Study on possible correlation of superconductivity with defects and superparamagnetism in undoped AFe$_{2}$As$_{2}$ with A$=$Ca, Sr and Ba

Extensive studies have been carried out on the induction of bulk superconductivity in the Fe-pnictide 122 system with a T$_{\mathrm{c}}$ up to 38 K through doping and/or pressure. However, non-bulk superconductivity has also been detected unexpectedly in undoped AFe$_{2}$As$_{2}$ where A $=$ Ca, Sr, and Ba with T$_{\mathrm{c}} =$ $\sim$12K, $\sim$22K and $\sim$23K, respectively. The reason for the observation remains unknown. Recently, systematic investigation shows that highly anisotropic superconductivity with a T$_{\mathrm{c}}$ up to 49 K and superparamagnetism occur in rare-earth doped Ca122. Further examination reveals slight deviation from the 1:2:2 stoichiometry which correlates closely with the occurrence of non-bulk superconductivity and superparamagnetism in these samples. We have therefore decided to investigate systematically the stoichiometry, defects, magnetism and superconductivity in undoped AFe$_{2}$As$_{2}$ single crystals under different synthesis conditions where A $=$ Ca, Sr, and Ba. Results will be presented and discussed.