  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
$\textit{et al.,}$ $\textit{Nature}$ $\textbf{578,}$ 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.
