Magnetic interactions in transition metal oxides with orbital degrees of freedom

We review the frustrated magnetic interactions in spin-orbital models which describe superexchange in transition metal oxides with orbital degeneracy, and analyze the reasons for the symmetry breaking in cubic perovskites. The superexchange in e(g) systems is dominated by orbital interactions responsible for the orbital ordering, and the A-type antiferromagnetic ordering follows at lower temperatures. Instead, a generic tendency towards dimerization, found already in the degenerate Hubbard model, occurs in t(2g) systems. In this case the quantum orbital fluctuations may stabilize orbital liquid states along one directions even in some undoped t(2g) systems, leading to the C-type antiferromagnetic order. The orbital liquid in manganites is triggered by doping. The present understanding of the spectroscopic parameters provides reliable information on the magnetic interactions, as shown on the example of magnons in ferromagnetic cubic and bilayer manganites.