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=${\mathit{J}}_{\mathit{z}}$/${\mathit{J}}_{\mathit{xy}}$, where ${\mathit{J}}_{\mathit{z}}$ and ${\mathit{J}}_{\mathit{xy}}$ 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 ${\lambda }_{\mathit{c}}$<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 λ<${\lambda }_{\mathit{c}}$; however, these degeneracies split for λ>${\lambda }_{\mathit{c}}$ 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. © 1996 The American Physical Society.