ON THE ZERO THICKNESS LIMIT OF THIN FERROMAGNETIC FILMS WITH SURFACE ANISOTROPY ENERGY

We discuss the behaviour, when the thickness ε tends to 0, of thin ferromagnetic films with surface anisotropy energy. The model equations are given by the Landau–Lifshitz equation coupled to Maxwell equations with magnetic polarization. We consider two types of materials: flat and slender cylinders. Two scalings for the surface anisotropy coefficient are used. In the first one it is assumed that the coefficient is of order ε while in the second one we suppose that it is of order 1. We prove global existence of solutions and show that the zero-thickness limit induces new effects. For example, for slender media we get a nonlocal effect for the magnetic excitation while for flat media we obtain a one-dimensional magnetic field.