  Iron telluride (FeTe), a relative of the iron based high temperature
superconductors, displays unusual magnetic order and structural transitions.
Here we explore the idea that strong correlations may play an important role in
these materials. We argue that the unusual orders observed in FeTe can be
understood from a picture of correlated local moments with orbital degeneracy,
coupled to a small density of itinerant electrons. A component of the
structural transition is attributed to orbital, rather than magnetic ordering,
introducing a strongly anisotropic character to the system along the diagonal
directions of the iron lattice. Double exchange interactions couple the
diagonal chains leading to the observed ordering wavevector. The incommensurate
order in samples with excess iron arises from electron doping in this scenario.
The strong anisotropy of physical properties in the ordered phase should be
detectable by transport in single domains. Predictions for ARPES, inelastic
neutron scattering and hole/electron doping studies are also made.
