We report muon spin rotation ($mu$SR) measurements of single crystal Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and Sr(Fe$_{1-x}$Co$_x$)$_2$As$_2$. From measurements of the magnetic field penetration depth $lambda$ we find that for optimally- and over-doped samp
les, $1/lambda(Tto 0)^2$ varies monotonically with the superconducting transition temperature T$_{rm C}$. Within the superconducting state we observe a positive shift in the muon precession signal, likely indicating that the applied field induces an internal magnetic field. The size of the induced field decreases with increasing doping but is present for all Co concentrations studied.
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 int
erplay 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.
Zero-field (ZF) muon spin relaxation ($mu$SR) measurements have revealed static commensurate magnetic order of Fe moments in NdOFeAs below $T_{N} sim 135$ K, with the ordered moment size nearly equal to that in LaOFeAs, and confirmed similar behavior
in BaFe$_{2}$As$_{2}$. In single crystals of superconducting (Ba$_{0.55}$K$_{0.45}$)Fe$_{2}$As$_{2}$, $mu$SR spectra indicate static magnetism with incommensurate or short-ranged spin structure in $sim$ 70 % of volume below $T_{N} sim$ 80 K, coexisting with remaining volume which exhibits superfluid-response consistent with nodeless gap below $T_{c}sim 30$ K.
