Defect-Associated Superconductivity in (Pr,Ca)Fe$_{2}$As$_{2}$

The superconductivity in rare earth doped CaFe$_{2}$As$_{2}$ remains puzzled. As reported before, there are two distinguishable superconductive transitions at 20 K and 49 K, respectively, and the 49 K superconductivity can be better modeled as Josephson-Junction-Arrays (JJA). The H- and T-dependencies of the ac/dc magnetization are further explored here. The data suggest that the effective lower-critical-fields at both $c$- and \textit{ab}-directions are below 1 Oe down to 5 K, in agreement with previous JJA assumption. The \textit{ac} susceptibility below the critical field is highly anisotropy, suggesting a thin-disk-like morphology of the JJA's. The associated weak-links, however, appear to be broken above 20 K by a \textit{dc} bias as small as 10 Oe. The \textit{ac} response at higher bias fields, therefore, will be dominated by the isolated superconducting islands of JJA. It is interesting to note, therefore, that the \textit{ac} susceptibility remains highly anisotropic at high fields, but is much weaker than that expected from the field-cooled magnetization. We interpret this as the result of sub-micron size, thin-disk-like local superconductivity, $i.e.$ Defect-associated superconductivity.