Strong pinning in high-temperature superconducting films

Detailed measurements of the critical current density ${j}_{c}$ of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ films grown by pulsed laser deposition reveal the increase of ${j}_{c}$ as a function of film thickness. Both this thickness dependence and the field dependence of the critical current are consistently described using a generalization of the theory of strong pinning of Ovchinnikov and Ivlev [Phys. Rev. B 43, 8024 (1991)]. From the model, we deduce values of the defect density ${(10}^{21} {\mathrm{m}}^{\ensuremath{-}3})$ and the elementary pinning force, which are in good agreement with the generally accepted values for ${\mathrm{Y}}_{2}{\mathrm{O}}_{3}$ inclusions. In the absence of clear evidence that the critical current is determined by linear defects or modulations of the film thickness, our model provides an alternative explanation for the rather universal field dependence of the critical current density found in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ films deposited by different methods.