# Route Towards Dirac and Weyl Antiferromagnetic Spintronics

## TL;DR

This review explores how antiferromagnetic order enables the integration of topological matter and spintronics, highlighting the role of complex symmetries in realizing Dirac and Weyl antiferromagnets with novel quantum effects.

## Contribution

It introduces the concept of antiferromagnetic topological spintronics, combining topological quasiparticles with antiferromagnetic symmetries, supported by ab initio predictions and experimental observations.

## Key findings

- Identification of Dirac and Weyl antiferromagnets such as SrMnBi2, CuMnAs, Mn3Ge
- Observation of quantum Hall effect in EuMnBi2
- Large anomalous Hall effect in Mn3Ge

## Abstract

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, e.g., for topological relativistic quasiparticles and the newly discovered N\'{e}el 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 $\textit{ab initio}$ calculations in predictions of examples of Dirac, and Weyl antiferromagnets: SrMnBi$_{\text{2}}$, CuMnAs, and Mn$_{\text{3}}$Ge. Lastly, we illustrate the interplay of Dirac quasiparticles, topology and antiferromagnetism on: (i) the experimentally observed quantum Hall effect in EuMnBi$_{\text{2}}$, (ii) the large anomalous Hall effect in Mn$_{\text{3}}$Ge, and (iii) the theoretically predicted topological metal-insulator transition in CuMnAs.