Influence of surface anisotropy on the magnetization of the Heisenberg ferromagnet

We examine theoretically the influence of surface anisotropy on the magnetization of the Heisenberg ferromagnet in its outermost layers. Emphasis is on the case where the surface spins sense an easy axis normal to the surface and at temperatures where spin-wave theory may be applied. For parameters in the range of those that emerge from recent analyses of Fe surfaces and interfaces, we find the influence of surface anisotropy to be very modest, except at rather low temperatures (10-K range). A key element in the analysis is a cancellation between the surface spin-wave contribution to the magnetization and that from a ‘‘hole’’ produced in the density of the bulk waves, when the surface wave is removed from the bulk spin-wave bands. Our theoretical analysis is based on a Green’s-function method.