unit cell of a spinel. In an [$\textrm{A}\textrm{B}_2\textrm{O}_4$]{} spinel, the A metal ions are in a tetrahedral $\textrm{AO}_4$ environment that constitutes a diamond lattice, the B metal ions form edge-sharing $\textrm{BO}_6$ octahedra arranged in a pyrochlore lattice. ](spinel){width="1\columnwidth"}

In spinel vanadates – [$\textrm{A}^{2+}\textrm{V}^{3+}_2\textrm{O}^{2-}_4$]{} – the vanadium ion is situated in a octahedral environment surrounded by oxygen ions. The crystal field of the oxygen ions splits the fivefold degenerate $d$ orbitals into $e_g$ and the $t_{2g}$ states with the $e_g$ orbitals lying higher than the $t_{2g}$ orbitals. The vanadium ions possess two $3d$ electrons that are distributed over the three degenerate $t_{2g}$ orbitals, namely $d_{xy}$, $d_{xz}$, and $d_{yz}$. This distribution of electrons results in one hole which can occupy any of the three degenerate $t_{2g}$ orbitals resulting in a three-fold orbital degeneracy. This orbital occupancy introduces an additional spin-orbit coupling term to the Hamiltonian. [@McClure59:9; @Abragam:book]

Because of the cooperative Jahn-Teller effect [@Kaplan:book; @Gehring1975] for materials with an orbital degeneracy, a structural phase transition accompanied by orbital ordering [@Radaelli2005; @Pandy11] sets in for [[$\textrm{Mg}\textrm{V}_2\textrm{O}_4$]{}]{} below a temperature $T_{OO}$. For $T < T_{OO}$ one of the crystallographic axes – which is conventionally taken along $c$ – compresses with $c/a=0.9941 <1$, lowering the 