Cooperative order in the weakly magnetic domain of LaFeAsO_{1-x}F_{x} near the doping phase boundary

Spatial phase separation into mesoscopic domains of non-magnetic [superconducting (SC) below Tc = 25.5 K] and two kinds of magnetic phases, one showing disordered spin density wave (d-SDW) order and another associated with glassy weak magnetism (WM), are observed below ~100 K by muon spin rotation (muSR) in LaFeAsO1-xFx for x = 0.057(3) which is near the boundary of these phases on the doping phase diagram. In contrast to the competing order observed in the regular SDW phase of Ba(Fe1-xCox)2As2, the WM domain exhibits cooperative coupling of superconducting and magnetic order parameters as inferred from strong diamagnetism and associated negative shift of muSR frequency just below Tc.