Quantum creep and pinning properties of oxygen-deficient ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{{\mathit{x}}_{\mathit{n}}}$ films

A high sensitivity capacitance torquemeter has been used for a comprehensive investigation of the induced current densities and dynamic relaxation rates in a ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{{\mathit{x}}_{\mathit{n}}}$ film with nominal oxygen content varying between ${\mathit{x}}_{\mathit{n}}$=6.55 and ${\mathit{x}}_{\mathit{n}}$=7.0. The dynamic relaxation rate Q does not extrapolate to zero at T=0 K, indicating the presence of quantum creep. By changing the oxygen content of the film it is possible to investigate the relation between the quantum creep rate Q(0) and the normal-state resistivity ${\mathrm{\rho }}_{\mathit{n}}$(0) at low temperature. Although Q(0) increases monotonically with ${\mathrm{\rho }}_{\mathit{n}}$, it is found that Q(0) is not proportional to ${\mathrm{\rho }}_{\mathit{n}}$(0), in contrast to the predictions of a theory based on dissipative tunneling of collectively pinned single vortices [Blatter et al., Rev. Mod. Phys. 66, 1125 (1994)]. The experimental results imply that in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ quantum creep takes place in a transition regime between Hall tunneling and dissipative tunneling. For lower oxygen contents the quantum creep regime moves towards the dissipative limit. For each oxygen content the characteristic pinning energy ${\mathit{U}}_{\mathit{c}}$(0) at T=0 is obtained by a linear extrapolation to T= 0 K of the T/Q versus T curves. The critical current density ${\mathit{j}}_{\mathit{c}}$ at T=0 is determined independently by a linear extrapolation of the measured ln${\mathit{j}}_{\mathit{s}}$ versus T curves. A power-law relation ${\mathit{U}}_{\mathit{c}}$(0)∝[${\mathit{j}}_{\mathit{c}}$(0)${]}^{\mathit{p}}$ with p≊ 0.5 is found, indicating single vortex pinning at higher temperatures. This is confirmed by a detailed analysis of the measured current densities and relaxation rates by means of the generalized inversion scheme developed by Schnack et al. [Phys. Rev. B 48, 13 178 (1993)]. For ${\mathit{x}}_{\mathit{n}}$≥ 6.6 at ${\mathit{B}}_{\mathit{e}}$= 0.6 T and for ${\mathit{x}}_{\mathit{n}}$≥ 6.7 at ${\mathit{B}}_{\mathit{e}}$= 2.0 T the calculated temperature dependence of ${\mathit{j}}_{\mathit{c}}$ and