Table Of ContentMAGNETISM
A Treatise on Modern Theory and Materials
Volume I:
Magnetic Ions in Insulators, Their Interactions,
Resonances, and Optical Properties.
Volume HA:
Statistical Models, Magnetic Symmetry, Hyperfine
Interactions, and Metals.
Volume MB:
Interactions and Metals.
Volume IV:
Exchange Interactions among Itinerant Electrons.
MAGNETISM
EDITED BY George T. Rado
Magnetism Branch
U.S. Naval Research Laboratory
Washington, D.C.
Harry Suhl
Department of Physics
University of California, San Diego
La Jolla, California
Spin Arrangements and
. ... Crystal Structure,
w
Volume III ' ,
Domains, and
Micromagnetics
ACADEMIC PRESS
1963
New York and London
COPYRIGHT © 1963, BY ACADEMIC PRESS INC.
ALL RIGHTS RESERVED.
NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM,
BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS, WITHOUT
WRITTEN PERMISSION FROM THE PUBLISHERS.
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United Kingdom Edition published by
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LIBRARY OF CONGRESS CATALOG CARD NUMBER: 63-16972
Second Printing, 1972
PRINTED IN THE UNITED STATES OF AMERICA
Contributors to Volume III
Numbers in parentheses refer to the page on which the author's contribution begins.
C. P. Bean. (271), General Electric Research Laboratory, Schenectady, New York
E. F. Bertaut. (149), Laboratoire d'Electrostatique et de Physique du Métal, Institut Fourier,
et Centre d'Études Nucléaires, Grenoble, France
P. G. de Gennes*. (115) CEN de Saclay, Gif-sur-Yvette, France
J. F. Dillon Jr. (415), Bell Telephone Laboratories, Murray Hill, New Jersey
N. Goldberg. (553), Univac Division, Sperry Rand Corp., Blue Bell, Pennsylvania
John B. Goodenough. (1), Lincoln Laboratory, Massachusetts Institute of Technology,
Lexington, Massachusetts
E. M. Gyorgy. (525), Bell Telephone Laboratories, Murray Hill, New Jersey
I. S. Jacobs. (271), General Electric Research Laboratory, Schenectady, New York
C. J. Kriessman. (553), Univac Division, Sperry Rand Corp., Blue Bell, Pennsylvania
R. Nathans. (211), Brookhaven National Laboratory, Upton, New York
S. J. Pickart. (211), U. S. Naval Ordnance Laboratory, Silver Spring, Maryland and
Brookhaven National Laboratory, Upton, New York
S. Shtrikman**. (395), The Franklin Institute for Research and Development, Philadelphia,
Pennsylvania
J. Samuel Smart. (63), International Business Machines Corp., Thomas J. Watson Research
Center, Yorktown Heights, New York
Donald O. Smith. (465), Lincoln Laboratory, Massachusetts Institute of Technology,
Lexington, Massachusetts
D. Trêves (395), Department of Electronics, The Weizmann Institute of Science, Rehovoth,
Israel
E. P. Wohlfarth. (351), Department of Mathematics, Imperial College, London, England
* Present Address: Faculté des Sciences, Orsay (S. et O.), France
* * Present Address: Department of Electronics, The Weizmann Institute of
Science, Rehovoth, Israel
Preface
This treatise attempts to provide an up-to-date and reasonably
concise summary of our understanding of magnetically ordered materials.
Thus it deals almost exclusively with ferromagnetism, ferrimagnetism,
and antiferromagnetism, i.e., with cooperative phenomena characterized
by ordered arrangements of magnetic moments subject to strong mutual
interactions.
Although research in magnetism during the past fifteen years has
experienced a tremendous expansion, the existing books cover only a
few areas of present knowledge. Many of the available review articles
are addressed to small circles of specialists, and the periodical literature
is voluminous and highly dispersed. The need for a consolidation of
almost all theoretical and experimental aspects of magnetically ordered
materials is the motivation for the present work. It is hoped that students
with physics or chemistry backgrounds as well as professionals will find
this treatise useful for study and reference.
As shown by the Table of Contents, the unusually broad scope of
this work includes the most diverse aspects of ferromagnetism, ferri-
magnetism, and antiferromagnetism in insulators as well as in metals.
The chapters range from discussions of quantum mechanical and
abstract statistical models to the analysis of actual magnetic structures,
from the theory of spin interactions in solids to the phenomenology of
ferromagnets, and from electronic and nuclear resonance effects to
neutron diffraction and optical phenomena in magnetically ordered
materials. An effort was made to represent both theoretical and experi-
mental points of view, to discuss each topic selectively rather than
encyclopedically, and to incorporate in most chapters a discussion of
the fundamentals. Since the most recent theories and materials are
covered, several chapters deal with subjects, controversial and
otherwise, which did not even exist a few years ago. While some aspects
of the current technological applications of magnetism are also treated,
the emphasis is on their physical basis, potentialities, and limitations.
In order to emphasize the recent developments and to cover the whole
field of magnetically ordered materials, various recognized and active
specialists were invited to write the chapters. Efforts were made to
vu
viii PREFACE
establish a reasonable amount of coherence among the chapters and
to minimize unnecessary duplication. For practical reasons, on the
other hand, no attempt was made to establish a uniform notation through-
out the exposition or to achieve unity of approach and style.
The three volumes of the work bear the following partially descriptive
subtitles:
Volume I: Magnetic Ions in Insulators, Their Interactions, Reso-
nances, and Optical Properties.
Volume II: Statistical Models, Magnetic Symmetry, Hyperfine Inter-
actions, and Metals.
Volume III: Spin Arrangements and Crystal Structure, Domains, and
Micromagnetics.
The publication schedule calls for Volume III to appear first, followed
by Volumes I and II.
The editors wish to express their deep appreciation to the authors who
prepared the chapters, even while pursuing active research programs.
Thanks are also due to V. J. Folen, D. R. Fredkin, and N. R. Werthamer
for editorial assistance, and to Academic Press for friendly cooperation.
June, 1963 G. T. RADO
H. SUHL
Contents of Volume I
Spin Hamiltonians
K. W. H. STEVENS
Exchange in Insulators
P. W. ANDERSON
Weak Ferromagnetism
TORU MORIYA
Anisotropy and Magnetostriction of Ferromagnetic and Antiferromagnetic
Materials
JUNJIRO KANAMORI
Magnetic Annealing
JOHN C. SLONCZEWSKI
Optical Spectra in Magnetically Ordered Materials
SATORU SUGANO and Υυκιτο ΤΑΝΑΒΕ
Optical and Infrared Properties of Magnetic Materials
KENNETH A. WICKERSHEIM
Spin Waves and Other Magnetic Modes
L. R. WALKER
Antiferromagnetic and Ferrimagnetic Resonance
SIMON FONER
Ferromagnetic Relaxation and Resonance Line Widths
C. WARREN HAAS and HERBERT B. CALLEN
Ferromagnetic Resonance at High Power
RICHARD W. DAMON
Microwave Devices
KENNETH J. BUTTON and THOMAS S. HARTWICK
Author Index—Subject Index
xiii
Contents of Volume II
Antiferromagnetism in Metals and Alloys
A. ARROTT
Statistical Mechanics of Ferromagnetism
R. BROUT
Statistical Mechanics of Critical Behavior in Magnetic Systems
C. DOMB
Hyperfme Fields in Metals
A. J. FREEMAN - R. E. WATSON
Exchange Interactions in Metals
C. HERRING
Nuclear Resonance in Antiferromagnetics
V. JACCARINO
On s-d and s-f Interactions
T. KASUYA
Magnetic Symmetry
W. OPECHOWSKI
Nuclear Resonance in Ferromagnetic Materials
A. M. PORTIS
Magnetism and Superconductivity
H. SUHL
XV
1.
Magnetism and Crystal Structure in Nonmetals
John B. Goodenough
Lincoln Laboratory*
Massachusetts Institute of Technology,
Lexington, Massachusetts
I. Some Important Nonmetallic Structures 1
1. Cubic Structures 2
2. Hexagonal Structures 14
3. Tetragonal Structures: Rutile (Ti0 ) 22
2
II. Description of Outer Electrons 24
1. The Free Atom 24
2. Solids 26
III. Applications to Magnetism 37
1. Site Preference Energies 37
2. Electron Ordering Transitions 47
References 59
I. Some Important Nonmetallic Structures
Crystal structure must be considered whenever the relationship
between chemistry and a particular phenomenological, magnetic param-
eter is desired. Although the design of practical materials requires
consideration of many extrinsic structural parameters—such as shape
and size of the specimen or the shape, size, orientation, distribution,
and intrinsic character of impurities or imperfections—these aspects
of structure are not considered in this chapter. Further, the relationship
between the intrinsic aspects of structure that are discussed here and
specific magnetic phenomena is made in those chapters where these
phenomena are discussed. For example, the relationship of structure
to crystalline anisotropy and magnetostriction is given in Chapter 4
* Operated with support from the U. S. Army, Navy, and Air Force.
1
2 JOHN B. GOODENOUGH
of Volume I; the structure dependence of weak ferromagnetism due
to an anisotropic superexchange that cants the atomic moments is given
in Chapter 3 of Volume I; magnetic order, which depends upon the
number and symmetrical arrangement of near neighbors as well as the
relative strengths of the couplings between them, is discussed in Chapters
4 and 5 of this volume; and the structural dependence of the magnetic
coupling between neighboring atomic moments is discussed in Chapter 2
of this volume, as well as in Chapter 2 of Volume I and in Volume II.
Therefore this chapter is confined to a description of several important,
nonmetallic structures (Section I) and of the types of distortion that may
be encountered in these structures as a result of electron ordering
(Section III). In order to discuss the various types of cation and electron
ordering that are encountered, it is necessary to review briefly (Section II)
two descriptions of the outer electrons and the domain of applicability
of each.
1. Cubic Structures
a. Rocksalt, zincblende, and antifluorite. Frequently the ions or
atoms of a compound are so arranged that one constituent forms a close-
packed array. In Fig. 1 is shown the cubic close-packed (fee) lattice.
L£v
à-
FIG. 1. The face-centered cubic lattice with inscribed octahedral interstice. Eight
tetrahedral interstices are defined by the eight octahedral faces and the respective corner
atoms toward which they face.
It contains two types of interstices: octahedral with coordination six
and tetrahedral with coordination four. It is apparent from Fig. 1 that
interstices of the same type share common edges and corners; those
of different type, common faces. The octahedral interstices, which are
located at the body-center and cube-edge positions, also form a fee
lattice whereas the tetrahedral sites, which are twice as numerous,
form a simple cubic lattice.
