Fig. 4

Pinning length in (Y,Gd)Ba₂Cu₃O_7−x film. a Creep rate versus film thickness at different temperatures for (Y,Gd)Ba₂Cu₃O_7−x (YGdBCO) film on a log – log plot. The dotted lines are linear fits for \(d \le L_{\mathrm{c}}^{\mathrm{mp}}(T)\). b Effective pinning length \(L_{\mathrm{c}}^{\mathrm{mp}}\) at 0.3 and 1 T. (See Supplementary Information for all 0.3 T data). The circles and diamonds show points extracted from the U^*(d) data. The inset shows an example of how \(L_{\mathrm{c}}^{\mathrm{mp}}\) was extracted for T = 10–25 K at 1 T. Linear fits to this data (solid lines) and extrapolations (dashed lines) defining \(L_{\mathrm{c}}^{\mathrm{mp}}(T,H)\) are shown. c Difference in creep rate of thinned film and that of the original film (d = 900 nm) versus the ratio of the film thickness to the effective pinning length, \(d{\mathrm{/}}L_{\mathrm{c}}^{\mathrm{mp}}(T)\). Creep rate increases sharply when film becomes thinner than \(L_{\mathrm{c}}^{\mathrm{mp}}\). The insets illustrate the bulk (right panel) and truncated (left panel) pinning volumes, applicable for \(d > L_{\mathrm{c}}^{\mathrm{mp}}\) and \(d < L_{\mathrm{c}}^{\mathrm{mp}}\), respectively