Self-consistent evaluation of effective Coulomb interaction U and its utilization to understand the degree of localization of electrons in vanadium spinels

In present work, we try to understand the degree of localization of electrons in AV2O4 (A = Zn, Cd and Mg) compounds by using self-consistent calculated effective Coulomb interaction (Ueff) between localized electrons of V atom. The suitable values of d-linearization energy (Ed) of impurity V atom for calculating the Ueff for these compounds are found to be ≥44eV above the Fermi level. Corresponding to these values of Ed, the self-consistently calculated values of effective ULSDA (UPBEsol) for ZnV2O4, MgV2O4 and CdV2O4 are ∼5.7 (∼5.9), ∼6.0 (∼6.2) and ∼5.6 (∼5.7) eV, respectively. The calculated values of tUeff (t is the transfer integral between neighboring sites) increases with decreasing V-V distance from CdV2O4 to MgV2O4 to ZnV2O4, which are consistent with the experimentally reported band gap. The tUeff for ZnV2O4, MgV2O4 and CdV2O4 are found to be ∼0.023, ∼0.02 and ∼0.018, respectively, which indicates that the degree of localization of electrons is largest for CdV2O4 and smallest for ZnV2O4 as compared to MgV2O4. The calculated values of lattice parameters aLSDA (aPBEsol) are found to be ∼1.7% (∼0.6%), ∼2.0% (∼0.7%) and ∼2.4% (∼0.7%) smaller than aexp for CdV2O4, MgV2O4 and ZnV2O4, respectively, which indicates that the PBEsol functional predicts the lattice parameters in good agreement with the experimental data. The present study shows the importance of Ueff in understanding the degree of localization of electrons in these compounds.