Abstract
In Chapter 1 we have briefly considered the fundamentals of the Jahn—Teller effect and have discussed some of its manifestations for isolated Jahn—Teller centers. One of the main conclusions of Chapter 1 is that the Jahn—Teller effect does not induce static distortions. A distorted nuclear configuration does actually correspond to a certain electronic state of the degenerate term, but such distorted equilibrium configurations (potential energy minima) are not always unique, and dynamic averaging over them restores the initial high symmetry. On the other hand, it has been noted that even slight low-symmetry perturbations (external fields, random strains, etc.) in Jahn—Teller situations can tend to localize the system at one of the minima and bring about significant distortions. In this situation it would be interesting to know whether interaction between Jahn—Teller centers, as in the case, e.g., of a crystal with an ionic sublattice whose ground state is degenerate, can lead to localization and a net distortion. In such a multicenter Jahn—Teller situation it is also reasonable to expect phase transitions similar to those accompanying spin ordering, the only difference is that pseudospins specified in a basis of orbital states should be addressed in this case. The investigation of such phase transitions due to ordering of the orbital components of degenerate electronic states of lattice ions is the main purpose of this book. For phase transitions to occur, there must be interaction between electronic states of different sites. In this chapter we shall discuss the mechanisms of such interaction.
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References
L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory [in Russian], Nauka, Moscow (1974) [3rd English ed.: Pergamon Press, New York-Oxford (1977)].
D. C. Mattis, The Theory of Magnetism, Harper and Row, New York (1965).
R. W. White and T. H. Geballe, Long-Range Order in Solids, Academic Press, New York-London (1979).
P. M. Levy, in: Magnetic Oxides, Part 1, D. J. Graik, ed., Wiley, New York-London-(1975), p. 181.
U. Fano and G. Racah, Irreducible Tensorial Sets, Academic Press, New York (1959).
A. J. Freeman and R. E. Watson, Phys. Rev. 124, 1439 (1961).
G. M. Copland and P. M. Levy, Phys. Rev. B. 1, 3043 (1970).
H. Kramers, Physica (Utrecht) 1, 182 (1934).
J. Goodenough, Magnetism and the Chemical Bond, Interscience Publishers, New York-London (1963).
P. W. Anderson, Phys. Rev. 115, 2 (1959).
K. I. Kugel and D. I. Khomskii, Sov. Phys. JETP 37, 725 (1973).
D. I. Khomskii and K. I. Kugel, Solid State Commun. 13, 763 (1973).
K. I. Kugel and D. I. Khomskii, Sov. Phys. Solid State 17, 285 (1975).
D. I. Khomskii and K. I. Kugel, Phys. Status Solidi B 79, 441 (1977).
K. I. Kugel and D. I. Khomskii, Sov. Phys. Usp. 136, 231 (1982).
K. Hirakawa and Y. Kurogi, Prog. Theor. Phys. (Suppl.), 46, 147 (1970).
Y. Ito and J. Akimitsu, J. Phys. Soc. Jpn. 40, 1333 (1976).
Le Dang Khoi and P. Veillet, Phys. Rev. B. 11, 4128 (1975).
W. Kleeman and Y. Farge, J. Phys. (Paris) 36, 1293 (1975).
C. Lacroix, J. Phys. C: Solid State Phys. 13, 5125 (1980).
S. V. Vonsovskii and Yu. A. Izyumov, Sov. Phys. Usp. 5, 547 (1963).
K. P. Sinha and N. Kumar, Interactions in Magnetically Ordered Solids, Oxford University Press (1980).
M. A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954).
T. Kasuya, Prog. Theor. Phys. 16, 45 (1956).
K. Yosida, Phys. Rev. 106, 893 (1957).
M. B. Stearns, Phys. Rev. 129, 1136 (1963).
M. B. Stearns, Phys. Rev. 8, 4383 (1973).
M. I. Darby, Am. J. Phys. 37, 354 (1969).
E. L. Nagaev, Physics of Magnetic Semiconductors [in Russian], Nauka, Moscow (1979).
P. M. Levy, Solid State Commun. 7, 1813 (1969).
B. C. Carlson and G. S. Rushbrooke, Proc. Cambridge Philos. Soc. 46, 626 (1950).
W. P. Wolf and R. J. Birgeneau, Phys. Rev. 166, 376 (1968).
J. M. Baker, Rep. Prog. Phys. 34, 109 (1971).
R. J. Elliott and K. W. H. Stevens, Proc. R. Soc. London Ser. A 218, 553 (1953).
R. J. Birgeneau, J. Phys. Chem. Solids 28, 2429 (1967).
R. J. Birgeneau, Phys. Rev. Lett. 19, 160 (1967).
S. A. Al’tshuler and B. M. Kozyrev, Electron Paramagnetic Resonance of Compounds of Transition Elements [in Russian], Nauka, Moscow (1972) translation of 1961 edition: Academic Press, New York (1964).
K. Sigihara, J. Phys. Soc. Jpn. 14, 1231 (1959).
L. K. Aminov and B. I. Kochelaev, Sov. Phys.-JETP 15, 903 (1962).
D. H. McMahon and R. H. Silsbee, Phys. Rev. 135A, A91 (1964).
R. Orbach and M. Tachiki, Phys. Rev. 158, 524 (1967).
J. M. Baker and A. E. Mau, Can. J. Phys. 45, 403 (1967).
H. A. Jahn, Proc. R. Soc. London Ser. A 164, 117 (1938).
V. R. Pekurovskii and S. I. Andronenko, Sov. Phys. Solid State 26, 2066 (1984).
B. Z. Malkin and V. R. Pekurovskii, in: Proceedings of the 17th All-Union Conference on the Physics of Magnetic Phenomena [in Russian], Vol. 3, Donetsk (1985), p. 230.
S. J. Allen, Phys. Rev. 166, 530 (1968).
B. G. Vekhter and M. D. Kaplan, in: Spectroscopy of Crystals [in Russian], Nauka, Leningrad (1978), p. 149.
G. A. Gehring and K. A. Gehring, Rep. Prog. Phys. 38, 1 (1975).
R. Englman and B. Halperin, Phys. Rev. B. 2, 75 (1970).
B. Halperin and R. Englman, Phys. Rev. B. 3, 1698 (1971).
R. J. Elliott, in: Proceedings of the International Conference on Light Scattering in Solids, M. Balkanski, ed., Flammarion, Paris (1971), p. 351.
B. G. Vekhter and M. D. Kaplan, Phys. Lett. A 43, 398 (1973).
E. Sigmund and M. Wagner, Z. Phys. 268, 245 (1974).
M. Wagner, Phys. Lett. A 53, 1 (1975).
G. Z. Wenzel, Z. Phys. B. 36, 133 (1973).
J. Kanamori, J. Appl. Phys. 31, Suppl., 14 (1960).
E. Pytte, Phys. Rev. B. 3, 3503 (1971).
N. Hugenholtz, Quantum Theory of Many-Body Systems [Russian translation], Mir, Moscow (1967) [Rep. Prog. Phys. 28, 201 (1965)].
K.-H. Hock, G. Schroder, and H. Thomas, Z. Phys. B. 30, 403 (1978).
Z. A. Kazey, P. Novak, and V. I. Sokolov, Sov. Phys. JETP 56, 854 (1982).
S. Hirotsu, J. Phys. C.: Solid State Phys. 10, 967 (1977).
W. J. A. Maaskant and W. G. Haije, J. Phys. C.: Solid State Phys. 19, 5295 (1986).
W. G. Haije and W. J. A. Maaskant, J. Phys. C.: Solid State Phys. 19, 6943 (1986).
W. G. Haije and W. J. A. Maaskant, J. Phys. C.: Solid State Phys. 20, 2089 (1987).
D. Muller, G. Heger, and D. Reinen, Solid State Commun. 17, 1249 (1975).
D. Reinen, Solid State Commun. 21, 137 (1977).
Y. Noda, M. Mori, and Y. Yamada, Solid State Commun. 19, 1071 (1976).
Y. Noda, M. Mori, and Y. Yamada, J. Phys. Soc. Jpn. 45, 954 (1978).
M. A. Ivanov, V. Ya. Mitrofanov, L. D. Falkovskaya, and A. Ya. Fishman, J. Magn. Magn. Mater. 36, 26 (1983).
F. Mehran and K. W. H. Stevens, Phys. Rev. B 27, 2899 (1983).
Z. Jirak, Phys. Rev. B. 35, 5437 (1987).
Y. Yamada, in: Electron-Phonon Interactions and Phase Transitions, T. Riste, ed., Plenum Press, New York-London (1977).
Yu. A. Izyumov, V. E. Naish, and R. P. Ozerov, Neutron Diffraction Examination of Magnetic Materials [in Russian], Vol. 2, Atomizdat, Moscow (1981).
E. J. Verwey, P. W. Haayman, and N. C. Romeijin, J. Chem. Phys. 15, 181 (1947).
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Kaplan, M.D., Vekhter, B.G. (1995). Interaction of Jahn—Teller Centers. In: Cooperative Phenomena in Jahn—Teller Crystals. Modern Inorganic Chemistry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1859-4_2
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DOI: https://doi.org/10.1007/978-1-4615-1859-4_2
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