  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 to describe the detection of magnon spin Nernst effect with boundary
conditions reflecting real device geometry. Thanks to the spin 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 favorable than
electronic detection.
