Mixed-State Hall Effect in an Extreme Type-II Superconductor

Measurements of mixed-state transverse and longitudinal voltages at $T=1.2\mathrm{}°$K, $0<H<\mathrm{}39\mathrm{}$ kG, $0<J<\mathrm{}800\mathrm{}$ A/${\mathrm{cm}}^2$ on an extremely high-$\kappa$ type-II alloy superconductor Ti-16 at.% Mo ($\kappa =68\mathrm{}$, $T_c=4.2\mathrm{}°$K, zero-temperature upper critical field $H_{c20\mathrm{}}=63\mathrm{}$ kG) show that the high-$J$, nearly $J$-independent, mixed-state Hall-angle tangent ${tan\theta }_m\mathrm{}\left(H\right)\mathrm{}$ is much larger than the normal-state value ${tan\theta }_n\mathrm{}\left(H\right)\mathrm{}$. At the highest applied magnetic field, the reduced Hall-angle tangent $P_m(\frac{H}{H_{k20\mathrm{}}}=0.35)=\frac{\left[{tan\theta }_m\right(H=39\mathrm{} \mathrm{kG}\left)\right]}{\left[{tan\theta }_n\right(H_{k20\mathrm{}}\left)\right]}\approx 0.6$, where $H_{k20\mathrm{}}=111\mathrm{}$ kG is determined by the measured reduced flux-flow resistivity $\frac{{\rho }_f\mathrm{}\left(H\right)\mathrm{}}{{\rho }_n}=\frac{H}{H_{k20\mathrm{}}}$. This contrasts with previous results pertinent to pure or low-$\kappa$ materials where $H_{k20\mathrm{}}\approx H_{c20\mathrm{}}:P_m\mathrm{}\left(0.35\right)\mathrm{}\approx 0.35$ (Bardeen-Stephen theory), (1) (Nozières-Vinen theory), 0.35 (Nb measurements of Fiory and Serin), (2) (Nb-Ta measurements of Niessen et al.).