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.
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V. Cannella and J. A. Mydosh: Phys. Rev. B6, 4220 (1972).
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).
D. Sherrington and S. Kirkpatrick: Phys. Rev. Lett. 32, 1972 (1975); Phys. Rev. B17, 4384 (1978).
D. J. Thouless, P. W. Anderson and R. G. Palmer: Phil. Mag. 35, 593 (1977).
G. Parisi: Phys. Lett. A 73, 203 (1979); Phys. Rev. Lett. 43, 1754 (1979); J. Phys. A 13, 1101 (1980).
G. Parisi, G. Toulouse: J. Phys. Lett. 41, L361 (1980).
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).
J. L. van Hemmen: Phys. Rev. Lett. 49, 409 (1982).
R. E. Walstedt: Physica 109 & 110B, 1924 (1982).
R. E. Walstedt and L. R. Walker: Phys. Rev. Lett. 47, 1624 (1981).
H. E. Stanley and T. A. Kaplan: Phys. Rev. Lett. 17, 913 (1966).
N. D. Mermin and A. Wagner: Phys. Rev. Lett. 17, 1133 (1966).
R. E. Walstedt and L. R. Walker: J. Appl. Phys. 53, 7985 (1982).
L. R. Walker and R. E. Walstedt: J. Mag. Mag. Mat. 31–34, 1289 (1983).
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).
The asterisk is used to denote quantities expressed in the reduced units of our model.
T *G 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.
L. R. Walker and R. E. Walstedt: Phys. Rev. B 22, 3816 (1980).
D. L. Martin: Phys. Rev. B20, 368 (1979).
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* < T *G . That this is the case may be seen in Fig. 3.
S. F. Edwards and P. W. Anderson: J. Phys. F5, 965 (1975).
J. Souletie: Heidelberg Colloquium on Spin Glasses 1983.
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).
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).
R. V. Chamberlin, M. Hardiman, L. A. Turkevich, and R. Orbach: Phys. Rev. B 25, 6720 (1982).
H. Sompolinsky and A. Zippelius: Phys. Rev. B 25, 6860 (1982).
The RKKY and dipolar interaction are defined here as \( - A\vec n_i \cdot \vec n_j \) cos(2kFrij)/r3 3ij 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.
J. Souletie and R. Tournier: J. Low Temp. Phys. 1, 95 (1969).
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.
K. Binder, Z. Phys. B. 26, 339 (1977).
In previous work (Ref. 18) the rotational modes were omitted from the spectra shown because of their limited importance for the macroscopic case.
B. I. Halperin and W. M. Saslow: Phys. Rev. B 16, 2154 (1977).
S. A. Roberts: J. Phys. C 15, 4755 (1981).
A. J. Bray and M. A. Moore: J. Phys. C 14, 2629 (1981).
I. Morgenstern and K. Binder: Phys. Rev. Lett. 43, 1615 (1980); Phys. Rev. B 22, 288 (1980).
A. P. Young: Phys. Rev. Lett. 50, 917 (1983).
F. Mezei: J. App. Phys. 53, 7654 (1982).
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Walstedt, R.E. (1983). Spin glass behavior in finite numerical samples. In: van Hemmen, J.L., Morgenstern, I. (eds) Heidelberg Colloquium on Spin Glasses. Lecture Notes in Physics, vol 192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12872-7_49
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DOI: https://doi.org/10.1007/3-540-12872-7_49
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