Effect of Magnetic Impurities in Crystalline and Amorphous 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, 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 pure crystalline state 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.