We analyze the influence of the single-ion easy-axis anisotropy on the phase states and elementary excitation spectra of a ferrimagnet with sublattices with S = 1 and sigma = 1/2 and a non-Heisenberg (bilinear and biquadratic in spins) exchange interaction for the sublattice with S = 1. It is shown that for various relations between material parameters of the system, a phase with vector order parameters (ferrimagnetic phase) and the phase characterized by the vector as well as tensor order parameters (quadrupole-ferrimagnetic phase) can be realized. It is shown that the inclusion of single-ion anisotropy changes the phase transition type as compared to that in an isotropic non-Heisenberg ferrimagnet. We have constructed the phase diagram and determined the condition for the compensation of sublattice spins, as well as the behavior of the elementary excitation spectra near the phase-transition line and near the spin-compensation line. In the vicinity of the spin-compensation line, the magnon spectra are "antiferromagnetically similar."
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