Magnetism; Volume I, Magnetic Ions in Insulators, Their Interactions, Resonances, and Optical Properties A Treatise on Modern Theory and Materials

688 Pages·1963·39.857 MB·English

by  George T. Rado, Harry Suhl

MAGNETISM
A Treatise on Modern Theory and Materials
Volume I:
Magnetic Ions in Insulators. Their Interactions,
Resonances, and Optical Properties.
Volume II:
Statistical Models, Magnetic Symmetry, Hyperfine
Interactions, and Metals. In preparation
Volume III:
Spin Arrangements and Crystal Structure, Domains
and Micromagnetics. 1963
MAGNETISM
EDITED BY George T. Rado
Magnetism Branch
U.S. Naval Research Laboratory
Washington, D.C.
Harry Suhl
Department of Physics
University of California
La Jolla, California
Magnetic Ions
in Insulators
Volume I Their Interactions
Resonances
and Optical Properties
1963 ACADEMIC PRESS
New York San Francisco London
A Subsidiary of Harcourt Brace Jovanovich, Publishers
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.
ACADEMIC PRESS INC.
Ill Fifth Avenue, New York 3, New York
United Kingdom Edition published by
ACADEMIC PRESS, INC. (LONDON) LTD.
24/28 Oval Road, London NW1
Library of Congress Catalog Card Number: 63-16972
PRINTED IN THE UNITED STATES OF AMERICA
Contributors to Volume I
Numbers in parentheses refer to the page on which the author's contribution begins.
P. W. Anderson (25), Bell Telephone Laboratories, Murray Hill, New Jersey
K. J. Button (621), National Magnet Laboratory, Massachusetts Institute of Technology,
Cambridge, Massachusetts
H. B. Callen (449), Department of Physics, University of Pennsylvania, Philadelphia,
Pennsylvania
R. W. Damon* (551), Microivave Associates, Incorporated, Burlington, Massachusetts
S. Foner (383), National Magnet Laboratory, Massachusetts Institute of Technology,
Cambridge, Massachusetts
C. W. Haas** (449), Remington Rand Univac, Division of Sperry Rand Corporation,
Blue Bell, Pennsylvania, awe? University of Pennsylvania, Philadelphia, Pennsylvania
Thomas S. Hartwick (621), Aerospace Corporation, £7 Segundo, California
J. Kanamori (127), Department of Physics, Faculty of Science, Osaka University, Naka-
noshima, Osaka, Japan
T. Moriya (85), Institute for Solid State Physics, University of Tokyo, Azabu, Tokyo
J. C. Slonczewski (205), International Business Machines Corporation, Thomas F. Watson
Research Center, Yorktown Heights, iVew Yor£
K. W. H. Stevens (1), University of Nottingham, England
S. Sugano (243), The Institute for Solid State Physics, The University of Tokyo, Azabu,
Tokyo, Japan
Y. Tanabe (243), Department of Physics, Tokyo Institute of Technology, Tokyo, Japan
R. L. Walker (299), Bell Telephone Laboratories Incorporated, Murray Hill, New Jersey
K. A. Wickersheim (269), Department of Physics, University of California, Los Angeles,
California
* Present Address: Sperry Rand Research Center, Sudbury, Massachusetts
* Present Address: Central Research Department, E. I. duPont de Nemours and
Company, Wilmington, Delaware
P reface
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 abstract quantum mechanical
and 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
vii
Vlll 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, in most cases 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.
G. T. Rado
H. Suhl
Contents of Volume II (Tentative)
Statistical Mechanics of Critical Behavior in Magnetic Systems
C. Domb
Statistical Mechanics of Ferromagnetism
R. Brout
Magnetic Symmetry
W. Opechowski - R. Guccione
Nuclear Resonance in Ferromagnetic Materials
A. M. Portis
Nuclear Resonance in Antiferromagnetics
V. Jaccarino
Hyperfine Fields in Metals
A. J. Freeman - R. E. Watson
Exchange Interactions in Metals
C. Herring
On s-d and s-f Interactions
T. Kasuya
Magnetism and Superconductivity
H. Suhl
Antiferromagnetism in Metals and Alloys
A. Arrott
Author Index
Subject Index
xiii
Contents of Volume III
Magnetism and Crystal Structure in Nonmetals
John B. Goodenough
Evaluation of Exchange Interactions from Experimental Data
J. Samuel Smart
Theory of Neutron Scattering by Magnetic Crystals
P. G. de Gennes
Spin Configuration of Ionic Structures: Theory and Practice
E. F. Bertaut
Spin Arrangements in Metals
R. Nathans and S. J. Pickart
Fine Particles,Thin Films and Exchange Anisotropy-Effects of Finite Dimensions
and Interfaces on the Basic Properties of Ferromagnets
I. S. Jacobs and C. P. Bean
Permanent Magnet Materials
E. P. WOHLFARTH
Micromagnetics
S. Shtrikman and D. Treves
Domains and Domain Walls
J. F. Dillon, Jr.
The Structure and Switching of Permalloy Films
Donald O. Smith
Magnetization Reversal in Nonmetallic Ferromagnets
E. M. Gyorgy
Preparation and Crystal Synthesis of Magnetic Oxides
C. J. Kriessman and N. Goldberg
Author Index
Subject Index
XV
t.
Spin Hamiltonians
K. W. H. Stevens
University of Nottingham, England
I. Introduction................................................................................... ............................ 1
II. The Magnetic Lattice................................................................ ............................................ 3
III. The Spin Hamiltonian................................................................ ............................................ 4
IV. Crystal Field Theory................................................................ ............................................10
V. Nuclear Hyperfine Structure................................................. ............................................15
VI. Pairs of Ions................................................................................... ............................................17
VII. The Rare Earths......................................................................... ............................................21
VIII. Final Remarks.............................................................................. ............................................22
References........................................................................................ ............................................22
I. Introduction
The traditional method of studying paramagnetics, by susceptibility
measurements, has been supplemented very considerably over the past
decade by the development of the technique of electron spin resonance.
Very detailed knowledge is now available about the properties of magnetic
ions in a wide variety of lattices (See Orton [1], Bleaney and Stevens [2],
Bowers and Owen [3], Griffith [4], and Low [5] for comprehensive
reviews). Present developments suggest that before long equally detailed
information will be available about interactions between the ions.
At the same time that the experimental work was proceeding theoretical
studies were also undertaken, and this has led to a detailed and accurate
theory of electron spin resonance, which can fairly easily be extended
to account for the paramagnetic susceptibilities of the salts. In the course
of this work the important concept of a spin Hamiltonian, which first
1
2 K. W. H. STEVENS
appears in the work of Van Vleck [6] and will be discussed at length,
has been developed. It has proved to be of considerable value, for a mass
of experimental information can be summed up succinctly in a spin
Hamiltonian in just the way that the theoretician finds most acceptable,
and the experimentalist reasonably comprehensible! Thus the concept
of a spin Hamiltonian is well established in the study of the high tem­
perature properties of ionic salts.
One of the earliest ideas introduced into ferromagnetism was that of
an assembly of localized moments coupled together by suitable inter­
actions, chosen so that at low enough temperatures the moments would
be aligned. Above the Curie temperature thermal agitation would destroy
all long-range order and the substance would show Curie-Weiss type
susceptibility. The development of the band theory of solids, with the
requirement that each electron moves in an orbit which extends
throughout the solid, is difficult to reconcile with the concept of localized
moments and the theories of ferromagnetism have tended to divide
into two kinds, localized and nonlocalized, with occasional attempts
to combine the two concepts. In the ionic salts the concept of localized
moments is widely accepted, much more so than it is in the metals, and
in spite of the fact that in the salts the same requirements of periodicity
obtain, they are usually ignored, and the discussion is invariably given
using a localized model and a spin Hamiltonian.
In a book devoted mainly to the cooperative phenomena in magnetism
it is relevant to ask what purpose is served by a chapter which discusses
the paramagnetic properties of salts, using the concept of localized
moments. For there is some doubt whether localized moments exist in
ferromagnetics, and in any case the emphasis is on the cooperative
states of the systems, rather than the highly disorganized states occupied
in the paramagnetic temperature region. The justification is that most
paramagnetic salts, when they are cooled sufficiently, do show coopera­
tive phenomena, and there is no reason to suppose that anything very
drastic happens to the individual ions when this occurs. They simply
have their moments aligned, albeit more usually antiferromagnetically
than ferromagnetically, and the difference is primarily one in statistical
behavior. Thus it seems that, if a detailed description of, for example,
antiferromagnetism in MnO is required, a satisfactory approach should
be obtainable from (a) a knowledge of the low-lying states of the indi­
vidual manganese ions, using a localized model, (b) a knowledge of the
interactions between pairs of localized manganese moments, and (c) an
accurate treatment by statistical mechanics of the implications of the
model. The information required in (a) will probably be summed up
in a spin Hamiltonian and the attraction of the spin Hamiltonian for­