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The electronic structures of the cubic and tetragonal$\mathrm{MnV}_2\mathrm{O}_4$ have been studied by using hybrid-exchange densityfunctional theory. The computed electronic structure of the tetragonal phaseshows an anti-ferro orbital ordering on V sites and a ferrimagnetic groundstate (the spins on V and Mn are anti-aligned). These results are in a goodagreement with the previous theoretical result obtained from the local-densityapproximation+$U$ methods [S. Sarkar, et. al., Phys. Rev. Lett. 102, 216405(2009)]. Moreover, the electronic structure, especially the projected densityof states of the cubic phase has been predicted with a good agreement with therecent soft x-ray spectroscopy experiment. Similar to the tetragonal phase, thespins on V and Mn in the cubic structure favour a ferrimagnetic configuration.Most interesting is that the computed charge densities of the spin-carryingorbitals on V in the cubic phase show an exotic orbital ordering, i.e., aferro-orbital ordering along [110] but an anti-ferro-orbital ordering along[$\overline{1}$10].

physical review. b, condensed matter and materials physics

A hybrid-exchange density-functional theory study of the electronic  structure of $\mathrm{MnV}_2\mathrm{O}_4$: Exotic orbital ordering in the  cubic structure