The Pair Approximation method for the ferromagnetic Heisenberg model with spin $S=1$ and arbitrary range of interactions. Application for the magnetic semiconductor CrIAs

TL;DR

This paper develops a Pair Approximation method for the spin-1 ferromagnetic Heisenberg model with arbitrary interaction range, including anisotropy and external field, and applies it to a hypothetical magnetic semiconductor CrIAs.

Contribution

The paper introduces a generalized Pair Approximation formalism for spin-1 systems with arbitrary interactions, incorporating anisotropy and external fields, and applies it to a predicted material.

Findings

Thermodynamic properties of CrIAs are calculated.

The method provides self-consistent thermodynamic quantities.

Numerical results are discussed in context of the material.

Abstract

The Pair Approximation method has been formulated for the isotropic ferromagnetic Heisenberg model with spin $S=1$. The exchange interactions of arbitrary range have been taken into account. The single-ion anisotropy has been considered as well as the external magnetic field. Within the method, the Gibbs free-energy has been derived, from which all thermodynamic properties can be self-consistently obtained. In order to illustrate the developed formalism, the numerical calculations have been performed for CrIAs planar magnetic semiconductor, a hypothetical material whose existence has been recently predicted by the Density Functional Theory-based calculations. For this model material, all the relevant thermodynamic magnetic properties have been studied. The numerical results have been presented in the figures and discussed.