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. 2018 Nov 12;8:16675. doi: 10.1038/s41598-018-34526-0

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Contour plots of m_z in a system with an internal fluctuating magnetic field, mimicking thermal effects at T = 100 K, and a superimposed external field, which is indicated in the right bottom corner. (a) Thermal fluctuations induce irregularities in zero field, but this does not prevent the system from reaching (b) the hexagonal state. (c) Via defect-induced melting, (d) some skyrmions invert their polarization, as illustrated in Fig. 5.