Stochastic homogenization of micromagnetic energies

Abstract

Nowadays, magnetic materials play an important role in modern technology. Such materials find applications in the construction of electric and medical devices, and data storage to name a few. Very often, the efficiency of the device is based on the magnetic properties of the materials used. From a mathematical viewpoint, the study of these materials is challenging since the material-dependent parameters vary at a very small scale. This suggests carrying out a homogenization procedure. In this talk, we provide an effective description of magnetic composites whose heterogeneities are randomly distributed. More specifically, in the framework of Gamma-convergence and stochastic two-scale convergence, we analyse how the bulk Dzyaloshinskii-Moriya interaction affects the magnetic properties of composite ferromagnetic materials.