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, {λ}=Jz/Jxy, where Jz and Jxy 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 λc1. 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 {λ}λc; however, these degeneracies split for {λ}>λc 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. {} 1996 The American Physical Society.