Different Behavior of Magnetic Impurities in Crystalline and Ammorphous States of Superconductors

It has been observed that the effect of magnetic impurities in a superconductor is drastically different depending on whether the host superconductor is in a crystalline or an amorphous state. Based on the recent theory of Kim and Overhauser (KO), it is shown that as the system is getting disordered, the initial slope of the $T_{c}$ depression is decreasing by a factor $\sqrt{\ell/\xi_{0}}$, when the mean free path $\ell$ becomes smaller than the BCS coherence length $\xi_{0}$, which is in agreement with experimental findings. In addition, for a superconductor in a crystalline state in the presence of magnetic impurities the superconducting transition temperature $T_{c}$ drops sharply from about 50% of $T_{c0}$ (for a pure system) to zero near the critical impurity concentration. This {\sl pure limit behavior} was indeed found by Roden and Zimmermeyer in crystalline Cd. Recently, Porto and Parpia have also found the same {\sl pure limit behavior} in superfluid He-3 in aerogel, which may be understood within the framework of the KO theory.