Magnetism Driven by Anion Vacancies in Superconducting $\alpha$--FeSe$_{1-x}$

To study the microscopic electronic and magnetic interactions in the substoichiometric iron chalcogenide FeSe$_{1-x}$ which is observed to superconduct at x~1/8 up to $T_c$=27 K, we use first principles methods to study the Se vacancy in this nearly magnetic FeSe system. The vacancy forms a ferrimagnetic cluster of eight Fe atoms, which for the ordered x=1/8 alloy leads to half metallic conduction. Similar magnetic clusters are obtained for FeTe$_{1-x}$ and for BaFe$_2$As$_2$ with an As vacancy, although neither of these are half metallic. Based on fixed spin density results, we suggest the low energy excitations in FeSe$_{1-x}$ are antiparamagnon-like with short correlation length.