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. 2017 Dec 1;7:16785. doi: 10.1038/s41598-017-16935-9

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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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(a) Synchrotron XRD intensity pattern (filled red circles) observed for K₃Cu₃AlO₂(SO₄)₄ at room temperature, the result of Rietveld refinement using the computer program RIETAN-FP²² (black solid line), and difference between the calculated and observed intensities (blue solid line). The green vertical bars indicate the position of Bragg reflection peaks. The inset shows the crystal structure of K₃Cu₃AlO₂(SO₄)₄ featuring a large inter-chain spacing. (b) The diamond chain of K₃Cu₃AlO₂(SO₄)₄, which consists of Cu²⁺ ions (grey spheres) along the a-axis with nearby oxygen (red spheres) and sulfur ions (yellow spheres). (c) Effective spin model of K₃Cu₃AlO₂(SO₄)₄ with the nearest-neighbor exchange couplings J _i (i = 1 to 5), and the next nearest-neighbor exchange couplings of J _m, J _d, and $J_{d}'$ . (d) Spin configuration of the ground state for K₃Cu₃AlO₂(SO₄)₄.