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.