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In the present work, we investigate the applicability of the LSDA+$U$ methodin understanding the electronic and magnetic properties of a geometricallyfrustrated ZnV$_2$O$_4$ compound, where the delicate balance of electrons,lattice, orbital and spin interactions play an important role in deciding itsphysical properties. In the ferromagnetic solution of the compound, only onetype of orbital solution is found to exist in all ranges of $U$ studied here.However, in antiferromagnetic (AFM) phase, two types of orbital solutions,AFM(OS1) and AFM(OS2), exist for $U >$3 eV. If the difference of the electronicoccupancy of $d_{xz}$ and $d_{yz}$ orbitals is less than 0.25, then AFM(OS1)solution is stabilized, whereas for higher values AFM(OS2) solution isstabilized. The use of unconstrained calculations within the fully localizeddouble counting scheme is unable to predict the AFM ground state for $U\leqslant$3 eV. Our results clearly suggest the importance of constrainedcalculations in understanding the electronic and magnetic properties of acompound, where various competing interactions are present. In the AFMsolution, the orbital ground state of the compound changes with varying $U$,where AFM(OS1) is found to be the ground state for $U \leqslant$3 eV and forhigher values of $U$, AFM(OS2) is the ground state. The analysis of the bandgap suggests that the AFM(OS2) is the real ground state of the compound.

journal of magnetism and magnetic materials

Limitations of unconstrained LSDA+$U$ calculations in predicting the  electronic and magnetic ground state of a geometrically frustrated  ZnV$_{2}$O$_{4}$ compound