Critical current, magnetization relaxation and activation energies for YBa₂Cu₃O₇ and YBa₂Cu₄O₈ films

By means of high-sensitivity capacitance torque magnetometers we have measured the superconducting current j_s and the dynamic magnetic-moment relaxation of YBa₂Cu₃O₇ and YBa₂Cu₄O₈ films of typically 100 nm thickness at temperatures between 2 K and T_c in magnetic fields up to 6 T. For the measurements of the dynamic relaxation rate Q≡d ln j_s/d ln (dB_e/dt) magnetic-field sweep rates were varied between 0.5 and 40 mT/s. At low fields (typically 0.5 T) the dynamical relaxation rate exhibits a plateau at Q≈0.06 in YBa₂Cu₃O₇ and 0.04 in YBa₂Cu₄O₈. At high fields (B_e=μ₀H_e≈ 6 T) the plateaus have completely disappeared and Q increases almost linearly with increasing temperature. At all fields a sharp increase up to Q≊1 is observed when the irreversibility line is approached. By means of the generalized inversion scheme (GIS), the j_s(T, B_e) and Q (T, B_e) data are used to determined the current dependent activation energy U (j, T, B_e) for thermally activted flux creep. Although the GIS does not make any a priori assumptions about the explicit functional dependences on T and j, the U(j, T=0, B_e) function derived from the experimental data by means of the GIS can remarkably well be described with the collective-creep interpolation formula U(j)=(U_c/μ)[(j_c/j)^μ-1] with μ≈0.6 for currents j>0.15j_c (T=0, B_e) where J_c(T=0, B_e) is the critical current at T=0, and wi U_c depending on B_e. At lower current densities U(j, T=0, B_e) does not diverge as j^-0.6 but shifts gradually to a weaker ln(j_c/j) dependence. At low temperatures the current and relaxation data cannot be explained in terms of a thermally activated flux-motion model. Quantum creep has an influence up to ∼13 K.