Fokker-Planck approach to thermal fluctuations in antiferromagnetic systems

TL;DR

This paper introduces a Fokker-Planck framework for modeling thermal fluctuations and spin dynamics in two-dimensional antiferromagnetic systems with uniaxial anisotropy, combining classical spin models with stochastic equations.

Contribution

It develops a novel Fokker-Planck approach integrated with Landau-Lifshitz-Gilbert dynamics to analyze thermal effects in antiferromagnets, including spin-wave and resistance fluctuation modeling.

Findings

Derived equations for spin polarization and correlations.

Applied methodology to spin-wave dynamics.

Formulated a model for resistance fluctuations.

Abstract

We develop a Fokker-Planck approach to describe the dynamics of staggered magnetization and thermal fluctuations in a two-dimensional antiferromagnetic system with uniaxial anisotropy. Beginning with a classical model for the antiferromagnetic system, we incorporate a Landau-Lifshitz-Gilbert equation augmented by Langevin fields to account for thermal fluctuations, and we derive the Fokker-Planck equation governing the probability distribution function of the spin configuration. Employing the mean-field approximation, we derive the equations of motion for the spin polarization and the two-time spin-spin correlation functions. The methodology is applied to the study of spin-wave dynamics and to the formulation of a phenomenological model for resistance fluctuations in two-dimensional antiferromagnetic semiconductors.