Orbital Ordering and Orbital Fluctuations in Transition Metal Oxides

We summarize some characteristic features of the frustrated magnetic interactions in spin-orbital models adequate for cubic transition metal oxides with orbital degeneracy. A generic tendency towards dimerization, found already in the degenerate Hubbard model, is confirmed for $t_{2g}$ but not for $e_g$ systems. In the $t_{2g}$ case the quantum orbital fluctuations are more pronounced and contribute to a stronger competition between different magnetic and orbital states. Therefore the orbital liquid states exist in some undoped $t_{2g}$ systems, while in the manganites such states can be triggered only by doping.