Homogenization of ferromagnetic multilayers in the presence of surface energies

Santugini-Repiquet, Kévin

ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 305-330.

We study the homogenization process of ferromagnetic multilayers in the presence of surface energies: super-exchange, also called interlayer exchange coupling, and surface anisotropy. The two main difficulties are the non-linearity of the Landau-Lifshitz equation and the absence of a good sequence of extension operators for the multilayer geometry. First, we consider the case when surface anisotropy is the dominant term, then the case when the magnitude of the super-exchange interaction is inversely proportional to the interlayer distance. We establish the homogenized equation in these two situations.

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