Nonlinear Hall resistivity in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ films near the vortex-glass transition

The Hall electric field ${\mathit{E}}_{\mathit{y}}$ is observed to be a strongly nonlinear function of the current density ${\mathit{J}}_{\mathit{x}}$ in the vicinity of the vortex-glass transition of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ films in a magnetic field. Much like the longitudinal electric field ${\mathit{E}}_{\mathit{x}}$,${\mathit{E}}_{\mathit{y}}$ apears to scale critically with ${\mathit{J}}_{\mathit{x}}$, with a Hall-related critical exponent λ=3.4±0.3. Furthermore, the Hall resistivity ${\mathrm{\rho }}_{\mathit{x}\mathit{y}}$=${\mathit{E}}_{\mathit{y}}$/${\mathit{J}}_{\mathit{x}}$ and the longitudinal resistivity ${\mathrm{\rho }}_{\mathit{x}\mathit{x}}$=${\mathit{E}}_{\mathit{x}}$/${\mathit{J}}_{\mathit{x}}$ are found to obey ${\mathrm{\rho }}_{\mathit{x}\mathit{y}}$∝${\mathrm{\rho }}_{\mathit{x}\mathit{x}}^{2.0\pm 0.2}$ over a wide range of current densities and temperatures. The results quantitatively verify recent theoretical predictions.