Magnon Hall Effect
Thermal Hall conductivity κ_xy from magnon Berry curvature
Magnon Hall Effect: spin waves (magnons) in magnetic insulators with Dzyaloshinskii-Moriya Interaction (DMI) acquire Berry curvature Ω(k) in momentum space.
Thermal Hall conductivity: κ_xy = −(k_B²T/ℏV)Σ_k c_2(n_B(ε_k)) · Ω_k, where c_2 is the transport distribution function and n_B is Bose-Einstein.
Two-band honeycomb model: Kitaev-like magnon bands with avoided crossing gap ∝ DMI. Berry curvature peaks near band crossings.
κ_xy changes sign at low T (topological magnon contribution) and peaks near T where magnon density is maximum.