Universal behavior of the Hall resistivity of single crystalline ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{x}}$ in the thermally activated flux flow regime

The Hall resistivity ${\mathrm{\rho }}_{\mathit{H}}$ and the longitudinal resistivity ρ of single crystalline ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{\mathit{x}}$ are measured in the thermally activated flux flow regime. It is shown that ${\mathrm{\rho }}_{\mathit{H}}$ scales to a universal function of ρ: ${\mathrm{\rho }}_{\mathit{H}}$(T)=A[ρ(T)${]}^{\mathrm{\beta }}$, where β=2±0.1 and A is a positive and magnetic field independent coefficient for magnetic fields from 1 to 5 T. A resistivity-squared dependence of ${\mathrm{\rho }}_{\mathit{H}}$ can be explained by the recent theory of Vinokur, Geshkenbein, Feigel’man, and Blatter in terms of weak pinning of a vortex liquid.