The dynamics of domain wall Skyrmions

TL;DR

This paper numerically studies domain wall Skyrmions in a (2+1)-dimensional O(3) sigma model, exploring their stability, dynamics, and scattering behavior, revealing effective one-dimensional interactions and complex multi-wall phenomena.

Contribution

It provides the first numerical analysis of domain wall Skyrmions in a potential-driven O(3) sigma model, including their dynamics and scattering properties.

Findings

Scattering with Skyrmions on the same wall is effectively one-dimensional.

Low-speed Skyrmion scattering resembles sine-Gordon kink interactions.

Complex multi-wall Skyrmion scattering events are observed.

Abstract

It has recently been shown that Skyrmions with a fixed size can exist in theories without a Skyrme term, providing the Skyrmion is located on a domain wall. Here we numerically compute domain wall Skyrmions of this type, in a (2+1)-dimensional O(3) sigma model with a potential term. Moreover, we investigate Skyrmion dynamics, to study both Skyrmion stability and the scattering of multi-Skyrmions. We demonstrate that scattering events in which both Skyrmions remain on the same domain wall are effectively one-dimensional, and at low speeds are well-approximated by kink scattering in the integrable sine-Gordon model. However, more exotic fully two-dimensional scatterings are also presented, in which Skyrmions that are initially on different domain walls emerge on the same domain wall.