It is well-known that strongly nonlinear topologically nontrivial excitations (solitons) play a special role in low-dimensional magnetic systems. For example, kinks in 1D systems are responsible for the destruction of long-range order at finite temperatures, and the presence of vortices in 2D systems gives rise to a special type of phase transition -- the Berezinskii-Kosterlitz-Thouless transition. Experimental observation of soliton signatures in the response functions is usually based on the fact that translational motion of solitons leads to the the so-called soliton central peak, for review see ,,. Another possibility is to look for internal degrees of freedom of solitons, such as magnon modes localized on a soliton. Resonances at characteristic frequencies of an internal motion can be observed in electron spin resonance or inelastic neutron scattering (INS) experiments. In 1D such effects of ``soliton magnetic resonance'' were detected in the Ising-type antiferromagnet (AFM) CsCoCl , and were predicted theoretically for Heisenberg AFMs . In 3D, magnon modes localized on domain walls in AFMs were observed in thulium orthoferrite . Presently, no experimentally testable examples of internal soliton dynamics in 2D are known. Moreover, only a quasi-local mode has been predicted for solitons in isotropic , XY-type, and easy-plane Heisenberg,, 2D ferromagnets (FM).
The aim of the present Letter is to draw attention to the fact that in classical easy-plane Heisenberg 2D AFMs ``out-of-plane'' vortices have finite-frequency truly localized internal modes which may be detectable in resonance or INS experiments. We also numerically obtain the vortex-magnon S-matrix in the long-wavelength region, analyzing linearized perturbations of the vortex structure, for continuum and discrete lattice models.