Spin-pumping in superconductor-antiferromagnetic insulator bilayers

We study theoretically spin pumping in bilayers consisting of superconductors and antiferromagnetic insulators. We consider both compensated and uncompensated interfaces and include both the regular scattering channel and the Umklapp scattering channel. We find that at temperatures close to the critical temperatures and precession frequencies much lower than the gap, the spin-current is enhanced in superconductors as compared to normal metals. Otherwise, the spin-current is suppressed. The relevant precession frequencies where the spin-current in SC/AFI is enhanced compared to NM/AFI is much lower than the typical resonance frequencies of antiferromagnets, which makes the detection of this effect experimentally challenging. A possible solution lies in the shifting of the resonance frequency by a static magnetic field.