Critical currents, magnetic relaxation and pinning in Nd$Ba_2$$Cu_3$$O_{7-\delta}$ films with BaZr$O_3$ generated columnar defects*

The critical current density $J_c$ and the magnetic relaxation (creep) properties have been studied for a set of $NdBa_2Cu_3O_{7-\delta}$(NdBCO) films doped with $BaZrO_3$ (BZO) nanoparticles to form columnar defects. The dependence of $J_c$ on the magnitude and orientation of the applied magnetic field $H_{app}$ (0-6.5 T) and temperature T (5 K-$T_c$) was investigated. The normalized flux-creep rate $S = -d ln(J)/d ln(t)$ was determined as a function of T. The current dependence of the effective activation energy $U_{eff}(J)$ was derived using the formalism developed by Maley. The results are well described by an inverse power law type barrier of the form $U_{eff}(J)\sim U_0(J_0/J)^{\mu}$ with fitted values for the pinning energy scale $U_0$ and the glassy exponent $\mu$. When comparing values for these parameters in the BZO-doped samples with those for their undoped control counterparts, the most striking difference is the larger scale of current density $J_0$ in the doped samples (a factor of 2.4 higher), while the other pinning parameters do not differ strongly. In the BZO-doped materials, the pinning energy scale $U_0$ increases with vortex density and $J_0$ decreases, with both following simple power law dependences on the field.