The Application of Axial Ising Models to the Description of Modulated Order

  • Julia Yeomans
Part of the NATO ASI Series book series (NSSB, volume 166)


In this paper I aim to review work on simple Ising models, the axial Ising models, which provide a useful phenomenological representation of modulated order in many compounds. The prototype of these systems is the axial next nearest neighbor Ising or ANNNI model and the first part of the article is devoted to a description of its phase diagram with emphasis on the features which might be observed experimentally. I then discuss the extent to which this behavior is in fact seen in polytypes, binary alloys and a ferrimagnet, cerium antimonide.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.J. Elliott, Phys. Rev. 124, 346 (1961).ADSCrossRefGoogle Scholar
  2. 2.
    M.E. Fisher and W. Selke, Phys. Rev. Lett. 44, 1502 (1980).ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    M.E. Fisher and W. Selke, Phil. Trans. Roy. Soc. 302, 1 (1981).ADSCrossRefGoogle Scholar
  4. 4.
    J. von Boehm, and P. Bak, Phys. Rev. Lett. 42, 122 (1979).ADSCrossRefGoogle Scholar
  5. 5.
    P. Bak and J. von Boehm, Phys. Rev. B21, 5297 (1980).ADSCrossRefGoogle Scholar
  6. 6.
    P. M. Duxbury and W. Selke, J. Phys. A. Math. Gen. 16, L741 (1983).ADSCrossRefGoogle Scholar
  7. 7.
    W. Selke and P. M. Duxbury, Z. Phys. B57, 49 (1984).ADSCrossRefGoogle Scholar
  8. 8.
    A. Szpilka and M. E. Fisher, Phys. Rev. Lett. 57 1044 (1986)ADSCrossRefGoogle Scholar
  9. 9.
    M. H. Jensen and P. Bak, Phys. Rev. B27, 6853 (1983).ADSCrossRefGoogle Scholar
  10. 10.
    A. Aharony and P. Bak, Phys. Rev. B23, 4770 (1981).ADSCrossRefGoogle Scholar
  11. 11.
    J. Villain and M. Gordon, J. Phys. C. Solid St. Phys. 13, 3117 (1980).ADSCrossRefGoogle Scholar
  12. 12.
    R. Bruinsma and A. Zangwill, Phys. Rev. Lett. 55, 214 (1985).ADSCrossRefGoogle Scholar
  13. 13.
    A. Zangwill and R. Bruinsma, Comments on Condensed Matter Physics. In press.Google Scholar
  14. 14.
    D. de Fontaine and J. Kulik, Acta. Metall. 33, 145 (1985).CrossRefGoogle Scholar
  15. 15.
    D. Broddin, G. van Tendeloo, J. van Landuyt, S. Amelinckx, R. Portier, M. Guymont and A. Loiseau. Phil. Mag. A54 395 (1986).ADSCrossRefGoogle Scholar
  16. 16.
    A. Loiseau, G. van Tendeloo, R. Portier and F. Ducastelle, J. de Physique, 46, 595 (1985).CrossRefGoogle Scholar
  17. 17.
    M. Guymont and D. Gratias, Acta Cyst. A35, 181 (1979).CrossRefGoogle Scholar
  18. 18.
    J. Kulik, S. Takeda and D. de Fontaine, Acta Metall. 35, 1137 (1987). preprint.CrossRefGoogle Scholar
  19. 19.
    G. van Tendeloo, this volume.Google Scholar
  20. 20.
    D. de Fontaine, A. Finel, S. Takeda and J. Kulik in “Noble Metals Symposium”, New York AIME meeting, eds. Massalski, Bennett, Pearson and Chang (1985).Google Scholar
  21. 21.
    H. Saro and R. S. Toth, Phys. Rev. 127, 469 (1962).ADSCrossRefGoogle Scholar
  22. 22.
    B. L. Gyorffy and G. M. Stocks, Phys. Rev. Lett. 50, 374 (1983).ADSCrossRefGoogle Scholar
  23. 23.
    A. R. Verma and P. Krishna, “Polymorphism and Polytypism in Crystals”, Wiley, New York.Google Scholar
  24. 24.
    G. S. Zdhanov and Z. Minervina, J. Phys. (Moscow) 9, 151 (1945).Google Scholar
  25. 25.
    D. Pandey and P. Krishna, J. Cyst. Growth Charact. 7, 213 (1984).CrossRefGoogle Scholar
  26. 26.
    S. Ramasesha, Pramana 23, 745 (1984).ADSCrossRefGoogle Scholar
  27. 27.
    J. Smith, J. M. Yeomans and V. Heine in Proc. N.A.T.O.A.S.I. on “Modulated Structure Materials,” ed. T. Tsakalakos (Dordrecht, Nijhoff), p. 23.Google Scholar
  28. 28.
    G. D. Price and J. M. Yeomans, Acta Cryst. B40, 448 (1984).CrossRefGoogle Scholar
  29. 29.
    J. M. Yeomans and G. D. Price, Bull. Min. 109, 3 (1986).Google Scholar
  30. 30.
    N. W. Jepps and T. F. Page, J. Cryst. Growth Charact. 7, 259 (1984).CrossRefGoogle Scholar
  31. 31.
    H. Horiuchi, K. Horioka and N. Moriraoto, J. Mineral. Soc. Japan 2, 253 (1980).Google Scholar
  32. 32.
    M. Akaogi, S. Akimoto, K. Horioka, K. Takahashi and H. Horiuchi, J. Solid St. Chem. 44, 257 (1982).ADSCrossRefGoogle Scholar
  33. 33.
    G. D. Price, S. C. Parker and J. M. Yeomans, Acta Cryst. B41, 231 (1985).CrossRefGoogle Scholar
  34. 34.
    G. Meier, P. Fischer, W. Halg, B. Lebech, B. D. Rainford and O. Vogt, J. Phys. C. Solid St. Phys. 11, 1173 (1978).ADSCrossRefGoogle Scholar
  35. 35.
    J. Rossat-Mignod, P. Burlet, H. Bartholin, O. Vogt and R. Langier, J. Phys. C. Solid St. Phys. 13, 6381 (1980).ADSCrossRefGoogle Scholar
  36. 36.
    W. Selke, M. N. Barreto and J. M. Yeomans, J. Phys. C. Solid. St. Phys. 18, L393 (1985).ADSCrossRefGoogle Scholar
  37. 37.
    M. N. Barreto and J. M. Yeomans, Physica 134A, 84 (1985).ADSCrossRefGoogle Scholar
  38. 38.
    H. Roeder and J. M. Yeoman, J. Phys. C. Solid St. Phys. 18, L163 (1985).ADSCrossRefGoogle Scholar
  39. 39.
    P. Bak, S. Coppersmith, Y. Shapir, S. Fishman and J. M. Yeomans, J. Phys. C. Solid St. Phys. 18, 3911 (1985).ADSCrossRefGoogle Scholar
  40. 40.
    J. P. Jamet and P. Lederer, J. Physique Lett. 44, L257 (1983).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Julia Yeomans
    • 1
  1. 1.Department of Theoretical PhysicsOxfordEngland

Personalised recommendations