The spectra of coupled magnetoelastic waves in a biaxial ferromagnet with biquadratic interaction are investigated. The phase diagrams of the system under investigation are constructed as functions of biquadratic exchange. It is shown that for a strong Heisenberg exchange (exceeding the biquadratic interaction), phase transitions in the system occur only through a decrease in the magnitude of the magnetization vector. For a strong biquadratic exchange (exceeding the Heisenberg interaction), orientational phase transitions are possible, which are reduced to a reorientation of the principal axis of the tensor of quadrupole magnetic moments.
The spectral and thermodynamic properties of a biaxial ferromagnetic crystal are investigated at different temperatures. It is shown that, depending on the direction of the external magnetic field, in the case of a large single-ion anisotropy (much greater than the exchange interaction) there can be both a reorientation phase transition and a transition involving a decrease in the modulus of the magnetization vector. In the first case the elastic and magnetic subsystems actively interact, which leads to the softening of a transverse polarized phonon mode at the point of the orientational phase transition; in the second case the magnon and phonon branches do not interact, and the phase transition takes place through a magnon mode. The phase diagram of a highly anisotropic biaxial ferromagnet is constructed for an arbitrary orientation of the external magnetic field and for arbitrary temperatures.
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