Enhancement of superconductivity by external magnetic field in magnetic alloys

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.