# Dynamics and inertia of a skyrmion in chiral magnets and interfaces: A linear response approach based on magnon excitations

## TL;DR

This paper develops a linear response theory for skyrmion dynamics in chiral magnets, revealing how magnon modes influence inertia and response to different external drives, with implications for skyrmion control.

## Contribution

It introduces a comprehensive magnon-based linear response framework to analyze skyrmion inertia and dynamics under various external stimuli.

## Key findings

- Magnon modes with angular momentum |m|=1 govern skyrmion center dynamics.
- Skyrmion inertia is mainly determined by continuum magnon spectrum.
- Skyrmion responds almost instantaneously to magnetic field gradients and spin transfer torques.

## Abstract

Taking all the magnon modes into account, we derive the skyrmion dynamics in response to a weak external drive. A skyrmion has rotational symmetry and the magnon modes can be characterized by an angular momentum. For a weak distortion of a skyrmion, only the magnon modes with an angular momentum $|m|=1$ govern the dynamics of skyrmion topological center. The skyrmion inertia is determined by the magnon modes in the continuum spectrum. For a skyrmion driven by a magnetic field gradient or by a spin transfer torque generated by a current, the dynamical response is practically instantaneous. This justifies the rigid skyrmion approximation used in Thiele's collective coordinate approach. For a skyrmion driven by a spin Hall torque, the torque couples to the skyrmion motion through the magnons in the continuum and damping, therefore the skyrmion dynamics shows sizable inertia in this case. The trajectory of a skyrmion is an ellipse for an ac drive of spin Hall torque.