Enhanced Antiferromagnetic Exchange between Magnetic Impurities in a Superconducting Host

Abstract

It is generally believed that superconductivity only weakly affects the indirect exchange between magnetic impurities. If the distance r between impurities is smaller than than the superconducting coherence length $(r \lesssim \xi)$ , this exchange is thought to be dominated by RKKY interactions, identical to the those in a normal metallic host. This perception is based on a perturbative treatment of the exchange interaction. Here, we provide a non-perturbative analysis and demonstrate that the presence of Yu-Shiba-Rusinov bound states induces a strong $1/r^2$ anti-ferromagnetic interaction that can dominate over conventional RKKY even at distances significantly smaller than the coherence length $(r\ll \xi )$. Experimental signatures, implications and applications are discussed.Physic