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The recent discovery and subsequent developments of FeAs-basedsuperconductors have presented novel challenges and opportunities in the questfor superconducting mechanisms in correlated-electron systems. Central issuesof ongoing studies include interplay between superconductivity and magnetism aswell as the nature of the pairing symmetry reflected in the superconductingenergy gap. In the cuprate and RE(O,F)FeAs (RE = rare earth) systems, thesuperconducting phase appears without being accompanied by static magneticorder, except for narrow phase-separated regions at the border of phaseboundaries. 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 astrong static magnetic order in a partial volume fraction. The superfluidresponse from the remaining paramagnetic volume fraction of(Ba$_{0.5}$K$_{0.5}$)Fe$_{2}$As$_{2}$ exhibits a nearly linear variation in Tat low temperatures, suggesting an anisotropic energy gap with line nodesand/or multi-gap effects.

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$_{2}$