Susceptibility and order parameter for a superconductor with coupled magnetic impurities.

Abstract

The influence of impurity pair interactions in superconductors is calculated in the spin-glass regime of 1--10 % magnetic-impurity concentrations. We use the s-d Hamiltonian to represent the exchange coupling J of an impurity spin to the conduction electrons; this term leads to the Ruderman-Kittel-Hasuya-Yosida (RRKY) coupling among impurities, and yields major modifications in the superconducting order parameter as well as the conduction-electron susceptibility. As the impurity concentration is increased, ferromagnetic RKKY coupling among impurities causes a reentrant form of the superconductivity order parameter and a corresponding large increase in the susceptibility. Antiferromagnetic RKKY interactions tend to counteract the isolated impurity suppression of the superconducting transition temperature and thus favor the persistence of superconductivity at higher impurity concentrations in contrast to the dilute-limit theory of Abrikosov and Gor'kov. In certain situations, the antiferromagnetic impurity coupling may in fact allow materials to be superconducting which would otherwise be expected to be normal metals. These results are applied to experiments on rare-earth compounds.