Enhancement of superconductivity by external magnetic field in magnetic alloys

TL;DR

This paper develops a theoretical model for the critical magnetic field in magnetic alloy superconductors, verifies it against experimental data, and demonstrates how external magnetic fields can enhance superconductivity by counteracting magnetic impurities.

Contribution

The paper introduces an asymptotic solution for the thermodynamics of magnetic impurity-laden BCS superconductors and validates it with experimental data, revealing the magnetic field's role in enhancing superconductivity.

Findings

Good agreement between theory and experiment for small impurity concentrations.

Introduction of effective temperature improves model accuracy at higher impurity levels.

External magnetic field can counteract impurity effects, increasing the critical temperature.

Abstract

An asymptotic solution of the thermodynamics of a BCS superconductor containing spin 1/2 and 7/2 magnetic impurities, obtained recently in Ref. 1 is exploited to derive the expressions for critical magnetic field $H_{\mathrm{c}}(T)$ . The credibility of the resulting theoretical equations, which depend on the magnetic coupling constant $g$ and impurity concentration $c$, is verified on the experimental data for the following superconducting alloys: LaCe, ThGd and SmRh$_{4}$B$_{4}$. Good quantitative agreement with experimental data is found for sufficiently small values of $c$. The discrepancies between theoretical and experimental values of $H_{\mathrm{c}}(T)$ for larger values of $c$ in case of LaCe and ThGd are reduced by introducing the concept of the effective temperature $\tilde{T}$, which accounts for the Coulomb interactions between the electron gas and impurity ions. At low temperatures, the critical magnetic field is found to increase with decreasing temperature $T$. This enhancement of the critical magnetic field provides evidence of the Jaccarino-Peter effect, which was experimentally observed in the Kondo systems like LaCe, (La$_{1-x}$Ce$_{x}$)Al$_{2}$ and also in the pseudoternary compounds, including Sn$_{1-x}$Eu$_{x}$Mo$_{6}$S$_{8}$, Pb$_{1-x}$Eu$_{x}$Mo$_{6}$S$_{8}$ and La$_{1.2-x}$Eu$_{x}$Mo$_{6}$S$_{8}$. The effect of an external magnetic field ${\mathcal H}$ on a BCS superconductor perturbed by magnetic impurities was also studied. On this grounds, by analyzing the dependence of superconducting transition temperature $T_{\mathrm{c}}$ on ${\mathcal H}$ of (La$_{1-x}$Ce$_{x}$)Al$_{2}$, we have shown, that for certain parameter values, external magnetic field compensates the destructive effect of magnetic impurities.