In view of recent controversy regarding the orbital order in the frustrated spinel ${\mathrm{ZnV}}_2{\mathrm{O}}_4$, we analyze the orbital and magnetic ground state of this system within an ab initio density functional theory approach. While $\mathrm{\text{local density approximation}}+\mathrm{\text{Hubbard}}U$ calculations in the presence of a cooperative Jahn-Teller distortion stabilize an $A$-type staggered orbital order, the consideration of relativistic spin-orbit (SO) effects unquenches the orbital moment and leads to a uniform orbital order with a net magnetic moment close to the experimental one. Our results show that ab initio calculations are able to resolve the existing discrepancies in previous theories and that it is the SO coupling along with electronic correlations which play a significant role in determining the orbital structure in these materials.

• Received 22 January 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.126401