Inelastic scattering of low-energy electrons by spin excitations on ferromagnets

We develop a multiple-scattering description of the inelastic scattering by spin excitations of low-energy electrons reflected from the surface of a ferromagnetic material. The scattering efficiency per unit solid angle is expressed in terms of an appropriately defined frequency- and wave-vector-dependent susceptibility of the near surface region of the crystal. The formalism may thus be applied to the scattering by either Stoner excitations, or spin waves, provided the appropriate dynamic response functions are available. We report quantitative studies of the excitation cross sections for spin waves on the Fe(100) surface, and on the Ni(110) surface. The scattering efficiencies we calculate are compared to those for exciting (short-wavelength) surface phonons on such surfaces, in electron-loss studies in the impact regime. We then comment on possible application of electron-loss spectroscopy to the study of spin excitations on magnetic surfaces, and in ultrathin films.