The effects of magnetic impurities in superconductors

A microscopic theory based on a Kondo Hamiltonian with strong longitudinal coupling is presented for the behaviour of a superconductor containing magnetic impurities mainly at low temperatures. The free energy is calculated in terms of a perturbation expansion to second order in the inverse of the longitudinal coupling constant and to all orders in the transverse coupling constant. This allows a discussion of the initial decrease in transition temperature, specific heat jump, zero temperature order parameter and critical magnetic field to first order in the impurity concentration in the limits of both strong and weak transverse coupling. The Green's Function is then calculated and the t-matrix is extracted in order to discuss the case of a finite concentration of impurities. Thermodynamic properties at low temperatures are shown to have the same functional dependence on impurity concentrations as in the Hartree-Fock treatment of the non-magnetic Anderson model. Knowledge of the Green's Function also allows a discussion of the spatial dependence of the order parameter at high and low temperatures and at large and small distances from the impurity. (U.K.)