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. 2017 Jun 22;7:4060. doi: 10.1038/s41598-017-03391-8

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© The Author(s) 2017

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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Overview of the NEB method. A summary of the Nudged Elastic Band method in a system parametrised by two variables. The surface height indicates the energy plotted for all points in this two-dimensional phase space. A set of specific magnetic configuration is shown through spheres, each being one image of the method. For a particular image Y _i of the initial energy band, we show the effective (total) force G, the gradient component perpendicular to the band ∇ _μ E|_⊥ (μ = μ _s s as the magnetic moment, see Methods for details), the tangent to the band t and the spring force F. The height of the surface E _i = E(Y _i) shows the energy of image i. At the extrema of the band, the magnetic configurations are fixed and localised at energy minima.