Homogenization of ferromagnetic multilayers in the presence of surface energies
ESAIM: Control, Optimisation and Calculus of Variations, Volume 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.

DOI: 10.1051/cocv:2007010
Classification: 35B27, 35K60
Keywords: ferromagnetism, multilayers, Landau-Lifshitz equation, micromagnetic model
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Santugini-Repiquet, Kévin. Homogenization of ferromagnetic multilayers in the presence of surface energies. ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 2, pp. 305-330. doi : 10.1051/cocv:2007010. http://www.numdam.org/articles/10.1051/cocv:2007010/

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