Scaling of voltage-current characteristics of thin-film Y-Ba-Cu-O at low magnetic fields

We have measured voltage-current characteristics for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ thin films in magnetic fields from 5 T to ambient, including some in the millitesla range. In all cases, the resistivity–current density isotherms can be separated into two classes: those which exhibit upward curvature, and have constant resistivity at low currents, and those which exhibit downward curvature at all currents. These two classes of isotherms are separated by a field-dependent temperature ${\mathit{T}}_{\mathit{g}}$. For each field, the isotherms scale in a manner consistent with a three-dimensional vortex-liquid to vortex-glass phase transition. The region that can be scaled is several kelvin at 5 T and narrows with decreasing field. The low-current resistivity above ${\mathit{T}}_{\mathit{g}}$ varies as ‖1-T/${\mathit{T}}_{\mathit{g}}$ ${\mathrm{\Vert }}^{\mathit{s}}$ with s≊7.4 at all fields, but the critical scaling exponents z and ν become field dependent below about 10 mT.