Vortex motion induced by lattice defects in two-dimensional easy-plane magnets

In this work we investigate the dynamics of planar vortices in the presence of nonmagnetic impurities in a two-dimensional magnet with $XY$ symmetry. We use analytical as well spin dynamics simulation methods. Our results indicate that vortices are attracted by defects in the lattice. Trapped by the nonmagnetic impurities they execute nonharmonic oscillations. In the regime of small oscillations our analytical results predict that the frequency is proportional to the inverse of the linear size of the system, in quite good agreement with numerical calculations. Although such oscillations barely can be observed in thermodynamic limit, it should be easy to be detected in nanoscale systems. We also consider the vortex motion near a line of nonmagnetic impurities. In such case, the vortex oscillates back and forth along the impurity line.