On the bilinear exchange coupling in ferromagnetic multilayers

We investigate a mathematical model describing the bilinear interlayer exchange coupling (IEC) of ferromagnets through spacers. We propose an extension in the case of the Maxwell system of the results obtained in Hamdache K and Tilioua M (2004 SIAM J. Appl. Math. 64 1077-97). The model couples the Landau-Lifshitz-Gilbert (LLG) equations with the Maxwell system. The Hoffmann interfacial boundary condition is considered to take into account bilinear IEC. The behavior of the electromagnetic field in the two cases of a thin and large nonmagnetic spacer is discussed. For example we obtain that the magnetic field in the nonmagnetic spacer vanishes in the case of a thin spacer. However the electric field depends explicitly on the initial data. Various other convergence results are also given