Orbital order and fluctuations in Mott insulators

Basic mechanisms controlling orbital order and orbital fluctuations in transition metal oxides are discussed. The lattice driven classical orbital picture, e.g. like in manganites LaMnO3, is contrasted to the quantum behavior of orbitals in frustrated superexchange models as realised in pseudocubic titanites ATiO3 and vanadates AVO3. In YVO3, the lattice and superexchange effects strongly compete - this explains the extreme sensitivity of magnetic states to temperature and doping. Lifting the t2g orbital degeneracy by a relativistic spin-orbital coupling is considered on example of the layered cobaltates. We find that the spin-orbital mixing of low-energy states leads to unusual magnetic correlations in a triangular lattice of the CoO2 parent compound. Finally, the magnetism of sodium-rich compounds Na1-xCoO2 is discussed in terms of a spin/orbital polaronic liquid. (author)