# Stability and Phase Transition of Skyrmion Crystals Generated by Dzyaloshinskii-Moriya Interaction

## TL;DR

This paper investigates the formation and stability of skyrmion crystal phases in a two-dimensional magnetic system influenced by Dzyaloshinskii-Moriya interaction, magnetic field, and temperature, revealing phase transitions and slow relaxation dynamics.

## Contribution

It demonstrates the existence of a skyrmion crystal ground state in a 2D Heisenberg model with Dzyaloshinskii-Moriya interaction and studies its finite-temperature stability through Monte Carlo simulations.

## Key findings

- Skyrmion crystal ground state identified in certain (D, H) regions.
- Skyrmion phase remains stable at finite temperatures with slow relaxation dynamics.
- Transition from skyrmion crystal to paramagnetic state occurs at finite temperature.

## Abstract

We generate a crystal of skyrmions in two dimensions using a Heisenberg Hamiltonian including the ferromagnetic interaction J, the Dzyaloshinskii-Moriya interaction D, and an applied magnetic field H. The ground state (GS) is determined by minimizing the interaction energy. We show that the GS is a skyrmion crystal in a region of (D, H). The stability of this skyrmion crystalline phase at finite temperatures is shown by a study of the time-dependence of the order parameter using Monte Carlo simulations. We observe that the relaxation is very slow and follows a stretched exponential law. The skyrmion crystal phase is shown to undergo a transition to the paramagnetic state at a finite temperature.