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 sequenceof 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 establishthe homogenized equation in these two situations.
