Low-temperature behaviour of magnetic impurities in superconductors: I

Abstract

For pt.I see ibid., vol.10, p.1507 (1980). The method used by the authors in a previous paper to calculate the free energy of a superconductor containing spin-1/2 magnetic impurities has been extended to calculate the thermal Green function to order ( pi nu 0jz)-2 and to infinite order in Jperpendicular to . The finite impurity concentration behaviour is found to be functionally the same as that arising from the non-magnetic Anderson model. The graph of the transition temperature versus the impurity concentration is found to have a finite tail which should lead to the observation of a third transition temperature in re-entrant superconductors. The spatial variation of the order parameter is investigated in the limits of high (T approximately=Tc) and low (T<<Tc) temperatures for both long and short distances from the impurity. In addition, a numerical analysis of the initial decrease in Tc for intermediate temperatures shows qualitative agreement with previous high-temperature theories.