Temperature dependence of the spectra of elementary excitations for anisotropic S = 1 ferromagnetic

The dynamics of an easy-plane S = 1 ferromagnetic was investigated at finite temperatures taking into account the considerable quantum reduction of the spin. It is shown that in the case considered, in addition to the two known modes, standard transverse and longitudinal, a new branch appears due to the nonzero probability of transitions of a magnetic ion between the excited energy levels at finite temperatures. This mode is highly suppressed at low temperatures, because the population of the excited energy level decreases exponentially with decreasing temperature. However, when the finite temperature is lower than the Curie temperature TC, but is comparable with the energy of the exchange integral J, this mode contributes considerably to the energy consumption and exhibits high dispersion.