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Homogenization of Composite Ferromagnetic Materials

Nowadays, nonhomogeneous and periodic ferromagnetic materials are the subject of a growing interest. Actually such periodic configurations often combine the attributes of the constituent materials, while sometimes, their properties can be strikingly different from the properties of the different constituents. In this talk, after a brief review of some basic ideas in homogenization theory, I will introduce the micromagnetic model of magnetized matter. In this framework I will present the results of a recent work (joint with F. Alouges) concerning the rigorous derivation of the homogenized Gibbs-Landau free energy functional associated to a composite periodic ferromagnetic material, i.e. a ferromagnetic material in which the heterogeneities are periodically distributed inside the media. I thus describe the Γ-limit of the Gibbs-Landau free energy functional, as the period over which the heterogeneities are distributed inside the ferromagnetic body shrinks to zero.

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