Orbital ordering and frustrations

Orbital ordering occurs in many transition metal compounds with Jahn-Teller ions (Cu2+, Mn3+, low-spin Ni3+, Ti3+ etc). It plays an important role in these materials. At the same time, exchange interactions in orbitally degenerate systems are inherently frustrated, even in materials with simple crystal lattices. We discuss the origin of this frustration, considering in detail materials with cubic and triangular lattices of transition metal ions. We also discuss possible types of ground states of such systems, e.g., disordered orbital liquids and ordering due to the order-from-disorder mechanism.