Coexistence of incommensurate magnetism and superconductivity in Fe_{1+y}Se_xTe_{1-x}

We report an investigation into the superconducting and magnetic properties of Fe_{1+y}Se_{x}Te_{1-x} single crystals by magnetic susceptibility, muon spin rotation, and neutron diffraction. We find three regimes of behavior in the phase diagram for 0\leq x\leq 0.5: (i) commensurate magnetic order for x< 0.1, (ii) bulk superconductivity for $x\lesssim 0.1$, and (iii) a range \sim 0.25\leq x\leq 0.45 in which superconductivity coexists with static incommensurate magnetic order. The results are qualitatively consistent with a two-band mean-field model in which itinerant magnetism and extended s-wave superconductivity are competing order parameters.