The Jahn—Teller Effect

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


In solving the Schrödinger equation, when several wave functions ϕ i correspond to the same energy E, such a state is called degenerate. Degeneracy is always associated with the existence of some symmetry element. The three p functions of the hydrogen atom serve as an example. Their degeneracy is due to the fact that such a system has spherical symmetry: Rotation about any axis through the nucleus leaves the Hamiltonian invariant, while transforming the p functions into each other. Such threefold degeneracy persists even if the free atom is in an external field of cubic symmetry created, for example, by six point charges forming an octahedral pattern around the nucleus. In fact, it is readily verified that cubic group operations transform the surrounding charges into each other, i.e., they leave the Hamiltonian invariant while once again transforming the three p functions into each other. At the same time, the distortion of the octahedron along the z axis (extension or compression) decreases the symmetry from cubic to tetragonal, partially lifting the degeneracy: E(p z ) ≠ E(p x ) = E(p y ). In turn, the twofold degeneracy remaining in the tetragonal group can be lifted by orthorhombic perturbations.


Yttrium Iron Garnet Electronic Function Vibronic Coupling Adiabatic Potential Vibronic Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Pergamon Press, New York-Oxford (1977).Google Scholar
  2. 2.
    H. A. Jahn and E. Teller, Proc. R. Soc. London A161, 220 (1937).Google Scholar
  3. 3.
    E. Ruch and A. Schonhofer, Theor. Chim. Acta, 3, 291 (1965).CrossRefGoogle Scholar
  4. 4.
    E. Blount, J. Math. Phys. 12, 1890 (1971).CrossRefGoogle Scholar
  5. 5.
    S. Sigano, Y. Tanabe, and H. Kamimura, Theory of Multiplets of Transition Metal Ions in Crystals, Academic Press, New York (1970).Google Scholar
  6. 6.
    M. Born and R. Oppenheimer, Ann. Phys. 84, 457 (1927).CrossRefGoogle Scholar
  7. 7.
    H. C. Longuet-Higgins, Adv. Spectrosc. 2, 429 (1961).Google Scholar
  8. 8.
    R. Englman, The Jahn—Teller Effect in Molecules and Crystals, Wiley-Interscience, New York (1972).Google Scholar
  9. 9.
    G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 3, Van Nostrand, Princeton (1966).Google Scholar
  10. 10.
    A. D. Liehr, J. Phys. Chem. 62, 471 (1963).CrossRefGoogle Scholar
  11. 11.
    R. Renner, Z. Phys. 92, 172 (1934).CrossRefGoogle Scholar
  12. 12.
    U. Opik and M. H. L. Pryce, Proc. R. Soc. A238, 425 (1957).Google Scholar
  13. 13.
    I. B. Bersuker, B. G. Vekhter, and I. Ya. Ogurtsov, Sov. Phys. Usp. 18, 569 (1975).CrossRefGoogle Scholar
  14. 14.
    W. Moffit and W. Thorson, Phys. Rev. 106, 1251 (1956).Google Scholar
  15. 15.
    M. Caner and R. Englman, J. Chem. Phys. 44, 4054 (1966).CrossRefGoogle Scholar
  16. 16.
    A. Ceulemens, J. Chem. Phys. 87, 5374.Google Scholar
  17. 17.
    W. Moffitt and A. D. Liehr, Phys. Rev. 106, 1155 (1956).Google Scholar
  18. 18.
    H. Uehara, J. Chem. Phys. 45, 4536 (1966).CrossRefGoogle Scholar
  19. 19.
    M. C. M. O’Brien, Proc. R. Soc. London A281, 323 (1964).Google Scholar
  20. 20.
    F. S. Ham, Solid State Phys. 2, 1163 (1989).Google Scholar
  21. 21.
    R. S. Dagis and I. B. Levinson, Optics and Spectroscopy, Vol. 3: Molecular Spectroscopy [in Russian], Nauka, Moscow (1967), p. 3.Google Scholar
  22. 22.
    B. P. Martinenas and R. S. Dagis, Theor. Exp. Chem. 5, 81 (1969).CrossRefGoogle Scholar
  23. 23.
    J. H. Van Vleck, Phys. Rev. 57, 426 (1940).CrossRefGoogle Scholar
  24. 24.
    B. G. Vekhter, Opt. Spectrosc. 63, 130 (1987).Google Scholar
  25. 25.
    S. Estreicher and T. L. Estle, Phys. Rev. B 30, 7 (1984).CrossRefGoogle Scholar
  26. 26.
    L. A. Rebane and O. I. Sild, in Defects in Insulating Crystals, V. M. Turkevich and K. K. Shvarts, eds. [in Russian], Riga (1981), p. 617.Google Scholar
  27. 27.
    P. Thalmeier and B. Luthi, in Handbook on the Physics and Chemistry of Rare Earths, Vol. 13 (1988).Google Scholar
  28. 28.
    V. Dohm and P. Fulde, Z. Phys. B. 21, 369 (1975).CrossRefGoogle Scholar
  29. 29.
    I. B. Bersuker and V. Z. Polinger, Sov. Phys. JETP 39, 1023 (1974).Google Scholar
  30. 30.
    M. C. M. O’Brien, J. Phys. C: Solid State Phys. 4, 2524 (1971).CrossRefGoogle Scholar
  31. 31.
    W. Thorson, J. Chem. Phys. 29, 938 (1958).CrossRefGoogle Scholar
  32. 32.
    B. Weinstock and G. L. Goodman, Adv. Chem. Phys. 9, 169 (1968).CrossRefGoogle Scholar
  33. 33.
    I. B. Bersuker and B. G. Vekhter, Ferroelectrics, 19, 137 (1978).CrossRefGoogle Scholar
  34. 34.
    R. E. Peierls, Quantum Theory of Solids, Oxford University Press, Oxford (1955).Google Scholar
  35. 35.
    R. H. Friend and D. Jerome, J. Phys. C: Solid State Phys. 12, 1441 (1979).CrossRefGoogle Scholar
  36. 36.
    D. A. Kirzhnits and Ya. A. Nepomnyashchiy, Sov. Phys. JETP 32, 1191 (1971).Google Scholar
  37. 37.
    V. A. Kochelap, V. N. Sokolov, and B. Yu. Vengalis, Phase Transitions in Semiconductors with Strain-Induced Electron-Phonon Interaction [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
  38. 38.
    J. J. Hallers and G. Vertogen, Phys. Rev. Lett. 27, 404 (1971).CrossRefGoogle Scholar
  39. 39.
    C. Weber, M. Wagner, and E. Sigmund, Phys. Status Solidi (b), 141, 529 (1987).CrossRefGoogle Scholar
  40. 40.
    L. M. Falikov and R. A. Harris, J. Chem. Phys. 51, 3153 (1969).CrossRefGoogle Scholar
  41. 41.
    M. M. Mestechkin, Instability of the Hartree-Fock Equation and Molecular Instability [in Russian], Naukova Dumka, Kiev (1986).Google Scholar
  42. 42.
    I. Ya. Ogurtsov, Article deposited at the All-Union Institute of Scientific and Technical Information, VINITI Deposit No. 5797-B-88 (1988).Google Scholar
  43. 43.
    A. K. Zvezdin, V. M. Matveev, A. A. Mukhin, and A. I. Popov, Rare-Earth Ions in Magnetically Ordered Crystals [in Russian], Nauka, Moscow (1985).Google Scholar
  44. 44.
    A. K. Zvezdin, A. A. Muchin, and A. I. Popov, JETP 45, 573 (1977).Google Scholar
  45. 45.
    A. K. Zvezdin, A. A. Muchin, and A. I. Popov, JETP Lett. 23, 240 (1976).Google Scholar
  46. 46.
    E. M. Henley and W. Therring, Elementary Quantum Field Theory, McGraw-Hill, New York (1962).Google Scholar
  47. 47.
    F. S. Ham, in: Electron Paramagnetic Resonance, Plenum Press, New York (1972), p. 1.Google Scholar
  48. 48.
    A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clarendon, Oxford (1970).Google Scholar
  49. 49.
    S. Washimia, Phys. Rev. Lett. 28, 5561 (1972).Google Scholar
  50. 50.
    K. Sasaki and Y. Obata, J. Phys. Soc. Jpn. 28, 1157 (1970).CrossRefGoogle Scholar
  51. 51.
    B. G. Vekhter, Sov. Phys. Solid State 15, 354 (1973).Google Scholar
  52. 52.
    B. G. Vekhter, in: Proceedings of the Second All-Union Conference on Solid State Physics [in Russian], Moscow (1969), p. 49.Google Scholar
  53. 53.
    I. B. Bersuker, Phys. Lett. 20, 589 (1966).CrossRefGoogle Scholar
  54. 54.
    I. B. Bersuker and I. Ya. Ogurtsov, Adv. Quantum Chem. 18, 1 (1986).CrossRefGoogle Scholar
  55. 55.
    Ya. E. Perlin and B. S. Tsukerblat, Electron-Vibration Interaction Phenomena in the Optical Spectra of Impurity Paramagnetic Ions [in Russian], Shtiintza, Kishinev (1974).Google Scholar
  56. 56.
    R. E. Coffman, Phys. Lett. 21, 381 (1966).CrossRefGoogle Scholar
  57. 57.
    R. E. Coffman, J. Chem. Phys. 48, 609 (1968).CrossRefGoogle Scholar
  58. 58.
    I. B. Bersuker, Sov. Phys. JETP 17, 836 (1963).Google Scholar
  59. 59.
    M. D. Sturge, in: Solid State Physics, F. Seitz, D. Turnbull, and H. Ehrenreich, eds., Academic Press, New York (1967), p. 91.Google Scholar
  60. 60.
    Yu. E. Perlin and M. Wagner (eds.), The Dynamical Jahn—Teller Effect in Localized Systems, North-Holland, Amsterdam (1984).Google Scholar
  61. 61.
    R. C. LeCraw and R. L. Comstock, in: Physical Acoustics, Vol. 3B: Lattice Dynamics, Warren P. Mason, ed., Academic Press, New York-London (1966), p. 127.Google Scholar
  62. 62.
    E. M. Gyorgy, M. D. Sturge, D. B. Fraser, and R. C. LeCraw, Phys. Lett. 15, 19 (1965).CrossRefGoogle Scholar
  63. 63.
    E. M. Gyorgy, R. C. LeCraw, and M. D. Sturge, J. Appl. Phys. 37, 1303 (1966).CrossRefGoogle Scholar
  64. 64.
    Z. A. Kazey, P. Novak, and V. I. Sokolov, Sov. Phys. JETP 56, 854 (1982).Google Scholar
  65. 65.
    V. V. Hyzhnyakov and N. N. Kristofell, in: The Dynamical Jahn—Teller in Localized Systems, Yu. E. Perlin and M. Wagner, eds., North-Holland, Amsterdam (1984), p. 383.Google Scholar
  66. 66.
    W. Ulrici, in: The Dynamical Jahn—Teller Effect in Localized Systems, Yu. E. Perlin and M. Wagner, eds., North-Holland, Amsterdam (1984), p. 439.Google Scholar
  67. 67.
    A. L. Natadze, A. I. Ryskin, and B. G. Vekhter, in: The Dynamical Jahn—Teller Effect in Localized Systems, Yu. E. Perlin and M. Wagner, eds., North-Holland, Amsterdam (1984), p. 347.Google Scholar
  68. 68.
    K. A. Kikoin and V. N. Flerov, Transition Metal Impurities in Semiconductors, World Scientific, 1994.Google 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

Personalised recommendations