Two components of critical current in YBa$_2$Cu$_3$O$_{7-\delta}$ films
  Combined action of weak and strong pinning centers on the vortex lattice complicates magnetic behavior of a superconductor since temperature and magnetic field differently affect weak and strong pinning. In this paper we show that contributions of weak and strong pinning into magnetization of the layered superconductor YBa$_2$Cu$_3$O$_{7-\delta}$ can be separated and analyzed individually. We performed a careful analysis of temperature behavior of the relaxed superconducting current $J$ in YBa$_2$Cu$_3$O$_{7-\delta}$ films which revealed two components of the current $J = J_1 +J_2$. A simple method of separation of the components and their temperature dependence in low magnetic fields are discussed. We found that $J_1$ is produced by weak collective pinning on the oxygen vacancies in CuO$_2$ planes while $J_2$ is caused by strong pinning on the Y$_2$O$_3$ precipitates. $J_1$ component weakly changes with field and quasi-exponentially decays with temperature, disappearing at $T \simeq 30$--40~K. Rapid relaxation of $J_1$ causes formation of the normalized relaxation rate peak at $T \simeq 20$~K. $J_2$ component is suppressed by field as $J_2\propto B^{-0.54}$ and decays with temperature following to the power law $J_2\propto(1 - T/T_\mathrm{dp} )^\alpha$ where $T_\mathrm{dp}$ is the depinning temperature. Detailed comparison of the experimental data with pinning theories is presented. 
A. V. Kuznetsov, I. I. Sanninkov and A. A. Ivanov
cond-mat.supr-con