Superconductivity coexisting with phase-separated static magnetic order in (Ba,K)Fe$_{2}$As$_{2}$, (Sr,Na)Fe$_{2}$As$_{2}$ and CaFe$_{2}$As$_{2}$

The recent discovery and subsequent developments of FeAs-based superconductors have presented novel challenges and opportunities in the quest for superconducting mechanisms in correlated-electron systems. Central issues of ongoing studies include interplay between superconductivity and magnetism as well as the nature of the pairing symmetry reflected in the superconducting energy gap. In the cuprate and RE(O,F)FeAs (RE = rare earth) systems, the superconducting phase appears without being accompanied by static magnetic order, except for narrow phase-separated regions at the border of phase boundaries. By muon spin relaxation measurements on single crystal specimens, here we show that superconductivity in the AFe$_{2}$As$_{2}$ (A = Ca,Ba,Sr) systems, in both the cases of composition and pressure tunings, coexists with a strong static magnetic order in a partial volume fraction. The superfluid response from the remaining paramagnetic volume fraction of (Ba$_{0.5}$K$_{0.5}$)Fe$_{2}$As$_{2}$ exhibits a nearly linear variation in T at low temperatures, suggesting an anisotropic energy gap with line nodes and/or multi-gap effects.