Magnonic topological insulators in antiferromagnets

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 Néel 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 Z2 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.

Non-Hermitian topology of spontaneous magnon decay

“…In this paper, we propose that magnonic systems may be a nearly ideal platform to realize non-Hermitian topological states. Topological magnon states have been widely discussed in the Hermitian context [37][38][39][40][41][42][43][44][45][46][47]. One of the peculiarities of topological magnons compared to their electronic cousins is that they appear as excited states and therefore they are sub- ject to the non-universal effects of interactions [42,44,47].…”

Spin currents and magnon dynamics in insulating magnets

“…Since the underlying Berry curvature 25,94,95,[122][123][124][125][126][127][128]213 is a local quantity that reflects the geometric properties of the Bloch wavevector-space, it can be expected that quantum Hall effects emerge also in magnonic systems. A Landau level is 31 formed also in Dirac magnon systems. Taking that into account to exploit quantum Hall effects of Dirac magnons and to reveal their relativistic effects (e.g., quantum anomaly) via magnon transport is certainly an interesting future direction 214 .…”

“…In this paper, we instead describe many magnon counterparts of electron transport (see Table I for a comparison). We review our past works on spin transport in insulating magnets and also add new insights to it [18][19][20][21][22][23][24][25][26][27][28][29][30][31] . The bosonic nature of magnons enables, however, excited magnons to dynamically condensate 32 .…”

“…[47]. Therefore, this analogy leads to the whole phenomenology of Hall effects such as the magnonic 'quantum' Hall effect 31,119,120 , the thermal Hall effect in skyrmion lattices 25 , the Hall effect in frustrated magnets 121 , and the magnonic topological insulators 94,95,[122][123][124][125][126][127][128][129] and their associated topologically protected edge states.…”

Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices

“…In this way, we show that the single-particle topological properties of the underlying SSH model are transferred to the bosonic magnonic excitations. Such a transfer of topological band properties to interacting-particle settings is reminiscent of that discussed in [23,24], in the context of topological doublons, and in [25,26] in the context of topological polarons; see also [27][28][29][30][31][32] on interplays between topological properties and magnons.…”