Effects of annealing and doping concentration on the critical current density and superconducting properties of $Ba(Fe_{1-x}Co_x)_2As_2$ and $Ba_{0.5}Sr_{0.5}(Fe_{1-y}Co_y)_2As_2$*

We report on the study we have made in order to better understand the intrinsic nature of superconductivity and pinning mechanisms in $Ba(Fe_{1-x}Co_x)_2As_2$ with various cobalt concentration and in $Ba_{0.5}Sr_{0.5}(Fe_{1-y}Co_{y})_2$. The critical current density $J_c$(as functions of temperature, and applied magnetic field) for different x values of 0.04, 0.08, and 0.15 (underdoped, optimally doped and overdoped respectively) is determined magnetically. From the $J_c (H)$ analysis, we see that $J_c$ slowly decays with respect to H in all the samples. We also found that $J_c$ in the annealed compared to the as-grown sample is enhanced in the underdoped and the optimally doped $Ba(Fe_{1-x}Co_x)_2As_2$ while there is no difference in the overdoped $Ba(Fe_{1-x}Co_x)_2As_2$ and the $Ba_{0.5}Sr_{0.5}(Fe_{1-y}Co_{y})_2$. Analysis of the $J_c$(T) data shows a weak pinning feature rather than correlated pinning. The pinning force $F_p$ as a function of the irreversible field $H_{irr}$ is also analyzed to gain further insights into the pinning mechanism.