  One of the most famous proximity effects at ferromagnet/superconductor (F/S)
interfaces is partial conversion of singlet superconductivity to triplet
pairing correlations. Due to the presence of macroscopic exchange field in the
ferromagnet the Cooper pairs penetrating into the ferromagnet from the
superconductor acquire a finite momentum there. The finite-momentum pairing
manifests itself, in particular, as a nonmonotonic dependence of the critical
temperature of the bilayer on the thickness of the F layer. Here we predict
that despite the absence of the macroscopic exchange field the critical
temperature of the antiferromagnet/superconductor (AF/S) bilayers also exhibit
nonmonotonic (oscillating) dependence on the AF layer thickness. It is a
manifestation of the proximity-induced Neel-type triplet correlations, which
acquire finite total pair momentum and oscillate in the AF layer due to the
Umklapp electron scattering processes at the AF/S interface. Our prediction can
provide a possible explanation for a number of recently published experimental
observations of the critical temperature of AF/S bilayers.
