Eur. Phys. J. B 22, 291-300 (2001)
https://doi.org/10.1007/s100510170106

Spin-wave theory for finite classical magnets and superparamagnetic relation

Laboratoire de Magnétisme et d'Optique, Université de Versailles St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France

Corresponding author: ^a kachkach@physique.uvsq.fr

Received: 1 December 2000
Published online: 15 August 2001

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 between the induced magnetization m of the magnetic particle and its intrinsic magnetization M for the Ising and isotropic classical models ( 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 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 if , as confirmed by our Monte Carlo calculations. At 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.