An analytical model for the effective magnetic properties of a thin film consisting of a few layers of particles with arbitrary permeability and the stochastical initial magnetization is presented. The model is magnetostatic and implies the explicit averaging of the true field. It is shown that it works for all possible thicknesses of the film (arbitrary number of particles across the film) and there is no need for surface-to-bulk transition. The surface effect leading to the change of the reflective properties of the thin film compared to the prediction of the traditional theory is significant for a sparse arrangement of the grains and vanishes when these are touching. The method is verified by comparison with the model of the lattice of magnetic scattering centers.
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Simovski et al. (2002) studied this question.