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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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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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.
The authors declare no competing interests.
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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