Curie Temperature of Anisotropic Ferromagnetic Films

TL;DR

This paper investigates how the Curie temperature in anisotropic ferromagnetic films varies with thickness, anisotropy, and dimensionality, using an exactly solvable classical spin model to understand finite-size effects and crossover behaviors.

Contribution

It provides an analytical and numerical analysis of the dimensional crossover of Curie temperature in ferromagnetic films within an exactly solvable uniaxial model, highlighting the role of anisotropy and dimensionality.

Findings

Finite-size corrections follow mean-field exponents for d>4.

For 3<d<=4, corrections are governed by the isotropic D=∞ model.

In low dimensions (d<=3), magnetic order vanishes as anisotropy approaches zero.

Abstract

Dimensional crossover of ordering in ferromagnetic films with both periodic and free boundary conditions is studied for the exactly solvable uniaxial model of classical D-component spin vectors in the limit D \to \infty. Analytical and numerical solution of the exact equations describing this model shows that for lattice dimensionalities d>4, finite-size corrections to the bulk values of T_c are characterized by the mean-field exponents and anisotropy-dependent amplitudes. For d =< 4, the mean-field behavior is only realized in the region \kappa_c N >> 1, where \kappa_c is the dimensionlesss inverse transverse (with respect to the easy axis) bulk correlation length at T_c and N is the number of layers in the film. In the region \kappa_c N << 1 and the dimensionality range 3 < d =< 4, finite-size corrections are described by the universality class of the isotropic D=\infty model. For d =< 3, magnetic ordering vanishes in the isotropic limit, \kappa_c \to 0, since the film behaves as an object of dimensionality d'=d-1 =< 2 and long-wavelength fluctuations destroy the order. Here the suppression of T_c of a film can be substantial, depending on the competition between the weakening anisotropy and the increasing film thickness. For thick films, T_c becomes small only for very small anisotropy.