The scattering of a skyrmion configuration on asymmetric holes or barriers in a model Landau-Lifshitz equation

TL;DR

This paper investigates how baby skyrmions scatter when encountering asymmetric holes or barriers within a Landau-Lifshitz model, revealing complex dynamics influenced by potential inhomogeneities and energy conservation aspects.

Contribution

The study extends previous work by analyzing skyrmion interactions with asymmetric potential obstructions, highlighting the effects of barrier height, width, and binding energy on skyrmion behavior.

Findings

Skyrmions deform and orbit boundaries when crossing barriers.

Critical barrier parameters can unbind skyrmions.

Energy oscillations correlate with angular momentum non-conservation.

Abstract

This current work is an extension to work previously done by the authors. The dynamics of a baby skyrmion configuration, in a model Landau-Lifshitz equation, was studied in the presence of various potential obstructions. The baby skyrmion configuration was constructed from two Q=1 hedgehog solutions to the new baby Skyrme model in $(2+1)$ dimensions. The potential obstructions were created by introducing a new term into the Lagrangian which resulted in a localised inhomogeneity in the potential term's coefficient. In the barrier system the normal circular path was deformed as the skyrmions traversed the barrier, after which the skyrmions orbited the boundary of the system. For critical values of the barrier height and width the skyrmions were no longer bound although the unbound behaviour is not clearly distinct from the bound. In the case of a potential hole the dynamics of baby skyrmions is dependent upon the binding energy of the system. Depending upon its value, the skyrmions' behaviour varies. The angular momentum must be modified to ensure overall conservation. We show that there exists a link between the oscillation in the skyrmion's energy density and the periods of non-conservation of the angular momentum in Landau-Lifshitz models.