COMPARISON OF VORTEX NORMAL-MODES IN EASY-PLANE FERROMAGNETS AND ANTIFERROMAGNETS

The spin-wave modes associated with magnetic vortices in classical eas y-plane ferromagnets (FM's) and antiferromagnets (AFM's) are studied n umerically and compared. We determine the modes about a static vortex through numerical diagonalization on circular systems containing up to several hundred spins on a square lattice, as a function of the aniso tropy parameter, lambda=J(z)/J(xy), where J(z) and J(xy) are the near- neighbor exchange couplings of the indicated spin components. In the F M system, a quasilocal mode is associated with the instability of vort ices to transform between in-plane and out-of-plane types at a critica l anisotropy lambda(c)<1. In the AFM system, the corresponding instabi lity mode is a true local mode for the out-of-plane vortex. Both syste ms have degenerate pairs of modes for lambda<lambda(c); however, these degeneracies split for lambda>lambda(c) in the FM system but not in t he AFM system. We relate this to the presence of a gyrovector for the FM out-of-plane vortex and corresponding orbital motions associated wi th the translation modes, both of which are absent for the AFM out-of- plane vortices.