Spatial Variation of the Magnetization Across a Ferromagnetic Thin Film in the Bethe-Peierls-Weiss Approximation

Abstract

The variation of the magnetization across a ferromagnetic film as a function of temperature and film thickness has been calculated in the Bethe-Peierls-Weiss approximation. In this approximation the Heisenberg exchange interaction between a given spin and the shell consisting of its nearest neighbors is treated exactly. The interaction of this shell with the rest of the sample is treated approximately, as an interaction with a molecular field. The extension to thin films was made by allowing this molecular field to vary across the film in the manner used by Valenta for the molecular-field approximation. The finite thickness of the film had little effect on the temperature variation of the magnetization, reducing the Curie temperature by only a few percent from the bulk value even for films as thin as eight layers. The spatial falloff of the magnetization at the surface was even more abrupt than in the molecular-field case and almost independent of film thickness. For a film of twenty layers, the magnetization fell at the surface to 60% of its value at the center and almost the entire drop occurred within four layers. The temperature dependence was found to be very sensitive to the method of determining the molecular field.