Ginzburg-Landau Parameters of Type-II Superconductors

Specific heats in a magnetic field were measured for three specimens of niobium, a 50% Nb-50% Ta specimen, and an In + 1.9% Bi specimen. These data were supplemented by magnetization measurements on one niobium specimen. From the data, two Ginzburg-Landau parameters are calculated: $K_1$, determined by the magnitude of the upper critical field, and $K_2$, determined by the slope of the magnetization curve at this field. For the niobium specimens, $K_2$ exceeds $K_1$ at all temperatures below the transition temperature, in qualitative agreement with the theory of pure type-II superconductors of Maki and Tsuzuki. The ratio $\frac{K_2}{K_1}$ at a given temperature is largest in the purest Nb and less in impure Nb. In the pure specimens, the temperature dependence of $K_1$ is more rapid than predicted by theory, the experimental value of $K_1\mathrm{}\left(0\right)\mathrm{}$ being about 25% larger than the theoretical value of 0→K. For the alloy specimens, $K_2\sim K_1$, over the temperature range measured, and both parameters increase with decreasing temperature. This result contradicts the inequality $K_2<K$ (where $K$ is the Ginzburg-Landau parameter at $T_c$) derived by Maki for type-II superconductors of short electron mean free path.