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.