TiOCl, an orbital-ordered system?

We present first principles density functional calculations and downfolding studies of the electronic and magnetic properties of the layered quantum spin system TiOCl. We discuss explicitely the nature of the exchange pathes and attempt to clarify the concept of orbital ordering in this material. An analysis of the electronic structure of slightly distorted structures according to the phononic modes allowed in this material suggests that this system is subject to large orbital fluctuations driven by the electron-phonon coupling. Based on these results, we propose a microscopic explanation of the behavior of TiOCl near the phase transition to a spin-gapped system.