Doping-induced metallicity and coexistence of magnetic subsystems in {K$_{2}$Fe$_{4+x}$Se$_{5}$}

Electronic structure calculations are used to analyze the electronic and magnetic properties in {K$_{2}$Fe$_{4+x}$Se$_{5}$}. Fe atoms can be divided into two distinct groups. The $x{=}0$ (parent) compound forms an insulating, collinear, local moment phase with high N{\'{e}}el temperature. We show that large biquadratic exchange coupling and exchange-elastic interactions stabilize the magnetic order. For $x{>}0$ the additional Fe atoms fill vacancy sites. They form impurity bands for small $x$, which broaden as $x$ increases. They determine the states at the Fermi level and may be viewed as a magnetic subsystem separate from the host. Spin fluctuations are prevalent because magnetic interactions between the `defect' and the `parent' atoms are relatively weak, while chemical fluctuations are prevalent for low $x$. Fluctuations of either type leads to the formation of a weakly metallic state. The unusual coexistence of the two magnetic subsystems offers a new perspective as to how superconductivity and strong antiferromagnetism can coexist. We argue that spin fluctuations of the impurity subsystem share common features with the Fe-pnictide superconductors.