Local voltage-current characteristics in high-$T_c$ superconductors

Local electric field versus current density $\mathrm{}(E-j)\mathrm{}$ curves were measured in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_{4\mathrm{-}\mathrm{\delta }}$ single crystals using a miniature Hall-sensors array. Measurements in the field range corresponding to the anomalous magnetization peak in these crystals reveal remarkably different $E-j$ characteristics below and above the peak, indicating a crossover in the flux-creep mechanism. Similar $E-j$ behavior, as observed here in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_{4\mathrm{-}\mathrm{\delta }},$ is expected universally in every superconductor exhibiting the anomalous peak.