Topological Aspects of Antiferromagnets

V. Bonbien, Fengjun Zhuo, A. Salimath, O. Ly, A. Abbout, A. Manchon

Published 2021-02-02Version 1

We review the topological phenomena that have been recently uncovered in antiferromagnetic materials. The scope of this work covers electronic and magnonic transport, as well as topologically non-trivial magnetic solitons and fractional excitations. We emphasize that while the term topology refers to a global property that reflects the gauge flux endowed by a quantum state, it is routinely used to designate properties emerging from the local geometry of the quantum states in momentum and spin spaces. In this review, we adopt this convention. In the introduction, we provide a short overview of antiferromagnetic spintronics, briefly highlighting its main features, and discuss the difference between topology and geometry. In the second section, we describe of the symmetry properties of antiferromagnets and how they impact their band structure, Berry curvature and conductivity tensor. In the third section, we show how these symmetries generate anomalous electronic and magnonic transport, focusing on the most recently discovered phenomena: anomalous Hall effect, magnetic spin Hall effect, crystal Hall effect and their magnonic counterpart. In the fourth section, we discuss the realization of electronic and magnonic topological insulators based on antiferromagnetic materials. In the fifth section, the emergence of topological solitons in antiferromagnets in one and two dimensions is addressed and their dynamical properties are presented. In the sixth section, we describe the emergence of topologically non-trivial magnetic excitations in quantum antiferromagnets, focusing on eloquent examples such as fermionic spinons in kagom\'e lattices, Majorana fermions in Kitaev honeycomb lattices and magnetic monopole in pyrochlores. In the seventh section, we provide perspectives on the promises of the field.