Vortex pinning in the frozen vortex lattice in YBa₂Cu₃O_7-x films

The inductance of vortices L_V(T, B) in YBa₂Cu₃O_7-x films is studied for temperature 8<T<85 K, and magnetic field 0<B<6 T with the goal of identifying the morphology of the vortex pinning sites and the type of the glass phase below the vortex lattice melting transition B_g(T). The key feature that distinguishes point, linear, and planar pinning sites is how rapidly L_V increases when thresholds in T and B are crossed. We find that, below a threshold field B_p(T)<B_g(T), the effective pinning force on each vortex is independent of B. At B_p<B<B_g, L_V increases as B², whereas at B≈B_g, L_V diverges faster than B² following a scaling law on f, consistent with a phase transition between a glass and a liquid vortex state. Although the value of the threshold field, B_p≈8(1-T/T_C) T, is consistent with any type of pinning defect, the increase of L_V∝B² for B>B_p is much less rapid than predicted for collective pinning of vortices by point defects. Linear and planar defects are possible explanations, but the necessary theoretical calculations are currently absent.