Theoretical determination of Ising-type transition by using the Self-Consistent Harmonic Approximation

TL;DR

This paper applies the Self-Consistent Harmonic Approximation (SCHA) to easy-axis magnetic models, providing a theoretical framework to determine transition temperatures and other properties, validated against experiments and simulations.

Contribution

It extends the use of SCHA to easy-axis magnetic models, offering both semiclassical and quantum approaches for analyzing transition temperatures and magnetic properties.

Findings

SCHA accurately predicts transition temperatures for various magnetic materials.

The method agrees well with experimental and Monte Carlo data.

Provides insights into spin-wave spectra and critical exponents.

Abstract

Over the years, the Self-Consistent Harmonic Approximation (SCHA) has been successfully utilized to determine the transition temperature of many different magnetic models, particularly the Berezinskii-Thouless-Kosterlitz transition in two-dimensional ferromagnets. More recently, the SCHA has found application in describing ferromagnetic samples in spintronic experiments. In such a case, the SCHA has proven to be an efficient formalism for representing the coherent state in the ferromagnetic resonance state. One of the main advantages of using the SCHA is the quadratic Hamiltonian, which incorporates thermal spin fluctuations through renormalization parameters, keeping the description simple while providing excellent agreement with experimental data. In this article, we investigate the SCHA application in easy-axis magnetic models, a subject that has not been adequately explored to date. We obtain both semiclassical and quantum approaches of the SCHA for a general anisotropic magnetic model and employ them to determine various quantities such as the transition temperature, spin-wave energy spectrum, magnetization, and critical exponents. To verify the accuracy of the method, we compare the SCHA results with experimental and Monte Carlo simulation data for many distinct well-known magnetic materials.