lattice. Because this theory has been found to predict a symmetry for the structural lattice which is incompatible with measurements [@Wheeler10], a different model was devised by O. Tchernyshyov [@Tcherny04], treating the spin-orbit interaction to be dominating, followed by the Jahn-Teller, and – on the weakest scale – the Kugel-Khomskii interaction. It predicts an orbital ordering where one of the electrons on each vanadium ion occupies a complex superposition of $d_{xz}$ and $d_{yz}$. For both models [@Tsunetsugu03; @Tcherny04], the spin of the vanadium electron in the $d_{xy}$ orbital orders antiferromagnetically along chains in the $\left[110\right]$ and $\left[1\overline{1}0\right]$ directions on the pyrochlore lattice. In the $bc$ and $ac$ planes, an up-up-down-down spin pattern forms below the Néel temperature $T_N < T_{OO}$. The magnetic moments point along the $c$ axis of the crystal and a strong (weak) magnetic coupling is obtained for perpendicular (parallel) chains. In the model by Tchernyshyov [@Tcherny04], geometric frustration of the spins in the perpendicular chains on the pyrochlore lattice gives rise to two (plus two time-reversed) degenerate ground states.

Neutron inelastic scattering and diffraction experiments by Wheeler *et al.* [@Wheeler10] found a mixture of both of these models, a real and a complex superposition of the $d_{xz}$ 