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Anomalous Hall antiferromagnets

Abstract

The Hall effect, in which a current flows perpendicular to an electrical bias, has been prominent in the history of condensed matter physics. Appearing variously in classical, relativistic and quantum guises, the Hall effect has — among other roles — contributed to the establishment of the band theory of solids, to research on new phases of interacting electrons and to the phenomenology of topological condensed matter. The dissipationless Hall current requires time-reversal symmetry breaking. When this symmetry breaking is due to an externally applied magnetic field, the effect is referred to as the ordinary Hall effect; when it is due to a non-zero internal magnetization (ferromagnetism), it is referred to as the anomalous Hall effect. The Hall effect has not usually been associated with antiferromagnetic order. More recently, however, theoretical predictions and experimental observations have identified large Hall effects in some compensated magnetic crystals, governed by neither of the global magnetic-dipole symmetry-breaking mechanisms mentioned above. The goal of this Review is to systematically organize the present understanding of anomalous antiferromagnetic materials that generate a Hall effect — which we call anomalous Hall antiferromagnets — and to discuss this class of materials in a broader fundamental and applied research context. Our motivation is twofold: first, because Hall effects that are not governed by magnetic-dipole symmetry breaking are at odds with the traditional understanding of the phenomenon, the topic deserves attention on its own. Second, this new incarnation of the Hall effect has placed it again in the middle of an emerging field in physics, at the intersection of multipole magnetism, topological condensed matter and spintronics.

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Fig. 1: Experimental discovery of the Hall effect in the compensated non-collinear magnet Mn3Sn.
Fig. 2: Collinear and non-collinear archetype structures of anomalous Hall antiferromagnets, and magnetic multipoles.
Fig. 3: Typical compensated collinear structures with multisublattice \({\mathcal{T}}\)-symmetry breaking.
Fig. 4: Comparison of Berry curvatures in a model ferromagnet and in an anomalous Hall antiferromagnet.
Fig. 5: Band structure, Berry curvature and Hall effect calculations in a metallic compensated collinear magnet.
Fig. 6: Band structure, Berry curvature and Hall effect calculations in metallic compensated non-collinear magnets and in a compensated non-coplanar magnetic Chern insulator.

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Acknowledgements

This work was supported by the Ministry of Education of the Czech Republic grants LNSM-LNSpin and LM2018140, the Czech Science Foundation grant no. 19-28375X, the EU FET Open RIA grant no. 766566 and the German Research Foundation SPIN+X (DFG SFB TRR 173) and Elasto-Q-Mat (DFG SFB TRR 288).

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Šmejkal, L., MacDonald, A.H., Sinova, J. et al. Anomalous Hall antiferromagnets. Nat Rev Mater 7, 482–496 (2022). https://doi.org/10.1038/s41578-022-00430-3

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