Thermodynamically-consistent mesoscopic model of the ferro/paramagnetic transition

TL;DR

This paper introduces a thermodynamically consistent mesoscopic model for micromagnetics that incorporates thermo-magnetic coupling and uses Young measures to handle fine spatial oscillations, with proven existence of weak solutions.

Contribution

It presents a novel continuum model that combines thermodynamics and micromagnetics with a mesoscopic approach using Young measures, and proves the existence of solutions.

Findings

Model successfully incorporates thermo-magnetic effects.

Existence of weak solutions established via backward Euler discretization.

Provides a framework for efficient computational implementation.

Abstract

A continuum evolutionary model for micromagnetics is presented that, beside the standard magnetic balance laws, includes thermo-magnetic coupling. To allow conceptually efficient computer implementation, inspired by relaxation method of static minimization problems, our model is mesoscopic in the sense that possible fine spatial oscillations of the magnetization are modeled by means of Young measures. Existence of weak solutions is proved by backward Euler time discretization.