Spin glass versus superconductivity

A superconductor with interacting paramagnetic impurities is considered. The impurities are coupled via the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. At a temperature ${T}_{g},$ the system of magnetic impurities forms a spin-glass state. We study the effect of the spin-spin interactions on the superconducting transition point at $Tl{T}_{g}.$ We show that superconducting properties depend on the state of the spin system via spin-spin autocorrelation functions. With the help of the Keldysh technique, a general nonequilibrium Gor'kov equation is derived. Possible aging effects in the superconducting transition point are discussed. The equilibrium superconducting transition point is found explicitly and shown to be shifted towards higher temperatures and impurity concentrations compared to the classical Abrikosov-Gor'kov curve. The corresponding shift of the superconducting quantum critical point is quite small (about 10%). A method of calculating spin-spin correlation function is suggested. The method combines the ideas of random mean-field method and virial expansion. We calculate analytically the first virial term for the spin-spin correlator for the quantum Heisenberg spin glass with the RKKY interactions in the quasiequilibrium regime.