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 < \xi), this exchange is thought to be dominated by RKKY interactions, identical to the those in a normal metallic host. This perception is based upon 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. Experimental signatures, implications and applications are discussed.
Categories: cond-mat.mes-hall cond-mat.str-el cond-mat.supr-con