Melting and Freezing of a Skyrmion Lattice

TL;DR

This study uses Monte Carlo simulations to analyze the melting and freezing behavior of skyrmion lattices across different system sizes, revealing size-dependent hysteresis, reversible phase transitions, and complex defect-driven mechanisms.

Contribution

It provides the first comprehensive simulation-based analysis of skyrmion lattice melting, highlighting size effects, hysteresis, and defect dynamics in phase transitions.

Findings

Large systems show hysteresis similar to experiments.

Small systems exhibit reversible sharp phase transitions.

Melting involves grain formation and defect dynamics.

Abstract

We report comprehensive Monte-Carlo studies of the melting of skyrmion lattices in systems of small, medium, and large sizes with the number of skyrmions ranging from $10^{3}$ to over $10^{5}$. Large systems exhibit hysteresis similar to that observed in real experiments on the melting of skyrmion lattices. For sufficiently small systems which achieve thermal equilibrium, a fully reversible sharp solid-liquid transition on temperature with no intermediate hexatic phase is observed. A similar behavior is found on changing the magnetic field that provides the control of pressure in the skyrmion lattice. We find that on heating the melting transition occurs via a formation of grains with different orientations of hexagonal axes. On cooling, the fluctuating grains coalesce into larger clusters until a uniform orientation of hexagonal axes is slowly established. The observed scenario is caused by collective effects involving defects and is more complex than a simple picture of a transition driven by the unbinding and annihilation of dislocation and disclination pairs.