  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.
