Magnon spectrum and phase transitions in easy-plane magnets

The method of two-time delaying Green’s functions is used to study the magnon spectrum and stability boundary (from the divergence of the transverse magnetic susceptibility) of the paramagnetic phase of easy-plane magnets with one-ion anisotropy in a magnetic field perpendicular to the easy plane. The behavior of the phase boundary in the low-frequency region is studied. An equation is derived for the line along which the energy of low-frequency magnons vanishes for arbitrary quasi-momenta. The coordinates of the line terminal on the phase curve are obtained. The change in the shape of the phase boundary with a decrease in the spatial dimension is considered.

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