Unified theory of phase separation and charge ordering in doped manganite perovskites

A unified theory is developed to explain various types of electronic collective behaviors in doped manganites R$_{1-x}$X$_x$MnO$_3$ (R = La, Pr,Nd etc. and X = Ca, Sr, Ba etc.). Starting from a realistic electronic model, we derive an effective Hamiltonianis by ultilizing the projection perturbation techniques and develop a spin-charge-orbital coherent state theory, in which the Jahn-Teller effect and the orbital degeneracy of e$_g$ electrons in Mn ions are taken into account. Physically, the experimentally observed charge ordering state and electronic phase separation are two macroscopic quantum phenomena with opposite physical mechanisms, and their physical origins are elucidated in this theory. Interplay of the Jahn-Teller effect, the lattice distortion as well as the double exchange mechanism leads to different magnetic structures and to different charge ordering patterns and phase separation.