  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 to convert a bulk spin
current into boundary spin accumulation, which determines the spin injection
rate into detectors through imperfect transmission. We formulate a diffusive
theory of the magnon spin Nernst effect with boundary conditions reflecting
real device geometry. Thanks to the diffusion effect, the output signals in
both electronic and optical detection grow rapidly with an increasing system
size in the transverse dimension, which eventually saturate.
Counterintuitively, the measurable signals are even functions of magnetic
field, yielding optical detection more reliable than electronic detection.
