In these notes we describe the homogenzation theory for ferromagnetic materials. A new phenomenon arises, in particular to take into account the geometric constraint that the magnetization is locally saturated.

We examine the theory of micromagnetics developed by W. F. Brown. We show that in the case often considered, with exchange energy omitted, the minimum of the free energy is not attained for uniaxial materials but is attained for cubic materials. A study of the minimizing sequences reveals that these accurately model many features of observed domain structure. Finally, we reexamine the so-called...

In this article, we give a glimpse on our last works in simulation of ferromagnetism phenomena. The main problems encountered in this type of computation are the demagnetization field and the microwave susceptibility computations. Difficulties for the demagnetization field come principally form the fact that the operator is nonlocal and the discretized operator gives a full matrix, we will focu...

The objective of this paper is to perform, by means of Γ -convergence and two-scale convergence, a rigorous derivation of the homogenized GIBBS-LANDAU free energy functional associated to a composite periodic ferromagneticmaterial, i.e. a ferromagneticmaterial in which the heterogeneities are periodically distributed inside the media. We thus describe the Γ -limit of the GIBBS-LANDAU free energ...

Ferromagnetic two-dimensional (2D) ultrathin nanosheets hold great promise for next generation electronics. Ferromagnetic metal-free materials that usually possess only an s/p electronic configuration with weak spin-orbit coupling and a large spin relaxation time, would play an important role in constructing future spintronic devices. However, the absence of an intrinsic spin ordering structure...