Abstract
We consider the magnon modes of a vortex-antivortex pair in a two-dimensional classical XY ferromagnet in the presence of a magnetic field applied along one of the in-plane axes. The exact analytical expressions for magnon modes of zero frequency are derived. The magnon waveforms of the continuum states are obtained using the Born approximation. The results can also be applied to anisotropic three-dimensional systems with a weak interlayer coupling constant.
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