Interacting Topological Magnons

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. Since spin excitations do not carry charge, they do not suffer from Joule heating and allow for 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.

I concentrate on magnons – the elementary spin excitations of ferromagnets – and demonstrate that interfacial Dzyaloshinskii-Moriya interaction (DMI) in chiral magnets leads to many-body effects without particle-number conservation. Selected implications are discussed: (i) interaction-stabilized topological gaps in the single-magnon spectrum (see Figure 1) [1], and (ii) a topological hybridization of particle number sectors that results in exotic topological hybrids of single-magnon and two-magnon bound states (see Figure 2) [2].

Figure 1: Tomographic cut of the single-magnon spectral function showing interaction-renormalized magnonic Dirac cones in ferromagnets on the honeycomb lattice. (a) The Dirac magnons remain massless in achiral magnets. (b) The Dirac magnon acquires a mass gap due to nonconserving interactions in chiral magnets.

Figure 2: One and two-magnon spectrum in spin-1/2 quantum magnets on the square lattice along high-symmetry lines of the Brillouin zone. (a) For isotropic Heisenberg exchange and without DMI, the single-magnon state is buried by the two-magnon continuum, below which there are two-magnon bound states (red bands). (b) In the limit of strong Ising anisotropy and DMI, single-magnon states and two-magnon bound states hybridize and topological band gaps emerge (blue bands). Chern numbers are indicated by yellow labels. 

[1] Mook A., Plekhanov K., Klinovaja J., and Loss D., (2021) "Interaction-Stabilized Topological Magnon Insulator in Ferromagnets," Phys. Rev. X 11, 021061.

[2] Mook A., Hoyer R., Klinovaja J., and Loss D., (2022), arXiv:2203.12374 (2022).