Surface spin pinnning model for magnetic properties of oxidized thin films on substrates

A simple model for oxidized thin ferromagnetic film deposited on a substrate based on the concept of surface spin pinning is proposed. A spin wave analysis of the spatial distribution of the magnetization through the film thickness, as well as of the total relative magnetization, is performed. Qualitative results are reported for three different cases: complete pinning of spins on both surfaces, one pinned and one free surface, and two free surfaces. It is shown that an appropriate choice of the surface anisotropy could account for various positions of standing spin wave resonances, even contradictory ones, as reported in the literature.