Complete $T_c$ suppression and Néel triplets-mediated exchange in antiferromagnet-superconductor-antiferromagnet trilayers

An antiferromagnetic insulator (AFI) bearing a compensated interface to an adjacent conventional superconductor (S) has recently been predicted to generate Néel triplet Cooper pairs, whose amplitude alternates sign in space. Here, we theoretically demonstrate that such Néel triplets enable control of the superconducting critical temperature in an S layer via the angle between the Néel vectors of two enclosing AFI layers. This angle dependence changes sign with the number of S monolayers providing a distinct signature of the Néel triplets. Furthermore, we show that the latter mediate a similarly distinct exchange interaction between the two AFIs' Néel vectors.