Superconductivity from magnetic fluctuations in FeTe_1-xSe_x-feedback of double stripe magnetism on itinerant spin excitations

Iron-chalcogenide superconductors exhibit an unusual double stripe antiferromagnetic parent phase with ordering vector Q_AF = (π/2,π/2) (in the one iron unit cell). In addition, magnetic excitations in optimally doped systems are peaked at momenta Q_SF = (π,0)/(0,π), which is in contrast to most other families of iron-based superconductors. There, both the magnetic order of the parent compounds and the magnetic fluctuations in the superconducting state have the same momentum Q_SF, which is taken as a strong argument in favor of spin-fluctuation induced superconductivity. Here, we model iron-chalcogenides as a system of itinerant electrons coupled to localized electrons responsible for the double stripe magnetism. We study the feedback of this unusual magnetic order on the itinerant spin excitations at Q_SF and show that they increase with decreasing magnetism. We make connection to recent INS experiments and reproduce qualitatively the behavior of magnetic excitations in FeTe_1-xSe_x from x=0 towards x=0.4.