Precision Measurement of Anisotropy in the Upper Critical Field of Superconducting Niobium

Abstract

A sensitive vibrating-coil magnetometer has been employed to investigate anisotropy in the upper critical field of pure niobium from 1.2°K to the transition temperature. The results are analyzed using a four-term Kubic harmonic expansion. This is sufficient to represent the data to within experimental error above a reduced temperature of $t\simeq 0.5$, although as the temperature is reduced, small but systematic deviations occur, indicating the presence of higher harmonics. The temperature dependences of the first four harmonics are presented and discussed. Both the temperature dependence of the $n\mathrm{th}$ harmonic, and the reduction of that harmonic by impurity scattering, increase as $n$ increases. Our observations are in qualitative accord with the detailed theory for upper-critical-field anisotropy due to Hohenberg and Werthamer. Where direct comparison is possible quantitative agreement is also obtained.