Diffusive Magnon Spin Nernst Effect in Antiferromagnets*

Magnon spin Nernst effect (SNE) has recently been proposed as a bulk effect in antiferromagnetic insulators without considering diffusions and boundaries. However, real experiments deal with situations far from the ideal bulk picture in that: 1) the system is finite and shares imperfect boundaries with the detecting leads; 2) both the electrons in the leads and the magnons are diffusive. To properly accommodate these complexities, we formulate a diffusive theory of the SNE of antiferromagnetic magnons under a realistic device geometry. By solving the coupled spin diffusion equations of magnons and electrons with a finite spin transmission across the boundaries, we find that the detectable signal can be much larger than that predicted by the bulk picture. Counterintuitively, the diffusive magnon SNE is even in the applied magnetic field, basing on which we conclude that optical detection is more reliable than electronic detection in real experiments.