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 ($n\mathrm{\ne }1\mathrm{/}2$) the system is unstable with respect to phase separation into charge ordered regions with $n=1\mathrm{/}2$ 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.