Vortex-vacancy interactions in two-dimensional easy-plane magnets

For a model with isotropic nearest-neighbor exchange combined with easy-plane exchange or single-ion anisotropies, the static effects of a magnetic vacancy site on a nearby magnetic vortex are analyzed on square, hexagonal, and triangular lattices. Numerical energy minimization and linear stability analysis using the vortex instability mode are employed. When the vortex is centered on a vacancy, the critical anisotropies where the stable vortex structure switches from out-of-plane to planar form are determined, and the vortex energies and magnetizations are found as functions of anisotropy. Consistent with square lattice calculations by Zaspel et al., the strength of anisotropy needed to stabilize a vortex in the planar form is reduced when the vortex is centered on a vacancy, for all three lattices studied. The vortex-on-vacancy energy is found to be smaller than the typical energy of a vortex centered between lattice sites in a system without vacancies. For a vortex separated from a vacancy, the energy found as a function of separation demonstrates an attractive potential between the two.