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Route towards Dirac and Weyl antiferromagnetic spintronics

Topological quantum matter and spintronics research have been developed to a large extent independently. In this review, we discuss a new role that the antiferromagnetic order has taken in combining topological matter and spintronics. This occurs due to the complex microscopic symmetries present in antiferromagnets that allow for, e.g., topological relativistic quasiparticles and the newly discovered Néel spin–orbit torques to coexist. We first introduce the concepts of topological semimetals and spin‐orbitronics. Secondly, we explain the antiferromagnetic symmetries on a minimal Dirac semimetal model and the guiding role of ab initio calculations in predictions of examples of Dirac and Weyl antiferromagnets: SrMnBi2, CuMnAs, and Mn3Ge. Lastly, we illustrate the interplay of Dirac quasiparticles, topology and antiferromagnetism on: (i) the experimentally observed quantum Hall effect in EuMnBi2; (ii) the large anomalous Hall effect in Mn3Ge; and (iii) the theoretically predicted topological metal–insulator transition in CuMnAs.