Interplay of charge and orbital ordering in manganese perovskites

A model of localized classical electrons coupled to lattice degrees of freedom and, via the Coulomb interaction, to each other has been studied to gain insight into the charge and orbital ordering observed in lightly doped manganese perovskites. Expressions are obtained for the minimum energy and ionic displacements caused by given hole and electron orbital configurations. The expressions are analyzed for several hole configurations, including that experimentally observed by Yamada et al. [Phys. Rev. Lett. 77, 904 (1996)] in ${\mathrm{La}}_{7/8}{\mathrm{Sr}}_{1/8}{\mathrm{MnO}}_3.$ We find that, although the preferred charge and orbital ordering depend sensitively on parameters, there are ranges of the parameters in which the experimentally observed hole configuration has the lowest energy. For these parameter values we also find that the energy differences between different hole configurations are on the order of the observed charge ordering transition temperature. The effects of additional strains are also studied. Some results for ${\mathrm{La}}_{1/2}{\mathrm{Ca}}_{1/2}{\mathrm{MnO}}_3$ are presented, although our model may not adequately describe this material because the high-temperature phase is metallic.