Frustration-enhanced spin Nernst conductivity in a single-layer honeycomb antiferromagnet.

• Spin Nernst effect current modifies by increasing frustration. • Spin Nernst current is remarkably enhanced with an increase in the strength of the second-nearest neighbor interaction, but one observes a decrease in the spin Nernst current by increasing the third-nearest neighbor Heisenberg interaction. We theoretically study the spin Nernst effect in collinear antiferromagnets on a honeycomb lattice with broken inversion symmetry. The broken inversion symmetry allows out-of-plane Dzyaloshinskii-Moriya interaction between the nearest neighbors. Within the semiclassical theory, the Dzyaloshinskii-Moriya exchange interaction, which generates an imbalance in the magnon distribution between the valley points, is the vital factor for producing a transverse net spin flow after a longitudinal temperature gradient. We predict that the spin Nernst effect current modifies by varying second- and third-nearest neighbor Heisenberg couplings of a single-layer honeycomb antiferromagnet. Our calculations show that the spin Nernst current is remarkably enhanced with an increase in the strength of the second-nearest neighbor interaction, but one observes a decrease in the spin Nernst current by increasing the third-nearest neighbor Heisenberg interaction. Our analysis indicates that this enhancement relies on the large Berry curvature due to the second-nearest neighbor interaction get frustrated the nearest-neighbor spins on the honeycomb lattice, in contrast, the third-nearest neighbor interaction stabilizes the Néel ordering. [ABSTRACT FROM AUTHOR]