Classical frustration and quantum disorder in spin-orbital models

Recently much attention is paid to the role of the orbital degrees of freedom in transition metal oxides as it remains unclear whether they can remain in a quantum disordered state at zero temperature. Discrete symmetry of the orbital sector counteracts the quantum melting, but especially in doped systems there are signs of dynamical frustration involving the spin-, charge-, and orbital sector simultaneously. It was discovered that even the simple Kugel–Khomskii (KK) model, describing eg degenerate Mott-insulators, is characterized by a point of perfect dynamical frustration on the classical level, reached in the absence of Hund’s rule and electron–phonon couplings. This frustration is lifted on the quantum level, and the true nature of the ground state is still unknown. At present there are two proposals: the KCuF3 phase, stabilized by an order-out-of-disorder mechanism; or spin orbital valence bond phases. It will be argued that at least in the Cu-based systems of this kind, the electron–phonon coupling is primarily responsible for driving the systems away from the special point in the phase diagram.