Enhancement of superconductivity by external magnetic field in magnetic alloys

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.