LOCALIZED MAGNON MODE OF INPLANE MAGNETIC VORTICES IN EASY-PLANE MAGNETS

We consider localized magnon modes of magnetic vortices in two-dimensi onal classical magnets, with exchange or single-ion easy-plane anisotr opy stronger than the critical value required to stabilize in-plane vo rtices. A discrete lattice ansatz for the structure of a magnon mode o n one vortex is analyzed. Its lowest eigenmodes are found to be identi cal with modes obtained from numerical diagonalization for ferro- (FM) and antiferromagnets (AFM), showing that the ansatz is exact. For the AFM model, one mode is found to be localized, with frequency reaching a size-independent asymptotic limit. A continuum treatment leads to a n effective Schrodinger problem that requires a small-radius cutoff du e to the singularity of the vortex core. We find, however, that it is not possible to choose this cutoff consistently to recover the exact l ocal mode frequency from the ansatz. This suggests that strong discret e lattice effects not well described by the usual continuum approximat ion always appear from the core of in-plane vortices.