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 spectra of the coupled magnetoelastic waves of an easy-plane ferromagnet with a negative biquadratic interaction are investigated. It is shown that in this case the existence region of the quadrupolar phase is narrowed substantially in comparison with the case of a positive biquadratic interaction. The phase diagram of the system is constructed.
The phase diagram of strongly anisotropic two-axis ferromagnet at arbitrary orientation of external magnetic field is built. It is demonstrated that together with a ferromagnetic phase there is possible the existence of phases with a tensorial order parameter: quadrupolar or quadrupolar-ferromagnetic phases. Spectra of bound magnetoelastic waves are investigated. Besides it is demonstrated that at large enough magnetoelastic interaction there is possible an active interaction of a magnetic subsystem with longitudinally polarized acoustic mode which becomes a soft mode at the point of orientational phase transition.
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