Comparison of vortex normal modes in easy-plane ferromagnets and antiferromagnets

The spin-wave modes associated with magnetic vortices in classical easy-plane ferromagnets (FM's) and antiferromagnets (AFM's) are studied numerically 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 anisotropy 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 FM system, a quasilocal mode is associated with the instability of vortices to transform between in-plane and out-of-plane types at a critical anisotropy lambda(c)<1. In the AFM system, the corresponding instability mode is a true local mode for the out-of-plane vortex. Both systems have degenerate pairs of modes for lambda<lambda(c); however, these degeneracies split for lambda>lambda(c) in the FM system but not in the AFM system. We relate this to the presence of a gyrovector for the FM out-of-plane vortex and corresponding orbital motions associated with the translation modes, both of which are absent for the AFM out-of-plane vortices.