Spherical Model for Anisotropic Ferromagnetic Films

TL;DR

This paper develops a spherical model to analyze how magnetic anisotropy influences the Curie temperature in ferromagnetic films with many layers, highlighting differences from the standard spherical model.

Contribution

It introduces a modified spherical model that incorporates magnetic anisotropy effects, providing new insights into the dimensional crossover in ferromagnetic films.

Findings

The model predicts a decrease in T_c with increasing layers due to anisotropy.

Inhomogeneous boundary conditions affect the Curie temperature differently than standard models.

The approach captures the transition from 3D to 2D magnetic behavior.

Abstract

The corrections to the Curie temperature T_c of a ferromagnetic film consisting of N layers are calculated for N \gg 1 for the model of D-component classical spin vectors in the limit D \to \infty, which is exactly soluble and close to the spherical model. The present approach accounts, however, for the magnetic anisotropy playing the crucial role in the crossover from 3 to 2 dimensions in magnetic films. In the spatially inhomogeneous case with free boundary conditions the D=\infty model is nonequivalent to the standard spherical one and always leads to the diminishing of T_c(N) relative to the bulk.