Phase separation in systems with charge ordering
  A simple model of charge ordering is considered. It is shown explicitly that at any deviation from half-filling ($n \neq 1/2$) the system is unstable with respect to phase separation into charge ordered regions with $n = 1/2$ and metallic regions with smaller electron or hole density. Possible structure of this phase-separated state (metallic droplets in a charge-ordered matrix)is discussed. The model is extended to account for the strong Hund-rule onsite coupling and the weaker intersite antiferromagnetic exchange. An analysis of this extended model allows us to determine the magnetic structure of the phase-separated state and to reveal the characteristic features of manganites and other substances with charge ordering. 
M.Yu. Kagan (1), K.I. Kugel (2), and D.I. Khomskii (3)((1) P.L.   Kapitza Institute for Physical Problems, Moscow, Russia, (...