Spin-wave dispersion in ferromagnetic semiconductor superlattices and thin films in the narrow-band limit

Bulk and surface magnetic excitations of the semi-infinite ferromagnetic semiconductor (FMS) superlattices and thin films described by Heisenberg and s-d model are analyzed using the transfer matrix method, developed in our previous work. Results are discussed in the narrow-band limit. The spin-wave frequencies for the semi-infinite narrow-band semiconductors are analyzed in both low- and high-frequency regions. Energies of localized excitations are compared to the bulk and the results of Green function formalism. Depending on the parameters of the system, the surface spin waves appear as “acoustical” and “optical”, and there are only some quantitative difference in the high-frequency region, comparing our method and the Green function method. In the framework of the same methodology, bulk and surface magnetic excitations of more complicated superlattices and thin films made of the FMS superlattices are analyzed in terms of dependence of the system parameters. It is shown that the s-d interaction governs the behavior of the systems. Dependence on bulk and surface parameters is discussed.