Reentrant behavior of superconducting alloys

TL;DR

This paper develops a mean-field theory for dirty BCS superconductors with magnetic impurities, revealing reentrant superconductivity, phase diagrams with five phases, and good agreement with experimental data on specific alloys.

Contribution

It introduces an improved mean-field approach to analyze reentrant behavior in superconducting alloys with magnetic impurities, extending previous models.

Findings

Identification of five distinct phases in the system.

Evidence of reentrant superconductivity and Jaccarino-Peter compensation.

Quantitative agreement with experimental data on specific alloys.

Abstract

A dirty BCS superconductor with magnetic impurities is studied. Asymptotic solution of the thermodynamics of such superconductor with spin $1/2$ and $7/2$ magnetic impurities, is found. To this end, the system's free energy $f(H, \beta)$ is bounded from above and below by mean-field type bounds, which are shown to coalesce almost exactly in the thermodynamic limit, provided the impurity concentration is sufficiently small. The resulting mean-field equations for the gap $\Delta$ and a parameter $\nu$, characterizing the impurity subsystem, are solved and the solution minimizing $f$ is found for various values of magnetic coupling constant $g$ and impurity concentration $x$. The phase diagrams of the system are depicted with five distinct phases: the normal phase, unperturbed superconducting phase, perturbed superconducting phase with nonzero gap in the excitation spectrum, perturbed gapless superconducting phase and impurity phase with completely suppressed superconductivity. Furthermore, evidence of reentrant superconductivity and Jaccarino-Peter compensation is found. The credibility of the theory is verified by testing the dependence of the superconducting transition temperature $T_{\text{c}}$ on $x$. Very good quantitative agreement with experimental data is obtained for several alloys: (La$_{1-x}$Ce$_{x}$)Al$_{2}$, (La$_{1-x}$Gd$_{x}$)Al$_{2}$ and (La$_{0.8-x}$Y$_{0.20}$)Ce$_{x}$. The theory presented improves earlier developments in this field.