# Nishikawa Hukushima Krauth 2017

### From Werner KRAUTH

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We study the melting of skyrmions in a two-dimensional Heisenberg chiral magnet with bi-axial Dzyaloshinskii--Moriya interactions. These topological excitations may form at zero temperature a triangular crystal with long-range positional order. However, we show using large-scale Monte Carlo simulations that at small finite temperature, the skyrmions rather form a typical two-dimensional solid: Positional correlations decay with distance as power laws while the orientational correlations remain finite. At higher temperature, we observe a direct transition from this two-dimensional solid to a liquid with short-range correlations. This differs from generic two-dimensional homogeneous particle systems, where a hexatic phase is realized between the solid and the liquid. | We study the melting of skyrmions in a two-dimensional Heisenberg chiral magnet with bi-axial Dzyaloshinskii--Moriya interactions. These topological excitations may form at zero temperature a triangular crystal with long-range positional order. However, we show using large-scale Monte Carlo simulations that at small finite temperature, the skyrmions rather form a typical two-dimensional solid: Positional correlations decay with distance as power laws while the orientational correlations remain finite. At higher temperature, we observe a direct transition from this two-dimensional solid to a liquid with short-range correlations. This differs from generic two-dimensional homogeneous particle systems, where a hexatic phase is realized between the solid and the liquid. | ||

+ | [http://dx.doi.org/10.1103/PhysRevB.99.064435 DOI: 10.1103/PhysRevB.99.064435] | ||

[http://arxiv.org/pdf/1710.11095 Electronic version (from arXiv)] | [http://arxiv.org/pdf/1710.11095 Electronic version (from arXiv)] | ||

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+ | [http://journals.aps.org/prb/pdf/10.1103/PhysRevB.99.064435 Journal version (subscription required)] |

## Current revision

**Y. Nishikawa, K. Hukushima, W. Krauth** **Solid-liquid transition of skyrmions in a two-dimensional chiral magnet**** arXiv:1710.11095 Physical Review B 99 064435 (2019)**

# Paper

**Abstract**
We study the melting of skyrmions in a two-dimensional Heisenberg chiral magnet with bi-axial Dzyaloshinskii--Moriya interactions. These topological excitations may form at zero temperature a triangular crystal with long-range positional order. However, we show using large-scale Monte Carlo simulations that at small finite temperature, the skyrmions rather form a typical two-dimensional solid: Positional correlations decay with distance as power laws while the orientational correlations remain finite. At higher temperature, we observe a direct transition from this two-dimensional solid to a liquid with short-range correlations. This differs from generic two-dimensional homogeneous particle systems, where a hexatic phase is realized between the solid and the liquid.

DOI: 10.1103/PhysRevB.99.064435