Magnetic impurities in superconductors: A theory with different predictions.

Abstract

The proclivity of paramagnetic solutes to degrade the transition temperature of a traditional singlet-pairing superconductor is studied anew. ${\mathit{T}}_{\mathit{c}}$ degradation is proportional to the (conduction electron) spin-disorder scattering rate, 1/${\mathrm{\ensuremath{\tau}}}_{\mathit{s}}$, caused by the solute spins. Accordingly the ${\mathit{T}}_{\mathit{c}}$ loss increases with solute concentration. The initial slope (versus 1/${\mathrm{\ensuremath{\tau}}}_{\mathit{s}}$) is found to depend on the superconductor and therefore is not the universal constant proposed by Abrikosov and Gor'kov. Instead the decrease is inversely proportional to \ensuremath{\lambda}, the electron-phonon coupling constant. Consequently a weak superconductor is doubly jeopardized by paramagnetic impurities: Its superconductivity is easily suppressed not only because ${\mathit{T}}_{\mathit{c}}$ is small to begin with, but also because the initial slope is steeper. Another unexpected consequence of the theory involves potential scattering which, acting alone, does not significantly influence ${\mathit{T}}_{\mathit{c}}$ (as surmised by Anderson). Nevertheless, the ${\mathit{T}}_{\mathit{c}}$ reduction caused by exchange scattering will be partially suppressed when the overall mean free path becomes smaller than the coherence length. This compensation has been demonstrated experimentally by comparing the influence of magnetic impurities in a pure host superconductor with that in a similar host having (also) nonmagnetic solutes. Such observed recovery of ${\mathit{T}}_{\mathit{c}}$, expected from this study, contradicts prior theories for magnetic solutes.