Magnonic topological insulators in antiferromagnets

TL;DR

This paper introduces a topological insulator concept for magnons in antiferromagnets, revealing helical edge states and novel thermomagnetic effects, with potential for experimental realization.

Contribution

It establishes a bosonic topological insulator model for magnons in antiferromagnets using the Aharonov-Casher effect and predicts observable edge states and thermomagnetic phenomena.

Findings

Magnonic quantum spin Hall effect with helical edge states.

Topological  number characterizes the AF phase.

Predicted thermomagnetic effects and magnonic Wiedemann-Franz law.

Abstract

Extending the notion of symmetry protected topological phases to insulating antiferromagnets (AFs) described in terms of opposite magnetic dipole moments associated with the magnetic N$\acute{{\rm{e}}} $el order, we establish a bosonic counterpart of topological insulators in semiconductors. Making use of the Aharonov-Casher effect, induced by electric field gradients, we propose a magnonic analog of the quantum spin Hall effect (magnonic QSHE) for edge states that carry helical magnons. We show that such up and down magnons form the same Landau levels and perform cyclotron motion with the same frequency but propagate in opposite direction. The insulating AF becomes characterized by a topological ${\mathbb{Z}}_{2}$ number consisting of the Chern integer associated with each helical magnon edge state. Focusing on the topological Hall phase for magnons, we study bulk magnon effects such as magnonic spin, thermal, Nernst, and Ettinghausen effects, as well as the thermomagnetic properties of helical magnon transport both in topologically trivial and nontrivial bulk AFs and establish the magnonic Wiedemann-Franz law. We show that our predictions are within experimental reach with current device and measurement techniques.