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It is generally believed that superconductivity only weakly affects theindirect exchange between magnetic impurities. If the distance r betweenimpurities is smaller than than the superconducting coherence length (r < \xi),this exchange is thought to be dominated by RKKY interactions, identical to thethose in a normal metallic host. This perception is based upon a perturbativetreatment of the exchange interaction. Here, we provide a non-perturbativeanalysis and demonstrate that the presence of Yu-Shiba-Rusinov bound statesinduces a strong 1/r^2 anti-ferromagnetic interaction that can dominate overconventional RKKY even at distances significantly smaller than the coherencelength. Experimental signatures, implications and applications are discussed.

Enhanced anti-ferromagnetic exchange between magnetic impurities in a superconducting host