Line shapes of “Mn and 59Co NMR rcsonancc spectra for fl-Mn--Co alloys at 1.4K. The scales of the intensities arc different for both nuclei [74 K 21.

0 b

Impurity-

Fig, 237. Magnetic hypcrfinc field, Hhyp, at 4.2 K derived from NMR experiments [74K 23. (a) For s9Co in fi-Co--Mn alloys, (b) for “Mn in p-Mn-based alloys.

1.0

I

10

0.8

2 0.6 z x ‘;10.4 t 0.2 . fee Co-O.Eot%Mn 0 bee Fe-O.4ot% Mn

0

0.2

0.4 7/r, -

0.6

0.8

Fig. 238. NMR frequency v, normalized to the frequency at 4.2 K for 55Mn in fee Co-O.8at% Mn and bee Fe0.4at% Mn. Also are shown the temperature dependcnccs of the reduced spontaneous magnetizations uJu(OK) of fee Co and bee Fe [74 K 33.

Ref. p. 4801

1.2.3.8 Co-Mn

399

-340 kOe I -350 c 25 w 12-360

-370 0 co

2.5

5.0 Mn-

7.5at%lO.O -

Fig. 240. Mean hyperfine field Hhypfor 55Mn in Co-Mn alloys at 1.6K [73 Y 11. 320

330

X0

350

360

370

380

Fig. 239. Spin-echo NMR spectra for “Mn alloys at 1.6K [73 Y 11.

MHz J+

in Co-Mn

375.0 MHz

I’

372.5 t 370.0 c z 367.5 w x 365.0 362.5 360.0 357.5

0 5

10

15 kOe 20

HOPPl -

Fig. 241. Spin-echo NMR frequency for “Mn in co 0,95Mn,,,, at 1.6K as dependent on an applied field. The straight line is drawn according to the relation: WAK,,, = - 1.05MHz/kOe [73 Y 11.

New Series lll/l9a

50

100

150 T-

200

250 K

Fig. 242. Temperature dependence of the NMR tiequency v, for 55Mn in fee Co-O.8at% Mn in zero applied magnetic field. HhYP=- 358.3(5)kOe at 4.2K [74K 31. Hhyp= - 357.52(15)kOe for 52Mn in fee Co at 1OmK [78Z 11.

Adachi

[Ref. p. 480

1.2.3.8 Co-Mn

400 80

I

P

PS p-Co-Mn 70.

I

I

l=l.bK 60

I

50

2 LO CT P 30

20

10

0 Mn

10

20 co -

3Ool%

LO

Fig. 243. Transverse or spin-spin relaxation time T, of “Co in P-Co--Mn alloys at 1.4K [74K 21.

1.5

JO” erg

mJ

cm?

K2%

5 I1

6.5

I 6.0 x 5.5

5.0

LO

80

120

160 rw

200

260

280 K 320

4.5 4.0

Hexagonal first order magnctocrystallinc anisotropy constant K, vs. tempcraturc for Co alloyed with small amounts of 3d transition elements. Measuring field strcncgth H,,,, =32kOe [64C I]. Fig.

244.

2

I

6 Impurity-

8

10 ot%

12

Fig. 245. Electronic specific heat coefficient 7 for Co alloyed with 3d transition elements [80G I].

Ref. p. 4801

1.2.3.9 Ni-Ti

Ti

Ni IO I

1800° “C

20 11

30 I

40 ,

Ni 50 I

60 I

70 I

80 wt% 90 I I

Ni -Ti

1720°C

1600

I 500 1153'C

1400 4

1300 a7.5)

1200

lot% 1100

800

600 500 0 Ti

IO

20

30

40

50 Ni -

60

70

80

90 at% 100 Ni

Fig. 246. Phase diagram of Ni-Ti alloys [SSh 1, p. lOSO]. Temperatures, in PC], and composition, in [at% Nil, and, in parentheses, in [wt% Nil, are given for special points of the phase diagram.

Landolt-BOrnstein New Series 111/19a

Ada&i

402

[Ref. p. 480

1.2.3.9 Ni-Ti 635 K 620

I 605 L-Y 590

560 0

0.5

1.0 Ti -

1.5 ot% 2.0

Fig. 247. Fcrromagnctic Curie tempcraturc Tc of NipTi alloys. derived from resistivity measurements[78 Y I]. Open circles:maximum in dc/dTand solid circles:“kinkpoint” technique.

Table 55.Change of the averagemagnetic moment per atom: pat,and of the Curie temperature Tc of Ni-3d transition metal alloys. x: impurity concentration. Impurity

Table 56. Mean magnetic moment per atom. j,,. for Ni-Ti alloys, as derived from saturation magnetization measurements at 4.2 K in fields up to 30kOe [75 G 11.

Mn

o... 5

Cr

o... 10

V Ti

O...lO 0...15

0.616 ‘) 0.528 0.404 0.329 0.271 0.203 0.149 0.103

dTc/dx K

dL,ldx PB

f2.4 +2.8 -4.4 -6.0 -5.2 -4.0

[32 S l] [62V l] [32 S l] [62V 1) [32S l] [32 S l]

- 11.0(5)[37 M l] -35

[37 M l]

-55(3) -21

[37 M l] [37 M l]

Table 57. Magnetic moment distribution for Ni-Ti alloys. P,,: average magnetic moment per atom derived from magnetization measurements in a field of 13kOe. PNiand pri: averagemagnetic moments of the Ni and Ti atoms, respectively, as derived from elastic diffuse scattering of polarized neutrons at room temperature [79 K 141.Magnetic moments in

Ni 2 4.8 6.1 8 10 12 14

x at%

bB1.

Ti at%

3.87 7.72

Pat

Ph’i

hi

RT

1

3.537 3.551

‘) [71 c43.

Adachi

RT

4.2 K

RT

0.383(5) 0.185(S)

0.444(5) 0.267(6)

0.402(7) 0.21(l)

- 0.08(2) -0.09(4)

403

1.2.3.9 Ni-Ti

Ref. p. 4801

0 i

nucleus Ni

nucleus Ni

:fi nucleus Ni

b

a

Fig. 248. Magnetic moment distribution in (a) the (100) plane and (b) the (110) plane of y-phase Ni,.,,Ti,,,,, obtained from polarized neutron diffraction scattering. At room temperature the average magnetic moment per atom is: &,=0.505(5)pr,. Localized 3d-moment of Ni atoms: pNi 3dx 0.595(3) un. Localized 3d-moment of Ti atoms : p:p z 0.05(20) us. Nonlocalized moment per atom : PnlN - -O.O78(8)un. Proportion of electron spins in E, orbitals: y = 0.203(5) [76 L 11.

-0.2 0 Ni

2

4

6 Ti -

8

10 at%

12

Fig. 249. Mean atomic moment per atom for Ni-3d transition metal alloys at 4.2 K as derived from magnetization measurements in magnetic fields up to 30 kOe [75 G 11.

0

4

8 Impurity

12 -

Eat%0

Fig. 250. Magnetic moment distribution for Ni-Ti alloys

at room temperature [79K 141. Open circles: magnetization measurements [37 M 11, open triangles: [79K 141, solid circles and open squares: neutron measurements: [79 K 141, solid triangle: [66 M 11.

Landolt-Bbmstein New Series lWl9a

Adachi

404

[Ref. p. 480

1.2.3.9 Ni-Ti Table 58. Electronic and lattice contributions, y and /?,respectively, to the molar specific heat of Ni-3d transition metal alloys in the temperature range 1...4 K [75 G 1). X

Ni, -$rr

Ni, -IV,

Ni, -,Ti,

Ni

0.005 0.01 0.02 0.035 0.17 0.30 0.005 0.0115 0.02 0.035 0.0507 0.0511 0.0685 0.073 0.08 0.09 0.094 0.10 0.11 0.116 0.15 0.18 0.02 0.048 0.067 0.08 0.10 0.12 0.14

Y

P

mJmol-’ Km2

mJ mol-’ Km4

7.287(2) 7.544(2) 7.989(2) 8.585(2) 7.389(2) 6.950(2) 7.203(2) 7.404(2) 7.641(2) 8.033(1) 8.277(2) 8.288(2) 8.390(2) 8.405(2) 8.652(3) 8.996(2) 9.344(2) 9.967(8) 9.992(9) 8.065(13) 4.789(1) 3.867(1) 7.453(2) 7.853(2) 7.972(2) 7.975(2) 8.154(2) 8.183(2) 8.219(10) 7.034(3)

Ada&i

0.0202(2) 0.0204(2) 0.0207(3) 0.021l(2) 0.0178(2) 0.0173(2) 0.0203(2) 0.0208(3) 0.0208(2) 0.0212(2) 0.0247(2) 0.0242(2) 0.0270(3) 0.0268(3) 0.0254(3) 0.0230(3) 0.0179(2) 0.0053(5) -0.0104(5) 0.0033(6) 0.0169(2) 0.0161(2) 0.0195(2) 0.0224(2) 0.0226(2) 0.0257(3) 0.0264(3) 0.0181(2) 0.0157(5) 0.0222(3)

405

1.2.3.10 Ni-V

Ref. p. 4801

Ni I.. 2ooo”

"'

V

v-

I’!

20 I

30 I

40 I

50 I

60 I

70 I

1900125)"1

Ni-V

1800

L--. .--

I

P

.g--._N

1600

=-

1453°C

1400

80wt%90 I I

z > 1

-J

1 / / +/

/

’

//

/:

I

I

?-

/’ x127OT /-47nj/UY.bl

Ni

?

141.31 151,5wt”/o/.)V

I 890 ‘C i.21 ’

\ I

1

17

Iv

6’ \ %:7

?I

I ?? I

I

1

1

0 Ni

IO

20

1

I

I

?

1 I i i/ II

30

40

50 v-

60

70

80

90at % 100 V

Fig. 251. Phase diagram ofNi-V alloys [58 h 1, p. 10561. Temperature, in c”C], and composition, in [at% V], and, in parentheses, in [wt% V], are given for characteristic points of the phase diagram.

I C

Fig. 252. Crystal structure of o-phase materials [54 B 11. The unit cell is composed of 30 atoms with five kinds of sites. Elements V, Cr and Mn prefer to occupy position M’,while Fe, Co and Ni prefer position M. M or M’means sites of mixed occupation.

Landolt-Biirnstein New Series 111/19a

Adachi

I I/

406

1.2.3.10 Ni-V

[Ref. p. 480

H”

.

1,

c-phase

.

co-v 00 co-v

2

. Co-Cr A Ni-V

0 6.0

I

6.3

6.6

6.9

I.2

1.5

Fig. 254. Paramagnetic susceptibility vs. average number n of4s and 3d electrons ncr atom for o-chase NT-V. Co-V and Co-0 alloys at room tempcratuie [69 M 21.’

J

6% K

11.0 mJ K2mol 10.5

550

I 153 Q 10.0

9.0

253 Ni

1i.V -

8.5

Fig. 253. Efkctive paramagnctic moment per atom. pcrr, and the paramngnctic Curie tcmpcraturc 0 for Ni alloys with small V and Ti concentrations [36 M I].

8.01 0

3

6

,L+

12

15 K2 18

Fig. 255. Tcmperaturc dcpcndencc ofthe specific heat C, of Ni ,,ssaV,,, t6 for various magnetic fields H,,,,. Since C,/T is plotted vs. T2 the curves can give an indication of the magnitude of the electronic specific heat coefficient [77 B 11.

Table 59. First-order magnetocrystalline anisotropy constant K,, and linear magnetostriction constants i.,,, and I., , I for Ni-Cr and Ni-V alloys [60 W 11. X

Ni Ni, -&rx 0.0147 0.0252 0.0408 Ni,-,V, 0.0128 0.0295 0.0393

K, 104ergcmm3

16100 10-6

300 K

300 K

-4.9 -1.1 -0.38 0 - 2.4 -0.73 -0.28

77K -73 -27 -17 - 6.5 -36 -18 -13

-55.8 -44.6 - 34.8 -20.6 -43.0 - 29.6 - 19.1

Adachi

1bill 10-6

3‘100

10-6

1 ‘1 11

10-6

77K -29.5 - 19.6 - 14.2 - 7.9 -21.0 - 13.4 - 6.5

-58 -46 -43 -35 -51 -39 -34

-37 -26 -21 -17 -29 -22 -15

Ref. p. 4801

1.2.3.10 Ni-V

407

Table 60. Specific heat parameters for fee Ni-Mn and fee Ni-V alloys, according to the equation C, = A + yT. Also the Debye temperature On is given [64G 11. X

Ni, -xMnx 0.20 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.30 0.40 0.60 0.75 Ni, -xV,

0.09 0.18 0.28 0.35 0.35 0.40

Landolt-Bbmstein New Series IIl/19a

Heat treatment

quenched from 11oo”c quenched from 11oo”c quenched from 11oo”c quenched from 1100“C quenched from 1100“C quenched from 1000“C and 2 h at 485°C quenched from 1000“C and 2 h at 485 “C quenched from 1000“C and 2 h at 485 “C quenched from 1100“C and 2.5 h at 535°C quenched from 11oo”c quenched from 1000“C quenched from 980 “C quenched from 1000“C quenched from 1150°C quenched from 1150°C quenched from 1150°C quenched from 1150°C quenched from 1150°C quenched from 1150°C

Magnetic field

y

rms dev.

A

@D

K

10-4calmol-1K-2

low4 cal mol-‘K-r

none

22.1

2.09

373

none

23.1

1.67

329

cooling to 1.4K

20.7

5.26

261

cooling and measurement none

21.5

3.80

266

22.7

3.02

279

none

18.5

3.80

313

cooling to 1.4K

18.1

3.65

291

cooling and measurement

18.3

3.14

315

none

23.5

0.36

422

none

16.7

2.81

356

none

8.0

4.74

312

none

9.9

3.34

311

none

15.9

3.99

307

none

19.3

7.05

398

none

9.5

3.22

479

none

10.2

0.40

388

none

10.7

0.50

422

none

10.7

0.40

421

none

11.5

1.00

419

Ada&i

0.30

0.50

[Ref. p. 480

1.2.3.11 Ni-Cr

408

1.2.3.11 Ni-Cr

cr -. 2ooo0 “.-

10 / I’C

20 /

Ni -Cr

30 I

40 4

Ni 50 I

Ni 80wt% 90 I I

70 I

60 I

o liauids

1600

j 5CO’C

\ \

Y-Y,

\ I I

Cr

50 Ni -

60

70

80

Fig. 256. Phase diagram ofNi-Cr alloys [SS h 1, p. 5421. Temperature, in [“C], and composition, in [at% Nil, and, in parentheses, in [wt% Ni], are given for characteristic points of the phase diagram.

Fig. 257. Magnetic mass susceptibility xp for Ni-Cr alloys at room temperature. I: quenched from 900 “C, II: annealed at 425 “C [57 K 11.

Adachi

Ni

Ref. p. 4801

1.2.3.11 Ni-Cr

409

Table 61. Paramagnetic properties of Ni-Cr alloys derived from the susceptibility vs. temperature curves given in Fig. 259, according to the equation: xp = x0 + C$( T- 0) [72 B 11. Cr [at%] C, [10M4cm3 Kg-‘]

@ CKI x0 [10e6cm3 g-i]

44

.I!" Y

11.0 22.2 96 4.09

11.5 17.6 89 3.92

12.0 14.7 51 4.70

12.5 12.2 48 4.37

13.1 9.9 2.5 4.85

13.5 11.2 -21 4.74

15.3 15.6 - 248 4.44

I

Ni-Cr

cm3

28 I 24 7 s20

0

16

250

500

750

1000 K 1250

T-

Fig. 259. Reciprocal mass susceptibility xi’ vs. temperature for Ni-Cr alloys. For the drawn curves, see Table 6 1 [72B 11.

00 Fig. 258. Inverse of the magnetic mass susceptibility, xi ‘, vs. temperature for Ni-Cr alloys. From the curves labelled a for 6 and 14wt% Cr the curves labelled b are obtained by correcting for a temperature-independent paramagnetic susceptibility x0 of 2.07. 10m6 and 3.82. 10m6gcmm3, respectively [36 M 11.

350 K 300

250

For Fig. 260, see page 413.

200 1 150

100

Fig. 261. Magnetic phase diagram of dilute Ni-Cr (dashed lines) and Cc&r (solid line) alloys. T-IC and L-IC denote transverse and longitudinal spin density wave states, respectively. AF means commensurate antiferromagnetic state. Circles: [68 E l] and triangles: [66 B 31.

Landolt-Bdmstein New Series 111/19a

Adachi

5c C 0 Cr

1

2

3 Co,Ni -

4

5 at%

410

1.2.3.11 Ni-Cr

3[ Gem 9

[Ref. p. 480

I

Ni - 5.6ot%Cr

2:

169

0

3

Cy

6

a

9

12 kOe 15

I

1=1.56K

9

12 kOe 15

H6

V

b

0

Ni

0

I

3

6

8

12 ot% 16

Cr -

Fig. 263. Average magnetic moment per atom. j,,. for NiCr alloys as determined from the magnetization in magnetic ticlds up to 30 kOe [72B I], see also [71 C 1, 32 S 1, 62 V I]. Bottom figure: extrapolated zero-field magnetic mass susceptibility xB at 0 K [72 B I].

I hli-91nt0/~~r

4

Hllat%Cr

1

0 C

5

10

15

20

25 kOe 30

Fig. 262. Magnetic moment per gram, o, as dependent on temperature and field strength [62 V I] : (a) Ni-5.6 at% Cr and (b) Ni-9.1 at% Cr.(c) Magnetic moment per gram: G, at 4.2 K, as dependent on composition and field strength [72B I].

H-

Adachi

Table 62. Saturation magnetic moment csand average magnetic moment per atom, pat, for Ni-Cr alloys at various temperatures [59 T 1-j. Cr at%

40 K) Gcm3g-’

1.70 3.28 6.74 8.75 11.2

50.9 43.7 29.0 21.9 15

0,(150K) Gcm3g-l 49.75 42.40 25.40 16.3

Ed0 K) uB 0.53 0.46 0.30 0.23 0.16

Table 64. Atomic magnetic moments as determined by polarized-neutron diffuse scattering measurementson Ni-Cr and Ni-V alloys [76 C l] and averagemagnetic moment per atom, P,, [72B 1, 71 C 1, 32s 11. T= 4.2 K, H = 57.3kOe. Cr

1 5 10 -

PB

5

0.570 0.375 0.100 0.346

Table 63. Average magnetic moment per atom, j&,,,and Curie temperature Tc for NiXr alloys [72 B 11,seealso [32S1,37M1,62Vl].T=4.2K. Cr at%

Pat PB

K

Ni 2.6 5.1 7.7 9.4 10.5 11.0 11.5 12.0 12.5

0.6155 0.4742 0.3487 0.2161 0.1268 0.0766 0.0548 0.0375 0.0221 0.0091

518 390 235 130 80 43 30 19 11

-0.20(6) -0.02(12) 0.05(6)

-0.065(48)

0.562 0.355 0.095 0.325

9 Ni Ni-1.7 at% Cr Ni-3.3 at% Cr Ni-5.0 at% Cr

Impurity-

Fig. 264.Amplitude ofthe spin density wave,p,, ofCr with various small additions of other 3d elements,as derived from neutron diffraction measurements[68 E 11.

Landolt-BOrnstein New Series 111/19a

T,

Table 65. g-factor of polycrystalline NiCr alloys, measured at room temperature and 35.6GHz [60A 11.

V

at%

411

1.2.3.11 Ni-Cr

Ref. p. 4801

Adachi

2.18 2.18 2.18 2.20

[Ref. p. 480

1.2.3.11 Ni-Cr

412

5 .w4 -cm3 mol

I

0 \\,

Ni - Cr I

L

3 I hk x 2

I I 0.2

. OAB at%Ni o Cl.98of% Ni

0.4

I

I

I

0.6

0.8

1.0

1

r/T& -

Fig. 265. Tempcraturc dependence of the relative sublatticc magnetic moment p,lp,(O K)for Ni-Cr alloys [68 E I].

0 a

Ni 12

d

3

F 10

8 I $6

0.9E I < a97 s

o Ni-Cu

0.9:

20

b NI

60

60 V. Cr. Cu -

80 ot% 100

Fig. 267. High-field magnetic susceptibility, xHF,at 4.2 K, (a)mcasured in magnetic fields up to 69 kOe for Ni-V and Ni-Cr alloys [75A I], and (b) measured in pulsed magnetic fields up to 300 kOe for Ni-Cr, Ni--V and Ni-Cu alloys [82S 21. 1

2 3 Impurity -

1 ot%

5

Fig. 266. Wavevector Q of the spin density waves in Cr with various small amounts ofothcr 3d elements [68 E I].

Ref. p. 4801

1.2.3.11 Ni-Cr

413

Table 66. High-field magnetic mass susceptibility xHF of Ni-Cr and Ni-Mn measured for field strengths up to 13 kOe [62 V 11. Cr

Mn

alloys at various temperatures and

XHF

10ms cm3 g-l at% 1.2...1.6K 0.9 5.6 9.1 2.1 -

-

2.8 0.5 0.9 12.5

5.6 11.3

20.0

2.5...3.2K

4.2 K 2.8 0.5 7.0 5.8 18.0 4.0

8.0

15K

20K

2.0 5.0

0 0 5.2

0 25.0

0 4.0

65K

0 9.2 0 140

77K

169K

300 K

0 1.5 7.0 0 0 150

0.7 2.0 2.6 6.2 3.7 140

1.4 4.0 1.5 7.5 4.0 12.0

3 .10-c 0 I -3 3 -6

-12 150

175

200

225

250 T-

275

300

325 K 350

Fig. 260. Linear thermal expansion coefficient tl= Al/l vs. temperature for Ni-Cr alloys. The arrows give the NCel temperature as determined by neutron diffraction. Measurements were made on single crystals [68 E I]. Fig. 268. Electronic specific heat coefficient y for Ni-3d transition metal alloys in the temperature range 1...4 K. The open and solid symbols reflect different analyses of the measuring results [75 G 11.

Landolt-Bbmsfein New Series lWl9a

1.2.3.12 Ni-Mn

Mn

[Ref. p. 480

Ni -

Ni

I

60

I /

I

II

60

I \i-. ,

50 J CL!.!.

LOO ’ II!

i I

i I

70

8owt% 90

q&! T

I I

\

!ji I 1 II

‘\: \moonPlic

353’

i

301 200 100 0

0 Mn

10

20

30

10

50 Ni -

60

70

80

90 ot% 100 Ni

Fig. 269.Phasediagram and crystal structuresof Mn -Ni alloys [SSh 1,p. 9393.yNi:fee,yhrn:fee-fct (Mn side),Phln: B-Mn structure.czhln: a-Mn structure, MnNi,: feeCu,Autype. MnNi (L): fct CuAu-type.Tempcraturc,in [“Cl, and composition, in [at%Ni] and, in parcnthcscs, in [wt%Ni], arc given for characteristic points of the phasediagram.

Adachi

Ref. p. 4801

1.2.3.12 Ni-Mn

415

100

60 Ni

65

70

75

80 Mn -

85

90

95at%100 Mn

200

300

400

500

600 K 700

Fig. 272. Reciprocal value of the paramagnetic volume susceptibility, x; ‘, vs. temperature T for Ni-Mn alloys, 21.6...35.9at% Mn [60K 11. See also Fig. 271.

Fig. 270. Tetragonal transition temperature ‘I; and NCel temperature TN of y-phase Ni-Mn alloys. t, : c/a > 1, t, : c/a< 1 [71 U 11, see also [7OU 11.

650 K K

Ni-Ag

1

600 61

550

I 51 500 Q L50

Ni

I

350

L50

550

T-

650

“C

750

\

Impurity -

Fig. 273. Paramagnetic Curie temperature 0 for various Ni alloys [36 M 11.

Fig. 271. Reciprocal value of the paramagnetic mass susceptibility, 1; ‘, vs. temperature for Ni-Mn alloys, 0...17.89at% Mn [36M 11. See also Fig. 272.

Landolt-Bbrnstein New Series 111/19a

.

Ada&i

416

1.2.3.12 Ni-Mn 8

[Ref. p. 480 I

kG Ni-Mn 7

j

6

/ a\

,I

'\ \

20 Mn -

25

onneoled

3 2 1 0 0 NI

a 14

N:

5

10

15

30

35w1%10

I

kG 13.

T=OK

0 b Ni

5

/

I

,'I

I

Impurity -

Fig. 274. Curie temperature T, of Ni-based 3d transition metal alloys [32 S 1. 37 M I].

10

15

20 Mn -

25

3d

4 35";;

:Ii

Fig. 276a. Saturation magnetization 4nM, for Ni-Mn alloys at room tempcraturc as a hmction ofcomposition. Open circles: quenched from 9OO”C, closed circles: anncalcd at 430°C. After [31 K I], from [51 b I]. Fig. 276b. Composition depcndencc of the saturation magnetization for Ni-Mn alloys at OK after various annealing proccsscs [53P I]. Heat treatment A: 2 h at 800 “C, then water-quenched; B: one week at 420 “C, one week cooling; C: I6 h at 550°C 250 h at 490°C 260 h at 420°C and 260 h cooling.

5

10

15 Mn -

20

25 at% 30

Fig. 275. Curie temperature vs. Mn concentration in disordered NiLMn alloys. I: [3l K I], 2: [37M I], 3: [58 K I], 4: [78 T I].

Adachi

Landoh-Aornclein Ke\r Sciirr 111’19a

Ref. p. 4801

1.2.3.12 Ni-Mn

50 Gcm3 9

417

Fig. 278a. Magnetization curves for disordered Ni o.7sMno.22 after cooling in zero magnetic field. No hysteresis is found for 4.2 and 40 K. For the intermediate temneratures the hvsteresis is similar to the one for 8 K [82kl]. -

I 30 b 20

I4

b

0

150

300

450 H-

a

600

750 Oe 900

0

150

300

450 H-

600

750 Oe 900

Fig. 277. Magnetic moment per gram, (r, vs. magnetic The isofield strength H for disordered Ni,,,,Mn,,,,. therms below T= 80 K (dashed lines) were obtained after cooling in zero field and are time-dependent [82A 11.

b -10

-40

b

H-

Fig. 278b. Hysteresis loops for disordered Ni-Mn alloys at 1.8K. Solid lines: specimens cooled in a magnetic field of 5 kOe applied parallel (left figures) and perpendicular (right figures) to the axis of measurement. Dashed lines: specimens cooled in zero field [59 K 21.

Land&-Bbmstein New Series lll/l9a

-50 -600

I

-400

-200

0

200

400 Oe fioo

HFig. 279. Hysteresis loops for the magnetization of disordered Ni,,,,Mn,,,, after cooling to 4.2 K in various magnetic fields Hcoo,[82A I], see also [59 K 21.

Adachi

418

1.2.3.12 Ni-Mn

[Ref. p. 480

l( k[ c 600

t1

,

I

I

RT

/I

I

\I

I

OrUeiPd

7 E I F I 3 2 1 0I 16

E;

I, = 275h

F

Ni-26.6at%Mn

600 I 18

I 20

I 22

I 21 b!n -

I 26

I 28

I

I I 30 OR32

Fig. 280. Effect of fast-neutron irradiation of initially ordersd Ni Mn alloys at room tcmpcraturc (neutron energy in excess of 0.5 MeV) on the magnetization 4rr.U in a magnetic field of 20 kOc. Maximum tempcrature of the specimen during radiation is 50 “C [54A I]. The integrated neutron flux during irradiation is indicated. Dashed lint: 4n1W for thermally disordcrcd Ni Mn alloy (annealing tempcraturc 1000°C). 0

150

300

150

600

K

750

Fig. 281. Temperature variations of the saturation magnetization of(a) Ni-24.6 at% Mn and (b) Ni-26.6 at% Mn alloys. The numbers in the figures indicate annealing time t, for (a) 427°C and (b) 445°C [SS H I].

100

200

300

100

500

600 K

I-

Fig. 282. Spontaneous magnetization 47cM, vs. tempcraturc for various homogeneous states of order of Ni,Mn alloys. The long-range order parameter S gives the ratio of the integrated intcnsitics of a fundamental and a superlattice reflection observed by neutron diffraction. S=O and S= 1 mean complete disorder and complete order, rcspcctivcly [66P I], see also [6l M I] and [SS K I].

Adachi

700

Ref. p. 4801

1.2.3.12 Ni-Mn

419

Table 67. Magnetic properties of stoichiometric NiMn. Phln,pNiand Hhyprefer to 0 K. For spin arrangement in the antiferromagnetic phase, see Fig. 288. Crystal structure fct CuAu-type I)

Magnetism

AF

TN K 1073(40) [68 K l]

PMn

PNi

fby,i5

5Mn)

PB

kOe

3.8(3) - 1. However, Y, is pressure-dependent, and hence it will be possible to find substances that become ferromagnetic at higher pressures, Y,, < - 1. Landolt-Bornstein New Series 111/19a

Misawa, Kanematsu

1.3.1 4d, 5d: introduction

492

[Ref. p. 517

To estimate the Stoner (Landau) enhancement factor F for 4d and 5d transition metals, one should single out lsrin from the observed susceptibility at 0 K. z (0 K). For that purpose one needseither to evaluate theoretical!) 3r to determine expcrimcntally xorhand x,p.orh.Such a procedure is not quite we!! defined except for Knightshift experiments and causes ambiguity. Here we adopt, as a very crude estimate, 21(OK) for zrpi,; the results for F calculated from the values of yoh.x (OK) and 3,on the basis of eq. (4) are listed in Table 1. It is concluded that, within the above-mentioned uncertainty, OSand Ru are in the weakly paramagnetic region, Pd is in the nearly ferromagnetic region and others are intermediate.

Table 1. Basic constants and susceptibility data for 4d and 5d transition metals. ~~(0K) and x,(20 “C): observed magnetic susceptibility at 0 K and 20 “C, respectively 7: observed electronic specific heat coefficient i.: electron-phonon interaction constant F: Stoner (Landau) enhanccmcnt factor. Rcfcrenccto each value of I,,(20 ‘C) is found in the corresponding place in the column of references.See[82 V 1, 81 S I] for referencesto the values of 7 and i. Crystal

~(0 K)

?

I.

structure

10-42

mJ molK’

Zr

hcp

1.06

2.77

0.4

3.9

Nb

bee

2.27

7.80

0.9

4.0

MO

bee

0.82

1.83

0.4

4.6

Tc Ru Rh

hcp hcp fee

1.07 0.39 0.95

6.28 2.8 4.64

0.4 -

1.4 -

Pd

fee

7.0

9.36

0.7

9.3

Hf

hcp

0.71

2.21

0.3

3.1

Ta

bee

1.54

6.15

0.7

3.1

w

bee

0.52

0.90

0.25

5.3

Re

hcp

0.63

2.35

0.4

2.7

OS Ir Pt

hcp fee fee

0.09 1.9s 2.06

2.35 3.19 6.48

0.4 0.3 0.6

0.4 5.9 3.7

F

Ref.

x,(20 -‘cl 10-45

‘) Sin_cle-crystalspecimens.(~“,,,(20‘C)+21,,,(20”C))/3

1.14 1.18‘) 1.26 2.02 2.09 0.65 0.73 1.07 0.34 1.01 1.06 5.25 5.4

1.17‘) 1.21 1.29 2.04 2.14 0.67 0.83 1.23 0.41 1.02 5.29 5.8

5.31

0.68 0.74 ‘) 1.50 1.54 0.52 0.54 0.56 0.68 0.10 0.23 1.87 1.91

0.70 0.75 1.52 1.62 0.53 0.59 0.65 0.71 1) 0.10 ‘) 0.27 1.89 2.0

0.70

is listed.

Misaaa, Kancmatsu

1.18 1.21 2.05 2.14 0.72 0.43 1.02

1.54 0.53 0.68 0.13 1.89 2.05

55Kl 6SVl 65S2 6532 54Al 61Kl 57Al SORl 61Kl SlAl 61 K 1 51Hl 61Kl

71Cl 6lKl 65Vl 53Kl 61Kl 77Pl 53Kl 7011 7011 5lHl

41Sl 62Tl

60Bl 70Tl

63Ml

61Kl 71Cl 53Kl 6lKl 75Al 57Al 54Al 52Wl 31Gl 60Bl 7811 60Bl

64Vl 55Kl 54Al 71Kl 6lKl 53Kl 61Kl 69Vl 73Gl 61Kl 51Hl 70Tl

65Vl

76Hl 71Kl 71Kl 31Gl 60Bl

51Hl 7lKl 71Kl 67Wl 6lKl 74Wl

Ref. p. 5171

1.3.2 4d, 5d: susceptibility

vs. temperature

493

1.3.2 Magnetic susceptibility The magnetic susceptibility of 4d and 5d transition metals and their mutual alloys is generally described by the formula x = kxe

+ Sorb + &-orb

+ &pin

9

(1)

is the diamagnetic susceptibility arising from the core electrons; xorb, xspmorb, and xspin are wherexcore paramagnetic susceptibilities arising from, respectively, the orbital angular momentum, the spin-orbit interaction term and the spin angular momentum. xspinis further decomposed into three parts (2)

Xspin=Xs+Xp+Xdf

where xs,x,, and xd refer to the paramagnetic susceptibility due to s, p, and d valence electrons, respectively. In each contribution the effect of Landau diamagnetism to the susceptibility is considered to be included. These formulae are obtained in the tight-binding approximation within the single-particle model. When the electron correlation arising from the electron-electron interaction is considered, the decomposition of x according to eqs. (1) and (2) contains some ambiguity. It is generally assumed that xd is mainly responsible for the temperature dependence of x. However, it is pointed out that the temperature variation of xspTorb and xorbis also rather significant [68 M 11.General studies for the temperature dependenceof x in which the effectsof the electron correlation, the spin-orbit coupling, etc., are taken into account are not available yet. Here we restrict ourselves to the temperature dependencearising from the spin paramagnetism of itinerant d electrons. When the electron-electron interaction is ignored, the temperature dependence of the susceptibility for a system of itinerant electrons is given by ~,,(T)=2p;

[D(E)

(

-g

>

dE

in terms of the density of states curve D(E) as a function of the single-particle energy E, where f is the Fermi distribution function. When the interaction is considered in the molecular-field approximation (the Stoner model), X(T) is given by

x(T)= 1-xoG’7 ZxoU)’

(4)

where I stands for the effective interaction between electrons. For temperatures low compared with the effective degeneracy temperature, eq. (4) can be expanded in even powers of T, as is the case for the free energy in the Sommerfeld asymptotic expansion,

x(T) = x0(1+PJ2> 9

(5)

where

x: xo=l-K’

x:=Q&%%),

K = 2p;ZD(E,),

and

For D primes denote differentiation with respect to energy and E, is the Fermi energy at zero temperature. According to this model, whether x(T) is an increasing function of Tat low temperatures or not depends on the sign of fl, i.e., whether v/j> v” or not. When one calculates x(T) on the basis of the density of states curve deduced from the observed electronic specific heat coefficient, one obtains &/aT H2 ' exx We define the magnetoresistivity e1I and the Hall resistivity ezl through the relations e~~=&~,(H>+exx(-H)l, e21

=ik?,,W)-e,x(-WI.

Observation of the magnetoresistivity of W reveals that u,,(T) is nearly proportional to T2; this shows that the scattering mechanism is mainly due to the electron-electron interaction [72 W 1-J.In the case of Re, there appears a break in the Hall resistivity vs. H curve; the break is considered to be a consequence of magnetic breakdown causing the appearance of new closed orbits [74 K 11.

Landolt-Bornstein New Series lll/l9a

Misawa, Kanematsu

1.3.8 4d, 5d: magnetoresistivity,

[Ref. p. 517

Hall effect

513

Table 7. Shape and volume magnetostriction and volume dependence of the magnetic susceptibility for transition metals and Pd-Rh alloys. u& for Pd-Rh alloys is assumedto be the samevalue as for Pd [83 F 11. T=4.2K. Sf

Xm 10m4cm3mol-’

VI& lOi ergmol-’

0, ait -xrn av

1.38 2.61 3.15 1.75

1.4 1.2 0.5 5.2 6.6 15.5 18.4

10-l* OeC2 V MO W Pd PhwRho.o, WmRho.o, Pdo.,,Rhm, Zr

-

0.5 4.7 3.4 90 100 80 90

16 1.9 0.4 105 200 520 680

4.8

-9.6

2.97 0.81 0.53 7.3 9.5 11.1 12.8 0.9 ‘) 1 1.492)

0.78

-2.4 ') 1 - 1.02)

‘) For x1. “1 For XII.

1.3.8 Magnetoresistance and Hall effect The magnetic field dependenceof the electrical conductivity tensor o(H) is described as follows. With the magnetic field (parallel to the z axis) along a high-symmetry direction, the conductivity tensor takes the form; c,.,(H) = a,,(H), o,,(H) = -o,,(H), and o,,(H) = a,,(H) = a,,(H) = a,,(H) = 0. These relations, coupled with the Onsager relation eij(H) = crji(-H), require that a,,(H) and a,,(H) be even and odd function of H, respectively. When the Fermi surfaceis closed,then, according to semiclassicalmagnetoresistancetheory [56 L 21,(T,, and (T,+, at high fields have the asymptotic form ax,(T) ~xxyjp

~xyN h - n&c + a,,(T) H

H3 '

where n, and n,, are the number of electrons and holes, respectively. The temperature dependenceof a,,(T) and u,,,(T) is subject to the nature of the scattering processesin metals. If the metal is compensated (n,=n,), gxy= ~x,UYH3. Inversion of the conductivity tensor gives the resistivity tensor Q(H). At high fields, 1 - xo’,,w ~uxx(T> H2 ' exx We define the magnetoresistivity e1I and the Hall resistivity ezl through the relations e~~=&~,(H>+exx(-H)l, e21

=ik?,,W)-e,x(-WI.

Observation of the magnetoresistivity of W reveals that u,,(T) is nearly proportional to T2; this shows that the scattering mechanism is mainly due to the electron-electron interaction [72 W 1-J.In the case of Re, there appears a break in the Hall resistivity vs. H curve; the break is considered to be a consequence of magnetic breakdown causing the appearance of new closed orbits [74 K 11.

Landolt-Bornstein New Series lll/l9a

Misawa, Kanematsu

1.3.8 4d, 5d: magnetoresistivity, Hall effect

514

[Ref. p. 517

IO2 e 6

0 I

2

108

I

z=6 s L

‘

0

0 il

2

-, 10 6-9 E Ilk

2

c

6

E

105

2

kOe4.10s

fHcp:lFig. 69. Magnetic field dcpcndence of the Hall rcsistivity of hJo for two samples; both axes are multiplied by the residual rcsistancc ratio r = R2031R,,, to produce a Kohler plot (r = 5050 in thcsc samples) [76 F I]. Fig. 70. Change in the magnctorcsistivity, A?,, =Q, ,(HApp,)--~, r(0). for two samples ofMo as a function of applied field; both axes arc multiplied by the residual reststance ratto r= Rz9, lR,, to product a Kohler plot (r = 5050). Circles: [76 F I]. solid lint: [62 F I]. 22.5 do8 Rem _

2

IO6

2

L

4 40'2 L-km Oe 3

Re

I 2

3

i

E

105

2 kOe4.

For Fig. 71, see p. 515.

17.5 I

6

f-Hopp~ -

I 2 c;

12.5

108

/q .

7.5

0”

2.5

0

a

IO

20

30

40 Hup:1-

50

60

70 kOe80

30"

60"

b @Fig. 72. (a) Magnetic field dependence ofthc Hall resistivity of Re. Curve I: Hvpp, along [lOiO] direction; 2: H,,,, along [I 1201 direction; 3: angle between H,,,, and the c axis is 45”; 4: Hllc [74K I]. (b) Hall constants of Re as a function of the angle 4 between H,,,, and the c axis: Curves I and 2 refer to field strengths below and above the break point (about 20 kOe) in (a). respectively [74K I].

Misawa, Kanematsu

Ref. p. 5171

1.3.9 4d, 5d: electronic specific heat

515

25 .I06

11

(is 23 I 22 Z F21 ,B s" 20 19 18

Fig. 71. H&, ,/err of W as a function of T2 for various values of the magnetic field [72 W 11.

6 17 0

5

IO

15

20 T2-

25

I 30

18.6 I 35 K*

1.3.9 Magnetic field dependence of the electronic specific heat coefficient The magnetic field dependence of the electronic specific heat coefficient, y(H), is related, according to thermodynamics, to the temperature dependenceof the magnetic susceptibility x(T). Since XH = - aF/aH and y= -aZF/3T2, where F(T, H) is the free energy of the system, one can obtain a thermodynamic relation:

where y is defined as the specific heat divided by temperature. If it is assumedthat x(T) behaveslike x(O)+ j3T2 at low temperatures, where /I is a constant, then, for H-0, one should expect y(H) = y(O) + fiH2 from eq. (1). As far as x(T) depends quadratically on T, the sameholds for the dependence of y(H) on H; one has

at T2 = H2 =O. By analysing the observed data on y(H) at low H and x(T) at low T one may examine the applicability of relation (2). Such a comparison has been made so far for LuCo,, Pd, and TiBe,; the results show that eq. (2) doesnot hold [82 B 1,83 M 11.This implies that the assumption that X(T) behaveslike x(0)+flT2, or, equivalently, y(H) behaveslike y(O)+ j?H2, is not valid. This difficulty may be avoided in the Fermi liquid model by considering that the temperature dependenceof x follows a T2 In T law becauseof the Fermi liquid effect [83 M 11. For 4d and 5d transition metals y(H) has been measured only for Pd; in accordance with the above statements, the observed y(H) does not follow a simple HZ law [Sl H 1, 83 M 11. 9.50 mJ molK2 9.25

I 9.00 x

Fig. 73. Magnetic field dependenceof the electronic specificheat coefficient of Pd [81 H 11.

8.50 0

30

60

90 HVP1 -

Landolt-Bbmstein New Series 111/19a

Misawa, Kanematsn

120 kOe 150

Ref. p. 5171

1.3.9 4d, 5d: electronic specific heat

515

25 .I06

11

(is 23 I 22 Z F21 ,B s" 20 19 18

Fig. 71. H&, ,/err of W as a function of T2 for various values of the magnetic field [72 W 11.

6 17 0

5

IO

15

20 T2-

25

I 30

18.6 I 35 K*

1.3.9 Magnetic field dependence of the electronic specific heat coefficient The magnetic field dependence of the electronic specific heat coefficient, y(H), is related, according to thermodynamics, to the temperature dependenceof the magnetic susceptibility x(T). Since XH = - aF/aH and y= -aZF/3T2, where F(T, H) is the free energy of the system, one can obtain a thermodynamic relation:

where y is defined as the specific heat divided by temperature. If it is assumedthat x(T) behaveslike x(O)+ j3T2 at low temperatures, where /I is a constant, then, for H-0, one should expect y(H) = y(O) + fiH2 from eq. (1). As far as x(T) depends quadratically on T, the sameholds for the dependence of y(H) on H; one has

at T2 = H2 =O. By analysing the observed data on y(H) at low H and x(T) at low T one may examine the applicability of relation (2). Such a comparison has been made so far for LuCo,, Pd, and TiBe,; the results show that eq. (2) doesnot hold [82 B 1,83 M 11.This implies that the assumption that X(T) behaveslike x(0)+flT2, or, equivalently, y(H) behaveslike y(O)+ j?H2, is not valid. This difficulty may be avoided in the Fermi liquid model by considering that the temperature dependenceof x follows a T2 In T law becauseof the Fermi liquid effect [83 M 11. For 4d and 5d transition metals y(H) has been measured only for Pd; in accordance with the above statements, the observed y(H) does not follow a simple HZ law [Sl H 1, 83 M 11. 9.50 mJ molK2 9.25

I 9.00 x

Fig. 73. Magnetic field dependenceof the electronic specificheat coefficient of Pd [81 H 11.

8.50 0

30

60

90 HVP1 -

Landolt-Bbmstein New Series 111/19a

Misawa, Kanematsn

120 kOe 150

1.3.10 4d, 5d: plastic deformation

516

[Ref. p. 517

1.3.10 Effect of plastic deformation on the susceptibility The plastic deformation alters substantially the magnetic properties of paramagnetic materials and may either increase (e.g.for V, Nb) or decreasethe susceptibility (e.g.for AI, Cu). Concerning 4d and 5d transition metals, the effect of the plastic deformation on the susceptibility has been measured for Zr, MO, Pd, W, etc.: [76D2. 80Dl. 8OSl]. When a cylindrical spccimcn oflength /is plastically dcformcd by A/along the axis, the susceptibility becomes a function of the degree of plastic deformation

~=Al/l;

the susceptibility

depends also on the direction of

deformation relative to the direction of an applied magnetic field. The plastic deformation increases the dislocation density p through which the susceptibility

changes [80 D 11.

0

0.5

1.0

1.5

1

2.0

2.5 kOe 3.0

HODD1 -

1.6 t -m ,x 51.3 1.0

0

1

2

3

6

5

6

7 kOe8

Hor4 -

Fig. 76. Susceptibility ratio of deformed and single crystal spccimcns for Pd and W as a function ofmagnetic

E-

Fig. 74. Relative variation ofthc susceptibility ofpolycrystnllinc Zr as a fimction of the degree of deformation at room tcmpcraturc: the direction of the deformation is (solid circles) pnrallcl to the magnetic field. and (open circles) pcrpcndicular to the mngnctic licld [SOS I].

0.6 10’

10”

10’

108

log

field for various values of the degreeof deformation. E, at room temperature [76 D 21.

lOlocm-210”

Fi_r. 7% x,(r)/~~ of MO as a function of dislocation density, ! at room tcmpcraturc, whcrc x,(w) is the susceptlhllity estrapolatcd to H= ~j in the zF vs. l/H curve and ,$ is the susceptibility of the undcformcd single crystal: [SOD I].

Misawa, Kanematsu

References for 1.3

1.3.11 References for 1.3 21 F 1 31Gl 33Hl 41 s 1 48Bl 51Hl 52Hl 52Wl 53Kl 54Al 54Hl 55Kl 56Ll 56L2 57Al 60Bl 6011 61 K 1 62Fl 62Jl 62Tl 63M 1 630 1 65Sl 6582 65Vl 66Nl 67Wl 68Fl 68Ml 68Vl 68Wl 69Dl 69Fl 69Vl 70Fl 70F2 7011 70Kl 70K2 70Ml 7OSl 70Tl 71Cl 71 G 1 71Kl 71Ml 71Nl 72Cl 72Wl 73Dl

Land&-Bdmstein New Series III/l%

Fo&x, G.: Ann. Phys. Paris 16 (1921) 174. Guthrie, A.N., Bourland, L.T.: Phys. Rev. 37 (1931) 303. de Haas, W.J., van Alphen, P.M.: Koninkl. Ned. Akad. Wetenschap. Proc. Ser. A36 (1933) 263. Squire, CF., Kaufmann, A.R.: J. Chem. Phys. 9 (1941) 673. Brauer, G.: Z. Anorg. Chem. 256 (1948) 10. Hoare, F.E., Walling, J.C.: Proc. Phys. Sot. (London) Sect. B64 (1951) 337. Hoare, F.E., Matthews, J.C.: Proc. R. Sot. London Ser. A212 (1952) 137. Wucher, J., Perakis, N.: C.R. Acad. Sci. 235 (1952) 419. Kriessman, C.J.: Rev. Mod. Phys. 25 (1953) 122. Asmussen, R.W., Soling, H.: Acta Chem. Stand. 8 (1954) 563. Hoare, F.E., Kouvelites, J.S.,Matthews, J.C., Preston, J.: Proc. Phys. Sot. (London) Sect. B 67 (1954) 728. Kriessman, C.J., McGuire, T.R.: Phys. Rev. 98 (1955) 936. Landau, L.D.: Zh. Eksp. Teor. Fiz. 30 (1956) 1058; Sov. Phys. JETP (English Transl.) 3 (1957) 920. Lifshitz, I.M., Azbel, M.I., Kaganov, M.I.: Zh. Eksp. Teor. Fiz. 31(1956) 63; Sov. Phys. JETP (English Transl.) 4 (1957) 41. Asmussen, R.W., Potts-Jensen, J.: Acta Chem. Stand. 11 (1957) 1271. Budworth, D.W., Hoare, F.E., Preston, J.: Proc. R. Sot. London Ser. A257 (1960) 250. van Itterbeek, A., Peelaers,W., Steffens,F.: Appl. Sci. Res. B8 (1960) 177. Kojima, H., Tebble, R.S., Williams, D.E.G.: Proc. R. Sot. London Ser. A260 (1961) 237. Fawcett, E.: Phys. Rev. 128 (1962) 154. Jones, D.W., McQuillan, A.D.: J. Phys. Chem. Solids 23 (1962) 1441. Taniguchi, S., Tebble, R.S., Williams, D.E.G.: Proc. R. Sot. London Ser. A265 (1962) 502. Manuel, A.J., St. Quinton, J.M.P.: Proc. R. Sot. London Ser. A273 (1963) 412. van Ostenburg, D.O., Lam, D.J., Shimizu, M., Katsuki, A.: J. Phys. Sot. Jpn. 18 (1963) 1744. Seitchik, J.A., Jaccarino, V., Wernick, J.H.: Phys. Rev. Al38 (1965) 148. Suzuki, H., Miyahara, S.: J. Phys. Sot. Jpn. 20 (1965) 2102. Volkenshtein, N.V., Galoshina, E.V.: Phys. Met. Metallogr. USSR (English Transl.) 20 (1965)No. 3,48. Narath, A., Fromhold, A.T., Jr., Jones, E.D.: Phys. Rev. 144 (1966) 428. Weiss, W.D., Kohlhaas, R.: Z. Angew. Phys. 23 (1967) 175. Foner, S., Doclo, R., McNiff, E.J., Jr.: J. Appl. Phys. 39 (1968) 551. Mori, N.: J. Phys. Sot. Jpn. 25 (1968) 72. Volkenshtein, N.V., Galoshina, E.V., Shchegolikhina, N.I.: Phys. Met. Metallogr. USSR (English Transl.) 25 (1968) No. 1, 166. Wunsch, K.M., Weiss, W.D., Kohlhaas, R.: Z. Naturforsch. 23a (1968) 1402. Doclo, R., Foner, S., Narath, A.: J. Appl. Phys. 40 (1969) 1206. Foner, S., McNiff, E.J., Jr.: Phys. Lett. A29 (1969) 28. Volkenshtein, N.V., Galoshina, E.V., Shchegolikhina, N.I.: Sov. Phys. JETP (English Transl.) 29 (1969) 79. Fawcett, E.: Phys. Rev. B2 (1970) 1604. Fawcett, E.: Phys. Rev. B 2 (1970) 3887. Isaacs, L.L., Lam, D.J.: J. Phys. Chem. Solids 31 (1970) 2581. Kanno, S.: Prog. Theor. Phys. 44 (1970) 813. Keller, R., Ortelli, J., Peter, M.: Phys. Lett. A31 (1970) 376. Misawa, S.: Phys. Lett. A32 (1970) 153. Shimizu, M.: Proc. 3rd IMR Symp. on Electronic Density of States,NBS Special Publ. 323 (1970)685. Treutmann, W.: Z. Angew. Phys. 30 (1970) 5. Collings, E.W., Ho, J.C.: Phys. Rev. B4 (1971) 349. Gersdorf, R., Muller, F.A.: J. Phys. Paris Suppl. C 1, 32 (1971) 995. Kohlhaas, R., Wunsch, K.M.: Z. Angew. Phys. 32 (1971) 158. Misawa, S.: Phys. Rev. Lett. 26 (1971) 1632. Narath, A., Weaver, H.T.: Phys. Rev. B3 (1971) 616. Collings, E.W., Smith, R.D.: J. Less-Common Met. 27 (1972) 389. Wagner, D.K.: Phys. Rev. B5 (1972) 336. van Dam, J.E.: Thesis, University of Leiden 1973.

Misawa, Kanematsu

518

Referencesfor 1.3

13G 1

Galoshina. E.V., Gorina, N.B., Polyakova, V.P., Savitskii, E.M., Shchcgolikhina, NJ., Volkenshtein. N.V.: Phys. Status Solidi (b) 58 (1973) K45. 74K 1 Kondorskii. E.I.. Galkina, OS., Cheremushkina, A.V., Usarov, U.T., Chuprikov, G.E.: Soviet Phys. JETP (English Transl.) 39 (1974) 1094. 14w 1 Weaver. H.T., Quinn, R.K.: Phys. Rev. BlO (1974) 1816. 75Al Alekseyeva.L.I.. Budagovskiy, S.S.,Bykov, V.N., Kondakhchan, LG., Povarova, K.P., Podolyan, N.I., Savitskiy, Ye.M.: Phys. Met. Metallogr. USSR (English Transl.) 40 (1975) No. 5, 87. EC 1 Cable. J.W., Wollan. E.O., Felcher, G.P., Brun, T.O., Hornfeldt, S.P.: Phys. Rev. Lett. 34 (1975) 278. 75H 1 Hioki. T., Kontani. M., Masuda. Y.: J. Phys. Sot. Jpn. 39 (1975) 958. 76B 1 Burzo. E., Lazar. D.P.: Solid State Commun. 18 (1976) 381. 76Dl Das. B.K., Stern. E.A., Lieberman, D.S.: Acta Metall. 24 (1976) 37. 76D 2 Deryagin. A.I., Pavlov, V.A., Vlasov, K.V., Shishmintsev, V.F.: Phys. Met. Metallogr.USSR (English Transl.) 41 (1976) No. 5, 183. 76F 1 Fletcher, R.: Phys. Rev. B 14 (1976) 4329. 76H I Hechtfischer, D.: Z. Phys. B 23 (1976) 255. 76M 1 Misawa. S., Kanematsu, K.: J. Phys. F6 (1976) 2119. 77B 1 Barnea. G.: J. Phys. F 7 (1977) 315. 77K 1 Karcher. R., Kiibler, U., Liiders, K., Sziics, Z.: Phys. Status Solidi (b) 84 (1977) 189. 77K2 Khan, H.R., Liiders, K., Raub, Ch.J., Sziics, Z.: Phys. Status Solidi (b) 84 (1977) K 33. 77P 1 Ploumbidis. D.: Z. Phys. B28 (1977) 61. Inoue. N., Sugawara, T.: J. Phys. Sot. Jpn. 44 (1978) 440. 7811 7SK 1 Kobler. U., Schober. T.: J. Less-Common Met. 60 (1978) 101. 7SM 1 Martins. J.M.V., Missell, F.P., Percira, J.R.: Phys. Rev. B 17 (1978) 4633. 7s M 2 Misawa. S.: J. Phys. F8 (1978) L263. 7ss 1 Shaham. M., El-Hanany, U., Zamir, D.: Phys. Rev. B17 (1978) 3513. 79K 1 Klyuyeva. LB., Kuranov, A.A., Chemerinskaya, L.S., Babanova, Ye.N., Bashkatov, A.N., Syutkin, P.N., Sidorenko, F.A., Gel’d, P.V.: Phys. Met. Metallogr. USSR (English Transl.) 47 (1979)No. 4, 46. 79s 1 Shaham, M.: Phys. Rev. B20 (1979) 878. SOD1 Deryagin. A.I., Nasyrov, R.Sh.: Phys. Met. Metallogr. USSR (English Transl.) 49 (1980) No. 6, 64. SOR 1 Radhakrishna. P., Brown, P.J.: J. Phys. F 10 (1980) 489. SOS1 Savin. V.I., Markin, V.Ya.. Deryavko, I.I., Yakutovich, M.V.: Phys. Met. Metallogr. USSR (English Transl.) 49 (19SO)No. 2, 170. SlAl Abart, J.?Voitlander. J.: Solid State Commun. 40 (1981) 277. SlGl Gerhardt. W., Razavi. F., Schilling. J.S., Hiiser, D., Mydosh, J.A.: Phys. Rev. B24 (1981) 6744. SlG2 Gygax, F.N., Hintermann, A., Riiegg. W., Schenck, A., Studer, W.: Solid State Commun. 38 (1981) 1245. 81 H 1 Hsiang. T.Y., Reister, J.W., Weinstock, H., Crabtree, G.W., Vuillemin, J.J.: Phys. Rev. Lett. 47 (1981) 523. SlMl Misawa, S.: J. Mag. Magn. Mater. 23 (1981) 312. SlSl Shimizu. M.: Rep. Prog. Phys. 44 (1981) 329. S2B1 Beal-Monod. M.T.: Physica 109, 1lOB (1982) 1837. 82Tl Takigawa, M.? Yasuoka. H.: J. Phys. Sot. Jpn. 51 (1982) 787. 82Vl Vonsovsky, S.V., Izyumov, Yu.A., Kurmaev, E.Z.: Superconductivity in Transition Metals, Berlin. Heidelberg. New York: Springer 1982, ch. 4. S3Fl Fawcett. E.. Pluzhnikov, V.: Physica 119B (1983) 161. S3M 1 Misawa, S.: J. Mag. Magn. Mater. 31-34 (1983) 361.

Misawa, Kanematsu

Ref. p. 5641

519

1.4.1.1 3dAd, 5d (group 4-7): introduction

1.4 Alloys and compounds of 3d elements and 4d or 5d elements 1.4.1 3d elements and Zr, Nb, MO or Hf, Ta, W, Re 1.4.1.1 Introduction a) Phase diagram and crystal structure Solubility and intermetallic compounds in binary systemsare shown in Table 1. As seenin the table, most of the 4d and 5d elements are not soluble in the 3d elements,but they can form intermetallic compounds. Among them the Laves phase compound, AB2, is the most important one. In particular, Laves phase compounds containing Fe or Co are extensively studied in respect of magnetism. Laves phases have one of the three following structure types: (i) Cl5 (cubic, MgCu, type), (ii) Cl4 (hexagonal, MgZn, type), (iii) C36 (hexagonal, MgNiz type). In the present alloy systems,Mg is replaced by one of the 4d or 5d elementsand a 3d element takesplace of Cu or Zn site. The C36 type rarely appears. In Fig. 1 the unit cells of the Cl5 and Cl4 crystals are shown. It is worthwhile to note that these AB, crystals have a close-packed structure of two kinds of atoms with different atomic sizes,ideally R, = 1.225Rn.The two types of Laves phases,Cl5 and C14, are due to a different sequenceof atom layers and hence the coordination number of each atom is the samefor both structures. The AB, compounds treated in this section have a finite range of a single phase in off-stoichiometric compositions. There is a trend that the off-stoichiometric field spreadswider to the B side. This trend may be understood as that the A atom having larger atomic size can be easily replaced by a B atom but not B by A. It should be noted that a slight deviation from the stoichiometry can give rise to significant effects on the magnetic properties. Therefore, it is likely that disagreementsin data on magnetic properties of these compounds may be due to a slight deviation from the stoichiometry introduced in their preparations.

a

0 Mg. Cu

b

Fig. 1. Crystal structure of Laves phasecompounds.(a) Cl 5 &IgCu, type, cubic, Fd3m): Both Mg and Cu have only one chemically equivalent site. It should be noted that the local symmetryof Cu is not cubic and hencethe Cu site has a non-zero electric field gradient, whose principal axis is along one of the [l 1l] directions. The asymmetryfactor q is zero. Therefore, ifa 3d atom at a Cu

Land&-Bdmstein New Series 111/19a

0

Mg 0 Zn

site is magnetized, it can take four magnetically different sites in maximum.(b) Cl4 (MgZn,, hexagonal, P6Jmmc): There are two Zn sites, 2a and 6h, respectively. The principal axis of the electric field gradient is along the c axis for the 2a site (q = 0) and in the c plane for the 6h sites

(tt$0) as shown by bold lines.

Shiga

Table 1. Equilibrium phases and solubility limits of binary alloys between 3cl and 4d or 5d elements. See [58 h I] if not otherwise noted. For intermetallic compounds, the crystal structure is given in parentheses. Hf

Zr Ti

V

Cr

Solid solution ‘) Low-temperature High-temperature V,Zr(C15) Zr in V 3at%

Cr,Hf

Eii (

Solid solution ‘) phase r (hcp) phase p (bee) V,Hf(Cl5)*)

>

z:i (

Ta

MO

Solid solution Solid solution Solid solution Martensitic transformation @-+a) on Ti-rich side Solid solution

Not soluble

Not soluble Cr,Zr

Nb

‘? 1

Miscibility gap V in Ta 36at% Ta in V lOat% ‘)

?

Ta in Cr l.Sat% Cr in Ta 9at% Cr,Ta(C15, C14)

Miscibility

W

Re

Not soluble ‘) Ti in W IOat%

Not soluble ‘) T&b4

7

V in Re 3at% Re in V 65at% VRe, ‘)

gap

Cr in Re 5at% Re in Cr 35 at% Cr,Re,o-phase ‘)

CrinW5at% WinCr2at%

Mn

Not soluble’) Mn,Zr(C14)

Mn,Hf(C14)

7

Mn,Ta(C14)

a-phase

?

Mn,,Re16’) o-phase

Fe

Not soluble Fe,Zr(ClS)

Not soluble ‘)

Fe,Nb(C14)

Fe,Ta(C14)

MO in Fe 4at% F+WD8s)

Fe,W(C14) hW2 Fe,W@8,)

Re in Fe 11 at% Fe,Re, o-phase

Co,Nb(C 15)

Co,Ta’)

COWDO,,) Co,Mo,W,)

Co,WDO

MO in Ni 13at% Ni,Mo Ni,Mo

W in Ni 12at% Ni,W

Fe,Hf(C14+ClS) co

Ni

Not soluble CoZr(CsCI) Co I *Zr,, Co,Zr CoZr,(CuAl,) Co,Zr(ClS) ‘)

Co,Hf Co,Hf(ClS) CoHf(CsC1) CoHf,(Ti,Ni)

Ni,Zr(AuBe,) Ni,Zr,, Ni,,Zr, Ni 1*Zr,, NiZr NiZr,(CuAl,)‘)

Ni,Hf Ni,Hfi, Ni,Hf, Ni,,Hf, Ni 1,Hf,,, NiHf NiHf,(AlCu,) ‘)

‘) [65e 11. ‘) [69s 11.

,cJ

Solid solution

Co7Wlm-3,)

‘) Ni,Nb NiNb

Ni,Ta(TiCu,) Ni,Ta,

Ni in Re 45 at% Re in Ni 5 at% ‘)

Ref. p. 5641

1.4.1.2 Ti, V-4d, 5d (group 4-6)

521

b) Magnetic properties Most of the alloys and the intermetallic compounds are Pauli paramagnetic except for some of the Fe alloys and intermetallic compounds which show ferro- or antiferromagnetism. However, they usually show a temperature-dependent susceptibility. In some cases,this looks like a Curie-Weiss law. This behavior may be ascribed to a high density of statesof the d band at the Fermi level. For thesecases,we use a term “nonmagnetic”, meaning a magnetic state in which no local-moment alignment, including ferro- and antiferromagnetism, takes place at the lowest temperature. c) Arrangement of substances Binary alloys and compounds are arranged in the order of increasing atomic number of the 3d element in thesesubstances.In each of the following subsections on Ti and V, Cr, Mn, Fe, Co and Ni alloys the sequenceof the 4d and 5d elements is: Zr, Hf, Nb, Ta, MO, W, Re. Ternary alloys are, in principle, placed after the binary alloys of their constituents. For example, the ternary alloy Fe-Co-Zr appears in the subsection on Co alloys after Co-Zr binary alloys. Exceptions are V-Fe-Zr and Cr-Co-Zr ternary alloys, which are found in the subsections on V and Cr alloys, respectively.

1.4.1.2 Ti and V alloys and compounds No alloys and intermetallic compounds other than nonmagnetic ones have been found so far. Most of them becomea superconductor at low temperatures. Fairly extensive studies including magnetic properties have been done becauseof the interest in superconductors, in particular, for Laves phase compounds of V,M (M = Zr, Hf, etc.). Survey Alloy

Composition

Property

Fig.

Ti, -xNb, Ti, -XM~, V, -xNbx VI -xMox V,Zr, V,Hf, V,Ta V, - ,Al,Zr V, -,Fe,Zr V, -,Fe,Hf V,Zr 1- ,Hf,

01x11.0 -O~x~1.0 OSxS1.0 -04x=0.5 at 4.2K [8OY I]. (a) At IOMHz. (b) In zero field.

Y-

Fig. 102. NMR spin-echo spectra of ‘lZr in (Fe, -$o,),Zr for x 5 0.2 at 4.2 K [81 W 11.The positions ofthe lines due to diffcrcnt Fe, Co neighborhoods of”Zr are indicated by vertical bars, labeled with the respective 48 MHz52 number of Fe and Co atom in the neighborhood.

YI.andol!-Rorncrein Ncu- Series 111/19a

1.4.1.6 CoAd, 5d (group 4-6)

Ref. p. 5641

559

Table 11. Magnetic and related properties of certain intermetallic compounds of Co-Hf, Co-Ta, and Co-Nb [82 B 11.For the compounds not showing magnetic ordering, the Pauli susceptibility is given instead of PC0and Tc Compound

Structure

a “)

Tc

Co,Hf Co,Hf C%,Hf, Co,Hf

Cl5 Cl5 Th6M%3 hexagonal

Co,Ta Co,Ta Co,Nb Co,Nb

Cl5 Cu,Au Cl5 Cl5

PC~

K

A

XP

. 10m6cm3g-l

PB

-

6.896

6.833 11.502 5.477 ‘) 8.070“) 6.761 6.788 6.773 6.717

7.8

40 499 600

0.12 0.66 1.14

-

12 10 7 0.17

‘) a, in hexagonal plane. ‘) c, along hexagonal axis. 3, RT.

7.0 8, I 6.9 D 6.8 27

28

29

30

a

31 Hf-

32

8 Oogo*Q

0

0 “&“*O

#*cl,

go@

0 .O 0.

O*“@w

4 0

b

50

100

150

33

34 at% 35

32.8 @New @.O& po*Q @ + 34.1at% Hf 200

250

TFig. 103.(a)Latticeparameterat room temperatureand(b) temperature dependenceof the susceptibility of cubic Laves phase Co-Hf alloys [73A 11. The sampleswere annealedat 1000“C for 6 days and then water quenched.

Landolt-BOrnstein New Series lll/l9a

Shiga

K

300

[Ref. p. 564

1.4.1.6 Co-4d, 5d (group 4-6)

560

__

9

I

2.5

H,;,,= 3 kOe

PB

250 kOe

I

I

( Fe,mxCox 12Hf 0

20

I

0

2.0 .

200

0 0

b

I= 4.2K 0

10 \ ‘\ 0

\

Co,Hf .’ ---___ 100 200

300

100

K 500

0

I 1.5 ” I%

I-

.

150

,)

.

I z IX

HhYP

,I .

100

1.0 4,

Fig. 103. Tcmpcraturc dcpcndcncc of the magnetization af Co,Hf (dashed line) and Coz,Hf, (solid lint) at 3 kOc [SZ B I-J.

4, -co 50

0.5 .

[

0.2

FI?,Hf

0

0.6

0.8

.O 1.0 Co,Hf

Fig. 105. Composition dependence ofthc avcragc ma_enetic moment per 3d atom and the mean hypcrfine ficld at “Fc of (Fc, -$o,),Hf with the Cl5 structure. T=4.2 K. The specimens were heat treated at I I50 “C for 2 days and at 700°C for I day [80 K 21.

For Fig. 106, see next page

co

0.4 x-

20

40 w-

60 wt% t 0

co

20

LO MO -

60 wt% 80

Fig. 107. Phase diagram and composition dcpcndcncc of the Curie temperature of Co-W and CO-MO alloys [32 K I].

Ref. p. 5641

1.4.1.6 CoAd,

5d (group 4-6)

561

6.78 A I 6.74 b

a

6.70 24

26

28

30 Ta -

32

34 at% 36

3.c gclj 9 3.c 2.E 1 2s

IO

b 1.5

I

1.0

15

H" IO

0.5

0

30

60

b

90 T-

120

150 K 180

Fig. 106. (a) Composition dependence of the lattice parameter at room temperature, (b) temperature dependence of the magnetization at 7.22 kOe and (c) the susceutibilitv at 7.22 kOe of cubic Laves phase Co-Ta alloys [74 I i].

15

IO

15

IO

5

50

1.60 t ,$.45

0

2.5

5.0 Ma,W -

7.5 at% 10.0

Fig. 108. Composition dependence of the average atomic moment of CO-MO and Co-W alloys [32 S 2,37 F 11. Landolt-Bdmvein New Series lWl9a

250 K 300

1.4.1.6 Nihld, 5d (group 4, 6)

562

[Ref. p. 564

Table 12. Magnetic and related properties of certain intermetallic compounds of Ni-Zr [82 A 11.Temperature dependenceof susceptibility is given in Figs. 109and 110. Except for Ni,Zr the susceptibility is temperature-independent. Compound

Structure type

xrn . 10e6cm3 mol- ’

Y mJmol-’ K-*

@D K

Zr NiZrz NiZr Ni, ,Zr, Ni,,Zr, Ni,,Zr, Ni,Zr NiiZr, Ni ,Zr

bee CuAlz CrB Ni, ,Zr, Ni,,Zr, Ni,,Zr, Ni,Sn Ni,Zr, AuBe,

131 95 72 79 13 19 89

2.80 4.85 2.0

291 216 270

2.5

351

1p8

5.75

485

‘) Weak ferromagnet.

10.0 4-6 3 Y I

x” 5.0 2.5

50

0

100

150 T-

200

250

Fig. 109.Tempcraturcdependenceofthc susceptibility of Ni -Zr compounds [82A I].

15 .10-6 -cm3 9 I 12

w’ H9

6 0

20

40

60

80

K 100

Fig. I IO.Tempcraturcdependenceofthc susceptibility of Ni,Zr at a high field (z60kOe) [82A I].

Shiga

K

300

1.4.1.6 NiAd, 5d (group 4, 6)

Ref. p. 5641

0.6 k

563

""600 K

0

0.4

400 Ni-W

0.2

lz

200

f

Ni

Mo.W-

Ni

Mo,W-

Fig. 111. Composition dependence of the average atomic moment and the Curie temperature of Ni-Mo and Ni-W alloys [32 S 1, 37 M 11.

Fig. 112. Temperature dependence of the susceptibility of Ni-Mo alloys with 18...lOOwt% MO for heating process. Arrows indicate phase boundary temperatures. T,: a-phase (fee) occurs. TP (x860 “C), TY (z91O”C) and T6 (c 1350 “C) correspond to the peritectic temperatures of, respectively, the P-phase (Ni,Mo), y-phase (Ni,Mo) and g-phase (NiMo). Ta (z 1350 “C) is the eutectic temperature .between aLphase -and g-phase: For alloys with less than 60 wt% MO. Axp, which is shown in the figure, has been added in order to avoid crossing curves [38 G 11.

600 meVW2

I

II

I

300

600

I

I

c

1.0 e----Mo

0.5I 0

900

1200 "C 1500

TNi

MO-

Fig. 113. Composition dependence of the spin-wave stifiess constant D at 4.2 K of Ni-Mo alloys [78 H 21. Land&BOrnstein New Series 111/19a

Shiga

Rcfcrcnces for 1.4.1

561

1.4.1.7 References for 1.4.1 General references 5Sh

I

5Spl 65el 69~1 8’fl

Hansen. M.: Constitution of Binary Alloys, New York: McGraw-Hi!! Inc. 1958. Pearson, W.B.: A Handbook of Lattice Spacings and Structures of Metals and Alloys, London: Pergnmon Press 1958. Elliott. R.P.: Constitution of Binary Alloys, 1st. supp!., New York: McGraw-Hill Inc. 1965. Shunk. F.A.: Constitution of Binary Alloys, 2nd. suppl., New York: McGraw-Hill Inc. 1969. Fischer. K.H., in: Landolt-Biirnstein. New Series(Hellwege, K.H., Olsen, J.L.. eds.),Berlin: Heidelberg. New York: Springer, vol. 1% (1982) 289.

Special references 32K 1 37Sl 37F 1 37hl 1 38G I 54 11’1 63 P 1 64B 1 64 B 2 64N 1 64 W 1 65B I 66H 1 66K 1 67B I 67L 1 68A I 65 A 2 6SK 1 68-I-l 69Al 69K 1 69 K 2 70Bl 70K 1 70K2 7ON 1 71Kl 72Al 72Cl 73Al 73B 1 741 I 7412 75D I 7511 76A I 76Cl 76F1 76L 1 77K 1

Koster. W., Tonn. W.: Z. Metallkd. 24 (1932) 296. Sadron. C.: Ann. Phys. Ser. 10, 17 (1932) 371. Farcns. T.: Ann. Phys. Ser. 11, 8 (1937) 146. Marinn. V.: Ann. Phys. Ser. 11, 7 (1937) 459. Grube. G.. Winklcr. 0.: Z. Elcctrochcm. 44 (1938) 423. Wilhelm, H.A.. Carlson. O.N.. Dickinson. J.M.: Trans. AIME 200 (1954) 915. Piqger, E.. Craig. R.S.: J. Chcm. Phys. 39 (1963) 137. Betsuyaku. H.. Komura. S., Betsuyaku, Y.: J. Phys. Sot. Jpn. 19 (1964) 1262. Booth. J.G.: Phys. Status Solidi 7 (1964) K 157. Nevitt. M.V., Kimball. C.W., Preston. R.S.: Proc. ICM, Nottingham 1964, p. 137. Werthcim. G.K.. Jaccarino, V., Wernick, J.H.: Phys. Rev. A 135 (1964) 151. Bu!yfcnko. A.K.. Gridncv, V.N.: Fiz. Met. Mctallovcd. 19 (1965) 205. Helmgcr. F.: Phys. Kondcns. Mater. 5 (1966) 285. Koehler. W.C.. Moon, R.M.. Trcgo. A.L., Mackintosh, A.R.: Phys. Rev. 151 (1966) 405. Bruckner. W.. Kleinstuck. K., Schulzc. G.E.R.: Phys. Status Solidi 23 (1967) 475. Lam. D.J.. Spokas. J.J., Van Ostenburg. D.O.: Phys. Rev. 156 (1967) 735. Abel, A.W., Craig. R.S.: J. Less-Common Met. 16 (1968) 77. Arajs, S.: J. App!. Phys. 39 (1968) 673. Kai. K.. Nakamichi. T., Yamamoto, M.: J. Phys. Sot. Jpn. 25 (1968) 1192. Tanaka, M.. Ito. N., Tokoro, T., Kanematsu, K.: J. Phys. Sot. Jpn. 25 (1968) 1541. Alfieri. G.T., Banks. E., Kanematsu, K.: J. Appl. Phys. 40 (1969) 1322. Kai, K.: Dr. Thesis. Tohoku Univ. 1969. Kancmntsu. K.: J. Phys. Sot. Jpn. 27 (1969) 849. Bender, D.. Muller. J.: Phys. Kondens Mater. 10 (1970) 342. Kai. K.. Nakamichi. T., Yamamoto, M.: J. Phys. Sot. Jpn. 29 (1970) 1094. Kanemntsu, K.. Fujita. Y.: J. Phys. Sot. Jpn. 29 (1970) 864. Nakamichi. T., Kai, K.. Aoki. Y., Ikedn, K., Yamamoto, M.: J. Phys. Sot. Jpn. 29 (1970) 794. Kancmatsu. K.: J. Phys. Sot. Jpn. 31 (1971) 1355. Aoki. Y., Nakamichi. T., Yamamoto, M.: Phys. Status Solidi (b) 53 (1972) K 137. Callings, E.W., Ho, J.C., Jaffee,R.I.: Phys. Rev. B5 (1972) 4435. Aoki. Y., Nakamichi, T., Yamamoto, M.: Phys. Status Solidi 56 (1973) K 17. Brouha. M.. Buschow, K.H.J.: J. App!. Phys. 44 (1973) 1813. Itoh. K.. Fujita. Y., Kanematsu, K.: J. Phys. Sot. Jpn. 36 (1974) 1024. Itoh. H., Aoki. Y.. Nakamichi, T., Yamamoto, M.: Z. Metallkd. 65 (1974) 149. DufTcr, P.. Sankar. S.G.. Rao. V.U.S.. Bergner, R.L., Obcrmyer, R.: Phys. Status Solidi (a) 31 (1975) 655. Ikeda. K., Nakamichi. T.: J. Phys. Sot. Jpn. 39 (1975) 963. Amamou. A., Caudron. R.. Costa. P., Friedt. J.M., Gautier, F., Loege!, B.: J. Phys. F6 (1976) 2371. Callings, E.W.. Smith. R.D.: J. Less-Common Met. 48 (1976) 187. Fukamichi. K.. Saito. H.: J. Jpn. Inst. Metals (in Japanese)40 (1976) 22. Livi, F.P., Rogers, J.D.. Viccaro, P.J.: Phys. Status Solidi (a) 37 (1976) 133. Kimura. Y.: Phys. Status Solidi (a) 43 (1977) K 141.

References for 1.4.1 77Ml 78Hl 78H2 78Pl 78P2 79Bl 79Kl 79K2 79Ml 79M2 79Sl 7982 8OJl 80Kl 80K2 80Ml 80M2 80Nl 8OSl 8OVl 8OYl 81Fl 81F2 81Gl 81Pl 81Vl 81V2 81Wl 81Yl 82Al 82Bl 82Fl 82F2 82F3 82Wl 83Al 83A2 83Hl 83Ml 83Nl 83Yl 85Fl

Muraoka, Y., Shiga, M., Nakamura, Y.: Phys.‘ Status Solidi (a) 42 (1977) 369. Hafstrom, J.W., Knapp, G.S., Aldred, A.T.: Phys. Rev. B 17 (1978) 2892. Hennion, M., Hennion, B.: J. Phys. F8 (1978) 287. Pop, I., Coldea, M., Rao, V.U.S.: Phys. Status Solidi (a) 49 (1978) 207. Pan, Y.M., Bulakh, I.Ye., Shevchenko, A.D., Latysheva, V.I.: Fiz. Met. Metalloved. 46 (1978) 741. Buschow, K.H.J., van Diepen, A.M.: Solid State Commun. 31 (1979) 469. Khan, H.R., Kobler, U., Luders, K., Raub, Ch.J., Szucs, Z.: Phys. Status Solidi (b) 94 (1979) K27. Kozhanov, V.N.,Romanov,Ye.I?, Verkhovskiy, S.V., Stepanov, A.P.: Fiz. Met. Metalloved 48 (1979) 1249. Muraoka, Y., Shiga, M., Nakamura, Y.: J. Phys. F9 (1979) 1889. Muraoka, Y.: Thesis submitted to Kyoto Univ. 1979. Shavishvili, T.M., Meskhishvili, A.I., Andriadze, T.D.: Fiz. Met. Metalloved. 47 (1979) 880. Shiga, M., Nakamura, Y.: J. Phys. Sot. Jpn. 47 (1979) 1446. Jacob, I., Davidov, D., Shaltiel, D.: J. Mag. Magn. Mater. 20 (1980) 226. Krischel, D., Thomas, L.K.: J. Phys. F 10 (1980) 115. van der Kraan, A.M., Gubbens, P.C.M., Buschow, K.H.J.: J. de Phys. 41 (1980) C 1-189. Marchenko, V.A., Polovov, V.M.: Zh. Eksp. Teor. Fiz. 78 (1980) 1062[Sov. Phys. JETP 51(1980) 535-J. Muraoka, Y., Shiga, M., Nakamura, Y.: J. Phys. F 10 (1980) 127. Nakamura, Y., Shiga, M.: J. Mag. Magn. Mater. 15-18 (1980) 629. Strom-Olsen, J.O., Wilford, D.F.: J. Phys. F 10 (1980) 1467. Verkhovskiy, S.V., Kozhanov, V.N., Stepanov, A.P., Romanow, Ye.P., Galoshina, E.V.: Fiz. Met. Metalloved. 49 (1980) 1234 [Phys. Met. Metallogr. (USSR) 49, No. 6 (1981) 941. Yamada, Y., Ohmae, H.: J. Phys. Sot. Jpn. 48 (1980) 1513. Fujii, H., Pourarian, F., Sinha. V.K., Wallace, W.E.: J. Phys. Chem. 85 (1981) 3112. Fujii, H., Pourarian, F., Wallace, W.E.: J. Mag. Magn. Mater. 24 (1981) 93. Grossinger, R., Hilscher, G., Wiesinger, G.: J. Mag. Magn. Mater. 23 (1981) 47. Pourarian, F., Fujii, H., Wallace, W.E., Sinha, V.K., Smith, H.K.: J. Phys. Chem. 85 (1981) 3105. Verkhovskiy, S.V., Kozhanov, V.N., Stepanov, A.P., Shevchenko, A.D., Pan, V.M., Bulakh, Lye.: Fiz. Met. Metalloved. 49 (1981) 553 [Phys. Met. Metallogr. (USSR) 49 No. 3 (1981) 911. Vincze, I., van der Woude, F., Scott, M.G.: Solid State Commun. 37 (1981) 567. Wiesinger, G., Oppelt, A., Buschow, K.H.J.: J. Mag. Magn. Mater. 22 (1981) 227. Yamada, Y., Ohira, K.: J. Phys. Sot. Jpn. 50 (1981) 3569. Amamou, A., Kuentzler, R., Dossmann, Y., Forey, P., Glimois, J.L., Feron, J.L.: J. Phys. F 12 (1982) 2509. Buschow, K.H.J.: J. Appl. Phys. 53 (1982) 7713. Fujii, H., Pourarian, F., Wallace, W.E.: J. Less-Common Met. 88 (1982) 187. Fujii, H., Pourarian, F., Wallace, W.E.: J. Mag. Magn. Mater. 27 (1982) 215. Fujii, H, Sinha, V.K., Pourarian, F., Wallace, W.E.: J. Less-Common Met. 85 (1982) 43. Wiesinger, G., Hilscher, G.: J. Phys. F 12 (1982) 497. Ahmed, MS., Hallam, G.C., Read, D.A.: J. Mag. Magn. Mater. 37 (1983) 101. Akselrod, Z.Z., Budzynski, M., Khazratov, T., Komissarova, B.A., Kryukova, L.N., Reiman, S.I., Ryasny, G.K., Sorokin, A.A.: Hyperfine Inter. 14 (1983) 7. Hirosawa, S., Pourarian, F., Sinha, V.K., Wallace, W.E.: J. Mag. Magn. Mater. 38 (1983) 159. Muraoka, Y., Shiga, M., Nakamura, Y.: Phys. Status Solidi (a) 78 (1983) 717. Nishihara, Y., Yamaguchi, Y.: J. Phys. Sot. Jpn. 52 (1983) 3630. Yamada, Y., Ohira, K.: J. Phys. Sot. Jpn. 52 (1983) 3646. Fujii, H., Okamoto, T., Wallace, W.E., Pourarian, F., Morisaki, T.: J. Mag. Magn. Mater. 46 (1985) 245.

Landolt-Bbrnstein New Series 111/19a

565

Shiga

1.4.2.1 3d-4d, 5d (group 8): 3d-rich alloys

[Ref. p. 648

1.4.2 3d elements and Ru, Rh, Pd or OS, Ir, Pt 1.4.2.1 3d-rich alloys Survey Alloy Cr, -,Ru,

Cr, -,Rh, Cr, -,Pd, Cr, -%os,

Cr, -Jrr

Crl -,Pt,

Mn, -xPd,

Fe, -A

co, -A Nil -A Ni, -,Ru, Ni, -IOs,

X

x50kOe: XHF=0.9. 10-6cm3g-’ for Cu,Au-type VPt,. and xHF=l.O. 10v6 cm3 g-’ for T&-type

100

0 0.4

Frame, Gersdorf

I

K

600

1.4.2.2.2 Cr-4d, 5d (group 8)

582

[Ref. p. 648

3 Gem: 9

2 I b

0

50

100

!

i'00

150

T-

K

250

Fig. 13.Variation of the spontaneousmagneticmoment per unit mass,U,with temperaturefor V(Ir, -rPtr)3 alloys [77 G 11.

Table 5. Experimental values for the coefficient 7 of the electronic term in the specific heat, and for the susceptibility xrnof various V-Pt compounds [82A 11. Compound

y mJ mol-’ K-’

Xm 10m6cm3mol- ’

V v,pt VPt vpt, vpt, Pt

9.9 7.19 3.38 2.00 3.24 6.6

286 220...250 148 118 ordered 237

Fig. 14.EstimatedaveragemagneticmomentofV atoms, j,., and of Pt atoms. j&,. together with the observed spontaneousmagneticmoment per formula unit, j, as a function of x in V(Ir, -XPtr)3[79 K I].

1.4.2.2.2 Cr alloys and compounds Thermomagnetic measurementshave been performed on concentrated Cr-M alloys (M: group VIII 4d or 5d element) over the whole composition range (Figs. 15 and 17).The susceptibility at room temperature strongly depends on the heat treatment as is indicated for Cr-Pd in Fig. 18. Cr-Pd and Cr-Pt have been studied in more detail. The fee Cr-Pd alloys in the composition range 25...35 at% Cr show mictomagnetic behavior (Fig. 21). Neutron diffraction measurementsreveal that the magnetic structure of ordered CrPt, is ferrimagnetic with two sublattices: the Cr atoms occupy one sublattice, the Pt atoms the other one, see Table 6. An antiferromagnetic structure in which Cr spins are antiferromagnetic within each layer was detected in the ordered CrPt compound (CuAuI-structure) at room temperature (Fig. 24). For the disordered systems superparamagnetic behavior is suggested[73 B 23.

Franse, Gersdorf

1.4.2.2.2 Cr-4d, 5d (group 8)

582

[Ref. p. 648

3 Gem: 9

2 I b

0

50

100

!

i'00

150

T-

K

250

Fig. 13.Variation of the spontaneousmagneticmoment per unit mass,U,with temperaturefor V(Ir, -rPtr)3 alloys [77 G 11.

Table 5. Experimental values for the coefficient 7 of the electronic term in the specific heat, and for the susceptibility xrnof various V-Pt compounds [82A 11. Compound

y mJ mol-’ K-’

Xm 10m6cm3mol- ’

V v,pt VPt vpt, vpt, Pt

9.9 7.19 3.38 2.00 3.24 6.6

286 220...250 148 118 ordered 237

Fig. 14.EstimatedaveragemagneticmomentofV atoms, j,., and of Pt atoms. j&,. together with the observed spontaneousmagneticmoment per formula unit, j, as a function of x in V(Ir, -XPtr)3[79 K I].

1.4.2.2.2 Cr alloys and compounds Thermomagnetic measurementshave been performed on concentrated Cr-M alloys (M: group VIII 4d or 5d element) over the whole composition range (Figs. 15 and 17).The susceptibility at room temperature strongly depends on the heat treatment as is indicated for Cr-Pd in Fig. 18. Cr-Pd and Cr-Pt have been studied in more detail. The fee Cr-Pd alloys in the composition range 25...35 at% Cr show mictomagnetic behavior (Fig. 21). Neutron diffraction measurementsreveal that the magnetic structure of ordered CrPt, is ferrimagnetic with two sublattices: the Cr atoms occupy one sublattice, the Pt atoms the other one, see Table 6. An antiferromagnetic structure in which Cr spins are antiferromagnetic within each layer was detected in the ordered CrPt compound (CuAuI-structure) at room temperature (Fig. 24). For the disordered systems superparamagnetic behavior is suggested[73 B 23.

Franse, Gersdorf

Ref. p. 6481

1.4.2.2.2 Cr-4d, 5d (group

8)

583

Survey

Cr, -.Ru, Cr, -xRh, Cr, -,Pd,

Cr, -,Os, Cr, -Jrx Cr, -xPt,

CrPt %.3%7 CrPt CrPt, CrPt, CrPt, Cr, -,Mn,Pt,

X

Property

Fig.

O<xI ) 252

0w 0 F11

I

20 at% 30

10 Ir -

Fig. 38. Magnetic phase diagram of y-phase Mn, -Jrx alloys [74Y I]. Fig. 39. Tempcraturc depcndencc of magnetic mass susceptibility )I~ and electrical resistivity e of the Mn,,,,Ir,,,, alloy (disordcrcd, y-phase). compared with the tcmpcraturc dependence ofsquarcd relative sublatticc magnetization MZ obtained from neutron diffraction. Arrows indicate the anomalies corresponding to the antifcrromagnctic transition [74Y 11.

Frame, Cersdorf

a80

6y,

Landolt-Rorn?lcin . ..

^

1.4.2.2.3 MnvId, 5d (group 8)

Ref. p. 6481 600 “C

593

16 THz

400

I *

200

0

-200 8000 G

20 THz

6000

16

t 2s 4000 #

I 12 ?

2000

0 10

8

30 at%

20

40

Mn-

Fig. 40. Saturation magnetization M, and Curie temperature Tc of Pt-Mn alloys near the 3: 1 composition [50 A 11. Fig. 41. Magnon dispersion relation of MnPt, in the three principal symmetry directions at a temperature of 80 K: (a): [loo]; (b): [llO] and (c): [ill]. The data are compared with the dispersion relation of FePd, at 4.2 K (solid curves) as measured by [77 S 11. Horizontal error bars refer to constant-E-type scanqvertical error bars refer to constant-Q-type scans [79P 11.

Landolt-Bornstein New Series 111/19a

Franse, Gersdorf

1.4.2.2.3 Mnwld, 5d (group 8)

594

Pt 0.t.t

a

b

‘

Mn0.0.0

Pi0 f.i

d

L11 2.2.2

[Ref. p. 648

f.o.0

o.+.o

e

Fig. 42. Sections of the magnetization distribution in MnPt, obtained by Fourier inversion of the polarized neutron diffraction data. Contours arc exprcsscd in [pn/A3]. Wavevector of momentum transfer: Q =4n(sinO)/%. (a) l/4 of the section on a basal plane including all reflections out to (sinO)/i.=0.75&‘, (b) l/4 ofthc section parallel to a basal plane through the center of the cell, including all rcflcctions out to (sin 0),/L=0.75 A - I, (c)same as (a), including all rcflcctions out to (sin0)/1.=0.85 A-‘, (d) same as (b), including all rcflcctions out to (sinO)j%=O.fGA-‘, (c) same as (c), integrated over a volume &Y3,where 26 is the edge of the cubic volume ccntcrcd at the point over which the avcragc is taken. 6=a/lO, and (f) same as (d), intcgratcd over a volume 8fi3 with S=a,/lO. In sections (a) to (d), the zero contour lines (dotted lines) enclose regions of ncgativc magnetic density, which rcachcs the lcvcl -0.025 pR/A3 at the center of the Pt site [69A I].

Frame, Cersdorf

Landoh-R6rnwin Nex Scrin 111’19n

Ref. p. 6481

1.4.2.2.3 Mn-4d,

MnPt

a

595

8)

Mn3Pt

b

l Mn oPt

F

E

MnP& I 70 at% Mn

G

H

Fig. 43. (a) Possible magnetic structures ofMnPt (CuAuItype of structure); the Mn and Pt atoms are represented by solid and open circles, respectively; structures II. ..IV correspond to, respectively, structures A. .C in Fig. 35; (b) possible magnetic structures of Mn,Pt (Cu,Au-type of structure); (c) magnetic phase diagram of the Mn-Pt system; the letters denote, for the ordered alloys, the stability regions of the various magnetic structures given in (a) and (b) [68 K 21, see also [74 R 11.A’: structure A in (b) with Mn on Pt-sites and vice versa. The dashed line represents TN for disordered Mn-Pt.

\ A’

c

5d (group

Pt -

IO 40-f cm3 9

120 .1o-g m3 kg 80

6 IO

120

8

100 80

hI

I 1: H" 8

120 I 100 .=g

I!

)OOD 01 0

0.2

0.4

120 80

8

0.6

0.8

1.0

x-

Fig. 45. Magnetic phase diagram of the Mn,Pt,-Jh, system; the letters denote, for the ordered alloys, the stability regions of the various magnetic structures given in Fig. 43b [68 K 21. The dashed line represents TN for disordered Mn,Pt, -,Rh,.

100

6

80

IO

120

8

100 80

6 0

200

400

600

800

1000"C 1200

i-

Fig. 44. Mass susceptibility xp vs. temperature for Mn-Pt alloys [63 Y 11. Landolt-BOrnstein New Series 111/19a

Frame, Gersdorf

1.4.2.2.4 Fe-4d, 5d (group 8)

596

[Ref. p. 648

1.4.2.2.4 Fe alloys and compounds

The FeRu and FeeOs systems,having the hcp phase boundary in the Fe-rich region, allow the study of the magnetic properties of Fe in the hcp phase. For both systemsthe internal magnetic field has been studied in the antifcrromagnetic state by means of MGssbaucr experiments (Fig. 48). Fe--Rh alloys near the equiatomic composition have the CsCI-type of structure. At low temperatures the alloys are antiferromagnctic with magnetic moments of 3.3p,, antiparallel on neighboring iron atoms. Above 320 K the magnetic structure transforms into a ferromagnetic state with magnetic moments of 3.17l.1,~ and 0.97pu on the Fe and Rh sites. respectively. The magnetic moment distribution for the nonstoichiometric Fe-rich compounds is shonn in Fig. 5 1. The antiferromagnctic-ferromagnetic and ferromagnetic-paramagnetic transition temperatures have been studied as a function of pressure for equiatomic FeRh and Fe,,,,,Rh,,,,,. The phasedia_eramof the Fc-Pd systemrevealstwo ordcrcd structures: FePd (CuAuI-type) and FePd,; both order ferromagnetically. For FePd the iron and palladium magnetic moments amount to 2.85pa and 0.35l.~a, respectively [65 C 11.Different results for the atomic magnetic moments have been reported for ordered FePd,. At 300K: &=2.37(13)p,,. &=0.51(4)p,) [62P I]; in reference [65C 11: ~re=3.10~lj. &,=0.42p11. The ironrich FeePd alloys show excellent magnetic properties after an appropriate heat treatment and cold-drawing (Fig. 64). Fe-Pd alloys around 30at% Pd, whcrc the transition from the fee to the bee structure occurs, show typical Invar properties: anomalies in the thermal expansion below T, (Fig. 65) and large forced magnetostrictions. Fe&r alloys have been investi_patedin magnetization experiments in the composition range 30,..70at% Fe. In the Fe-Pt systemseveral types ofmagnetic order have been observed.The Curie temperature as a function of composition is given in Fig. 72. In Fig. 77 the basic types of magnetic structures for this systemare shown. In the composition range 24...36 at% Fe, a change in the type of antiferromagnetic order occurs from parallel iron moments in the (110) planes to parallel moments in the (100)or (010) planes. A value of 3.3 pa has been reported for the magnetic moment per iron atom in FePt, [63 B I]. Above 32at% Fe ferromagnetism becomes predominant. The saturation magnetization for ordered and disordered alloys is shown in Fig. 78. The magnetic ordering temperatures of the ordered and disordered FePt, phasedependson composition as indicated in Fig. 75 and Table 15.In the pseudobinary scrics of Fc(Pd,Pt 1-X)3a transition from a ferromagnetic state as in FePd, to an antiferromagnetic state as in FePt, occurs near x=0.5. In the intermediate region an additional magnetic transition from a high-temperature ferromagnetic to a low-temperature canted-ferrimagnetic structure is found (Figs. 93 and 94). The ordered equiatomic FePt alloy (CuAuI-type of structure) is hard to magnetize. A value for the mean atomic magnetic moment of 0.77 pn has been reported. By disordering FePt the bulk magnetization increasesconsiderably. From theseobservations ferrimagnetic order was concluded for the ordered compound. Neutron diffraction studies. however, point to Fe magnetic moments at 300 K of 2.8(1)p,,. parallel to the c axis. whereas Pt moments could not bc determined [73 K 51. In [74 M 23 the hypothetical values pFc= 2.75pr, and ijp,= -0.25 11,~ arc mcntioncd for the ordered FePt compound. The Fc-Pt alloys near the 25 at% Pt composition show invar characteristics aswell in the Cu,Au-type ordered state asin the disordered state.At low temperature these alloys undergo a martcnsitic transformation. The results of magnetic moment and Curie temperature studies on ordcrcd and disordcrcd alloys with 20,..30at% Pt arc given in Figs. 85, 86. Anomalies in the thermal expansion arc of a similar type as those in Fe-Ni invar alloys (Fig. 87). Survey X

Fe, -.A Fe, -,Rh,

0.1 <x 5.7

320

280

240

I 200 a, .> 2 160 -

1 P IQ 2.5

2 120

0 0 0 0 0 0 0c I. 3

80

40

. l -. .

1.5 0 Pd- 4at%Mn . Pd-6at%Mn A Pd 8ot%Mn

A*

2

1.0 0.5

A-b,~~A

A-----n.

0

4

T-

6

.A

8

a.

K

IO

0

3

6

9 8 WPl

Fig. 17. Temperature dependenceof the low-field ac susceptibility xLF for Pd-Mn alloys containing 4at%, 6 at% and 8 at% Mn. The position of the sharp peaksin xLFdefinesthe freezing temperature T, [77 Z 11.

Land&BCmctein NW Serier 111/19a

1

0%

!-n

0.35ot%Fe

2.0

nor?+--

l

/'/ fiSot%Mn.

12

15

T

18

-

Fig. 18. High-field magnetization, expressedas average magneticmomentper solute atom,jsolute,for Pd-Mn and Pd-@In, Fe)vs.applied flux density [79 M 1] at 1.5K and 4.2K, respectively.

Franse, Gersdorf

1.4.2.3 Mn4d, 5d (group 8)

638

[Ref. p. 648

I

Pd-Mn

I_

0 PJ

6

2

8 at%

10

E:n -

Fig. 19. Saturation magnetic moment j& as function of Mn concentration for Pd ~Mn alloys [79S I], see also [73 B 3, 75 D 1. 77C I]. and [78 F I]. Diffcrcnt symbols rcprcscnt data ofdifTcrcnt authors for PDFMn (lower solid line). For comparison the upper solid line shows jpc VS.Fe concentration for Pd Fc.

L50 mJ molK

LOO

150 100 50 0 0

3

9

6

12

15 K

18

TFig. 20. (a) Diffcrcncc Aa in the thermal expansion cocflicicnt bctwccn various Pd-Mn alloys and pure Pd. The ferromagnetic and spin-glass transition temperatures arc indicated by T, and T,, rcspcctivcly. (b) Excess specific heat AC = C,,,,, - Ghostof various Pd--Mn alloys. The broken curve represents the ferromagnetic contribution to AC for the Pd -2 at% Mn alloy, whcrcas the solid curve shows the antiferromagnetic cluster part [S 1 B I], seealso [Sl T I].

Ref. p. 6481

1.4.2.3 Mn, Fe-4d, 5d (group 8)

.10’5

639

Pt-Mn I

-cm3 9 ,

a

2.5 0

50

100

150

200

250

300

350

400

450

0

500

0.25

b

0.50 at% Mn c-

Fig. 21. (a) Impurity contribution Axp to the mass susceptibility as measured in low field vs. normalized temperature T/c for Pt-Mn alloys. (b) Paramagnetic Curie temperature 0 as function of impurity concentration c [77 T I], see also [69 M 11; for the specific heat data, see [74 S 11.

Table 4. Magnetic moment and Curie temperature for 1 at% solutions of Fe in 4d alloys from Ru to Pd [62 C 21. pFe: Fe magnetic moment calculated from the

relation p,“,,= pFe(PFe + gla) with g = 2. & : average Fe magnetic moment derived from saturation magnetization. Alloy

Ru RU o.,dWm km%,, Rudho., Ru o.zsRh,,,, Rh Rho.+&., Rhd%.ax bd’do., Rhd%.s Rho.,Pdo., Rbd’4,.,, Pd Pdo.,,Ag,.,,

Structure

hcp hcp hcp hcp

fee fee fee fee fee fee fee fee fee fee

PFe

0

PFe

T,

PB

K

PB

K

0.0 0.0 0.8 1.3 1.7 2.2 4.5 5.9 ') 7.1 ') 9.6')

-21(2) -13(2) -17(2) -14(2) -2 -2 1

11.4‘)

E(2)

7.1 9.5

12.7') 11.3 ') 8.3 1)

49(6)

10.8

55(3) 12

9.7 6.3

i) Determined by relating the magnetic susceptibility near T = 100 K.

Landolt-Bbrnstein New Series 111/19a

Frame, Gersdorf

11 27 39 39

11

to a Curie-Weiss law

1.00

[Ref. p. 648

1.4.2.3 Fe-4d, 5d (group 8)

640

1.0 Crm3

I

I

I

0.6

b

OX

Pd.T=l.ZgK / 0.i

8 15

10

5

0

20

kOe ;

H-o;?

=ig. 22. hJngnctization curvzs for various conccnlrations If Pd Fc alloys at 1.25K and 0.05 K. rcspcctivcly. The ron conrcntrntion is _pivenin ppm [71 C 21.

16 kOe 20

12

Fig. 23. Magnctizntion curves of high-purity Pd-Fc alloys at low tcmpcratuics [70 M 31. 25.0 ,103 9

I

I

I

0.1

0.2

0.3

Pd and

I

I

I

I

0.L

0.5

0.6(Gcm3/g)’

cm3 2o.c

17.5

15.c I b 12.: \ x 0

0.0’

0.02

0.03 at%

0.05

1O.I

Fe -

Pd

5 Gcir’ Pd-Fe 9 i 1

I

3

6

2

7.:

5.1

2!

CT2-

1 I 0.75

c c

PC

0.25

0.50

Fe-

I 1.00 ot% 1.25

Fe -

Fi_r.25. Saturation mayctic moment per unit mass o, and Curie constant C, of Pd Fc alloys [7 1C 2).

Fig. 24. H/a against ~7’ for Pd-O.l5at% Fe. The highfield points (I . ..I&5 kOc) arc marked with symbols denoting the tcmpcraturc of mcasurcmcnt. For the lowfield points (0...1.25 kOe) the tcmpcraturcs are marked on the figure. The straight lines making intcrccpts on the G* axis arc drawn through isothermal points for liclds above IOkOc [70M3].

Frame, Gersdorf

641

1.4.2.3 FewId, 5d (group 8)

Ref. p. 6481

Table 5. Atomic magnetic moments in Pd-Fe alloys [65 C 11.

3 7 25 50

0.234(7) 0.457(14) 1.00(3) 1.60(5)

2.92(H) 2.76(11) 2.64(H) 2.49(11)

2.9(3) 3.0(2) 2.9(2) 3.0(l)

3.07(U) 3.02(11) 2.98(15) 2.85(8)

0.15(l) 0.26(2) 0.34(5) 0.35(8)

‘) From large-angle neutron scattering data assuming no Pd contribution and the metallic Fe form factor.

0

200 T-

-100

300

K

400

Fig. 26. Variation of spontaneous magnetization gSwith temperature for Pd-Fe alloys; the iron content is given in the figure [60 C 21. K ox I Q 0.2

I

0 c*-

hy

0.6 K I 0.4 I-Y 0.2

0

0.2

Il.kot%Fe 0.6

0

IO

20

30

m%t%Fe)*50

c*-

C-

Fig. 27. Ferromagnetic Curie temperature ‘Kcand paramagnetic Curie temperature 0 for Pd-Fe alloys as function of Fe concentration c [7 1 C 21. Landolt-Bdmstein New Series lWl9a

Franse, Gersdorf

[Ref. p. 648

1.4.2.3 Fe-4d, 5d (group 8)

642

8 Fe -

4 PO6

12 at% 16

Fig. 28.Variation ofthc Curie point with iron content for Pd-Fe alloys [60 C 23.seealso [70 C I].

/

Pd- O.l6at%Fe

1

(

1

50

100

I

150

200

250 K 300

‘C -

2

1

6

8 7-

10

12

11 K 16

Fig. 30. Excessspecific hcnt AC= C’~llny-Chos, VS. T Pd O.l6at% Fc. Curve I: H ~%%~]?~ 3: H,,,,= I .8kOc, and 4: H,,,zt=?k& also [61 V I].

Fig. 29. Volume derivative of the Curie temperaturefor Pd-Co, Fc (a) and Pt-Co, Fe (b) alloys plotted vs. the Curie tcmpcraturc of the respectivealloy [74 M I]. Diffcrcnt size of the symbols indicates different authors.

for

Table 6. Alloy compositions and magnetic parameters for dilute Pd[Gcm3g-‘1 Pa, CPBI t% Ccd

0.51 2.7 0.36 0.013 2.5

5.17 104 5.30 0.18 3.5

10.2 218 10.52 0.34 3.4

15.2 315 15.37 0.48 3.2

20.1 19.6 0.59 3.0

Pd-Ni Solute content [at%]

T,CKl

2.5 12

os [Gcm3g-‘1 L, Cd

Psi bnl

5.55 88 7.37 0.14 2.5

11.78 177 14.50 0.26 2.2

18

mJ Krr:? 15

12 1 sg 6 .5% lolcl h?:t copxily

3

0

3

6

12

15

K 18

Fig. 40. Excess spccitic heat AC vs. T for Pt-0.5 at% Co. Curve I: H,,,,=O, 2: H,,,,=4.5 kOe. 3: Ha,,,=9 kOe, 4: H,,,,=18kOe,5: H,,,,=27kOe [73Nl].

Fig. 41. Inverse initial mass susceptibility 10 ’ vs. temperature for various Pd-Ni alloys. Solid circles [81 C I], open circles [78 S 11.

Frame, Gersdorf

Ref. p. 6481

1.4.2.3 Ni-4d, 5d (group 8)

647

Fig. 42. Magnetization curve at 2.4 K for various Pd-Ni alloys and for pure Pd. Solid circles [S 1 C 11; open circles [78 S 11; see also [74 C I] and [76 C 11. For pressure effect, see [75 B 1] and [76 B 11; for magnetostriction, see [SOH I].

0

1.00

IO

20

30

40

I

30 K

0

Pd-Ni

t

50 kOe 60

0.16 mJ K"mol I 0.12 a 0.10 0.08

Qcm ai% 7.5

r\

I 8000 'I z 6000 7 2 4000 4

D/I

1

j/-

5.0 I ? : 2.5 '

\ \I

AdI/\

.g -2

2

4

6

8 NI -

10

12

14at% 16

Fig. 43. The coefficients y and /I of the low-temperature specific heat, C,=yT+ pT3, of Pd-Ni alloys, plotted vs. Ni concentration [68 C 23, see also [83 Ill. For the de Haas-van Alphen effect, see [82 R 11;for spin fluctuations, see [83 B 11.

I

2000

I

0.06 0

0

0 24

20

4 16 0

Landolt-BOrnstein New Series ill/19a

1

2 NI -

3

at%

4

Fig. 44. (a) Inverse susceptibility &lNi of Pd-Ni alloys relative to xpdl of pure Pd as a function of Ni concentration: on the right Tc as a function of Ni concentration; (b) resistivity data for Pd-Ni alloys, plotted as l/cAA/A,, and AQ/Cvs. c; A is the coefficient of the T2 term in Q(T); AA and AQ are defined with respect to pure Pd; (c) incremental electronic specific heat vs. c [74M 31, see also [82B2].

Franse, Gersdorf

648

Rcfcrcnccs for 1.4.2

1.4.2.4 References for 1.4.2 3oc 1 32Sl 35Fl 35Gl 36F1 37M 1 40Gl 50Al 50K 1 52Kl 5SG1 5SG2 59Cl 59C2 60C 1 6OC2 61 B I 62B I 62Cl 62C2

Constant, F.W.: Phys. Rev. 36 (1930) 1654. Sadron. C.: Ann. Phys. Paris 17 (1932) 371. Friederich. E.. Kussmann. A.: Phys. Z. 36 (1935) 185. Grubc. G.. Winklcr. 0.: Z. Elektrochem. 41 (1935) 52. Fallot, M.: Ann. Phys. 6 (1936) 305; 7 (1937) 420; 10 (1938) 29. Marian. V.: Ann. Phys. Paris 7 (1937) 459. Gebhardt, E., Kbster, W.: Z. Mctallkd. 32 (1940) 252. Auwgrter. M., Kussmann. A.: Ann. Phys. 7 (1950) 169. Kussmann. A.. Rittbcrg. G. v.: Ann. Phys. 7 (1950) 173. Kiister. W., Horn. E.: Z. Mctallkd. 43 (1952) 444. Gerstenbcrg. D.: Ann. Phys. Leipzig 2 (1958) 236. Gerstenberg. D.: Z. Metallkd. 49 (1958) 476. Corliss. L.M., Hastings, J.M., Weiss, R.J.: Phys. Rev. Lett. 3 (1959) 211. Crangle. J.: J. Phys. Paris 20 (1959) 435. Crangle. J.. Parsons. D.: Proc. R. Sot. 255 (1960) 509. Crangle. J.: Philos. Mag. 5 (1960) 335. Bozorth. R.M.. Wolff. P.A., Davis, D.D., Compton, V.B., Wernick, J.H.: Phys. Rev. 122 (1961) 1157. Bozorth. R.M.. Davis. D.D., Wernick, J.H.: J. Phys. Sot. Jpn. 17, B-I (1962) 112. Cable. J.W., Wollan. E.D., Koehler, W.C., Child, H.R.: Phys. Rev. 128 (1962) 2118. Clogston. A.M., Matthias, B.T., Peter, M., Williams, H.J., Corenzwit, E., Sherwood, R.C.: Phys. Rev. 125 (1963) 541. Nagle. D.E.. Craig. P.P., Barrett, P., Cochran, D.F.R., Olsen, C.E., Taylor, R.B.: Phys. Rev. 125(1962) 62Nl 490. 62P 1 Pickart, S.J..Nathans. R.: J. Appl. Phys. 33 (1962) 1336. 63B 1 Bacon. G.E., Crangle. J.: Proc. R. Sot. London A272 (1963) 387. 63K 1 Kouvel, J.S.. Hart&us. C.C., Osika, L.M.: J. Appl. Phys. 34 (1963) 1095. 63 P 1 Pickart. S.J..Nathans. R.: J. Appl. Phys. 34 (1963) 1203. Yokoyama. T., Wuttig, M.: Z. Metallkd. 54 (1963) 308. 63Y1 Booth. J.G.: Phys. Status Solidi 7 (1964) K 157. 64B I Laar. B. van: J. Phys. Paris 25 (1964) 600. 64L1 Shaltiel. D., Wernick. J.H., Williams, H.J., Peter, M.: Phys. Rev. 135 (1964) A 1346. 64s 1 Shnltiel. D., Wernick. J.H.: Phys. Rev. 136 (1964) A 245. Shirane. G., Nathans, R., Chen, C.W.: Phys. Rev. 134 (1964) A 1547. 64S2 64V 1 Veal. B.W., Raync. J.A.: Phys. Rev. 135 (1964) A 442. Cable. J.W., Wollan. E.O., Koehler, WC.: Phys. Rev. 138 (1965) A755. 65Cl Crangle. J., Scott. W.R.: J. Appl. Phys. 38 (1965) 921. 65C2 Collins. M.F., Low, G.G.: Proc. Phys. Sot. (London) 86 (1965) 535. 65C3 Tsiovkin. Yu.N., Volkenstheyn. N.V.: Phys. Met. Metallogr. (USSR) 19, 3 (1965) 45. 65Tl 66C 1 Campbell. LA.: Proc. Phys. Sot. (London) 89 (1966) 71. 66G 1 Geballe. T.H., Matthias. B.T., Clogston, A.M., Williams, H.J., Sherwood, R.C., Maita, J.P.: J. Appl. Phys. 37 (1966) 1181. Koehler. W.C., Moon, R.M., Trego, A.L., Mackintosh, A.R.: Phys. Rev. 151 (1966) 405. 66K I 66K2 Krin, E.. KLdir. G., Pil. L., %lyom, J., Szab6, P.: Phys. Lett. 20 (1966) 331. 66K3 Krt-n. E.. S6lyom. J.: Phys. Lett. 22 (1966) 273. 66M I Menzinger. F., Paoletti. A.: Phys. Rev. 143 (1966) 365. 67Dl Dunlap, B.D., Dash. J.G.: Phys. Rev. 155 (1967) A460. 67M 1 Maley. M.P., Taylor. R.D.. Thompson, J.L.: J. Appl. Phys. 38 (1967) 1249. 67s 1 Sarachik. M.P., Shaltiel. D.: J. Appl. Phys. 38 (1967) 1155. 67S2 Segnan. R.: Phys. Rev. 160 (1967) A404. 67Tl Trousdale. W.L., Longworth, G., Kitchens, T.A.: J. Appl. Phys. 38 (1967) 922. 6SA 1 Alekseevskii. N.E., Samerskii, Yu.A., Kir’yanov, A.P., Tsebro, V.I.: JETP Lett. 8 (1968) 403. 6SB 1 Brinkman. W.F., Bucher, E., Williams, H.J., Matia, J.P.: J. Appl. Phys. 39 (1968) 547. 6SB2 Baggurley, D.M.S.. Robertson, J.A.: Phys. Lett. 27 A (1968) 516. 6SC 1 Comly, J.C.. Holden. T.M.. Low, G.G.: J. Phys. C 1 (1968) 458. 6SC2 Chouteau. G., Fourneaux. R.. Tournier, R., Lederer, P.: Phys. Rev. Lett. 21 (1968) 1082. 6SG 1 Gainon. D.. Sierra. J.: Phys. Lett. 26 A (1968) 601. Frame, Gersdorf

Referencesfor 1.4.2 68Hl 68Kl 68K2 68Ml 68Pl 68P2 68s 1 68Wl 69Al 69Cl 69Fl 69F2 69Kl 69K2 69K3 69Ml 69Nl 69Pl 69Rl 69Sl 69Tl 69Vl 69Wl 69W2 70Al 70A2 70Bl 70B2 7OCl 7OC2 7OJl 70Kl 70K2 70K3 7OLl 70Ml 70M2 70M3 70Nl 70N2 7OVl 7OWl 71 c 1 71C2 71c3 7111 7112 71Ll 71Ml 71M2 7101 71Sl 71S2 71s3 71Tl Land&B6msrein New Series 111/19a

649

Hicks, T.J., Pepper, A.R., Smith, J.H.: J. Phys. Cl (1968) 1683. Kussmann, A., Miiller, K., Raub, E.: Z. Metallkd. 59 (1968) 859. KrCn, E., Kadar, G., Pal, L., Sblyom, J., Szabo, P., Tarnoczi, T.: Phys. Rev. 171 (1968) 574. McDougal, M., Manuel, A.J.: J. Appl. Phys. 39 (1968) 961. Pal, L., KrCn, E., Kadar, G., Szabb, P., Tarnoczi, T.: J. Appl. Phys. 39 (1968) 538. Ponyatovskii, E.G., Kutsar, A.R., Dubovka, G.T.: Kristallografiya 12 (1967) 79 (Sov. Phys. Crystallogr. 12 (1968)). Shirley, D.A., Rosenblum, S.S.,Matthias, E.: Phys. Rev. 170 (1968) 363. Wayne, R.C., Bartell, L.C.: Phys. Lett. 28A (1968) 196. Antonini, B., Lucari, F., Menzinger, F., Paoletti, A.: Phys. Rev. 187 (1969) 611. Calow, J.S., Meads, R.E.: J. Phys. C2 (1969) 2120. Fujimori, H., Saito, H.: J. Phys. Sot. Jpn. 26 (1969) 1115. Fischer, G., Besnus, M.J.: Solid State Commun. 7 (1969) 1527. KrCn, E., KBdLr, G.: Phys. Lett. 29A (1969) 340. Kouvel, J.S., Forsyth, J.B.: J. Appl. Phys. 40 (1969) 1359. Kawatra, M.P., Skalski, S., Mydosh, J.A., Budnick, J.I.: J. Appl. Phys. 40 (1969) 1202. Miyaka, Y., Morishita, H., Watanabe, T.: J. Phys. Sot. Jpn. 27 (1969) 1071. Nagasawa, H.: J. Phys. Sot. Jpn. 27 (1969) 787. Palaith, D., Kimball, C.W., Preston, R.S., Crangle, J.: Phys. Rev. 178 (1969) 795. Rault, J., Burger, J.P.: C.R. Acad. Sci., Ser. B 269 (1969) 1085. Star, W.M., Nieuwenhuys, G.J.: Phys. Lett. 30A (1969) 22. Tu, P., Heeger, A.J., Kouvel, J.S., Comley, J.B.: J. Appl. Phys. 40 (1969) 1368. Vinokurova, L.I., Nikolayev, I.N., Mel’nikov, Ye.V., Adis’yevich, I.K., Reutov, Yu.B.: Phys. Met. Metallogr. (USSR) 28, 6 (1969) 147. Williams, G., Loram, J.W.: Solid State Commun. 7 (1969) 1261 and J. Phys. Chem. Solids 30 (1969) 1827. Wheeler, J.C.G.: J. Phys. C2 (1969) 135. Arajs, S., De Young, T.F., Anderson, E.E.: J. Appl. Phys. 41 (1970) 1426. Aldred, A.T., Rainford, B.D., Stringfellow, M.W.: Phys. Rev. Lett. 24 (1970) 897. Bucher, E., Brinkman, W., Maita, J.P., Cooper, A.S.: Phys. Rev. B 1 (1970) 274. Boerstoel, B.M., Baarle, C. van: J. Appl. Phys. 41 (1970) 1079. Clark, P.E., Meads, R.E.: J. Phys. C 3 (1970) S 308. Cable, J.W., Child, H.R.: Phys. Rev. B 1 (1970) 3809. Jayaraman, A., Rice, T.M., Bucher, E.: J. Appl. Phys. 41 (1970) 869. Kaneko, T., Fujimori, H.: J. Phys. Sot. Jpn. 28 (1970) 1373. Kawatra, M.P., Budnick, J.I.: Int. J. Magn. 1 (1970) 61. Kawatra, M.P., Mydosh, J.A., Budnick, J.A., Madden, B.: Proc. Low.Temp. (Kyoto) 12 (1970) 773. Loegel, B.: J. Phys. C3 (1970) S 355. McKinnon, J.B., Melville, D., Lee E.W.: J. Phys. C 3 (1970) S 46. Mizoguchi, T., Sasaki, T.: J. Phys. Sot. Jpn. 28 (1970) 532. McDougal, M., Manuel, A.J.: J. Phys. C3 (1970) 147. Nagasawa, H.: J. Phys. Sot. Jpn. 28 (1970) 1171. Nieuwenhuys, G.J., Boerstoel, B.M.: Phys. Lett. 33A (1970) 147. Vogt, E., Biilling, F., Treutmann, W.: Ann. Phys. 25 (1970) 280. Williams, G.: J. Phys. Chem. Solids 31 (1970) 529. Chakravorty, S., Panigrahy, P., Beck, P.A.: J. Appl. Phys. 42 (1971) 1698. Chouteau, G., Tournier, R.: J. Phys. Paris 32 (1971) C l-1002. Crangle, J., Goodman, G.M.: Proc. R. Sot. (London) A321 (1971) 477. Inoue, N., Nagasawa, H.: J. Phys. Sot. Jpn. 31 (1971) 477. Ivanova, G.V., Magat, L.M., Solina, L.V., Shur, Ya.S.: Phys. Met. Metallogr. (USSR) 32,3 (1971)92. Loram, J.W., Williams, G., Swallow, G.A.: Phys. Rev. B3 (1971) 3060. Matsumoto, M., Goto, T., Kaneko, T.: J. Phys. Paris 32 (1971) C 1419. Moon, R.M.: Int. J. Magnetism 1 (1971) 219. Ohno, H.: J. Phys. Sot. Jpn. 31 (1971) 92. Star, W.M.: Thesis, University of Leiden, Netherlands 1971. Stoelinga, S.J.M., Grimberg, A.J.T., Gersdorf, R., Vries, G. de: J. Phys. Paris 32 (1971) Cl-330. Swallow, G.A., Williams, G., Grassie, A.D.C., Loram, J.W.: J. Phys. Fl (1971) 511. Ttriplett, B.B., Phillips, N.E.: Phys. Lett. 37A (1971) 443. Frame, Gersdorf

650 71Vl 71Y 1 72B 1 72B2 72Cl 72Dl 72Fl 72Gl 72Ml 72Nl 72Sl 72Tl 73 Al 73A2 73Bl 73B2 73B3 73Dl 73Gl 7362 73Kl 73K2 73K3 73K4 73K5 73Nl 73s1 73Tl 73T2 74A1 74A2 74Bl 74B2 74B3 74C 1 74Dl 74Fl 7411 74Ml 74M2 74M3 74Nl 74Rl 74Sl 74S2 74s3 74Yl 74Y2 7421 75Al 75A2 75A3

Referencesfor 1.4.2 Vinokurova, L., Pardavi-Horvath, M.: Phys. Status Solidi (b) 48 (1971) K 31. Yamaoka. T., Mekata. M., Takaki, H.: J. Phys. Sot. Jpn. 31 (1971) 301. Boerstoel. B.M., Zwart, J.J., Hansen, J.: Physica 57 (1972) 397. Besnus. M.J., Herr, A.: Phys. Lett. 39 A (1972) 83. Claus, H.: Phys. Rev. B5 (1972) 1134. DeYoung. T.F., Arajs, S., Anderson, E.E.: AIP Conf. Proc. 5 (1972) 517. Ferrando, W.A., Segnan, R., Schindler, AI.: Phys. Rev. B5 (1972) 4657. Gillespie, D.J., Schindler, AI.: AIP Conf. Proc. 5 (1972) 461. Menzinger, F., Romanazzo, M., Sacchetti, F.: Phys. Rev. B5 (1972) 3778. Nieuwenhuys, G.J., Boerstoel, B.M., Zwart, J.J., Dokter, H.D., Berg, G.J. van den: Physica 62 (1972) 278. Star, W.M., Vroede, E. de, Baarle, C. van: Physica 59 (1972) 128. Tissier, B., Tournier, R.: Solid State Commun. 11 (1972) 895. Abdul-Noor, S.S.,Booth, J.G.: Phys. Lett. 43 A (1973) 381. Arajs, S., Rao, K.V., Astrom, H.U., DeYoung, T.F.: Physica Scripta 8 (1973) 109. Besnus. M.J., Meyer, A.J.P.: Phys. Status Solidi (b) 58 (1973) 533. Besnus. M.J., Meyer, A.J.P.: Phys. Status Solidi (b) 55 (1973) 521. Burger, J.P., McLachlan, D.S.: Solid State Commun. 13 (1973) 1563. DeYoung. T.F., Arajs, S., Anderson, E.E.: J. Less-Common Met. 32 (1973) 165. Goring, J.: Phys. Status Solidi (b) 57 (1973) K 7. Gillespie, D.J., Mackliet, C.A., Schindler, AI.: Amorphous Magnetism (Hooper, H., Graaf, A.M., de, eds.).New York: Plenum Press 1973, 343. Kao, F.C.C., Colp, M.E., Williams, G.: Phys. Rev. B8 (1973) 1228. Kao, F.C.C., Williams, G.: Phys. Rev. B7 (1973) 267. Kuentzler, R., Meyer, A.J.P.: Phys. Lett. 43 A (1973) 3. Kadomatsu, H., Fujii, H., Okamoto, T.: J. Phys. Sot. Jpn. 34 (1973) 1417. Kelarev, V.V., Vokhmyanin, A.P., Dorofeyev, Yu.A., Sidorov, S.K.: Phys. Met. Metallogr. (USSR) 35, 6 (1973) 1302. Nieuwenhuys, G.J., Pikart, M.F., Zwart, J.J., Boerstoel, B.M., Berg, G.J. van den: Physica 69 (1973) 119. Sumiyama, K., Graham, G.M., Nakamura, Y.: J. Phys. Sot. Jpn. 35 (1973) 1255. Tamminga. Y., Barkman, B., Boer, F.R. de: Solid State Commun. 12 (1973) 731. Tokunaga. T., Tange, H., Goto, M.: J. Phys. Sot. Jpn. 34 (1973) 1103. Alquit. G., Kreisler, A., Sadoc, G., Burger, J.P.: J. Phys. Paris Lett. 35 (1974) L69. Alberts, H.L., Beille, J., Bloch, D., Wohlfarth, E.P.: Phys. Rev. B9 (1974) 2233. Beille. J., Bloch. D., Besnus, M.J.: J. Phys. F4 (1974) 1275. Beille, J., Bloch, D., Kuentzler, R.: Solid State Commun. 14 (1974) 963. Baggurley, D.M.S., Robertson, J.A.: J. Phys. F4 (1974) 2282. Chouteau, G., Tournier, R., Mallard, P.: J. Phys. Paris 35 (1974) C4-185. Dubovka, G.T.: Sov. Phys. JETP 38 (1974) 1140. Fujimori, H., Hiroyoshi, H.: Solid State Commun. 15 (1974) 1287. Ito, Y., Sasaki, T., Mizoguchi, T.: Solid State Commun. 15 (1974) 807. Meier, J.S., Christoe, C.W., Wortmann, G., Holzapfel, W.B.: Solid State Commun. 15 (1974) 485. Men’shikov, A.Z., Dorofeyev, Yu.A., Kazantsev,V.A., Sidorov, S.K.: Phys. Met. Metallogr. (USSR)38, 3 (1974) 47. Murani, A.P., Tari, A., Coles, B.R.: J. Phys. F4 (1974) 1769. Nikolayev, I.N., Vinogradov, B.V., Pavlynkov, L.S.: Phys. Met. Metallogr. (USSR) 38, 1 (1974) 85. Ricodeau, J.A.: J. Phys. F4 (1974) 1285. Sacli, O.A., Emerson, D.J., Brewer, D.F.: J. Low Temp. Phys. 17 (1974) 425. Scherg. M., Seidel, E.R., Litterst, F.J., Gierish, W., Kalvius, G.M.: J. Phys. Paris 35 (1974) C6527. Schinkel, C.J., in: Physique sous Champs Magnttiques Intenses, Colloque du CNRS, Grenoble 1974, 25. Yamaoka, T.: J. Phys. Sot. Jpn. 36 (1974) 445. Yamaoka, T., Mekata, M., Takaki, H.: J. Phys. Sot. Jpn. 36 (1974) 438. Zavadskii, E.A., Medvedeva, L.I.: Sov. Phys. Solid State 15 (1974) 1595. Arajs, S., Moyer, CA., Kelly, J.R., Rao, K.V.: Phys. Rev. B 12 (1975) 2747. Abdul-Noor, S.S.,Booth, J.G.: J. Phys. F5 (1975) L 11. Arajs, S., Rao, K.V., Anderson, E.E.: Solid State Commun. 16 (1975) 331.

Frame, Gersdorf

References for 1.4.2 75A4 75Bl 75Cl 75C2 75Dl 75El 75Fl 75F2 7551 75Kl 75K2 75Ml 75M2 75M3 75Nl 75Sl 75S2 7583 7521 76Bl 76B2 76Cl 76Kl 76Ml 76Rl 76Tl 76Vl 76V2 77Cl 77C2 77Fl 77Gl 7762 77Kl 7701 77Rl 77R2 77Sl 7782 77Tl 7721 78Bl 78Cl 78Fl 7811 78Ml 78Nl 7801 78Pl 78P2 78Sl 78Tl 78Vl 78V2

651

Antonov, V.Ye., Dubovka, G.T.: Phys. Met. Metallogr. (USSR) 40, 3 (1975) 171. Beille, J., Chouteau, G.: J. Phys. F5 (1975) 721. Coles, B.R., Jamieson, H.C., Taylor, R.H., Tari, A.: J. Phys. F5 (1975) 565. Chen, C.W., Buttry, R.W.: AIP Conf. Proc. 24 (1975) 437. De Pater, C.J., Dijk, C. van, Nieuwenhuis, G.J.: J. Phys. F5 (1975) L 58. Eytel, L., Raghavan, P., Munnick, D.E., Raghavan, R.S.: Phys. Rev. B 11 (1975) 1160. Fukamichi, K., Saito, H.: J. Less-Common Met. 40 (1975) 357. Fujiwara, H., Tokunaga, T.: J. Phys. Sot. Jpn. 39 (1975) 927. Jamieson, H.C.: J. Phys. F5 (1975) 1021. Kadomatsu, H., Fujiwara, H., Ohishi, K., Yamamoto, Y.: J. Phys. Sot. Jpn. 38 (1975) 1211. Koon, N.C., Gubser, D.U.: AIP Conf. Proc. 24 (1975) 94. Menshikov, A., Tarnoczi, T., KrCn, E.: Phys. Status Solidi (a) 28 (1975) K 85. Martin, D.C.: J. Phys. F5 (1975) 1031. Muellner, W.C., Kouvel, J.S.: Phys. Rev. Bll (1975) 4552. Nieuwknhuys, G.J.: Adv. Phys. 24 (1975) 515. Strom-Olsen, J.O., Williams, G.: Phys. Rev. B 12 (1975) 1986. Star, W.M., Foner, S., McNiff Jr., E.J.: Phys. Rev. B 12 (1975) 2690. Swallow, G.A., Williams, G., Grassie, A.D.C., Loram, J.W.: Phys. Rev. Bll (1975) 337. Zweers, H.A., Berg, G.J. van den: J. Phys. F5 (1975) 555. Beille, J., Tournier, R.: J. Phys. F6 (1976) 621. Beille, J., Pataud, P., Radhakrishna, P.: Solid State Commun. 18 (1976) 1291. Chouteau, G.: Physica 84 B (1976) 25. Kortekaas, T.F.M., Franse, J.J.M.: J. Phys. F6 (1976) 1161. Maartense, I., Williams, G.: J. Phys. F6 (1976) L 121. Rao, K.V., Rapp, O., Johannesson, Ch., Budnick, J.I., Burch, T.J., Canella, V.: AIP Conf. Proc. 29 (1976) 346. Tsiovkin, Yu.N., Kourov, N.I., Volkenshteyn, N.V.: Phys. Met. Metallogr. (USSR) 42,2 (1976) 157. Vogt, E.: Phys. Status Solidi (a) 34 (1976) 11. Vinokurova, L., Vlasov, A.V., Pardavi-Horvath, M.: Phys. Status Solidi (b) 78 (1976) 353. Cable, J.W., David, L.: Phys. Rev. B 16 (1977) 297. Cable, J.W.: Phys. Rev. B 15 (1977) 3477. Franse, J.J.M.: Physica 86-88 B (1977) 283. Goto, T., Yamauchi, H.: J. Phys. Sot. Jpn. 43 (1977) 339. Goto, T.: J. Phys. Sot. Jpn. 43 (1977) 1848. Kortekaas, T.F.M., Franse, J.J.M.: Phys. Status Solidi (a) 40 (1977) 479. Oishi, K.: J. Sci. Hiroshima Univ. Ser. A41 (1977) 1. Roshko, R.M., Maartense, I., Williams, G.: J. Phys. F7 (1977) 1811; Physica 86-88B (1977) 829. Ryshenko, B.V., Sidorenko, F.A., Karpov, Yu.G., Gel’d, P.V.: Sov. Phys. JETP 46 (1977) 547. Smith, A.J., Stirling, W.G., Holden, T.M.: J. Phys. F7 (1977) 2411; Physica 86-88B (1977) 349. Savchenkova, S.F., Tsiovkin, Yu.N., Zolov, T.D., Volkenshteyn, N.V.: Phys. Met. Metallogr. (USSR) 43, 1 (1977) 188. Tholence, J.L., Wasserman, E.F.: Physica 86-88 B (1977) 875. Zweers, H.A., Pelt, W., Nieuwenhuys, G.J., Mydosh, J.A.: Physica 86-88 B (1977) 837. Beille, J., Bloch, D., Voiron, J.: J. Mag. Magn. Mater. 7 (1978) 271. Cable, J.W.: J. Appl. Phys. 49 (1978) 1527. Flouquet, J., Ribault, M., Taurian, V., Sanchez, J., Tholence, J.L.: Phys. Rev. B 18 (1978) 54. Inoue, N., Sugawara, T.: J. Phys. Sot. Jpn. 44 (1978) 440. Michelluti, B., Perrier de la Bathie, R., du Tremolet de Lacheisserie,E.: Solid State Commun. 28 (1978) 879. Nakamura, Y., Sumiyama, K., Shiga, M.: Inst. Phys. Conf. Proc. 39 (1978) 522. Ododo, J.C., Horvath, W.: Solid State Commun. 26 (1978) 39. Pardavi-Horvath, M., Vinokurova, L.I., Vlasov, A.V.: Inst. Phys. Conf. Proc. 39 (1978) 603. Ponomarev, B.K., Tiessen, V.G.: Phys. Status Solidi (b) 88 (1978) K 139. Sain, D., Kouvel, J.S.: Phys. Rev. B 17 (1978) 2257. Tokunaga, T., Fujiwara, H.: J. Phys. Sot. Jpn. 45 (1978) 1232. Verbeek, B.H., Nieuwenhuys, G.J., Stocker, H., Mydosh, J.A.: Phys. Rev. Lett. 40 (1978) 586. Vinokurova, L.I., Ivanov, V.Yu., Sagoyan, L.I., Rodionov, D.P.: Phys’Met. Metallogr. (USSR) 45,4, (1978) 869.

Land&-Biirnsfein New Series 111/19a

Frame, Gersdorf

652 7sv3 79Al 79Cl 79Gl 79K 1 79K2 79K3 79Ml 7901 79 P 1 79P2 79P3 79Rl 79Sl 79Wl 79w2 80Al 80B1 80Fl 80H 1 80Kl 80M 1 80M2 8001 8OPl 80R 1 8OYl 81Bl 81Cl 81 H 1 81 H2 81H3 8151 81Kl 81K2 81K3 81Pl 81Sl 81S2 81Tl 81 T2 81 v 1 81Wl 81 W2 82Al 82Bl 82B2 82H 1 82H2 82Jl 82Ll 8201 82Rl 82Tl 82Yl

Referencesfor 1.4.2 Verbeek, B.H., van Dijk, C., Nieuwenhuys, G.J., Mydosh, J.A.: J. Phys. Paris 39 (1978) C&918. Acker. F., Huguenin. R.: J. Mag. Magn. Mater. 12 (1979) 58. Cochrane, R.W., Strom-Olsen, J.O., Williams, G.: J. Phys. F9 (1979) 1165. Guy. C.N., Strom-Olsen. J.O.: J. Appl. Phys. 50 (1979) 7353. Kaaakami, M., Goto, T.: J. Phys. Sot. Jpn. 46 (1979) 1492. Kelly, J.R.. Moyer, C.A., Arajs, S.: Phys. Rev. B20 (1979) 1099. Kadomatsu, H., Fujiwara, H.: Solid State Commun. 29 (1979) 255. Mydosh, J.A., Roth, S.: Phys. Lett. 69A (1979) 350. Ododo. J.C.: J. Phys. F9 (1979) 1441. Paul, D.M., Stirling, W.G.: J. Phys. F9 (1979) 2439. Parette, G., Kajzar, F.: J. Phys. F9 (1979) 1867. Parra, R.E., Cable, J.W.: J. Appl. Phys. 50 (1979) 7522. Rainford, B.D.: J. Mag. Magn. Mater. 14 (1979) 197. Smit, J.J., Nieuwenhuys, G.J., Jongh, L.J. de: Solid State Commun. 30 (1979) 243. Williams, D.E.G., Lewin, B.G.: Z. Metallkd. 70 (1979) 441. Wu? M.K., Aitken, R.G., Chu, C.W., Huang, C.Y., Olsen, C.E.: J. Appl. Phys. 50 (1979) 7356. Aubert, G., Michelluti, B.: J. Mag. Magn. Mater. 15-18 (1980) 575. Bieber. A.?Charaki. A., Kuentzler, R.: J. Mag. Magn. Mater. 15-18 (1980) 1161. Franse, J.J.M., Hiilscher, H., Mydosh, J.A.: J. Mag. Magn. Mater. 15-18 (1980) 179. Hiilscher. H., Franse, J.J.M.: J. Mag. Magn. Mater. 15-18 (1980) 605. Kadomatsu. H., Kamimori, T., Tokunaga, T., Fujiwara, H.: J. Phys. Sot. Jpn. 49 (1980) 1189. Moyer, CA., Arajs, S., Eroglu, A.: Phys. Rev. B 22 (1977) 3277. Mydosh. J.A., Nieuwenhuys, G.J., in: Ferromagnetic Materials I (Wohlfarth, E.P., ed.), Amsterdam: North-Holland Publishing Company 1980, p. 71. Ododo, J.C.: J. Phys. F 10 (1980) 2515. Parra. R.E., Cable, J.W.: Phys. Rev. B21 (1980) 5494. Rouchy, J., du Tremolet de Lacheisserie, E., Genna, J.C.: J. Mag. Magn. Mater. 21 (1980) 69. Yamada. O., Ono, F., Arae, F., Arimune, H.: J. Mag. Magn. Mater. 15-18 (1980) 569. Brommer, P.E.. Franse,J.J.M., Geerken, B.M., Griessen,R., Holscher, H., Kragtwijk, J.A.M., Mydosh, J.A., Nieuwenhuys, G.J.: Inst. Phys. Conf. Ser. 55 (1981) 253. Cheung, T.D., Kouvel, J.S., Garland, J.W.: Phys. Rev. B23 (1981) 1245. Hedman. L., Moyer, CA., Kelly, J.R., Arajs, S., Kote, G., Garbe, K.: J. Appl. Phys. 52 (1981) 1643. Ho, SC., Maartense, I., Williams, G.: J. Phys. Fll (1981) 699, 1107. Hayashi. K., Mori, N.: Solid State Commun. 38 (1981) 1057. Jesser.R., Bieber. A., Kuentzler, R.: J. Phys. Paris 42 (1981) 1157. Kadomatsu, H., Tokunaga. T., Fujiwara, H.: J. Phys. Sot. Jpn. 50 (1981) 3. Kuentzler, R.: Inst. Phys. Conf. Ser. 55 (1981) 397. Kadomatsu, H., Tokunaga, T., Fujiwara, H.: J. Phys. Sot. Jpn. 50 (1981) 1409. Papoular, R., Debray, D.: J. Mag. Magn. Mater. 24 (1981) 106. Sate, T., Miyako, Y.: J. Phys. Sot. Jpn. 51 (1981) 1394. Sumiyama, K., Emoto, Y., Shiga, M., Nakamura, Y.: J. Phys. Sot. Jpn. 50 (1981) 3296. Thomson, J.O., Thompson, J.R.: J. Phys. Fll (1981) 247. Tsiovkin. Yu.N., Kourov, N.I., Volkenshtein, N.V.: Sov. Phys. Solid State 23 (1981) 1534. Vinokurova. L.I.. Vlasov, A.V., Kulikov, N.I., Pardavi-Horvath, M.: Hungarian Acad. Sci. Budapest 1981. Williams. D.E.G., Ziebeck, K.R.A., Hukin, D.A., Kollmar, A.: J. Phys. Fll (1981) 1119. Watanabe, K.: Phys. Status Solidi (a) 40 (1981) 697. Amamou, A., Kuentzler, R.: Solid State Commun. 43 (1982) 423. Burmester, W.L.. Sellmyer, D.J.: J. Appl. Phys. 53 (1982) 2024. Burke, SK., Cywinski, R., Lindley, E.J., Rainford, B.D.: J. Phys. Sot. Jpn. 53 (1982) 8079. Ho, S.C., Maartense, I., Williams, G.: J. Appl. Phys. 53 (1982) 2235. Hiroyoshi, H., Hoshi, A., Nakagawa, Y.: J. Appl. Phys. 53 (1982) 2453. Jesser,R., Kuentzler, R.: J. Appl. Phys. 53 (1982) 2726. Lynn. J.W., Rhyne, J.J., Budnick, J.I.: J. Appl. Phys. 53 (1982) 1982. Oishi. K., Asai. A., Fujiwara, H.: J. Phys. Sot. Jpn. 51 (1982) 3504. Roeland, L.W., Wolfrat, J.C., Mak, D.K., Springford, M.: J. Phys. F 12 (1982) L267. Takahashi, Y., Jacobs, R.L.: J. Phys. F12 (1982) 517. Yamada. O., Ono. F., Nakai, I., Maruyama, H., Arae, F., Ohta, K.: Solid State Commun. 42 (1982)473.

Franse, Gersdorf

References for 1.4.2 83Bl 83Cl 83Fl 8311 83Ml 8301 83Sl 83Tl 83T2 83Wl 83Yl 83Y2 83Y3

Land&Bbmstein New Series IW19a

653

Burke, S.K., Rainford, B.D., Lindley, E.J., Maze, 0.: J. Mag. Magn. Mater. 31-34 (1983) 545. Campbell, S.J., Hicks, T.J., Wells, P.: J. Mag. Magn. Mater. 31-34 (1983) 625. Fujiwara, H., Kadomatsu, H., Tokunaga, T.: J. Mag. Magn. Mater. 31-34 (1983) 809. Ikeda, K., Gschneider, Jr., K.A., Schindler, A.I.: Phys. Rev. B28 (1983) 1457. Matsui, M., Adachi, K.: J. Mag. Magn. Mater. 31-34 (1983) 115. Ono, F., Maeta, H., Kittaka, T.: J. Mag. Magn. Mater. 31-34 (1983) 113. Sumiyama, K., Shiga, M., Nakamura, Y.: J. Mag. Magn. Mater. 31-34 (1983) 111. Tino, Y., Iguchi, Y.: J. Mag. Magn. Mater. 31-34 (1983) 117. Takahashi, Y., Jacobs, R.L.: J. Mag. Magn. Mater. 31-34 (1983) 49. Williams, D.E.G., Ziebeck, K.R.A., Jezierski, A.: J. Mag. Magn. Mater. 31-34 (1983) 611. Yamada, O., Ono, F., Nakai, I., Maruyama, H., Ohta, K., Suzuki, M.: J. Mag. Magn. Mater. 31-34 (1983) 105. Yamada, O., Maruyama, H., Pauthenet, R., in: High Field Magnetism (Date, M., ed.), Amsterdam: North-Holland Publishing Company, 1983, p. 97. Yamada, 0.: Physica 119B (1983) 90.

Franse, Gersdorf