Skyrmion and Baby Skyrmion Formation from Domain Walls

TL;DR

This paper uses numerical simulations to explore how Skyrmions and Baby Skyrmions can form from domain wall collisions, proposing more stable formation methods and analyzing topological charge conservation in complex systems.

Contribution

It demonstrates that stable Skyrmion formation can occur via multi-segment domain wall interactions and analyzes topological charge conservation in dynamic networks.

Findings

Skyrmions can form from domain wall collisions under specific conditions.

Multi-segment domain wall interactions provide a more stable formation process.

Topological charge is conserved through boundary countercharges in complex systems.

Abstract

We numerically simulate the formation of $(2+1)$-dimensional baby Skyrmions and $(3+1)$-dimensional $SU(2)$ Skyrmions from domain wall collisions. It has been suggested that Skyrmion, anti-Skyrmion pairs can be produced from the interaction of two domain walls. This is confirmed, however it is also demonstrated that the process can require quite precise conditions. An alternative, more stable, formation process is proposed as the interaction of more than two segments of domain wall. This is simulated, requiring far less constraints on the initial conditions used. Finally domain wall networks are considered, demonstrating how Skyrmions may be produced in a complex dynamical system. We show that the local topological charge configurations, formed within the system, are countered by opposite winding on the boundary of the system to conserve topological charge.