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# Progress and prospects in magnetic topological materials

## Abstract

Magnetic topological materials represent a class of compounds with properties that are strongly influenced by the topology of their electronic wavefunctions coupled with the magnetic spin configuration. Such materials can support chiral electronic channels of perfect conduction, and can be used for an array of applications, from information storage and control to dissipationless spin and charge transport. Here we review the theoretical and experimental progress achieved in the field of magnetic topological materials, beginning with the theoretical prediction of the quantum anomalous Hall effect without Landau levels, and leading to the recent discoveries of magnetic Weyl semimetals and antiferromagnetic topological insulators. We outline recent theoretical progress that has resulted in the tabulation of, for the first time, all magnetic symmetry group representations and topology. We describe several experiments realizing Chern insulators, Weyl and Dirac magnetic semimetals, and an array of axionic and higher-order topological phases of matter, and we survey future perspectives.

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## Acknowledgements

Work from B.A.B. on magnetic topology is mainly supported by DOE grant no. DE-SC0016239. Further support comes from the Schmidt Fund for Innovative Research, Simons Investigator grant no. 404513, the Packard Foundation, the Gordon and Betty Moore Foundation through grant no. GBMF8685 towards the Princeton theory programme, the NSF-EAGER no. DMR 1643312, NSF-MRSEC nos DMR-1420541 and DMR2011750, ONR no. N00014-20-1-2303, BSF Israel US Foundation no. 2018226, and the Princeton Global Network Funds. C.F. was supported by the ERC Advanced grant no. 742068 ‘TOPMAT’ and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) 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). H.B. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 678702), and the German–Israeli Foundation (GIF, I-1364-303.7/2016).

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B.A.B., C.F. and H.B. wrote the review.

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## Supplementary information

### Supplementary Information

This Supplementary Information file contains Appendix A: Magnetic Group Theory and Magnetic Topology; Appendix B: Magnetic Topological Insulators: Correlated Chern Insulators in Moiré Systems; Appendix C: Semimetal Predictions; and additional references.

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Bernevig, B.A., Felser, C. & Beidenkopf, H. Progress and prospects in magnetic topological materials. Nature 603, 41–51 (2022). https://doi.org/10.1038/s41586-021-04105-x

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