Magnetically controlled electron localization in Eu-rich EuO

A calculation of the linear-response properties of an electron gas, coupled by the $s-f$ exchange interaction to a lattice of localized spins is presented. Coupled-charge and spin-density-response functions are determined in the random-phase approximation and used to compute a Mott-type instability of metallic Eu-rich EuO toward formation of magnetic polarons bound to oxygen vacancies. Critical carrier densities are obtained as a function of temperature and phase diagrams of the metallic and insulating states are presented and compared with existing theories and experimental results.