Cooperative Phenomena in Jahn - Teller Crystals

437 Pages·2012·35.681 MB·English

by  Michael D. Kaplan, Benjamin G. Vekhter

Cooperative
Phenomena in
Jahn-Teller Crystals
MODERN INORGANIC CHEMISTRY
Series Editor: John P. Fackler, Jr., Texas A&M University
CARBON-FUNCTIONAL ORGANOSILICON COMPOUNDS
Edited by Vaclav Chvalovsky and Jon M. Bellama
COOPERATIVE PHENOMENA IN JAHN-TELLER CRYSTALS
Michael D. Kaplan and Benjamin G. Vekhter
GAS PHASE INORGANIC CHEMISTRY
Edited by David H. Russell
HOMOGENEOUS CATALYSIS
WITH METAL PHOSPHINE COMPLEXES
Edited by Louis H. Pignolet
INORGANOMET ALLIC CHEMISTRY
Edited by Thomas P. Fehlner
THE JAHN-TELLER EFFECT AND
VIBRONIC INTERACTIONS IN MODERN CHEMISTRY
I. B. Bersuker
METAL INTERACTIONS WITH BORON CLUSTERS
Edited by Russel1 N. Grimes
MOSSBAUER SPECTROSCOPY
APPLIED TO INORGANIC CHEMISTRY
Volumes 1 and 2. Edited by Gary J. Long
Volume 3 • Edited by Gary 1. Long and Fernande Grandjean
MOSSBAUER SPECTROSCOPY
APPLIED TO MAGNETISM AND MATERIALS SCIENCE
Volume 1 • Edited by Gary J. Long and Fernande Grandjean
ORGANOMETALLIC CHEMISTRY OF THE
TRANSITION ELEMENTS
Florian P. Pruchnik
Translated from Polish by Stan A. Duraj
PHOTOCHEMISTRY AND PHOTOPHYSICS OF METAL COMPLEXES
D. M. Roundhil1
A Continuation Order Plan is available for this series. A continuation order will bring delivery
of each new volume immediately upon publication. Volumes are billed only upon actual
shipment. For further information please contact the publisher.
Cooperative
Phenomena in
Jahn-Teller Crystals
Michael D. Kaplan
Boston University
Boston, Massachusetts
Benjamin G. Vekhter
Northwestern University
Evanston, Illinois
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Llbrary of Congress Cataloglng-ln-Publlcatlon Data
Kaplan, Michael D.
Cooperatlve pheno~ena in Jahn-Teller crystals I Mlchael D. Kaplan,
BenJamln G. Vekhter.
p. cm. -- (Modern lnorganic chemlstryJ
Includes bibllographical references and index.
ISBN 978-14613-5755-1 ISBN 978-14615-18594 (eBook)
DOI 10.1007/978-14615-18594
1. Jahn-Teller effect. 2. Crysta!s. 1. Vekhter, BenJamin G.
II. Tlt!e. III. Serles.
OD461.K298 1995
530.4' 16--dc20 94-46426
CIP
©1995 Springer Science+Business Media New York
Originaily published by Plenum Press, New York in 1995
Softcover reprint of the hardcover 1 st edition 1995
10987654321
AII rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted in
any form or by any means, electronic, mechanical, photocopying, microfilming, recording,
or otherwise, without written permission from the Publisher
To our wives
Una and Sophie
with love and hope
Foreword
This book by Kaplan and Vekhter brings together the molecular world
of the chemist with the condensed matter world of the physicist. Prior
to the collapse of the Soviet Union, chemists in the West devoted lit
tle attention to relationships between molecular electronic structure and
solid-state vibronic phenomena. Treating quantum mechanical problems
wherein the adiabatic Born-Oppenheimer approximation fails was done by
"brute force." With bigger and better computers available in the West,
molecular orbital calculations were done on observed and conceived static
structures with little concern for any cooperativity of vibrational behavior
that might connect these states. While it had long been understood in the
West that situations do occur in which different static structures are found
for molecules that have identical or nearly identical electronic structures,
little attention had been paid to understanding the vibrational states that
could connect such structures. It was easier to calculate the electronic
structure observed with several possible distortions than to focus on ways
to couple electronic and vibrational behavior.
In the former Soviet Union, computational power was not as acces
sible as in the West. Much greater attention, therefore, was devoted to
conserving computational time by considering fundamental ways to han
dle the vibrational connectivity between degenerate or nearly degenerate
electronic states. The Jahn-Teller effect on structure, a situation wherein
the adiabatic approximation in the calculation of electronic structure fails,
became the focus of a strong theoretical group in Kishinev, Moldova, led
by 1. B. Bersuker (The lahn-Teller Effect and Vibronic Interactions in
Modern Chemistry, Plenum Press, New York, 1984). As a result, many
very important contributions to the understanding of Jahn-Teller related
phenomena came from the Academy of Sciences there.
The authors of this volume, Kaplan and Vekhter, have made important
contributions to the understanding of the Jahn-Teller effect in cooperative
systems. They have over 130 publications devoted completely to the mech
anism of structural phase transitions based on the cooperative Jahn-Teller
vii
viii Foreword
effect. These authors are experts in solid-state physics and have developed
a systematic theory of J ahn-Teller crystals in external fields. In this book
they have considered systems in which a fundamental understanding of
cooperative effects is established, systems in which many facts predicted
theoretically have been confirmed experimentally.
This is the first book in the realm of physics and chemistry that is de
voted completely to the microscopic theory of structural phase transitions
and to the cooperative Jahn-Teller effect. This theory is applied to the
analysis of different physical properties of various materials. As a result,
this book should be of special interest to scientists, engineers, and students
interested in any aspect of phase transformation. Finally it should be
noted that high-temperature superconductivity with ceramic cuprates and
fullerenes appears to owe its very existence to strong electron-phonon in
teractions such as those expected in Jahn-Teller systems, a topic discussed
in this book.
John P. Fackler, Jr.
College Station, Texas
Preface
The first notions of the cooperative Jahn-Teller effect as a viable mi
croscopic mechanism of structural transformations in solids were enunci
ated back in 1957 by Dunitz, Orgel, and McClure [IJ. Not long afterward,
in 1960, Kanamori published a fundamental paper [2J defining the basic
approach to the problem. Despite these early landmark efforts, the sys
tematic study of cooperative vibronic systems began at a much later date.
Not until the early 1970s, prompted by investigations at Oxford involving
scientists from various countries (see [3J and the references cited in [4]), did
comprehensive experimental and theoretical research begin on compounds
exhibiting the cooperative Jahn-Teller effect. The stimulating influence of
this group and its work led to widespread investigations of the properties of
Jahn-Teller compounds in several countries. By the middle of the 1970s the
foremost, and doubtless the most distinguishing, feature of this scientific
trend had been clearly delineated, viz.: myriad combinations of diverse, ex
perimentally observable, anomalous physical properties of crystals, along
with vast possibilities afforded by the theory for the interpretation and
prediction of those properties and their combinations.
Several reviews of the cooperative Jahn-Teller effect have been pub
lished [4-8], including the superb work of G. Gehring and K. Gehring [4J.
In addition, fundamental articles and entire book chapters have been de
voted to electron-phonon phase transitions [9-11J. At present, however, a
monograph dedicated especially to the subject is nonexistent in the world
literature.
In the meantime, we believe that the need exists for a detailed and
comprehensive study of this topic. The urgency of such an undertaking
derives not only from results that have important bearing on fundamental
and applied science, but also because the cooperative Jahn-Teller effect
is one of the few shining examples of the many ways in which microscopic
theory can contribute to our understanding of the properties of compounds
and hence fulfill our expectations for their prediction.
;x
x Preface
The existence of different "levels of microscopicity" in the theory is
well known. The cooperative Jahn-Teller effect is not a theory constructed
exclusively from "first principles." It is in fact based on the real elec
tronic structure and the real phonon spectrum of a crystal, and within
the scope of a very limited set of experimentally determined parameters of
a specific compound it describes a broad range of phenomena. Steps are
currently under way to formulate a theory of the properties of Jahn-Teller
compounds proceeding from first principles. Although serious difficulties
are encountered along the way, it will ultimately be possible, using mod
ern quantum-chemical methods [12], to formulate a complete microscopic
theory of materials science.
We shall not elaborate on the book's contents, which are best sum
marized in the Table of Contents. Naturally, we have been faced with the
usual problem of selecting the right material and, as usual, this has been
a subjective process. We have endeavored to treat what we regard as the
most interesting aspects of the cooperative Jahn-Teller effect. It might
be said that we have a strong bias toward our own work, but then-in
the words of Academician P. Kapitza-"The greatest interests of every in
dividual are his wife and his work, for were it not thus, work would be
impossible."
Nevertheless, we admit one departure from this underlying principle
of the selection process, namely in reference to the recent breakthrough
discovery of high-temperature superconductivity [13]. Like the discoverers
of this phenomenon, we believe that the properties of high-temperature su
perconductors have a definite bearing on the cooperative Jahn-Teller effect
(see the review [14] and the references cited therein). However, inasmuch
as the material accumulated to date is insufficient for the adoption of a
final position on this question, we have not included the relevant material
in the book.
Above all, we have attempted to focus on the qualitative side of the
phenomena in question rather than to present an exhaustive inventory of
all available results. In this light, it would be impossible to cite all the
appropriate published works, even if confined to the topics included in the
book. We apologize to the authors for any such omissions.
We are most grateful to all those colleagues and friends whose conver
sations have enabled us to take a definite stand regarding the microscopic
theory of structural phase transitions and who have encouraged us to write
this book. We deeply regret that we cannot acknowledge all of them. How
ever, special mention is due S. A. AI'tshuler, K. P. Belov, 1. B. Bersuker,
L. N. Bulaevskii, A. 1. Zvyagin, Z. A. Kazei, K. I. Kugel, A. P. Levanyuk,
B. Z. Malkin, 1. Va. Ogurtsov, Yu. E. Perlin, N. M. Plakida, V. Z. Polinger,
Yu. B. Rozenfel'd, V. I. Sokolov, D. 1. Khomskii, B. S. Tsukerblat, and
V. A. Shutilov for stimulating discussions.
We also express our sincere gratitude to our foreign colleagues, with
Preface xi
whom we have communicated at various stages during the preparation of
the book and with whose help we have been able to elucidate some vex
ing problems. First and foremost we acknowledge R. Englman, J. Fack
ler, G. Gehring, H. Kahle, O. Kahn, U. Maaskant, K. Miiller, P. Novak,
D. Reinen, E. Zigmund, and M. Wagner.
We would also like to thank V. D. Ashkinazi, A. V. Vasil'ev, and R. A.
Rozhkov for their substantial assistance in preparing the manuscript.
References
1. J. D. Dunitz and L. E. Orgel, J. Phys. Chem. Solids 3, 20 (1957); D. S. McClure,
J. Phys. Chem. Solids 3, 311 (1957).
2. J. Kanamori, J. Appl. Phys. 31, 14S (1960).
3. R. J. Elliott, R. T. Harley, W. Hayes, and S. R. P. Smith, Proc. R. Soc. London
Ser. A 328, 217 (1972).
4. G. A. Gehring and K. A. Gehring, Rep. Prog. Phys. 38, 1 (1975).
5. R. L. Melcher, in: Physical Acoustics: Principles and Methods, Vol. 12, W. P. Mason
and R. N. Thurston, eds., Academic Press, New York (1976), p. 1.
6. H. Thomas, in: Electron-Phonon Intemctions and Phase Transitions, T. Riste, ed.,
NATO Adv. Study Inst., Ser. B, Plenum Press, New York (1977), p. 245.
7. B. G. Vekhter and M. D. Kaplan, in: Spectroscopy of Crystals [in Russian], Nauka,
Moscow (1978), p. 143.
8. K. I. Kugel' and D. I. Khomskii, Usp. Fiz. Nauk 136, 621 (1982).
9. T. Riste (ed.), Electron-Phonon Intemctions and Phase Transitions, NATO Adv.
Study Inst., Ser. B, Plenum Press, New York (1977).
10. I. B. Bersuker, The Jahn-Teller Effect and Vibronic Intemctions in Modern Chem
istry, Plenum Press, New York (1984).
11. I. B. Bersuker and V. Z. Polinger Vibronic Intemctions in Molecules and Crystals,
Springer-Verlag, Berlin-New York (1989).
12. R. Hoffman, Solids and Surfaces, A Chemist's View of Bonding in Extended Struc
tures, VCH Verlagsgesellschaft, Weinheim (1988).
13. J. G. Bednorz and K. A. Muller, Z. Phys. B 64, 189 (1986).
14. M. D. Kaplan, in: High-Tempemture Superconductivity: Topical Problems, [in Rus
sian], Vol. 2, Leningrad State University, Leningrad (1989), p. 184.