Interacting Topological Magnons in Ferromagnets and Antiferromagnets*

Topological magnets support magnetic excitations with a topologically nontrivial spectrum. As a result, they exhibit chiral edge states akin to those known from the quantum Hall effect. These edge states are envisioned to facilitate backscattering-free information channels for magnetic signals [1]. Since spin excitations do not carry charge, they do not suffer from Joule heating and facilitate ultra-low energy computation. However, in contrast to electrons, there is no conservation law for spin excitations. This gives rise to particle number-nonconserving many-body interactions the influence of which on quasiparticle topology is an open issue of fundamental interest in the field of topological quantum materials. Herein, I concentrate on magnons - the elementary spin excitations of ferromagnets and antiferromagnets - and discuss several aspects of many-body effects caused by particle-number nonconservation. These include (i) quantum damping due to spontaneous quasiparticle decay [2], (ii) interaction-stabilized topological gaps in the single-particle spectrum [3], and (iii) a topological hybridization of states belonging to different particle number sectors [4]. These effects highlight the fundamental difference between electronic and magnonic topology.

[1] Alexander Mook, Sebastián A. Díaz, Jelena Klinovaja, and Daniel Loss, "Chiral Hinge Magnons in Second-Order Topological Magnon Insulators," Phys. Rev. B 104, 024406 (2021)

[2] Alexander Mook, Jelena Klinovaja, and Daniel Loss, "Quantum damping of skyrmion crystal eigenmodes due to spontaneous quasiparticle decay," Phys. Rev. Research 2, 033491 (2020)

[3] Alexander Mook, Kirill Plekhanov, Jelena Klinovaja, and Daniel Loss, "Interaction-Stabilized Topological Magnon Insulator in Ferromagnets," Phys. Rev. X 11, 021061 (2021)

[4] Alexander Mook, Rhea Hoyer, Jelena Klinovaja, and Daniel Loss, "Topological Hybridization of Magnons and Magnon Bound Pairs," arXiv:2203.12374 (2022)