Frustration in Systems with Orbital Degrees of Freedom

Abstract

We review the types of frustration encountered in Mott insulators with orbital degrees of freedom and discuss the physical consequences. We first survey the driving forces for the ordering of orbital degrees of freedom and then compare the generic features of typical orbital and typical spin Hamiltonians. A primary difference between the two is caused by the sensitivity of orbital interactions to the spatial orientation of the orbitals involved. This leads in general to highly anisotropic orbital Hamiltonians, to frustration of classical ordered states on unfrustrated lattices, and to enhanced quantum fluctuations. As a consequence of these effects, new types of symmetry can appear in orbital models, in particular in compass models. These intermediate symmetries lie midway between the extremes of global symmetries and local gauge symmetries. We discuss briefly the generic consequences of this very particular type of symmetry, and highlight in this context the relation between orbital models and the models of Kitaev for quantum computation. As a final topic, we include spin degrees of freedom into combined spin-orbital models and consider a number of ways in which the orbital frustration in real materials is lifted by the magnetic degrees of freedom. Orbital degrees of freedom boost the tendency to form disordered states or valence-bond phases. Enhanced quantum fluctuations and spin-orbital entanglement occur in the vicinity of quantum critical points, where different types of order compete with each other. Taken together, these phenomena demonstrate that orbital and spin-orbital physics contain a number of unconventional features and peculiar symmetries which are qualitatively different from the range of properties known in pure spin models with frustration, arising either from frustrated geometries or due to longer-range magnetic interactions.