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High-throughput calculations of magnetic topological materials

Nature volume 586, pages 702–707 (2020)Cite this article

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Abstract

The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators1,2,3, have directed fundamental research in solid-state materials. Topological quantum chemistry4 has enabled the understanding of and the search for paramagnetic topological materials5,6. Using magnetic topological indices obtained from magnetic topological quantum chemistry (MTQC)7, here we perform a high-throughput search for magnetic topological materials based on first-principles calculations. We use as our starting point the Magnetic Materials Database on the Bilbao Crystallographic Server, which contains more than 549 magnetic compounds with magnetic structures deduced from neutron-scattering experiments, and identify 130 enforced semimetals (for which the band crossings are implied by symmetry eigenvalues), and topological insulators. For each compound, we perform complete electronic structure calculations, which include complete topological phase diagrams using different values of the Hubbard potential. Using a custom code to find the magnetic co-representations of all bands in all magnetic space groups, we generate data to be fed into the algorithm of MTQC to determine the topology of each magnetic material. Several of these materials display previously unknown topological phases, including symmetry-indicated magnetic semimetals, three-dimensional anomalous Hall insulators and higher-order magnetic semimetals. We analyse topological trends in the materials under varying interactions: 60 per cent of the 130 topological materials have topologies sensitive to interactions, and the others have stable topologies under varying interactions. We provide a materials database for future experimental studies and open-source code for diagnosing topologies of magnetic materials.

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Fig. 1: Band structures of the ‘high-quality’ magnetic topological materials predicted by MTQC.
Fig. 2: Topological surface states of representative magnetic topological insulator and enforced semimetal phases.

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Data availability

All data are available in the Supplementary Information and at https://www.topologicalquantumchemistry.fr/magnetic. The codes required to calculate the character table of magnetic materials are available at https://www.cryst.ehu.es/cryst/checktopologicalmagmat.

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Acknowledgements

We thank U. Schmidt, I. Weidl, W. Shi and Y. Zhang. We acknowledge the computational resources Cobra in the Max Planck Computing and Data Facility (MPCDF), the HPC Platform of ShanghaiTech University and Atlas in the Donostia International Physics Center (DIPC). Y.X. is grateful to D. Liu for help in plotting some diagrammatic sketches. B.A.B., N.R., B.J.W. and Z.S. were primarily supported by a Department of Energy grant (DE-SC0016239), and partially supported by the National Science Foundation (EAGER grant DMR 1643312), a Simons Investigator grant (404513), the Office of Naval Research (ONR; grant N00014-14-1-0330), the NSF-MRSEC (grant DMR-142051), the Packard Foundation, the Schmidt Fund for Innovative Research, the BSF Israel US foundation (grant 2018226), the ONR (grant N00014-20-1-2303) and a Guggenheim Fellowship (to B.A.B.). Additional support was provided by the Gordon and Betty Moore Foundation through grant GBMF8685 towards the Princeton theory programme. L.E. was supported by the Government of the Basque Country (Project IT1301-19) and the Spanish Ministry of Science and Innovation (PID2019-106644GB-I00). M.G.V. acknowledges support from the Diputacion Foral de Gipuzkoa (DFG; grant INCIEN2019-000356) from Gipuzkoako Foru Aldundia and the Spanish Ministerio de Ciencia e Innovación (grant PID2019-109905GB-C21). Y.C. was supported by the Shanghai Municipal Science and Technology Major Project (grant 2018SHZDZX02) and a Engineering and Physical Sciences Research Council (UK) Platform Grant (grant EP/M020517/1). C.F. acknowledges financial support by the DFG under Germany’s Excellence Strategy through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (ct.qmat EXC 2147, project-id 390858490), an ERC Advanced Grant (742068 ‘TOPMAT’). Y.X. and B.A.B. were also supported by the Max Planck Society.

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Authors and Affiliations

  1. Max Planck Institute of Microstructure Physics, Halle, Germany

    Yuanfeng Xu & B. Andrei Bernevig

  2. Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Bilbao, Spain

    Luis Elcoro

  3. Department of Physics, Princeton University, Princeton, NJ, USA

    Zhi-Da Song, Benjamin J. Wieder, Nicolas Regnault & B. Andrei Bernevig

  4. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Benjamin J. Wieder

  5. Department of Physics, Northeastern University, Boston, MA, USA

    Benjamin J. Wieder

  6. Donostia International Physics Center, Donostia/San Sebastian, Spain

    M. G. Vergniory

  7. IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

    M. G. Vergniory

  8. Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France

    Nicolas Regnault

  9. School of Physical Science and Technology, ShanghaiTech University, Shanghai, China

    Yulin Chen

  10. ShanghaiTech Laboratory for Topological Physics, Shanghai, China

    Yulin Chen

  11. Clarendon Laboratory, Department of Physics, University of Oxford, Oxford, UK

    Yulin Chen

  12. State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics and Collaborative Innovation Center of Quantum Matter, Tsinghua University, Beijing, China

    Yulin Chen

  13. Max Planck Institute for Chemical Physics of Solids, Dresden, Germany

    Claudia Felser

  14. Center for Nanoscale Systems, Faculty of Arts and Science, Harvard University, Cambridge, MA, USA

    Claudia Felser

  15. Physics Department, Freie Universität Berlin, Berlin, Germany

    B. Andrei Bernevig

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  1. Yuanfeng Xu
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  2. Luis Elcoro
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Contributions

B.A.B. conceived this work; Y.X. and M.G.V. performed the first-principles calculations. L.E. wrote the code for calculating the irreducible representations and checking the topologies of materials. Y.X., Z.S., B.J.W. and B.A.B. analysed the calculated results, B.J.W. determined the physical meaning of the topological indices with help from L.E., Z.S. and Y.X. C.F. performed chemical analysis of the magnetic topological materials. N.R. built the topological material database. All authors wrote the main text and Y.X. and Z.S. wrote the Methods and the Supplementary Information.

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Correspondence to B. Andrei Bernevig.

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This file contains Supplementary Sections 1–13, including 33 Supplementary Figures and 419 Supplementary Tables – see contents page for details.

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Xu, Y., Elcoro, L., Song, ZD. et al. High-throughput calculations of magnetic topological materials. Nature 586, 702–707 (2020). https://doi.org/10.1038/s41586-020-2837-0

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