Abstract
A cone phase appears as the ground state of uniaxial magnets with comparable second-order and fourth-order anisotropy constants. In such systems, specific vortex states can exist. The authors have studied magnetization oscillations in small cylindrical particles in a cone vortex state. The study has determined the frequencies of magnon excitations in the presence of a vortex in the cone phase of a ferromagnet. It has been established that there is a significant splitting of the doublets of modes with opposite values of the azimuthal number m, including modes with |m| > 1.
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