Correlation of superparamagnetism and self-assembled defects with non-bulk superconductivity up to 49 K in (Ca,Pr)Fe$_{2}$As$_{2}$ single crystal

We have found the unusual simultaneous occurrence of superparamagnetism and superconductivity single crystals of (Ca$_{1-x}$Pr$_{x}$)Fe$_{2}$As$_{2}$ with an x-independent Tc and a close correlation of the superconducting volume fraction with the magnetic cluster density and self-assembled As-defect density. The finding demonstrates a close relationship of superconductivity with superparamagnetism associated with the self-assemble defects. In addition, we have detected extremely large magnetic anisotropy, doping level independent Tc, the existence of mesoscopic-2D structures and Josephson-Junction Array couplings in the system. All these observations provide the physical basis of interfaces for the proposed interface-mechanism, and the best evidence for interface-enhanced superconductivity in a naturally occurring (vs artificially synthesized) material system to date.