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Spin-wave theory for finite classical magnets and superparamagnetic relation

H. Kachkachi·D. A. Garanin
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Abstract

Analytical calculations based on finite-size spin-wave theory and Monte Carlo (MC) simulations are performed to investigate the validity of the well-known relation m(H,T)=M(H,T)B_D[M(H,T)NH/T] between the induced magnetization m of the magnetic particle and its intrinsic magnetization M for the Ising and isotropic classical models [B_D(x) is the Langevin function, D is the number of spin components, N is the number of atoms in the particle]. It follows from general arguments and from our analytical results for the Heisenberg model at T << T_c that this relation is not exact for any finite D and nonzero temperature. Nevertheless, corrections to this formula remain very small practically in the whole range T > 1, as confirmed by our Monte Carlo calculations. At T <~ T_c/4 there is a good agreement between the MC and finite-size spin-wave calculations for the field dependence of m and M for the Heisenberg model with free boundary conditions.

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H. Kachkachi, D. A. Garanin. 2001-09-29. Spin-wave theory for finite classical magnets and superparamagnetic relation. https://doi.org/10.1007/s100510170106

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