Anharmonic Properties near Structural Phase Transitions

  • K. Alex Müller
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 77)


In these three lectures an attempt is made to describe, in a certain context, experimental evidence for anharmonic behavior near structural phase transitions (SPT’s): Theoretically, it is expected that systems with lower effective lattice dimensionality and shorter ranges of forces are, near TC, more dominated by correlated fluctuations (in space and time). Thus, intrinsic anharmonic behavior due to such correlated fluctuations is expected to become more pronounced, the lower the effective lattice dimensionality and the shorter the range of forces. The more important experiments on SPT’s carried out in the past decade are discussed in the above context. The manuscript is subdivided into three sections and progresses on the average, from higher to lower dimensionality and from earlier to more recent results.


Central Peak Structural Phase Transition Soft Mode Ultrasound Absorption Anharmonic Property 
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.


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  1. 1.
    From 1973 on, these volumes were edited by T. Riste with Noordhoff, Leiden, and Plenum, New York.Google Scholar
  2. 2.
    “Structural Phase Transitions and Soft Modes,” E. J. Samuelsen, E. Andersen, and J. Feder, eds., Universitetsforlaget, Oslo (1971);Google Scholar
  3. 2a.
    J. F. Scott, Rev. Mod. Phys. 46:83 (1974).ADSCrossRefGoogle Scholar
  4. 3.
    A. D. Bruce and R. A. Cowley, “Structural Phase Transitions,” Taylor and Francis Ltd., London, (1981).Google Scholar
  5. 4.
    “Structural Phase Transitions,” K. A. Müller and H. Thomas, eds., Current Topics in Physics 23, Springer, Berlin (1981).Google Scholar
  6. 5.
    K. A. Müller, in: “Dynamical Critical Phenomena and Related Topics,” p. 210, C. P. Enz, ed., Lecture Notes in Physics 104, Springer, Berlin (1979).CrossRefGoogle Scholar
  7. 6.
    W. Cochran, Adv. Phys. 9:387 (1960).ADSCrossRefGoogle Scholar
  8. 7.
    B. Berre, K. Fossheim, and K. A. Müller, Phys. Rev. Lett. 23:589 (1969).ADSCrossRefGoogle Scholar
  9. 8.
    K. A. Müller and W. Berlinger, Phys. Rev. Lett. 26:13 (1971).ADSCrossRefGoogle Scholar
  10. 9.
    T. Riste, E. J. Samuelsen, K. Otnes, and J. Feder, Solid State Commun. 9:1455 (1971).ADSCrossRefGoogle Scholar
  11. 10.
    S. M. Shapiro, J. D. Axe, G. Shirane, and T. Riste, Phys. Rev. B 6:4332 (1972).ADSCrossRefGoogle Scholar
  12. 11.
    J. K. Kjems, G. Shirane, K. A. Müller, and H. J. Scheel, Phys. Rev. B 8:1119 (1973).ADSCrossRefGoogle Scholar
  13. 12.
    Th. von Waldkirch, K. A. Müller, W. Berlinger, and H. Thomas, Phys. Rev. Lett. 28:503 (1972).ADSCrossRefGoogle Scholar
  14. 13.
    P. Hohenberg, (1971) unpublished.Google Scholar
  15. 14.
    R. A. Cowley, Ferroelectrics 6:163 (1974).CrossRefGoogle Scholar
  16. 15.
    J. Feder, in: “Local Properties at Structural Phase Transitions,” K. A. Müller and A. Rigamonti, eds., North-Holland, Amsterdam (1976) p. 312.Google Scholar
  17. 16.
    J. D. Axe, S. M. Shapiro, G. Shirane, and T. Riste, in: “Anharmonic Lattices, Structural Transitions and Melting,” T. Riste, ed., Noordhoff-Leiden, (1974) p. 23.Google Scholar
  18. 17.
    J. Töpler, B. Alefeld, and A. Heidemann, J. Phys. C 10:635 (1977).ADSCrossRefGoogle Scholar
  19. 18.
    C. N. W. Darlington and D. A. O’Connor, J. Phys. C 9:3561(1976) and “Lattice Dynamics,” Proc. Int. Conf., H. Balkanski, ed., Flammarion, Paris (1977) p. 750.Google Scholar
  20. 19.
    I. Hatta, M. Matsudo, and S. Sawada, J. Phys. C 7:L299 (1974).ADSCrossRefGoogle Scholar
  21. 20.
    A. Avogadro, G. Bonera, F. Borsa, and A. Rigamonti, Phys. Rev. B 9:3905 (1974).ADSCrossRefGoogle Scholar
  22. 21.
    F. Denoyer and R. Currat, “Neutron Inelastic Scattering,” Proc. Symp. IAEA, Vienna (1977) p. 273.Google Scholar
  23. 22.
    G. F. Reiter, W. Berlinger, K. A. Müller, and P. Heller, Phys. Rev. B 21:1 (1980).ADSCrossRefGoogle Scholar
  24. 23.
    R. Folk and F. Schwabl, Solid State Commun. 15:937 (1974).ADSCrossRefGoogle Scholar
  25. 24.
    B. I. Halperin and C. M. Varma, Phys. Rev. B 14:4030 (1976).ADSCrossRefGoogle Scholar
  26. 25.
    R. G. Petschek, Phys. Rev. B 22:1409 (1980).ADSCrossRefGoogle Scholar
  27. 26a.
    K. H. Hock and H. Thomas, Z. Phys. B 27:267 (1977).MathSciNetADSCrossRefGoogle Scholar
  28. 26b.
    H. Schmidt and F. Schwabl, Phys. Lett. 61A:476 (1977).ADSGoogle Scholar
  29. 27.
    J. B. Hastings, S. M. Shapiro, and B. C. Frazer, Phys. Rev. Lett. 40:237 (1978).ADSCrossRefGoogle Scholar
  30. 28.
    Y. Yacoby, Z. Phys. B 31:275 (1978) and references therein.ADSCrossRefGoogle Scholar
  31. 29.
    R. Currat, K. A. Müller, W. Berlinger, and F. Denoyer, Phys. Rev. B 17:2937 (1978).ADSCrossRefGoogle Scholar
  32. 30.
    K. B. Lyons and P. A. Fleury, Solid State Commun. 23:477 (1977).ADSCrossRefGoogle Scholar
  33. 31.
    E. Courtens, Phys. Rev. Lett. 37:1584 (1976).ADSCrossRefGoogle Scholar
  34. 32.
    T. Schneider and E. Stoll, Phys. Rev. Lett. 31:1254 (1973);ADSCrossRefGoogle Scholar
  35. 32a.
    T. Schneider and E. Stoll, Phys. Rev. B 13:1216 (1976).ADSCrossRefGoogle Scholar
  36. 33.
    S. Aubry, J. Chem. Phys. 62:3217 (1975); 64:3392 (1976).ADSCrossRefGoogle Scholar
  37. 34.
    T. R. Koehler, A. R. Bishop, J. A. Krumhansl, and J. R. Schrieffer, Solid. State Commun. 17:1515 (1975).ADSCrossRefGoogle Scholar
  38. 35.
    J. A. Krumhansl and J. R. Schrieffer, Phys. Rev. B 11:3535 (1975).ADSCrossRefGoogle Scholar
  39. 36.
    “Solitons and Condensed Matter Physics,” A.R. Bishop and T. Schneider, eds., Springer Series in Solid State Sciences, Springer, Heidelberg (1978).Google Scholar
  40. 37.
    T. Schneider and E. Stoll, Phys. Rev. B 16:2220 (1977).ADSCrossRefGoogle Scholar
  41. 38.
    T. Schneider and E. Stoll, Phys. Rev. B 10:2004 (1974).Google Scholar
  42. 39.
    A. D. Bruce, in: “Solitons and Condensed Matter-Physics,” A. R. Bishop and T. Schneider, eds., Springer, Heidelberg (1978) p. 116.CrossRefGoogle Scholar
  43. 40.
    A. D. Bruce, T. Schneider, and E. Stoll, Phys. Rev. Lett.:1284 (1979).Google Scholar
  44. 41.
    E. Stoll, Phys. Lett. 58A:121 (1976).ADSGoogle Scholar
  45. 42.
    M. E. Fisher, Rev. Mod. Phys. 46:597 (1974).ADSCrossRefGoogle Scholar
  46. 43.
    A. I. Larkin and D. E. Khmel’nitskii, Sov. Phys.—JETP 29:1123 (1969).ADSGoogle Scholar
  47. 44.
    B. A. Strukov, Ferroelectrics 12:97 (1976);CrossRefGoogle Scholar
  48. 44a.
    K. H. Ehses and H. E. Müser, Ferroelectrics 12:247 (1976).CrossRefGoogle Scholar
  49. 45.
    A. Aharony and A. D. Bruce, Phys. Rev. Lett. 42:462 (1979).ADSCrossRefGoogle Scholar
  50. 46a.
    E. Courtens, Phys. Rev. Lett. 41:1171 (1978);ADSCrossRefGoogle Scholar
  51. 46b.
    E. Courtens, R. Gammon, and S. Alexander, Phys. Rev. Lett. 43:1026 (1979), and (c) to be published.ADSCrossRefGoogle Scholar
  52. 47.
    R. Folk, H. Iro, and F. Schwabl, Z. Phys. B 25:69 (1976).ADSCrossRefGoogle Scholar
  53. 48.
    Th. von Waldkirch, K. A. Müller, and W. Berlinger, Phys. Rev. B 5:4324 (1972)ADSCrossRefGoogle Scholar
  54. 48a.
    and Th. von Waldkirch, K. A. Müller, and W. Berlinger, Phys. Rev. B 15 7:1052 (1973).CrossRefGoogle Scholar
  55. 49.
    A. Abragam, in: “The Principles of Nuclear Magnetism,” Clarendon, Oxford (1961) Chap. 10, p. 424.Google Scholar
  56. 50.
    A. D. Bruce, K. A. Müller, and W. Berlinger, Phys. Rev. Lett. 42:185 (1979).ADSCrossRefGoogle Scholar
  57. 51.
    E. F. Steigmeier and H. Auderset, Solid State Commun. 12:565 (1973).ADSCrossRefGoogle Scholar
  58. 52.
    A theoretical rationale for Eq. (10) to hold is given by G. Meissner, N. Menyhàrd, and P. Szépfalusy in this issue.Google Scholar
  59. 53.
    G. M. Meyer, R. J. Nelmes, and I. Hutton, “Lattice Dynamics”, Proc. Int. Conf., H. Balkanski, ed., Flammarion, Paris (1977) p. 652.Google Scholar
  60. 54.
    A. D. Bruce and R. A. Cowley, Adv. Phys. 29:219 (1980).ADSCrossRefGoogle Scholar
  61. 55.
    K. B. Lyons and P. A. Fleury, Phys. Rev. B 17:2403 (1978).ADSCrossRefGoogle Scholar
  62. 56.
    A. Aharony and M. E. Fisher, Phys. Rev. B 8:3323 (1973);ADSCrossRefGoogle Scholar
  63. 56a.
    A.D. Bruce and A. Aharony, Phys. Rev. B 10: 2078 (1974).ADSCrossRefGoogle Scholar
  64. 57.
    R. Kind and K. A. Müller, Commun. Phys. 1:223 (1976) and new data analysis (unpublished).Google Scholar
  65. 58.
    Y. Luspin, J. L. Servoin, and F. Gervais, J. Phys. C 13:3761 (1980); J. L. Servoin, F. Gervais, and K. A. Müller, to be published.ADSCrossRefGoogle Scholar
  66. 59.
    W. G. Spitzer, R. C. Miller, D. A. Kleinman, and L. E. Howarth, Phys. Rev. 126:1710 (1962);ADSCrossRefGoogle Scholar
  67. 59a.
    J. Harada, J. D. Axe, and G. Shirane, Phys. Rev. B 4:155 (1971).ADSCrossRefGoogle Scholar
  68. 60.
    R. Comes, M. Lambert, and A. Guinier, Solid State Commun. 6:715 (1968).ADSCrossRefGoogle Scholar
  69. 60a.
    M. Lambert and R. Comes, Solid State Commun. 7:305 (1969).ADSCrossRefGoogle Scholar
  70. 61.
    A. M. Quittet and M. Lambert, Solid State Commun. 12:1053 (1973);ADSCrossRefGoogle Scholar
  71. 61a.
    D. Heiman and S. Ushioda, Phys. Rev. 9:2122 (1974).ADSCrossRefGoogle Scholar
  72. 62.
    M. Rousseau, J. Nouet, and R. Almairac, J. Phys. (Paris) 38:1423 (1977), see Table II.CrossRefGoogle Scholar
  73. 63.
    T. Nattermann, J. Phys. C 9:3337 (1976)ADSCrossRefGoogle Scholar
  74. 64a.
    J.Y. Buzaré, J. C. Fayet, W. Berlinger, and K. A. Müller, Phys. Rev. Lett. 42:465 (1979).ADSCrossRefGoogle Scholar
  75. 64b.
    K. A. Müller, W. Berlinger, J. Y. Buzaré, and J. C. Fayet, Phys. Rev. B 21:1763 (1980).Google Scholar
  76. 65.
    A. Bulou, H. Théveneau, A. Trokiner, and P. Papon, J. Phys. (Paris) 40:L277 (1979).CrossRefGoogle Scholar
  77. 66.
    R. Almairac, M. Rousseau, J. Y. Gesland, J. Nouet, and B. Hennion, J. Phys. (Paris) 38:1429 (1977).CrossRefGoogle Scholar
  78. 67.
    M. Rousseau, J. Phys. (Paris) 40:L439 (1979).CrossRefGoogle Scholar
  79. 68.
    A. D. Bruce, W. Taylor, and A. F. Murray, J. Phys. C 13:483 (1980).ADSCrossRefGoogle Scholar
  80. 69.
    E. Courtens, Phys. Rev. Lett. 29:1380 (1972).ADSCrossRefGoogle Scholar
  81. 70.
    H. J. Scheel, J. G. Bednorz, and P. Dill, Ferroelectrics 13:507 (1976).CrossRefGoogle Scholar
  82. 71.
    K. A. Müller, W. Berlinger, and H. J. Scheel, to be published.Google Scholar
  83. 72.
    N. S. Shiren and R. L. Melcher, in: “Phonon Scattering in Solids”, L. J. Challis, V. W. Rampton, and A. F. G. Wyatt, eds., Plenum, New York (1976) p. 405.CrossRefGoogle Scholar
  84. 73.
    K. Fossheim and R. M. Holt, Phys. Rev. Lett. 45:730 (1980).ADSCrossRefGoogle Scholar
  85. 74.
    K. K. Murata, Phys. Rev. B 13:4015 (1976).ADSCrossRefGoogle Scholar
  86. 75.
    F. A. Modine, E. Sonder, W. P. Unruh, C. B. Finch, and R. D. Westbrook, Phys. Rev. B 10:1623 (1974).ADSCrossRefGoogle Scholar
  87. 76.
    P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49:435 (1977).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1982

Authors and Affiliations

  • K. Alex Müller
    • 1
  1. 1.IBM Zurich Research LaboratoryRüschlikon-ZHSwitzerland

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