Vortex pinning by natural linear defects in thin films ofYBa2Cu3O7−δ

Abstract

The behavior of the superconducting current density ${j}_{s}(B,T)$ and the dynamical relaxation rate $Q(B,T)$ of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ thin films exhibits a number of features typical for strong pinning of vortices by growth induced linear defects. At low magnetic fields ${j}_{s}(B)$ and $Q(B)$ are constant up to a characteristic field ${B}^{*},$ that is directly proportional to the linear defect density ${n}_{\mathrm{disl}}.$ The pinning energy ${U}_{c}(B=0)\ensuremath{\approx}600\mathrm{K}$ can be explained by half-loop excitations determining the thermal activation of vortices at low magnetic fields. Extending the Bose glass theory [D. R. Nelson and V. M. Vinokur, Phys. Rev. B 48, 13 060 (1993)], we derive a different expression for the vortex pinning potential ${\ensuremath{\varepsilon}}_{r}(R),$ which is valid for all defect sizes and describes its renormalization due to thermal fluctuations. With this expression we explain the temperature dependence of the true critical current density ${j}_{c}(0,T)$ and of the pinning energy ${U}_{c}(0,T)$ at low magnetic fields. At high magnetic fields ${\ensuremath{\mu}}_{0}H\ensuremath{\gg}{B}^{*}$ the current density experiences a power law behavior ${j}_{s}(B)\ensuremath{\sim}{B}^{\ensuremath{\alpha}},$ with $\ensuremath{\alpha}\ensuremath{\approx}\ensuremath{-}0.58$ for films with low ${n}_{\mathrm{disl}}$ and $\ensuremath{\alpha}\ensuremath{\approx}\ensuremath{-}0.8$ to -1.1 for films with high ${n}_{\mathrm{disl}}.$ The pinning energy in this regime, ${U}_{c}(\mathrm{high}B)\ensuremath{\approx}60--200\mathrm{K}$ is independent of magnetic field, but depends on the dislocation density. This implies that vortex pinning is still largely determined by the linear defects, even when the vortex density is much larger than the linear defect density. Our results show that natural linear defects in thin films form an analogous system to columnar tracks in irradiated samples. There are, however, three essential differences: (i) typical matching fields are at least one order of magnitude smaller, (ii) linear defects are smaller than columnar tracks, and (iii) the distribution of natural linear defects is nonrandom, whereas columnar tracks are randomly distributed. Nevertheless the Bose glass theory, that has successfully described many properties of pinning by columnar tracks, can be applied also to thin films. A better understanding of pinning in thin films is thus useful to put the properties of irradiated samples in a broader perspective.