Geodesic
Homogenization of ferromagnetic multilayers in the presence of surface energies
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 305-330

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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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     author = {Santugini-Repiquet, K\'evin},
     title = {Homogenization of ferromagnetic multilayers in the presence of surface energies},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {305--330},
     publisher = {EDP-Sciences},
     volume = {13},
     number = {2},
     year = {2007},
     doi = {10.1051/cocv:2007010},
     mrnumber = {2306638},
     zbl = {1130.35310},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007010/}
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Santugini-Repiquet, Kévin. Homogenization of ferromagnetic multilayers in the presence of surface energies. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 305-330. doi: 10.1051/cocv:2007010

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