Hall Effect in Superconducting Niobium and Alloys

We have studied the Hall effect in niobium and some Nb-Ta alloys in the mixed state by calorimetric surface-resistance measurements. In certain conditions the tangent of the Hall angle is given by $\frac{({R_{+}}^2-{R_{-}}^2)}{\left(2\mathrm{}{R}_{+}{R}_{-}\right)}$ where $R_{+}$, $R_{-}$ are the surface resistances in right- and left-hand circularly polarized fields. The method of study is critically analyzed and its suitability for studying the mixed state is discussed. It is found that flux pinning causes the magnitude of the Hall angle to be overestimated, which is quite opposite to the influence of pinning on dc Hall-effect measurements. Interpreted like this, the data for moderately pure Nb are consistent with the Hall angle being independent of field in the mixed state. As increasing amounts of Ta are alloyed in, the mixed-state Hall angle becomes smaller compared with the normal state, and for ${\mathrm{Nb}}_{96.8}$ ${\mathrm{Ta}}_{3.2}$ it is approximately zero in $0.5H_{c2}$. The small and negative Hall angles which have been reported for impure Nb and Nb-rich alloys therefore probably represent the true flux-flow behavior, at least qualitatively, and are not primarily due to pinning. A Ta-rich alloy has a relatively large positive Hall angle as also previously reported by Niessen et al.