Magnon modes in the presence of solitons (vortices) in two-dimensional
(2D) easy-plane antiferromagnets are studied. The vortex-magnon scatt
ering matrix is obtained numerically. The analysis shows the presence
of a new localized mode with a well-defined frequency determined by th
e strength of the anisotropy. It may be possible to observe this mode
in resonance experiments for quasi-2D magnetic materials with a finite
density of vortices.