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. 2018 Jul 3;9:2591. doi: 10.1038/s41467-018-05054-2

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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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Fig. 1 — Crystal structure and the first Brillouin zone for Cu₃TeO₆. a Schematic for the centro-symmetric cubic crystal structure with the Ia-3 space group (no. 206). For simplicity, only Cu²⁺ ions with spins indicated by arrows are shown. Shades indicate hexagons formed by Cu²⁺ ions. The nearest-neighbour exchange interaction J₁ is indicated by a solid line. b The first Brillouin zone of the primitive unit cell with high-symmetry paths and points