Effect of Surface Pinning on the Magnetization of Thin Films

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Abstract
The effect of surface pinning, as manifested by a surface anisotropy field, on the magnetization of thin films is examined in detail for a simple cubic lattice of atoms having spin ½ coupled by pure exchange. The magnetization‐versus‐temperature curve is found to lie above that obtained in the absence of pinning. For very weak pinning (surface anisotropy field much less than surface exchange field), the magnetization is sensitive to film thickness falling off more rapidly than for bulk, in qualitative agreement with some experiments. For intermediate pinning, the magnetization is essentially independent of film thickness, following the bulk behavior, in qualitative agreement with other experiments. For very strong pinning (surface anisotropy field on the order of or greater than surface exchange field), the magnetization falls off slower than for bulk, again with a thickness dependence. As a consequence, one may interpret experimental results in terms of the degree of surface spin pinning. Physically it is not yet clear why the degree of pinning should behave in the required fashion.