Commensurate and incommensurate charge ordering in Perovskite manganites

Commensurate and incommensurate charge ordering in La1-xCaxMnO3 are investigated by high resolution electron microscopy at low temperatures. Commensurability of charge ordering is mainly determined by the doped charge carrier concentration x. Commensurate charge ordering arises due to periodic array of pairs of the Jahn-Teller distorted Mn3+O6 stripes. The discrete nature of the charge ordering gives rise to a few distinct commensurate periodicities of 2, 3, 4, and 5 time the lattice parameter a, of the orthorhombic cell, which correspond to the commensurate carrier concentrations for x = 1/2, 2/3, 3/4, and 4/5, respectively. An incommensurate charge ordered state with arbitrary carrier concentration occurs as a result of the fine random mixtures of the two adjacent commensurate configurations according to the lever rule.