In modern solid-state physics, it is common to classify systems according to the kind of degrees of freedom they have available, like electron (metals) or spin (magnetism). In crystals that can display the JTE, and before this effect is realised by symmetry-breaking distortions, it is found that there exists an orbital degree of freedom consisting of how electrons occupy the local degenerate orbitals. As initially discussed by Kugel and Khomskii, not all configurations are equivalent. The key is the relative orientation of these occupied orbital, in the same way that spin orientation is important in magnetic systems, and the ground state can only be realised for some particular orbital pattern. Both this pattern and the effect giving rise to this phenomenon is usually denominated orbital-ordering.
In order to predict the orbital-ordering pattern, Kugel and Khomskii used a particularisation of the Hubbard model. In particular they established how superexchange interactions, usually described by the Anderson–Kanamori–Goodenough rules, change in the presence of degenerate orbitals. Their model, using a pseudospin representation for the local orbitals, leads to a Heisenberg-like model in which the ground state is a combination of orbital and spin patterns. Using this model it can be shown, for example, that the origin of the unusual ground insulating ferromagnetic state of a solid like KCuF can be traced to its orbital ordering.
Even when starting from a relatively high-symmetry structure the combined effect of exchange interactions, spin–orbit coupling, orbital-ordering and crystal deformations activated by the JTE can lead to very low symmetry magnetic patterns with specific properties. For example, in CsCuCl an incommensurable helicoidal pattern appears both for the orbitals and the distortions along the -axis. Moreover, many of these compounds show complex phase diagrams when varying temperature or pressure.