Doping-induced metallicity and coexistence of magnetic subsystems in K2Fe4+xSe5

► We theoretically analyze the electronic and magnetic properties in K2Fe4+xSe5. ► The magnetic structure may be viewed as having two nearly independent subsystems. ► This may explain how superconductivity and strong antiferromagnetism can coexist. ► Spin fluctuations of the impurity subsystem share key features with the Fe-pnictides.