Spin Seebeck Effect near the Antiferromagnetic Spin-Flop Transition

We develop a low-temperature, long-wavelength theory for the interfacial spin Seebeck effect (SSE) in easy-axis antiferromagnets. The field-induced spin-flop (SF) transition of N'eel order is associated with a qualitative change in SSE behavior: Below SF, there are two spin carriers with opposite magnetic moments, with the carriers polarized along the field forming a majority magnon band. Above SF, the low-energy, ferromagnetic-like mode has magnetic moment opposite the field. This results in a sign change of the SSE across SF, which agrees with recent measurements on Cr${}_2$O${}_3$/Pt and Cr${}_2$O${}_3$/Ta devices [Li $\mathit{\text{et}}\mathit{\text{al.,}}$ $\mathit{\text{Nature}}$ $\mathbf{\text{578,}}$ 70 (2020)]. In our theory, SSE is due to a N'eel spin current below SF and a magnetic spin current above SF. Using the ratio of the associated N'eel to magnetic spin-mixing conductances as a single constant fitting parameter, we reproduce the field dependence of the experimental data and partially the temperature dependence of the relative SSE jump across SF.