Amplitudes for magnon scattering by vortices in two-dimensional weakly easy-plane ferromagnets

TL;DR

This paper investigates how magnons scatter off vortices in two-dimensional easy-plane ferromagnets, combining analytical and numerical methods to reveal universal scattering laws and physical explanations for observed phenomena.

Contribution

It provides a comprehensive analysis of vortex-magnon scattering, establishing general laws and explaining phenomena like Zeeman-like splitting and singular scattering behavior.

Findings

Splitting of doublets for modes with opposite m signs at long wavelengths.

Scattering amplitude σ_m proportional to wave number k as k diverges.

Physical explanation of scattering phenomena via effective magnetic field behavior.

Abstract

We study magnon modes in the presence of a vortex in a circular easy-plane ferromagnet. The problem of vortex-magnon scattering is investigated for partial modes with different values of the azimuthal quantum number m over a wide range of wave numbers. The analysis was done by combining analytical and numerical calculations in the continuum limit with numerical diagonalization of adequately large discrete systems. The general laws governing vortex-magnon interactions are established. We give simple physical explanations of the scattering results: the splitting of doublets for the modes with opposite signs of $m$, which takes place for the long wavelength limit, is an analogue of the Zeeman splitting in the effective magnetic field of the vortex. A singular behavior for the scattering amplitude, $\sigma_m\propto k$, takes place as $k$ diverges; it corresponds to the generalized Levinson theorem and can be explained by the singular behavior of the effective magnetic field at the origin.