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Phase transitions in diluted magnets: Critical behavior, percolation, and random fields

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Abstract

Transition metal halides provide realizations of Ising,XY, and Heisenberg antiferromagnets in one, two, and three dimensions. The interactions, which are of short range, are generally well understood. By dilution with nonmagnetic species such as Zn++ or Mg++ one is able to prepare site-random alloys which correspond to random systems of particular interest in statistical mechanics. By mixing two magnetic ions such as Fe++ and Co++ one can produce magnetic crystals with competing interactions-either in the form of competing anisotropies or competing ferromagnetic and antiferromagnetic interactions. In this paper the results of a series of neutron scattering experiments on these systems carried out at Brookhaven over the past several years are briefly reviewed. First the critical behavior in Rb2Mn0.5Ni0.5F4 and FecZn1−cF2 which correspond to two-dimensional and three-dimensional random Ising systems, respectively, are discussed. Percolation phenomena have been studied in Rb2MncMgl−cF4, Rb2CocMgl−cF4, KMncZl-cF3, and MncZnl−cF2 which correspond to two-and three-dimensional Heisenberg and Ising models, respectively. In these casesc is chosen to be in the neighborhood of the nearest-neighbor percolation concentration. Application of a uniform field to the above systems generates a random staggered magnetic field; this has facilitated a systematic study of the random field problem. As we shall discuss in detail, a variety of novel, unexpected phenomena have been observed.

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References

  1. R. J. Birgeneau, R. A. Cowley, G. Shirane, J. A. Tarvin, and H. J. Guggenheim,Phys. Rev. B 21:317 (1980).

    Google Scholar 

  2. H. Ikeda and K. Hirakawa,Solid State Commun. 14:529 (1974).

    Google Scholar 

  3. J. Als-Nielsen, R. J. Birgeneau, H. J. Guggenheim, and G. Shirane,J. Phys. C 9:L121 (1976).

    Google Scholar 

  4. See for example, J. W. Essam, inPhase Transitions and Critical Phenomena, C. Domb and M. S. Green, eds. (Academic, New York, 1972), Vol. II, p. 197; D. Stauffer,Phys. Rep. 54:1 (1979).

    Google Scholar 

  5. D. Stauffer,Z. Phys. B 22:161 (1976); H. E. Stanley, R. J. Birgeneau, P. J. Reynolds, and J. F. Nicoll,J. Phys. C 9:L553 (1976); T. C. Lubensky,Phys. Rev. B 15:311 (1977).

    Google Scholar 

  6. R. J. Birgeneau, R. A. Cowley, G. Shirane, J. A. Tarvin, and H. J. Guggenheim,Phys. Rev. B 21:317 (1980).

    Google Scholar 

  7. A. B. Harris,J. Phys. C 7:1671 (1974); A. B. Harris and T. C. Lubensky,Phys. Rev. Lett. 33:1540 (1974); T. C. Lubensky,Phys. Rev. B 11:3580 (1975); G. Grinstein and A. Luther,ibid. 13:1329 (1976); D. E. Khmel'nitskii,Zh. Eksp. Teor. Fiz. 68:1960 (1975) [Sov. Phys.-JETP 41:981 (1976)]; C. Jayaprakash and H. J. Katz,Phys. Rev. B 16:3987 (1977); K. E. Newman and E. K. Riedel,Phys. Rev. B 25:264 (1982); Giancarlo Jug,ibid. 27:609 (1983); V. Dotsenko and V. Dotsenko,Adv. Phys. 32:129 (1983).

    Google Scholar 

  8. H. Ikeda,J. Phys. Soc. Jpn. 50:3215 (1981).

    Google Scholar 

  9. R. J. Birgeneau, H. Yoshizawa, R. A. Cowley, G. Shirane, and H. Ikeda,Phys. Rev. B 28:1438 (1983).

    Google Scholar 

  10. G. M. Meyer and O. W. Dietrich,J. Phys. C 11:1451 (1978); R. A. Cowley and K. Carneiro,ibid. 13:3281 (1980).

    Google Scholar 

  11. R. J. Birgeneau, R. A. Cowley, G. Shirane, H. Yoshizawa, D. P. Belanger, A. R. King, and V. Jaccarino,Phys. Rev. B 27:6747 (1983).

    Google Scholar 

  12. For a review see A. Aharony, inMulticritical Phenomena, R. Pynn, ed. (Plenum, New York, 1984).

    Google Scholar 

  13. M. Thorpe,J. Phys. (Paris) 36:117 (1975).

    Google Scholar 

  14. Y. Endoh, G. Shirane, R. J. Birgeneau, and Y. Ajiro,Phys. Rev. B 19:1476 (1979); J. P. Boucher, C. Dupas, W. Fitzgerald, K. Knorr, and J. P. Renard,J. Phys. (Paris) 39:L-86 (1978).

    Google Scholar 

  15. A. Coniglio,Phys. Rev. Lett. 46:250 (1981).

    Google Scholar 

  16. R. A. Cowley, R. J. Birgeneau, G. Shirane, H. J. Guggenheim, and H. Ikeda,Phys. Rev. B 21:4038 (1980).

    Google Scholar 

  17. D. J. Wallace and A. P. Young,Phys. Rev. B 17:2384 (1978).

    Google Scholar 

  18. R. B. Stinchcombe,J. Phys. C 13:3723 (1980).

    Google Scholar 

  19. R. A. Cowley, G. Shirane, R. J. Birgeneau, E. C. Svennson, and H. J. Guggenheim,Phys. Rev. Lett. 39:894 (1977);Phys. Rev. B 22:4412 (1980).

    Google Scholar 

  20. O. Nikotin, P. A. Lingard, and O. W. Dietrich,J. Phys. C 2:1168 (1969).

    Google Scholar 

  21. G. Aeppli, S. M. Shapiro, R. J. Birgeneau, and H. S. Chen,Phys. Rev. B 25:4882 (1982);B 28:5160 (1983).

    Google Scholar 

  22. H. Maletta and P. Convent,Phys. Rev. Lett. 42:108 (1979); H. Maletta and W. Felsch,Z. Phys. B 37:55 (1980); H. Maletta, G. Aeppli, and S. M. Shapiro,Phys. Rev. Lett. 48:1490 (1982);J. Magn. Magn. Mat. 31–34:1367 (1983).

    Google Scholar 

  23. Y. Imry and S-k. Ma,Phys. Rev. Lett. 35:1399 (1975); A. Aharony, Y. Imry, and S-k. Ma,Phys. Rev. Lett. 37:1367 (1976); G. Grinstein,ibid. 37:944 (1976); A. P. Young,J. Phys. C 10:L257 (1977); G. Parisi and N. Sourlas,Phys. Rev. Lett. 43:744 (1979).

    Google Scholar 

  24. E. Pytte, Y. Imry, and D. Mukamel,Phys. Rev. Lett. 46:1173 (1981); K. Binder, Y. Imry, and E. Pytte,Phys. Rev. B 24:6736 (1981); D. Mukamel and E. Pytte,ibid. 25:4779 (1982); H. S. Kogon and D. J. Wallace,J. Phys. A 14:L527 (1981); J. Cardy (unpublished); A. Niemi,Phys. Rev. Lett. 49:1808 (1982).

    Google Scholar 

  25. G. Grinstein and S-k. Ma,Phys. Rev. Lett. 49:685 (1982); J. Villain,J. Phys. (Paris) 43:L551 (1982); A. Aharony and E. Pytte,Phys. Rev. B 27:5872 (1983).

    Google Scholar 

  26. S. Fishman and A. Aharony,J. Phys. C 12:L729 (1979).

    Google Scholar 

  27. P. Wong, S. von Molnar, and P. Dimon,J. Appl. Phys. 53:7954 (1982).

    Google Scholar 

  28. M. Hagen, R. A. Cowley, S. K. Satija, H. Yoshizawa, G. Shirane, R. J. Birgeneau, and H. J. Guggenheim,Phys. Rev. B 28:2602 (1983).

    Google Scholar 

  29. J. Cardy,Phys. Rev. B 29:505 (1984).

    Google Scholar 

  30. D. P. Belanger, H. Yoshizawa, V. Jaccarino, A. R. King, R. J. Birgeneau, R. A. Cowley, and G. Shirane (unpublished work).

  31. H. Yoshizawa, R. A. Cowley, G. Shirane, R. J. Birgeneau, H. J. Guggenheim, and H. Ikeda,Phys. Rev. Lett. 48:438 (1982).

    Google Scholar 

  32. P. Wong and J. Cable,Phys. Rev. B 28:5361 (1983) and unpublished work.

    Google Scholar 

  33. D. P. Belanger, A. R. King, and V. Jaccarino,Phys. Rev. Lett 48:1050 (1982); D. P. Belanger, A. R. King, V. Jaccarino, and J. L. Cardy,Phys. Rev. B 29:2522 (1983).

    Google Scholar 

  34. Y. Shapira,J. Appl. Phys. 53:1931 (1982); and private communication; Y. Shapira and N. F. Oliveira Jr.,Phys. Rev. B 27:4336 (1983); Y. Shapira, N. F. Oliviera Jr., and S. Foner (unpublished).

    Google Scholar 

  35. R. A. Cowley, H. Yoshizawa, G. Shirane, R. J. Birgeneau, M. Hagen, and D. P. Belanger (unpublished work).

  36. R. A. Cowley and W. J. L. Buyers,J. Phys. C 15:L1209 (1983).

    Google Scholar 

  37. P. Kettler and M. Steiner (private communication).

  38. H. Ikeda,J. Phys. C 16:L21 (1983); H. Ikeda and K. Kikuta,ibid. 16:L445 (1983).

    Google Scholar 

  39. I. B. Ferreira, A. R. King, V. Jaccarino, H. J. Guggenheim, and J. L. Cardy,Phys. Rev. B 28:5192 (1983).

    Google Scholar 

  40. E. Pytte (private communication) is currently carrying out such calculations.

  41. R. A. Cowley, R. J. Birgeneau, G. Shirane, and H. Yoshizawa,Proceedings of the Geilo Conference on Multicritical Phenomena, R. Pynn, ed. (in press) (Plenum, New York, 1984).

    Google Scholar 

  42. R. M. Fleming, D. E. Monoton, D. B. McWhan, and F. J. DiSalvo,Phys. Rev. Lett. 45:576 (1980); C. H. Chen, J. M. Gibson, and R. M. Fleming,Phys. Rev. B 26:184 (1982).

    Google Scholar 

  43. P. Wong, P. M. Horn, R. J. Birgeneau, and G. Shirane,Phys. Rev. B 27:428 (1983).

    Google Scholar 

  44. A. N. Bazhan and V. A. Ul'ganov,Zh. Eksp. Teor. Fiz. 79:186 (1980) [Sov. Phys.-JETP 52:94 (1980)]; D. Mukamel,Phys. Rev. Lett. 46:845 (1981).

    Google Scholar 

  45. P. Kettler, M. Steiner, H. Dachs, R. German, and B. Wanklyn,Phys. Rev. Lett. 47:1329 (1981).

    Google Scholar 

  46. R. M. Suter, M. W. Schafer, and P. M. Horn,Phys. Rev. B 26:1495 (1982).

    Google Scholar 

  47. R. J. Birgeneau and A. N. Berker,Phys. Rev. B 26:3751 (1982).

    Google Scholar 

  48. H. Rohrer and H. J. Scheel,Phys. Rev. Lett. 44:876 (1980). In this paper it is shown that random fields round the Ising transition as we expect.

    Google Scholar 

  49. Y. Imry, this issue,J. Stat. Phys. 34:849 (1984).

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts

    R. J. Birgeneau

  2. Department of Physics, University of Edinburgh, EH9 3JZ, Edinburgh, Scotland

    R. A. Cowley

  3. Brookhaven National Laboratory, 11973, Upton, New York

    G. Shirane & H. Yoshizawa

Authors
  1. R. J. Birgeneau
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  2. R. A. Cowley
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  3. G. Shirane
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  4. H. Yoshizawa
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Birgeneau, R.J., Cowley, R.A., Shirane, G. et al. Phase transitions in diluted magnets: Critical behavior, percolation, and random fields. J Stat Phys 34, 817–848 (1984). https://doi.org/10.1007/BF01009443

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