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. 2021 May 11;12:2723. doi: 10.1038/s41467-021-22857-y

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© The Author(s) 2021

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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Fig. 1 — a Magnetisation distribution of an isolated magnetic skyrmion. The magnetic moments far from the centre point antiparallel to the central spin, with intermediate moments winding away from the centre in case of a Bloch-type skyrmion (and point radially in case of a Neel-type skyrmion). b When a skyrmion is driven by an applied force F, it moves with a velocity v at an angle θ_SkH to the direction of the applied force. This angle is constrained to lie in the closed interval $[- 9 0^{\circ}, 9 0^{\circ}]$ , i.e., skyrmions cannot be driven backwards by a force that acts forwards.