Electronic structure study of vanadium spinels by using density functional theory and dynamical mean field theory

Theoretically, various physical properties of AV$_{2}$O$_{4}$ (A=Zn, Cd and Mg) spinels have been extensively studied for last 15 years. Besides of this, no systematic comparative study has been done for these compounds, where the material specific parameters are used. Here, we report the comparative electronic behaviour of these spinels by using a combination of density functional theory and dynamical mean-field theory, where the self-consistent calculated Coulomb interaction $U$ and Hund's coupling $J$ (determined by Yukawa screening $\lambda$) are used. The main features, such as insulating band gaps ($E_{g}$), degree of itinerancy of V 3$d$ electrons and position of lower Hubbard band are observed for these parameters in these spinels. The calculated values of $E_{g}$ for ZnV$_{2}$O$_{4}$, CdV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$ are found to be $\sim$0.9 eV, $\sim$0.95 eV and $\sim$1.15 eV, respectively, where the values of $E_{g}$ are close to experiment for ZnV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$. The position of lower Hubbard band are observed around $\sim$-1.05 eV, $\sim$-1.25 eV and $\sim$-1.15 eV for ZnV$_{2}$O$_{4}$, CdV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$, respectively, which are also in good agreement with the experimental data for ZnV$_{2}$O$_{4}$. The order of average impurity hybridization function of V site are found to be ZnV$_{2}$O$_{4}$$>$MgV$_{2}$O$_{4}$$>$CdV$_{2}$O$_{4}$. Hence, the degree of localization of V 3$d$ electrons is largest for CdV$_{2}$O$_{4}$ and smallest for ZnV$_{2}$O$_{4}$, which is in accordance with our earlier results. Hence, present work shows the importance of material specific parameters to understand the comparative electronic behaviour of these compounds.