Orbital state dependence of insulating manganites' magnetic ordering

In insulating manganites, a semi-empirical model of orbital structure is proposed. The model allows us to account for the non-linear and non-local effects of a crystal structure on the orbital ordering of a trivalent manganese sublattice. This allows the variation of only two parameters for each degenerated manganese ion. They include the main part - the linear vibronic interaction - and additional parts (as long-range Coulomb fields or non-linear vibronic interactions). This is why one can define the orbital structure with respect of the magnetic structure without explicit microscopic definition of the non-linear and non-local terms. The continuous changes to the orbital mixing parameters are important for magnetic structure description. Within the framework of orbitally-dependent superexchange interaction, magnetic structures dependent on orbital orderings are considered. For manganite crystals LaMnO3, BiMnO3, La0.5Ca0.5MnO3, La0.333Ca0.667MnO3, phase diagrams of the orbital and magnetic structures with an unchanged crystal structure are drawn. The role of orbital ordering in frustrated magnetic structures is emphasized. The insufficiency of the linear vibronic approach is shown.