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.

Figures (3)

• Figure 1: The polarization tensor, which corresponds to the first perturbative correction of the emergent gauge field $\mathcal{A}_\mu$.
• Figure 2: Momentum dependence of the transverse spin conductivity $\sigma^{xy}$ for different values of the coupling constant $\alpha$ and group velocities $v_M$. Blue, black, and red lines correspond to $\alpha=1, 0.8, \text{and }0.4$, respectively, while dashed lines stand for $v_M=v_M/2$. It is demonstrated the quantization at $p\rightarrow 0$ and its subsequent decay with increasing momentum. The reduction in the magnon group velocity $v_M$ suppresses this decay, thereby producing a broader plateau of near-quantized response.
• Figure 3: AC magnon spin conductivity as a function of the frequency $\omega$. Panel a) and b) show the real and imaginary part of the longitudinal response $\sigma^{xx}$, while c) and d) show the real and imaginary part of the Hall-like conductivity $\sigma^{xy}$. Blue, black, and red lines correspond to $\alpha=1, 0.8, \text{and }0.4$, respectively. Solid lines correspond to a Gilbert damping $\alpha_G = 10^{-5}$, while dashed lines stand for $\alpha_G = 3\times 10^{-2}$. Resonance occurs at the frequency determined by the magnon gap, i.e., $\Delta/\hbar=6\sqrt{3}DS/\hbar\approx 7.96\times 10^{2}$ GHz and the dissipation Gilbert damping $\alpha_G$ broadens this resonance. The imaginary parts reveal the threshold behavior associated with interband transitions for $\omega>\Delta/\hbar$.