Advertisement

Spin glass behavior in finite numerical samples

  • R. E. Walstedt
Theoretical Papers
Part of the Lecture Notes in Physics book series (LNP, volume 192)

Abstract

The main points of a numerical simulation study of the spin glass transition in Ruderman-Kittel-Kasuya-Yosida (RKKY) systems are summarized. New results are also presented as follows. An investigation of the lifetime of spin freezing in a sample of 960 spins yields results which resemble qualitatively, if not quantitatively, the behavior of macroscopic systems. In the absence of anisotropy, a gradual spin freezing is found to set in at low temperatures when rotational decay of the Edwards-Anderson (EA) order parameter q is eliminated. However, this freezing exhibits no transition feature and is thought to be a finite sample effect. A study of 50 randomly selected ground states for a system of 500 spins is also presented. Evidence is given for a model of closely similar ground state pairs in which a small defect region occurs inverted in the two states concerned. Upper limit exchange barriers separating ground states are found to be substantially less than the mean thermal energy residing on the spins in the barrier region at reduced temperature T* = T G * in a number of cases. Thus, the possibility of barrier transitions, which underlie the observed decay of q, magnetic remanence, torque and EPR parameters, etc., in the spin glass state, is shown to be a natural feature of a disordered, exchange coupled spin system.

Keywords

Spin Glass Defect Region Versus Versus Versus Versus Versus Progressive Collapse Minimize Energy Path 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. Cannella and J. A. Mydosh: Phys. Rev. B6, 4220 (1972).Google Scholar
  2. 2.
    K. Binder and D. Stauffer, to appear in Monte Carlo Methods in Statistical Physics II, Springer, Berlin-Heidelberg-New York; K. Binder and D. Stauffer: in Monte Carlo Methods in Statistical Physics (K. Binder, ed.) p. 301, Springer, Berlin-Heidelberg-New York 1979; K. Binder: in Fundamental Problems in Statistical Mechanics V, p. 21, ed. by E. G. D. Cohen, North-Holland, Amsterdam 1980; K. H. Fischer: Phys. Status Solidi (b).Google Scholar
  3. 3.
    D. Sherrington and S. Kirkpatrick: Phys. Rev. Lett. 32, 1972 (1975); Phys. Rev. B17, 4384 (1978).Google Scholar
  4. 4.
    D. J. Thouless, P. W. Anderson and R. G. Palmer: Phil. Mag. 35, 593 (1977).Google Scholar
  5. 5.
    G. Parisi: Phys. Lett. A 73, 203 (1979); Phys. Rev. Lett. 43, 1754 (1979); J. Phys. A 13, 1101 (1980).Google Scholar
  6. 6.
    G. Parisi, G. Toulouse: J. Phys. Lett. 41, L361 (1980).Google Scholar
  7. 7.
    D. J. Elderfield and D. Sherrington: J. Phys, A 15, L437 (1982); J. Phys. A 15, L513 (1982); J. Phys. C 15, L783 (1982); J. Phys. C, to be published (1983).Google Scholar
  8. 8.
    J. L. van Hemmen: Phys. Rev. Lett. 49, 409 (1982).Google Scholar
  9. 9.
    R. E. Walstedt: Physica 109 & 110B, 1924 (1982).Google Scholar
  10. 10.
    R. E. Walstedt and L. R. Walker: Phys. Rev. Lett. 47, 1624 (1981).Google Scholar
  11. 11.
    H. E. Stanley and T. A. Kaplan: Phys. Rev. Lett. 17, 913 (1966).Google Scholar
  12. 12.
    N. D. Mermin and A. Wagner: Phys. Rev. Lett. 17, 1133 (1966).Google Scholar
  13. 13.
    R. E. Walstedt and L. R. Walker: J. Appl. Phys. 53, 7985 (1982).Google Scholar
  14. 14.
    L. R. Walker and R. E. Walstedt: J. Mag. Mag. Mat. 31–34, 1289 (1983).Google Scholar
  15. 15.
    The anisotropy of 0.3 at % Mn in Cu is increased by a factor ≈5 by adding 0.1 at % Au (J. J. Préjean, M. J. Joliclerc and P. Monod: J. Phys. 41, 1127 (1980). The resulting change in TG is an increase by ≈5% (F. Milliken and S. J. Williamson: private communication).Google Scholar
  16. 16.
    The asterisk is used to denote quantities expressed in the reduced units of our model.Google Scholar
  17. 17.
    TG* is estimated by scaling the experimental transition temperature by a factor 2d2 V0S(S+1)/kB a3 (W. Y. Ching and D. L. Huber: J. Phys. F8, L63 (1978) where the RKKY 3 exchange term is written — JijSi ·, with Jij = V0cos(2kFrij)/rij 3.Google Scholar
  18. 18.
    L. R. Walker and R. E. Walstedt: Phys. Rev. B 22, 3816 (1980).Google Scholar
  19. 19.
    D. L. Martin: Phys. Rev. B20, 368 (1979).Google Scholar
  20. 20.
    This argument assumes the equivalence of classical and quantum thermal energies and ignores changes in the zero-point energy, which is large. The former assumption is reasonable for large spin quantum numbers. On the latter point, changes in the zero-point energy may be small if relatively few modes are excited for T* < TG*. That this is the case may be seen in Fig. 3.Google Scholar
  21. 21.
    S. F. Edwards and P. W. Anderson: J. Phys. F5, 965 (1975).Google Scholar
  22. 22.
    J. Souletie: Heidelberg Colloquium on Spin Glasses 1983.Google Scholar
  23. 23.
    D. A. Smith: J. Phys. F 4, L26 (1974); 5, 2168 (1975); F. A. Rozario and D. A. Smith: J. Phys. F 7, 439 (1977).Google Scholar
  24. 24.
    G. Toulouse and M. Gabay: J. Phys. Lett. (Paris) 42, L163 (1981); G. Toulouse, M. Gabay, T. C. Lubensky and J. Vannimenus: J. Phys. Lett. (Paris) 43, L109 (1982).Google Scholar
  25. 25.
    R. V. Chamberlin, M. Hardiman, L. A. Turkevich, and R. Orbach: Phys. Rev. B 25, 6720 (1982).Google Scholar
  26. 26.
    H. Sompolinsky and A. Zippelius: Phys. Rev. B 25, 6860 (1982).Google Scholar
  27. 27.
    The RKKY and dipolar interaction are defined here as \( - A\vec n_i \cdot \vec n_j \) cos(2kFrij)/r3ij3 and \( - D\left[ {\vec n_i \cdot \vec n_j /r_{ij}^3 - 3(\vec n_i \cdot \vec r_{ij} )(\vec n_j \cdot \vec r_{ij} )/n_{ij}^5 } \right]\) respectively. Dipolar interaction terms are limited to nearest neighbor pairs only. The results in this paper were obtained using D/A = 0.01.Google Scholar
  28. 28.
    J. Souletie and R. Tournier: J. Low Temp. Phys. 1, 95 (1969).Google Scholar
  29. 29.
    R. H. Heffner, M. Leon, M. E. Schillaci, D. E. MacLaughlin and S. A. Dodds: J. Appl. Phys. 53, 2174 (1982); R. H. Heffner, M. Leon and D. E. MacLaughlin: Proceedings of the Yamada Conference on Muon Spin Rotation and Associated Problems, Shimoda, Japan 1983.Google Scholar
  30. 30.
    K. Binder, Z. Phys. B. 26, 339 (1977).Google Scholar
  31. 31.
    In previous work (Ref. 18) the rotational modes were omitted from the spectra shown because of their limited importance for the macroscopic case.Google Scholar
  32. 32.
    B. I. Halperin and W. M. Saslow: Phys. Rev. B 16, 2154 (1977).Google Scholar
  33. 33.
    S. A. Roberts: J. Phys. C 15, 4755 (1981).Google Scholar
  34. 34.
    A. J. Bray and M. A. Moore: J. Phys. C 14, 2629 (1981).Google Scholar
  35. 35.
    I. Morgenstern and K. Binder: Phys. Rev. Lett. 43, 1615 (1980); Phys. Rev. B 22, 288 (1980).Google Scholar
  36. 36.
    A. P. Young: Phys. Rev. Lett. 50, 917 (1983).Google Scholar
  37. 37.
    F. Mezei: J. App. Phys. 53, 7654 (1982).Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • R. E. Walstedt
    • 1
  1. 1.Bell LaboratoriesMurray HillUSA

Personalised recommendations