Topological Magnons — Magnon Hall Effect & Edge States

In ferromagnets on a honeycomb lattice (e.g. CrI₃), Dzyaloshinskii-Moriya interaction (DMI) breaks time-reversal symmetry, giving magnon bands a non-zero Chern number. Magnons accumulate at edges — the magnon Hall effect. Analogous to the quantum Hall effect but for bosons at finite T.

Chern number: C=±1 | Magnon Hall conductivity: κ_xy > 0