Spin Nernst Effect of Antiferromagnetic Magnons in the Presence of Spin Diffusion

The magnon spin Nernst effect was recently proposed as an intrinsic effect in antiferromagnets, where spin diffusion and boundary spin transmission have been ignored. However, diffusion processes are essential for converting a bulk spin current into boundary spin accumulation, which determines the spin injection rate into detectors through imperfect transmission. We formulate a diffusive theory to describe the detection of the magnon spin Nernst effect with boundary conditions reflecting real device geometry. Because of the spin diffusion effect, the output signals in both electronic and optical detection grow rapidly with increasing system size in the transverse dimension, which eventually saturate. Counterintuitively, the measurable signals are even functions of magnetic field, making optical detection more favorable than electronic detection.

Figure 1

Illustration of system geometry and spin transmission processes at boundaries. A temperature gradient $\mathrm{\nabla }T$ generates a transverse pure spin current ${\mathbf{j}}_s$ through the SNE in the AFM (yellow region). The spin current injects into the metallic leads (gray region) on both sides through four different spin transmission processes depicted by Feynman diagrams (a)–(d). The injected spin currents are converted into detectable voltages along $x$ through the inverse SHE. The system length along $x$ is $L$; the AFM width and the lead width are $w$ and $d$, respectively.

Figure 2

Inverse SHE voltage resulting from the spin currents injected into the leads as a function of $w/{\lambda }_m$ and $d/{\lambda }_e$ for ${\eta }_m={\eta }_e=16$, which is estimated by using material parameters of ${\mathrm{Mn}\mathrm{PS}}_3$ (see the Appendix). Unit: $-{\mathrm{\partial }}_{x}T(\sigma {\theta }_{s}L/eG{\lambda }_e)$.

Figure 3

(a) Nonequilibrium density ${\rho }_{\uparrow ,\downarrow }$. Inset: equilibrium magnon density ${\rho }_{\uparrow ,\downarrow }^{\mathrm{eq}}$. (b) Nonequilibrium magnon spin density ${\rho }_s$ as a function of $y$ for open boundaries and $w=5{\lambda }_m$. Insets: nonequilibrium spin density on the right-hand edge ${\rho }_s(w/2)$ as a function of $w/{\lambda }_m$ (upper left); illustration of device geometry (lower right). Unit: $-2{\mathrm{\partial }}_{x}T(\sigma {\lambda }_m/D_m)$.