We theoretically propose a nonreciprocal spin Seebeck effect, i.e., nonreciprocal spin transport generated by a temperature gradient, in antiferromagnetic insulators with broken inversion symmetry. We find that nonreciprocity in antiferromagnets has rich properties not expected in ferromagnets. In particular, we show that polar antiferromagnets, in which the crystal lacks the spatial inversion symmetry, exhibit perfect nonreciprocity --- one-way spin current flow irrespective of the direction of the temperature gradient. We also show that nonpolar centrosymmetric crystals can exhibit nonreciprocity when a magnetic order breaks the inversion symmetry, and in this case, the direction of the nonreciprocal flow can be controlled by reversing the magnetic domain. As their representatives, we calculate the nonreciprocal spin Seebeck voltages for the polar antiferromagnet $α$-Cu$_2$V$_2$O$_7$ and the honeycomb antiferromagnet MnPS$_3$, while varying temperature and magnetic field.

5 pages, 3 figures