Transport of Dirac magnons driven by gauge fields

Abstract: We present a unified quantum field theory for Dirac magnons coupled to emergent gauge fields. At zero temperature, any space- and time-dependent gauge perturbation drives magnons out of equilibrium, generating spin currents and magnon accumulation without conventional thermal or chemical potential gradients. For a honeycomb ferromagnet, we derive closed-form expressions for the induced density and current. In the DC limit, the transverse spin conductivity quantizes to $σ^{xy}=α^2\text{sgn}(m)\hbar/4π$, a magnonic analog of the quantum Hall effect, where $m$ is the topological magnon mass and $α$ a dimensionless coupling constant. In the AC regime, the conductivity exhibits a sharp resonance when the drive frequency matches the topological gap $Δ$, signaling interband transitions. Our work establishes gauge fields as a versatile tool for controlling magnon transport and reveals topologically protected quantized responses.