Spurious Symmetry Enhancement in Linear Spin Wave Theory and Interaction-Induced Topology in Magnons.

Linear spin wave theory (LSWT) is the standard technique to compute the spectra of magnetic excitations in quantum materials. In this Letter, we show that LSWT, even under ordinary circumstances, may fail to implement the symmetries of the underlying ordered magnetic Hamiltonian leading to spurious degeneracies. In common with pseudo-Goldstone modes in cases of quantum order by disorder these degeneracies tend to be lifted by magnon-magnon interactions. We show how, instead, the correct symmetries may be restored at the level of LSWT. In the process we give examples, supported by nonperturbative matrix product based time evolution calculations, where symmetry dictates topological features but where LSWT fails to implement them. We also comment on possible spin split magnons in MnF_{2} and similar rutiles by analogy to recently proposed altermagnets.

Identifying and Constructing Complex Magnon Band Topology.

Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path toward coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials. We do this by adapting the topological quantum chemistry approach that has used constraints imposed by time reversal and crystalline symmetries to enumerate a large class of topological electronic bands. We show how to identify physically relevant models of gapped magnon band topology by using so-called decomposable elementary band representations, and in turn discuss how to use symmetry data to infer the presence of exotic symmetry enforced nodal topology.

Magnon Interference Tunneling Spectroscopy as a Probe of 2D Magnetism.

Probing two-dimensional single-layer quantum magnets remains a significant challenge. In this Letter, we propose exploiting tunneling spectroscopy in the presence of magnetic impurities to obtain information about the magnon dispersion relations in analogy to quasiparticle interference in nonmagnetic materials. We show that this technique can be used to establish the dispersion relations even for frustrated magnets, where the presence of an impurity generally leads to a nontrivial spin texture. Finally, we consider the problem of establishing Chern magnon bands in 2D magnets showing how tunable impurities allow one to probe the nature of the surface states.