Spin waves in a skyrmion crystal

TL;DR

This paper derives the low-frequency spin wave spectrum in skyrmion crystals, revealing how their elastic and topological properties influence their collective excitations.

Contribution

It provides a theoretical framework for understanding spin wave modes in skyrmion crystals, incorporating Berry-phase effects and elastic properties.

Findings

Identification of Goldstone modes as skyrmion displacements

Berry-phase term induces a gapped cyclotron mode

Dispersion relations influenced by elastic and topological factors

Abstract

We derive the spectrum of low-frequency spin waves in skyrmion crystals observed recently in noncentrosymmetric ferromagnets. We treat the skyrmion crystal as a superposition of three helices whose wavevectors form an equilateral triangle. The low-frequency spin waves are Goldstone modes associated with displacements of skyrmions. Their dispersion is determined by the elastic properties of the skyrmion crystal and by the kinetic terms of the effective Lagrangian, which include both kinetic energy and a Berry-phase term reflecting a nontrivial topology of magnetization. The Berry-phase term acts like an effective magnetic field, mixing longitudinal and transverse vibrations into a gapped cyclotron mode and a twist wave with a quadratic dispersion.