Insular superconductivity in Co-doped iron pnictide CaFe$_{1-x}$Co$_x$AsF

The presence of macroscopic phase separation between the superconducting and magnetic phases in \cfcaf is demonstrated by muon spin rotation (muSR) measurements conducted across their phase boundaries (x=0.05-0.15). The magnetic phase tends to retain the high transition temperature (T_m > T_c), while Co-doping induces strong randomness. The volumetric fraction of superconducting phase is nearly proportional to the Co content $x$ with constant superfluid density. These observations suggest the formation of superconducting "islands" (or domains) associated with Co ions in the Fe$_2$As$_2$ layers, indicating a very short coherence length.