Charge and orbital ordering in transition metal oxides

Transition metal oxides with strongly correlated d-electrons show an astonishing variety of properties. This is largely determined by an interplay of different degrees of freedom: charge, spin, orbital, lattice ones. Often there appear in them various superstructures. In this talk I will consider different types of superstructures in transition metal oxides, especially charge and orbital ordering, willdiscuss the main mechanisms leading to their formation and consider specific examples of superstructures in manganites, cobaltites and in some frustrated systems. Relative role of purely electronic mechanisms and of the electron-phonon interaction will be discussed. In particular, I will show that the elastic interactions can naturally lead to different superstructures, including stripes. Special features of charge and, especially, orbital ordering in frustrated systems, where frustrations may be caused both by the geometric structure of the lattice and by the special features of orbital interactions, will be considered, and it will be shown that the order-from-disorder mechanism can lead to a unique ordered ground state in many of these cases..