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.
Keywords: ferromagnetism, multilayers, Landau-Lifshitz equation, micromagnetic model
@article{COCV_2007__13_2_305_0, 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://www.numdam.org/articles/10.1051/cocv:2007010/} }
TY - JOUR AU - Santugini-Repiquet, Kévin TI - Homogenization of ferromagnetic multilayers in the presence of surface energies JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 305 EP - 330 VL - 13 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007010/ DO - 10.1051/cocv:2007010 LA - en ID - COCV_2007__13_2_305_0 ER -
%0 Journal Article %A Santugini-Repiquet, Kévin %T Homogenization of ferromagnetic multilayers in the presence of surface energies %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 305-330 %V 13 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007010/ %R 10.1051/cocv:2007010 %G en %F COCV_2007__13_2_305_0
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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