Theory of the surface magnetization profile and the low-energy, spin-polarized, inelastic electron scattering off insulating ferromagnets at finiteT

A semi-infinite Heisenberg ferromagnet with nearest-neighbor exchange interactions is studied at finite $T$. The Green functions are evaluated by extending the random-phase approximation to consider the spatial variation of the layer magnetization, which is calculated self-consistently at all temperatures up to $T_c$. Results for an fcc lattice with a (111) surface turn out qualitatively similar to previous results for a sc lattice with a (100) surface. In both cases the surface has the same $T_c$ as the bulk, irrespective of the difference between surface and bulk exchange constants. A survey is presented of a continued fraction representation for the Green functions in the mixed local-Bloch basis for the spin operators, related to the transfer-matrix formalism, which allows explicit evaluation of the diagonal Green function at each layer. The calculation was performed by truncating the spatial variation of the magnetization, at any $T$, at the third layer of the lattice. The currently available intense sources of spin-polarized electrons offer a possibility of obtaining quantitative information on the surface parameters. The differential cross section for low-energy electron scattering is calculated for the fcc lattice at zero momentum transfer. The curves show resonances near one or both ends of the bulk magnon energy band, depending on the surface exchange parameters.