Hole-vortex-magnon interactions in diluted layered antiferromagnets with planar symmetry

We investigate the scattering of spin wave or magnon modes on planar vortices pinned on holes in two-dimensional (2D) easy-plane antiferromagnets. Numerical methods on a discrete lattice and analytical calculations in a continuum model are considered. Numerical calculations use systems centered on a lattice site, whose spin is removed. The continuum treatment is based on a simple approach that solves the equations of motion on a 2D support manifold not simply connected (i.e., containing a circular hole, which can be seen as a spin vacancy). The phase shifts for the scattered states are obtained and a comparison between numerical and analytical results is discussed. The vortex instability local mode is analyzed as a function of the hole size by several approaches. Its frequency is found to go to zero at a critical hole size. Larger holes are found to be more effective for stabilizing vortices in the planar configuration.