Magnon modes and magnon-vortex scattering in two-dimensional easy-plane ferromagnets

TL;DR

This paper investigates magnon modes and their scattering by vortices in two-dimensional easy-plane ferromagnets, combining analytical and numerical methods to connect theoretical predictions with simulation results.

Contribution

It introduces a comprehensive analysis of magnon-vortex interactions, deriving a scattering matrix and a collective coordinate model that aligns with molecular dynamics simulations.

Findings

Identification of quasi-local translational magnon modes

Derivation of a vortex motion equation matching simulations

Dependence of vortex parameters on boundary conditions

Abstract

We calculate the magnon modes in the presence of a vortex in a circular system, combining analytical calculations in the continuum limit with a numerical diagonalization of the discrete system. The magnon modes are expressed by the S-matrix for magnon-vortex scattering, as a function of the parameters and the size of the system and for different boundary conditions. Certain quasi-local translational modes are identified with the frequencies which appear in the trajectory X(t) of the vortex center in recent Molecular Dynamics simulations of the full many-spin model. Using these quasi-local modes we calculate the two parameters of a 3rd-order quation of motion for X(t). This equation was recently derived by a collective variable theory and describes very well the trajectories observed in the simulations. Both parameters, the vortex mass and a factor on the third time derivative of X(t), depend strongly on the boundary conditions.