Surface Magnons and Analytic Continuation in the Cubic Systems

Abstract

Magnetic excitations localized on the (001) surface of a cubic Heisenberg ferromagnet are considered theoretically by extending previous calculations by several authors, where only a simple cubic spin lattice was considered, to b. c. c. and f. c. c. spin lattices. The method can be easily generalized to any crystal symmetry, or any orientation of the axis of magnetization, assumed normal to the surface. This extension of the theory makes it possible to undertake in the future a comparison of theoretical calculations of the surface magnon despersionrelation, with, for instance, results of experiments with inelastic low energy electron diffraction on surfaces of, e. g. , some ferromagnetic rare-earth salts. The relationship has been shown between the surface spectrum and the analytic continuation to the complex k 3 plane of the bulk magnon dispersion relation, where a very close analogy can be found with the theory of surface electronic states in semiconductors.