Interaction of Jahn—Teller Centers

  • Michael D. Kaplan
  • Benjamin G. Vekhter
Part of the Modern Inorganic Chemistry book series (MICE)


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.


Local Distortion Anisotropic Exchange Incommensurate Phase Vibronic Coupling Indirect Exchange 
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  1. 1.
    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)].Google Scholar
  2. 2.
    D. C. Mattis, The Theory of Magnetism, Harper and Row, New York (1965).Google Scholar
  3. 3.
    R. W. White and T. H. Geballe, Long-Range Order in Solids, Academic Press, New York-London (1979).Google Scholar
  4. 4.
    P. M. Levy, in: Magnetic Oxides, Part 1, D. J. Graik, ed., Wiley, New York-London-(1975), p. 181.Google Scholar
  5. 5.
    U. Fano and G. Racah, Irreducible Tensorial Sets, Academic Press, New York (1959).Google Scholar
  6. 6.
    A. J. Freeman and R. E. Watson, Phys. Rev. 124, 1439 (1961).CrossRefGoogle Scholar
  7. 7.
    G. M. Copland and P. M. Levy, Phys. Rev. B. 1, 3043 (1970).CrossRefGoogle Scholar
  8. 8.
    H. Kramers, Physica (Utrecht) 1, 182 (1934).CrossRefGoogle Scholar
  9. 9.
    J. Goodenough, Magnetism and the Chemical Bond, Interscience Publishers, New York-London (1963).Google Scholar
  10. 10.
    P. W. Anderson, Phys. Rev. 115, 2 (1959).CrossRefGoogle Scholar
  11. 11.
    K. I. Kugel and D. I. Khomskii, Sov. Phys. JETP 37, 725 (1973).Google Scholar
  12. 12.
    D. I. Khomskii and K. I. Kugel, Solid State Commun. 13, 763 (1973).CrossRefGoogle Scholar
  13. 13.
    K. I. Kugel and D. I. Khomskii, Sov. Phys. Solid State 17, 285 (1975).Google Scholar
  14. 14.
    D. I. Khomskii and K. I. Kugel, Phys. Status Solidi B 79, 441 (1977).CrossRefGoogle Scholar
  15. 15.
    K. I. Kugel and D. I. Khomskii, Sov. Phys. Usp. 136, 231 (1982).CrossRefGoogle Scholar
  16. 16.
    K. Hirakawa and Y. Kurogi, Prog. Theor. Phys. (Suppl.), 46, 147 (1970).CrossRefGoogle Scholar
  17. 17.
    Y. Ito and J. Akimitsu, J. Phys. Soc. Jpn. 40, 1333 (1976).CrossRefGoogle Scholar
  18. 18.
    Le Dang Khoi and P. Veillet, Phys. Rev. B. 11, 4128 (1975).CrossRefGoogle Scholar
  19. 19.
    W. Kleeman and Y. Farge, J. Phys. (Paris) 36, 1293 (1975).CrossRefGoogle Scholar
  20. 20.
    C. Lacroix, J. Phys. C: Solid State Phys. 13, 5125 (1980).CrossRefGoogle Scholar
  21. 21.
    S. V. Vonsovskii and Yu. A. Izyumov, Sov. Phys. Usp. 5, 547 (1963).CrossRefGoogle Scholar
  22. 22.
    K. P. Sinha and N. Kumar, Interactions in Magnetically Ordered Solids, Oxford University Press (1980).Google Scholar
  23. 23.
    M. A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954).CrossRefGoogle Scholar
  24. 24.
    T. Kasuya, Prog. Theor. Phys. 16, 45 (1956).CrossRefGoogle Scholar
  25. 25.
    K. Yosida, Phys. Rev. 106, 893 (1957).CrossRefGoogle Scholar
  26. 26.
    M. B. Stearns, Phys. Rev. 129, 1136 (1963).CrossRefGoogle Scholar
  27. 27.
    M. B. Stearns, Phys. Rev. 8, 4383 (1973).CrossRefGoogle Scholar
  28. 28.
    M. I. Darby, Am. J. Phys. 37, 354 (1969).CrossRefGoogle Scholar
  29. 29.
    E. L. Nagaev, Physics of Magnetic Semiconductors [in Russian], Nauka, Moscow (1979).Google Scholar
  30. 30.
    P. M. Levy, Solid State Commun. 7, 1813 (1969).CrossRefGoogle Scholar
  31. 31.
    B. C. Carlson and G. S. Rushbrooke, Proc. Cambridge Philos. Soc. 46, 626 (1950).CrossRefGoogle Scholar
  32. 32.
    W. P. Wolf and R. J. Birgeneau, Phys. Rev. 166, 376 (1968).CrossRefGoogle Scholar
  33. 33.
    J. M. Baker, Rep. Prog. Phys. 34, 109 (1971).CrossRefGoogle Scholar
  34. 34.
    R. J. Elliott and K. W. H. Stevens, Proc. R. Soc. London Ser. A 218, 553 (1953).CrossRefGoogle Scholar
  35. 35.
    R. J. Birgeneau, J. Phys. Chem. Solids 28, 2429 (1967).CrossRefGoogle Scholar
  36. 36.
    R. J. Birgeneau, Phys. Rev. Lett. 19, 160 (1967).CrossRefGoogle Scholar
  37. 37.
    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).Google Scholar
  38. 38.
    K. Sigihara, J. Phys. Soc. Jpn. 14, 1231 (1959).CrossRefGoogle Scholar
  39. 39.
    L. K. Aminov and B. I. Kochelaev, Sov. Phys.-JETP 15, 903 (1962).Google Scholar
  40. 40.
    D. H. McMahon and R. H. Silsbee, Phys. Rev. 135A, A91 (1964).CrossRefGoogle Scholar
  41. 41.
    R. Orbach and M. Tachiki, Phys. Rev. 158, 524 (1967).CrossRefGoogle Scholar
  42. 42.
    J. M. Baker and A. E. Mau, Can. J. Phys. 45, 403 (1967).CrossRefGoogle Scholar
  43. 43.
    H. A. Jahn, Proc. R. Soc. London Ser. A 164, 117 (1938).CrossRefGoogle Scholar
  44. 44.
    V. R. Pekurovskii and S. I. Andronenko, Sov. Phys. Solid State 26, 2066 (1984).Google Scholar
  45. 45.
    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.Google Scholar
  46. 46.
    S. J. Allen, Phys. Rev. 166, 530 (1968).CrossRefGoogle Scholar
  47. 47.
    B. G. Vekhter and M. D. Kaplan, in: Spectroscopy of Crystals [in Russian], Nauka, Leningrad (1978), p. 149.Google Scholar
  48. 48.
    G. A. Gehring and K. A. Gehring, Rep. Prog. Phys. 38, 1 (1975).CrossRefGoogle Scholar
  49. 49.
    R. Englman and B. Halperin, Phys. Rev. B. 2, 75 (1970).CrossRefGoogle Scholar
  50. 50.
    B. Halperin and R. Englman, Phys. Rev. B. 3, 1698 (1971).CrossRefGoogle Scholar
  51. 51.
    R. J. Elliott, in: Proceedings of the International Conference on Light Scattering in Solids, M. Balkanski, ed., Flammarion, Paris (1971), p. 351.Google Scholar
  52. 52.
    B. G. Vekhter and M. D. Kaplan, Phys. Lett. A 43, 398 (1973).CrossRefGoogle Scholar
  53. 53.
    E. Sigmund and M. Wagner, Z. Phys. 268, 245 (1974).CrossRefGoogle Scholar
  54. 54.
    M. Wagner, Phys. Lett. A 53, 1 (1975).CrossRefGoogle Scholar
  55. 55.
    G. Z. Wenzel, Z. Phys. B. 36, 133 (1973).Google Scholar
  56. 56.
    J. Kanamori, J. Appl. Phys. 31, Suppl., 14 (1960).CrossRefGoogle Scholar
  57. 57.
    E. Pytte, Phys. Rev. B. 3, 3503 (1971).CrossRefGoogle Scholar
  58. 58.
    N. Hugenholtz, Quantum Theory of Many-Body Systems [Russian translation], Mir, Moscow (1967) [Rep. Prog. Phys. 28, 201 (1965)].Google Scholar
  59. 59.
    K.-H. Hock, G. Schroder, and H. Thomas, Z. Phys. B. 30, 403 (1978).CrossRefGoogle Scholar
  60. 60.
    Z. A. Kazey, P. Novak, and V. I. Sokolov, Sov. Phys. JETP 56, 854 (1982).Google Scholar
  61. 61.
    S. Hirotsu, J. Phys. C.: Solid State Phys. 10, 967 (1977).CrossRefGoogle Scholar
  62. 62.
    W. J. A. Maaskant and W. G. Haije, J. Phys. C.: Solid State Phys. 19, 5295 (1986).CrossRefGoogle Scholar
  63. 63.
    W. G. Haije and W. J. A. Maaskant, J. Phys. C.: Solid State Phys. 19, 6943 (1986).CrossRefGoogle Scholar
  64. 64.
    W. G. Haije and W. J. A. Maaskant, J. Phys. C.: Solid State Phys. 20, 2089 (1987).CrossRefGoogle Scholar
  65. 65.
    D. Muller, G. Heger, and D. Reinen, Solid State Commun. 17, 1249 (1975).CrossRefGoogle Scholar
  66. 66.
    D. Reinen, Solid State Commun. 21, 137 (1977).CrossRefGoogle Scholar
  67. 67.
    Y. Noda, M. Mori, and Y. Yamada, Solid State Commun. 19, 1071 (1976).CrossRefGoogle Scholar
  68. 68.
    Y. Noda, M. Mori, and Y. Yamada, J. Phys. Soc. Jpn. 45, 954 (1978).CrossRefGoogle Scholar
  69. 69.
    M. A. Ivanov, V. Ya. Mitrofanov, L. D. Falkovskaya, and A. Ya. Fishman, J. Magn. Magn. Mater. 36, 26 (1983).CrossRefGoogle Scholar
  70. 70.
    F. Mehran and K. W. H. Stevens, Phys. Rev. B 27, 2899 (1983).CrossRefGoogle Scholar
  71. 71.
    Z. Jirak, Phys. Rev. B. 35, 5437 (1987).CrossRefGoogle Scholar
  72. 72.
    Y. Yamada, in: Electron-Phonon Interactions and Phase Transitions, T. Riste, ed., Plenum Press, New York-London (1977).Google Scholar
  73. 73.
    Yu. A. Izyumov, V. E. Naish, and R. P. Ozerov, Neutron Diffraction Examination of Magnetic Materials [in Russian], Vol. 2, Atomizdat, Moscow (1981).Google Scholar
  74. 74.
    E. J. Verwey, P. W. Haayman, and N. C. Romeijin, J. Chem. Phys. 15, 181 (1947).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Michael D. Kaplan
    • 1
  • Benjamin G. Vekhter
    • 2
  1. 1.Boston UniversityBostonUSA
  2. 2.Northwestern UniversityEvanstonUSA

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