Isotope effect in superconductingβ-phase gallium

Abstract

The superconductive isotope effect in $\beta$-phase Ga has been investigated in small single spheres of ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$ and ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$. The difference in transition temperatures is $\Delta T_c=73\mathrm{}\pm 3$ mK. Assuming a dependence on the mean isotopic mass of the form $T_c\sim M^{-\alpha }$, this yields $\alpha =0.43\mathrm{}\pm 0.02$. The transition temperatures are $T_c^{69}=6.10\mathrm{}\pm 0.02$ K and $T_c^{71}=6.02\mathrm{}\pm 0.02$. Our previously published value for $T_c$ in $\beta$-Ga is too low owing to an incorrect thermometer calibration. The correct value is $T_c^{\beta }=6.07\mathrm{}\pm 0.03$ K for natural $\beta -\mathrm{Ga}$. $H_c\mathrm{}\left(T\right)\mathrm{}$ has been measured both for ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$ and ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$. At $T=0\mathrm{}$, the difference in critical field is $H_0^{69}-H_0^{71}=5\mathrm{}\pm 2$ Oe, in agreement with the similarity principle. Within the experimental accuracy, the deviation of $H_c\mathrm{}\left(T\right)\mathrm{}$ from a parabola is independent of isotopic mass, yielding $D{\left(t^2\right)}_{max}=-0.021\mathrm{}\pm 0.004$. The slope ${\left(\frac{d{H}_c}{\mathrm{dT}}\right)|}_{T_c}=155\mathrm{}\pm 2$ Oe/K, independent of isotopic mass to this accuracy. These results show $\beta$-Ga to be a rather typical weak-coupling superconductor.