Anisotropy effects in tantalum, niobium, and vanadium down to the millikelvin temperature range

Abstract

Experiments on the transition fields to the normal conducting state were made on single crystals of Ta, Nb, and V in the temperature range between 40 mK and the transition temperature. In tantalum results are presented on the thermodynamic quantitiesT _c, μ₀ H _c(T),D(t), and γ in the clean limit and as a function of impurity concentration at low impurity levels (<0.15 at %). Special attention is paid to the phase transition between type I and type II superconductivity, which occurs at a certain conversion temperatureT*<T _c in materials with κ(T _c)<1/√2. This transition is found to be strongly anisotropic because of theH _c2 anisotropy effect appearing in the type II superconducting state. It is shown that atT=0 no signs of type II superconductivity will appear for κ(T _c)⩽0.44, whereas type II superconductivity will be found in every crystal direction for κ(T _c)⩾0.50. The analysis ofH _c2 anisotropy in Ta in terms of cubic harmonic functions demonstrates that the first anisotropic expansion coefficienta ₄ remains finite atT*, whereas the second,a ₆, vanishes when type II superconductivity disappears. No significant values of any higher order coefficient could be detected in Ta. For Nb and V the temperature dependence of the anisotropy coefficientsa ₄,a ₆,a ₈, anda ₁₀ was established in the entire temperature range. The diversity of results clearly indicates that different microscopic mechanisms contribute to the observedH _c2 anisotropy effect in these materials.