Phase separation in doped systems with spin-state transitions

Spin-state transitions, observed in many transition-metal compounds containing Co³⁺ and Fe²⁺, may occur with the change in temperature and pressure but also with doping, in which case the competition of single-site effects and kinetic energy of doped carriers can favor a change in the spin state. We consider this situation in a simple model, formally resembling that used for manganites in Kugel, Rakhmanov, and Sboychakov, Phys. Rev. Lett. 95, 267210 (2005). Based on such a model, we predict the possibility of a jumplike change in the number of Co³⁺ ions undergoing spin-state transition caused by hole doping. A tendency to the electronic phase separation within a wide doping range is demonstrated. Phase diagrams with the regions of phase separation are constructed at different values of the characteristic parameters of the model.