Field dependence of the superconductive penetration depth in tin up to the superheating limit

The superconductive penetration depth $\delta (T, H)$ has been studied as a function of temperature and field in single tin spheres, 15-30 μm in diameter. A mutual-inductance method was used with the 75-kHz measuring field parallel to the static field. When properly normalized, the variation of the transition signal with $T$ and $H$ is then proportional to $\frac{d\left[\overline{\delta }\right(T, H)\times H]}{\mathrm{dH}}$, where $\overline{\delta }$ is the penetration depth averaged over the sphere surface. The results are independent of sphere diameter, and thus characteristic of bulk tin. In zero field, we find $\delta \mathrm{}\left(T\right)=\frac{{\delta }_0}{{[1-{\left(\frac{T}{T_c}\right)}^4]}^{\frac{1}{2}}}$, with ${\delta }_0=520\mathrm{}\pm 30$ Å. The field dependence was studied for temperatures close to $T_c$ and fields up to the ideal bulk superheating field $H_{\mathrm{sh}}\cong 2.76H_c$, corresponding to a Ginzburg-Landau parameter $\kappa =0.093\mathrm{}\pm 0.001$. The penetration depth increases sharply as the field approaches $H_{\mathrm{sh}}$, but stays finite, while its derivative diverges. We find $\frac{\delta \left(H_{\mathrm{sh}}\right)}{\delta \mathrm{}(H=0\mathrm{})\mathrm{}}=1.51\mathrm{}\pm 0.04$. Averaged over the sphere, we have $\frac{\overline{\delta }\left(H_{\mathrm{sh}}\right)}{\overline{\delta }\mathrm{}(H=0\mathrm{})\mathrm{}}=1.19\mathrm{}\pm 0.01$. The field dependence is rather well described by one-dimensional Ginzburg-Landau theory in the low-$\kappa$ limit. The results indicate that the surface order parameter ${\psi }_s$ is depressed by (30-50)% at $H_{\mathrm{sh}}$. In "weak" fields, $H\le 1.5H_c$, the data are consistent with the customary quadratic field dependence.