Magnon spectrum in ferromagnets with a skyrmion

TL;DR

This paper investigates the spin wave excitations in a two-dimensional ferromagnet with a skyrmion, revealing unique zero modes linked to conformal symmetry breaking.

Contribution

It introduces a modified semiclassical quantization approach for lattice models to analyze magnon spectra in skyrmion-hosting ferromagnets.

Findings

Identification of three zero modes associated with conformal symmetry.

Derivation of the magnon dispersion relation in the skyrmion background.

Demonstration of a non-negative magnon spectrum.

Abstract

The analysis of the spin wave excitations in two-dimensional isotropic Heisenberg ferromagnet is performed with a single skyrmion in the ground state. We employ the ideas of semiclassical quantization method, duly modified for the use of the lattice model and Maleyev-Dyson boson representation of spin operators. The resulting Schr\"odinger equation for magnons describes the dispersion and wave functions of spin-wave excitations with strictly non-negative spectrum. In contrast to usual ferromagnet, we demonstrate the existence of three zero modes, corresponding to conformal symmetries spontaneously violated by the skyrmion configuration.