Superparamagnetism and interfacial superconductivity in rare earth Pr-doped Ca122

To better understand the origin of the non-bulk superconductivity with an unusually high onset-T$_{c}$ (49 K) and its superconducting behavior in the rare earth Pr-doped Ca122 [(Ca$_{1-x}$Pr$_{x})$Fe$_{2}$As$_{2}$], detailed chemical analyses and magnetization measurements on both the as-synthesized and annealed single crystals were carried out. A small but non-negligible As-deficiency and superparamagnetic clusters (SPCs) were detected in the superconducting as-synthesized crystals, suggesting that the SPCs originate from the As vacancies. The magnetic moment of the SPC were found to be insensitive to the doping level x, while the SPC density (n) is zero for x \textless 0.05 in the non-superconducting region and increases monotonically with x for x \textgreater 0.1 in the superconducting region. The superconducting volume fraction (f) was shown to be very closely related with n. Noticeable inter-cluster interactions, from antiferromagnetic for x \textless 0.05 (non -SC region) to weakly ferromagnetic for x \textgreater 0.1 (SC region) were found, suggesting that the defects are ordered. Systematically annealing the crystals over 500-920${^\circ}$ simultaneously suppress both n and f. Therefore, we propose that the ordered vacancies, and the associated interfaces, are responsible for the rather high onset-T$_{c}$.