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

TL;DR

This study investigates how magnetic vacancies influence vortex stability and energy in two-dimensional easy-plane magnets across different lattice types, revealing vacancy-induced stabilization and attractive vortex-vacancy interactions.

Contribution

It provides a detailed analysis of vortex-vacancy interactions, including critical anisotropies and energy profiles, across square, hexagonal, and triangular lattices, which was not previously comprehensively studied.

Findings

Vacancies lower the anisotropy needed for vortex stabilization.

Vortex energy is reduced when centered on a vacancy.

Attractive potential exists between vortices and vacancies.

Abstract

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.