Magnetic Order in Transition Metal Oxides with Orbital Degrees of Freedom

We investigate the frustrated magnetic interactions in cubic transition metal oxides with orbital degeneracy. The $e_g$ orbitals order easier and their ordering explains the $A$-type antiferromagnetic phase in KCuF${}_3$ and LaMnO${}_3$. In $t_{2g}$ systems the magnetic order changes at a transition from an orbital liquid to orbital ordered states. The fluctuations of $t_{2g}$ orbitals play a prominent role in LaVO${}_3$ and YVO${}_3$, where they compete with the Jahn-Teller effect and trigger the C-type antiferromagnetic order.