Spectrum of elementary excitations in compounds formed by a rare-earth metal and a transition metal

On the basis of the generalized model of a ferromagnetic metal with single-ion anisotropy a study is made of hexagonal ferromagnets that are compounds of a rare-earth metal and a transition metal with $S=1$, where $S$ is the spin of an individual rare-earth ion, and easy axis anisotropy. It is shown that there are two types of elementary excitation in these compounds: a Fermi excitation (Stoner) and a Bose excitation (spin wave). The existence of three spin-wave branches is established. Equations are obtained for the order parameters. The calculations are made by the Green's function method for longitudinal and transverse magnetic fields.