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Intrinsic and extrinsic central-peak properties near structural phase transitions

  • K. A. Müller
Panel on the Central Peak Problem
Part of the Lecture Notes in Physics book series (LNP, volume 104)

Abstract

This review assesses the occurrence of slow collective dynamics above TC in structural phase transitions, distinct from normal-, under-, or over-damped soft modes. This is done mainly from an experimental point of view but proper reference to important theoretical progress is given. After a reference to important theoretical progress is given. After a reminiscence of the first observation of a central peak (c.p.) in SrTiO3 and its possible origin, computer simulations and strongly anharmonic (soliton)-type theories related to this phenomenon will be discussed. Then, the results of theories in which slowly-relaxing defects are coupled to the order parameter are given. A comparison with existing experiments above TC indicates that the width of c.p's have extrinsic origins, i.e., are impurity dominated. In contrast, electron paramagnetic resonance (EPR) measurements of the distribution of the order parameter in SrTiO3 prove the existence of short-range order clusters in this displacive system at TC. This short-range order accounts quantitatively for the non-vanishing c.p's in hydrogen-bounded ferro-electrics are put into perspective regarding their critical dimensionaly. Examples of magnetic centers which relax slowly in these ferroelectrics, are discussed.

Keywords

Nuclear Magnetic Resonance Electron Paramagnetic Resonance Central Peak Structural Phase Transition Soft Mode 
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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References

  1. 1.
    L. Landau, E. Lifshitz: Physique Statistique (MIR editions, Moscow 1967)Google Scholar
  2. 2.
    W. Cochran: Advances in Physics 9, 387 (1960)Google Scholar
  3. 3.
    E.J. Samuelsen, E. Andersen, J. Feder (eds.): Structural Phase Transitions and Soft Modes, (Oslo, 1971); J.F. Scott: Rev. Mod. Phys. 46, 83 (1974)Google Scholar
  4. 4.
    K.A. Müller, W. Berlinger: Phys. Rev. Lett. 26, 13 (1971)CrossRefGoogle Scholar
  5. 5.
    M.E. Fisher: Rev. Mod. Phys. 46, 597 (1974)CrossRefGoogle Scholar
  6. 6.
    T. Riste, E.J. Samuelsen, K. Otnes, J. Feder: Solid State Commun. 9, 1455 (1971)CrossRefGoogle Scholar
  7. 7.
    S.M. Shapiro, J.D. Axe, G. Shirane, T. Riste: Phys. Rev. B 6, 4332 (1972)CrossRefGoogle Scholar
  8. 8.
    J.K. Kjems, G. Shirane, K.A. Müller, H.J. Scheel: Phys. Rev. B 8, 1119 (1973)CrossRefGoogle Scholar
  9. 9.
    P. Hohenberg: (1971) unpublishedGoogle Scholar
  10. 10.
    R.A. Cowley: Ferroelectrics 6, 163 (1974)Google Scholar
  11. 11.
    Th. von Waldkirch, K.A. Müller, W. Berlinger, H. Thomas: Phys. Rev. Lett. 28, 503 (1972)CrossRefGoogle Scholar
  12. 12.
    J. Feder: In Local Properties at Structural Phase Transitions, ed. by K.A. Müller and A. Rigamonti (North-Holland, Amsterdam 1976) p.312; a more recent paper by R. Bausch and B.I. Halperin: Phys. Rev. B 18, 190 (1978), vindicates earlier nonlinear coupling theories of the thermal diffusion modeGoogle Scholar
  13. 13.
    J.D. Axe, S.M. Shapiro, G. Shirane, T. Riste: In Anharmonic Lattices, Structural Transitions and Melting, ed. by T. Riste (Noordhoff-Leiden, 1974) p.23Google Scholar
  14. 14.
    G. Shirane, J.D. Axe: Phys. Rev. Lett. 27, 1803 (1971)CrossRefGoogle Scholar
  15. 15.
    T. Schneider, E. Stoll: Phys. Rev. Lett. 31, 1254 (1973); Phys. Rev. B 13, 1216 (1976)CrossRefGoogle Scholar
  16. 16.
    S. Aubry: J. Chem. Phys. 62, 3217 (1975); 64, 3392 (1976)CrossRefGoogle Scholar
  17. 17.
    T.R. Koehler, A.R. Bishop, J.A. Krumhansl, J.R. Schrieffer: Solid State Commun. 17, 1515 (1975)CrossRefGoogle Scholar
  18. 18.
    J.A. Krumhansl, J.R. Schrieffer: Phys. Rev. B 11, 3535 (1975)CrossRefGoogle Scholar
  19. 19.
    A.R. Bishop, T. Schneider (eds.): Solitons and Condensed Matter Physics, Springer Series in Solid State Sciences (Springer, Berlin, Heidelberg, New York 1978)Google Scholar
  20. 20.
    T. Schneider, E. Stoll: Phys. Rev. Lett. 36, 1501 (1976); Phys. Rev. B 17, 1302 (1978); Phys. Rev. Lett. 41, 964 (1978)CrossRefGoogle Scholar
  21. 21.
    Th. von Waldkirch, K.A. Müller, W. Berlinger: Phys. Rev. B. 7, 1052 (1973)CrossRefGoogle Scholar
  22. 22.
    R. Folk, F. Schwabl: Solid State Commun. 15, 937 (1974)CrossRefGoogle Scholar
  23. 23.
    B.I. Halperin, C.M. Varma: Phys. Rev. B 14, 4030 (1976)CrossRefGoogle Scholar
  24. 24.
    H. Thomas in Ref. 3Google Scholar
  25. 25.
    K.H. Höck, H. Thomas: Z. Physik B 27, 267 (1977)CrossRefGoogle Scholar
  26. 26.
    H. Schmidt, F. Schwabl: Phys. Lett. A 61, 476 (1977)CrossRefGoogle Scholar
  27. 27.
    T. Schneider, E. Stoll: Phys. Rev. B 16, 2220 (1977)CrossRefGoogle Scholar
  28. 28.
    K.A. Muller: IBM Internal Report RZ982 (1978)Google Scholar
  29. 29.
    J. Töpler, B. Alefeld, A. Heidemann: J. Phys. C 10, 635 (1977)Google Scholar
  30. 30.
    C.N.W. Darlington, W.J. Fitzgerald, D.A. O'Connor: Phys. Lett. 54A, 35 (1975); C.N.W. Darlington, D.A. O'Connor: J. Phys. C 9, 3561 (1976) and Lattice Dynamics, Proc. Int. Conf., ed. by H. Balkanski (Flammarion, Paris 1977) p.750Google Scholar
  31. 31.
    K.B. Lyons, P.A. Fleury: Solid State Commun. 23, 477 (1977). The 15 GHz central peak was confirmed by C.B. Su, with Brillouin scattering (Thesis, Brandeis University 1979) unpublishedCrossRefGoogle Scholar
  32. 32.
    E. Courtens: Phys. Rev. Lett. 37, 1584 (1976)CrossRefGoogle Scholar
  33. 33.
    K.A. Müller, W. Berlinger, C.H. West, P. Heller: Phys. Rev. Lett. 32, 160 (1974)CrossRefGoogle Scholar
  34. 34.
    G.F. Reiter, W. Berlinger, K.A. Müller, P. Heller: (to be submitted for publication)Google Scholar
  35. 35.
    K. Aso: J. Appl. Phys. Jpn., 15, 1243 (1976)Google Scholar
  36. 36.
    R. Currat, K.A. Müller, W. Berlinger, F. Denoyer: Phys. Rev. B 17, 2937 (1978)CrossRefGoogle Scholar
  37. 37.
    J.B. Hastings, S.M. Shapiro, B.C. Frazer: Phys. Rev. Lett. 40, 237 (1978)CrossRefGoogle Scholar
  38. 38.
    O.F. Schirmer, K.A. Müller: Phys. Rev. B 7, 2986 (1973)Google Scholar
  39. 39.
    I. Hatta, M. Matsubo, S. Sawada: J. Phys. C 7, L 299 (1974)Google Scholar
  40. 40.
    K. Hanisch, M. Drosg: Phys. Lett. 58A, 415 (1976)Google Scholar
  41. 41.
    K. Gesi, J.D. Axe, G. Shirane, A. Linz: Phys. Rev. B 5, 1933 (1972)Google Scholar
  42. 42.
    F. Denoyer, M. Lambert, A. Comes, R. Currat: Solid State Commun. 18, 441 (1976); F. Denoyer, R. Currat: Neutron Inelastic Scattering, Proc. Symp. IAEA (Vienna 1977) p.273Google Scholar
  43. 43.
    A. Avogadro, G. Bonera, F. Borsa, A. Rigamonti: Phys. Rev. B 9, 3905 (1974)Google Scholar
  44. 44.
    R. Almairac, M. Rousseau, J.Y. Gesland, J. Nouet, B. Hennion: J. de Physique 38, 1429 (1977)Google Scholar
  45. 45.
    R.A. Cowley, J.D. Axe, M. Iizumi: Phys. Rev. Lett. 36, 806 (1976)Google Scholar
  46. 46.
    P.A. Fleury, K.B. Lyons: Phys. Rev. Lett. 37, 1088 (1976)Google Scholar
  47. 47.
    D.J. Lockwood, J.W. Arthur, W. Taylor, T.J. Hosea: Solid State Commun. 20, 703 (1976)Google Scholar
  48. 48.
    Y. Yacoby: Lattice Dynaamics, Proc. Int. Conf., ed by M. Balkanski (Flammarion, Paris 1977) p.453; Y. Yacoby, S. Just: Solid State Commun. 15, 715 (1974)Google Scholar
  49. 49.
    Y. Yacoby, Z. Physik B 31, 275 (1978)Google Scholar
  50. 50.
    U.T. Höchli, H.E. Weibel, L.A. Boatner: Phys. Rev. Lett. 41, 1440 (1978)Google Scholar
  51. 51.
    E.F. Steigmeier, G. Harbeke, R.K. Wehner: Light Scattering in Solids, ed. by M. Balkanski (Flammarion, Paris 1971) p.396Google Scholar
  52. 52.
    A.D. Bruce: In SoLitons and Condensed-Matter Physics, ed. by A.R. Bishop, T. Schneider (Springer, Berlin, Heidelberg, New York 1978) p.116Google Scholar
  53. 53.
    E. Stoll: Phys. Lett. 58A, 121 (1976)Google Scholar
  54. 54.
    Th. von. Waldkirch, K.A. Müller, W. Berlinger: Phys. Rev. B 7, 1052 (1973)CrossRefGoogle Scholar
  55. 55.
    E.S. Kirkpatrick, K.A. Müller, R.S. Rubins: Phys. Rev., A86, 135 (1964)Google Scholar
  56. 56.
    A. Abragam: The Principles of Nuclear Magnetism (Clarendon, Oxford 1961) Chap.10Google Scholar
  57. 57.
    Th. von Waldkirch, K.A. Müller, W. Berlinger: Phys. Rev. B 5, 4324 (1972)Google Scholar
  58. 58.
    F. Schwabl: Phys. Rev. Lett. 28, 500 (1972); Z. Phys. 254, 57 (1972)Google Scholar
  59. 59.
    K.A. Müller, W. Berlinger, M. Capizzi, H. Gränicher: Solid State Commun. 8, 549 (1970)Google Scholar
  60. 60.
    K.A. Müller: In Anharmonic Lattices, Structural Transitions and Melting, ed. by T. Riste (Noordhoff-Leiden, 1974)Google Scholar
  61. 61.
    E. Courtens: Phys. Rev. Lett. 29, 1380 (1972)Google Scholar
  62. 62.
    K.A. Müller, W. Berlinger: Phys. Rev. Lett. 29, 715 (1972)Google Scholar
  63. 63.
    T. Schneider, E. Stoll: Phys. Rev. B 10, 2004 (1974)Google Scholar
  64. 64.
    A.D. Bruce, T. Schneider: Phys. Rev. B 16, 3991 (1977)Google Scholar
  65. 65.
    A.D. Bruce, K.A. Müller, W. Berlinger: Phys. Rev. Lett. 42, 185 (1979)Google Scholar
  66. 66.
    E.F. Steigmeier, H. Auderset: Solid State Commun. 12, 565 (1973)CrossRefGoogle Scholar
  67. 67.
    Y. Yacoby, S. Yust, W.W. Kruhler: Ferroelectrics 12, 117 (1976)Google Scholar
  68. 68.
    A theoretical rationale for Eq.(12) to hold has been given in the paper by F. Szépfalusy at this conferenceGoogle Scholar
  69. 69.
    G.M. Meyer, R.J. Nelmes, I. Hutton: Lattice Dynamics, Proc. Int. Conf., ed by H. Balkanski (Flammarion, Paris 1977) p.652Google Scholar
  70. 70.
    A. Bunde, L. Lam: Z. Phys. B 28, 225 (1977)Google Scholar
  71. 71.
    N. Lagakos, H.Z. Cummins: Phys. Rev. B 10, 1063 (1974)Google Scholar
  72. 72.
    R.A. Cowley, G.J. Coombs, R.S. Katiyar, J.F. Ryan, J.F. Scott: J. Phys. C 4, L 203 (1971)Google Scholar
  73. 73.
    L.N. Durvasula, R.W. Gammon: Phys. Rev. Lett. 38, 1081 (1977)Google Scholar
  74. 74.
    E. Courtens: Phys. Rev. Lett. 39, 561 (1977)Google Scholar
  75. 75.
    E. Courtens: Phys. Rev. Lett. 41, 1171 (1978)Google Scholar
  76. 76.
    T. Yagi, H. Tanaka, I. Tatsuzaki: Phys. Rev. Lett. 38, 609 (1977)Google Scholar
  77. 77.
    M. Mehring, D. Suwelack: Phys. Rev. Lett. 42, 317 (1979)Google Scholar
  78. 78.
    R. Blinc, P. Cevc, M. Schara: Phys. Rev. 159, 411 (1967)Google Scholar
  79. 79.
    R. Blinc, B. Zeks: In Soft Modes in Ferroelectrics and Antiferroelectrics, ed. by E.P. Wohlfarth (North-Holland, Amsterdam 1974)Google Scholar
  80. 80.
    N.S. Dalal, C.A. McDowell, R. Srinivasan: Mol. Phys. 24, 1052 (1972); J. Chem. Phys. 60, 3787 (1974)Google Scholar
  81. 81.
    N.S. Dalal, J.A. Hebden, D.E. Kennedy, C.A. McDowell: J. Chem. Phys. 66, 4425 (1977)Google Scholar
  82. 82.
    B. Lamotte, J. Gaillard, O. Constantinescu: J. Chem. Phys. 57, 3319 (1972)Google Scholar
  83. 83.
    G.J. Adriaenssens: J. Mag. Res. 25, 511 (1977)Google Scholar
  84. 84.
    L.V. Gonzaga, A.S. Chaves, R. Blinc, G.M. Ribeiro, R. Gazzinelli, G. Rius: Solid State Commun. 27, 495 (1978)Google Scholar
  85. 85.
    R. Blinc, P. Cevc, G. Cevc: J. Chem. Phys. 70, 153 (1979)Google Scholar
  86. 86.
    K.A. Müller, N.S. Dalal, W. Berlinger: Phys. Rev. Lett. 36, 1504 (1976)Google Scholar
  87. 87.
    K.A. Müller, W. Berlinger: Phys. Rev. Lett. 37, 916 (1976)Google Scholar
  88. 88.
    J. Gaillard, P. Gloux, K.A. Müller: Phys. Rev. Lett. 38, 1216 (1977)Google Scholar
  89. 89.
    K.A. Müller, W. Berlinger: Z. Phys. B 31, 151 (1978)Google Scholar
  90. 90.
    90.D.J. Newman, W. Urban,: Adv. Phys. 24, 793 (1975)Google Scholar
  91. 91.
    E. Siegel, K.A. Müller: Bull. Am. Phys. Soc. 24, 509 (1979)Google Scholar
  92. 92.
    R. Blinc, J.L. Bjorkstam: Phys. Rev. Lett. 23, 788 (1969)Google Scholar
  93. 93.
    J.L. Bjorkstam: Adv. Mag. Res. 7, 1 (1974)Google Scholar
  94. 94.
    G.J. Adriaenssens: Phys. Rev. B 12, 5116 (1975)Google Scholar
  95. 95.
    R. Blinc: Ferroelectrics 20, 121 (1978); R. Blinc, J. Slak, F.C. Sa Barreto, A.S.T. Pires: Phys. Rev. Lett. 42, 1000 (1979)Google Scholar
  96. 96.
    R. Binder: Solid State Commun. 24, 4011 (1977)Google Scholar
  97. 97.
    G.J. Adriaenssens, J.L. Bjorkstam: Phys. Status Solidi A 18, 129 (1973), and private communicationGoogle Scholar
  98. 98.
    J. Peterson: to be publishedGoogle Scholar
  99. 99.
    M.E. Fisher: Rev. Mod. Phys. 46, 597 (1975)Google Scholar
  100. 100.
    R. Folk, H. Iro, F. Schwabl: Z. Phys. B 25, 69 (1976)Google Scholar
  101. 101.
    S.K. Ma: Modern Theory of Critical Phenomena, ed. by W. A Benjamin Inc. (London, Amsterdam)Google Scholar
  102. 102.
    A.I. Larkin, D.E. Khmelnitskii: JETP 56, 2087 (1969)Google Scholar
  103. 103.
    B.A. Strukov:Ferrolectrics 12, 97 (1976)Google Scholar
  104. 104.
    T. Schneider (private communication)Google Scholar
  105. 105.
    D.W. Bechtle, J.F. Scott, D.J. Lockwood: Phys. Rev. B 18, 6213 (1978)Google Scholar

Additional Literature

  1. -.
    R.L. Armstrong, C.A. Martin: Phys. Rev. Lett. 35, 294 (1975); R.L. Armstrong, D. Mintz, M. D'Iorio: Phys. Rev. B 15, 2840 (1977) New Evidence for the Formation of Dynamic Clusters at Temperatures in the Vicinity of a Structural Phase Transition Google Scholar
  2. -.
    C.P. Enz: Helv. Phys. Acta 47, 749 (1974) Theory of Coupled Hydrodynamic Modes Applied Above Structural Phase Transitions Google Scholar
  3. -.
    I.Ohnari, S. Takada: Progr. Theor. Phys. Jpn. 61, 11 (1979) Central Peak and Thermal Diffusion Mode near a _Structural Phase Transition Google Scholar
  4. -.
    G.F. Reiter, N. Tzoar: Phys. Rev. B 14, 208 (1976) Critical Fluctuations in the Weakly Anharmonic Crystal Model Google Scholar
  5. -.
    E. Šimánek, R. Ward: Solid State Commun. 18, 841 (1976) On the Hydrodynamic Theory of a Central Peak in Displacive Structural Phase Transitions Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • K. A. Müller
    • 1
  1. 1.IBM Zurich Research LaboratoryRüschlikonZwitzerland

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