Computational modeling of magnetic hysteresis with thermal effects

TL;DR

This paper presents a computational model for magnetic hysteresis that incorporates thermal effects, capturing microstructure formation and temperature-dependent magnetic properties, validated through 2D simulations aligned with experimental data.

Contribution

It introduces a thermo-magnetic model combining microstructure microstates with temperature effects, including a discretization scheme and MATLAB implementation.

Findings

Microstructures are encoded via Young measures.

Model captures temperature-dependent transition to paramagnetism.

Simulation results qualitatively match experimental observations.

Abstract

We study computational behavior of a mesoscopic model describing temperature/external magnetic field-driven evolution of magnetization. Due to nonconvex anisotropy energy describing magnetic properties of a body, magnetization can develop fast spatial oscillations creating complicated microstructures. These microstructures are encoded in Young measures, their first moments then identify macroscopic magnetization. Our model assumes that changes of magnetization can contribute to dissipation and, consequently, to variations of the body temperature affecting the length of magnetization vectors. In the ferromagnetic state, minima of the anisotropic energy density depend on temperature and they tend to zero as we approach the so-called Curie temperature. This brings the specimen to a paramagnetic state. Such a thermo-magnetic model is fully discretized and tested on two-dimensional examples. Computational results qualitatively agree with experimental observations. The own MATLAB code used in our simulations is available for download.