Commensurate States and Pattern Switching via Liquid Crystal Skyrmions Trapped in a Square Lattice

TL;DR

This study uses simulations to demonstrate diverse skyrmion liquid crystal states in a periodic obstacle array, revealing transitions between ordered and disordered structures influenced by external parameters.

Contribution

It introduces a new way to realize and control various skyrmion crystal states using a periodic obstacle lattice, highlighting their relation to commensurate effects in other physical systems.

Findings

Identification of hexagonal, square, dimer, trimer, and quadrimer skyrmion arrangements.

Transitions between different crystalline states as external field and obstacle size vary.

Observation of mixed and disordered skyrmion structures.

Abstract

Using continuum based simulations we show that a rich variety of skyrmion liquid crystal states can be realized in the presence of a periodic obstacle array. As a function of the number of skyrmions per obstacle we find hexagonal, square, dimer, trimer and quadrimer ordering, where the $n$-mer structures are a realization of a molecular crystal state of skyrmions. As a function of external field and obstacle radius we show that there are transitions between the different crystalline states as well as mixed and disordered structures. We discuss how these states are related to commensurate effects seen in other systems, such as vortices in type-II superconductors and colloids interacting with two dimensional substrates.