Investigation of magnon dispersion relations and neutron scattering cross sections with special attention to anisotropy effects

A general bilinear two-Bose Hamiltonian is diagonalized and the result used in a discussion of non-imteracting spin waves in a two-sub-lattice ferromagnet having not negligible anisotropy in the spin interaction. Model-independent functions suitable for the analysis of experimental dispersion curves are suggested. The magnon cross section for unpolarized neutrons is calculated and shown to be dependent on the anisotropy in the spin interaction. Thus in principle it allows the detection of anisotropy in the exchange interaction. Some remarks are made concerning antiferromagnetic and plane-helical structure. A numerical calculation is performed for terbium on the basis of the Kaplan-Lyons Hamiltonian with added crystalline anisotropy. The non-istropic exchange part is shown to have a small effect on the dispersion curves, and it turns out that radical changes of the Ruderman-Kittel-type functions for the exchange interaction seem to be necessary for agreement with experimental dispersion curves be obtained. The effect of the anisotropy in the cross section is estimated and shown to be important for small magnon energies.