Spin-wave theory for finite classical magnets and superparamagnetic relation |
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Authors: | H Kachkachi DA Garanin |
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Institution: | (1) Laboratoire de Magnétisme et d'Optique, Université de Versailles St. Quentin, 45 avenue des états-Unis, 78035 Versailles, France, FR |
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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
DM(H, T)
H/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, 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 < T
c if ≫ 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.
Received 1st December 2000 |
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Keywords: | PACS 75 50 Tt Fine particle systems – 75 10 Hk Classical spin models |
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