Self-consistent evaluation of effective Coulomb interaction of V atom and its importance to understand the comparative electronic behaviour of vanadium spinels

TL;DR

This study computes the effective Coulomb interaction for vanadium atoms in spinel compounds to better understand their electronic behavior, revealing the regimes of electron localization and the accuracy of lattice parameter predictions.

Contribution

It provides a self-consistent evaluation of the effective Coulomb interaction ($U_{ef}$) in vanadium spinels, linking $t/U_{ef}$ ratios to electron localization and validating PBEsol lattice predictions.

Findings

$U_{ef}$ values are around 5.6-6.2 eV for the compounds.

$rac{t}{U_{ef}}$ ratios indicate localized electrons in CdV$_{2}$O$_{4}$.

PBEsol functional predicts lattice parameters within 2.4% of experimental data.

Abstract

In present work, we try to understand the importance of effective Coulomb interaction ($U_{ef}$) between localized electrons of V atom to understand the comparative electronic behaviour of AV$_{2}$O$_{4}$ (A=Zn, Cd and Mg) compounds. The suitable values of $d$-linearization energy ($E_{d}$) of impurity V atom for calculating the $U_{ef}$ for these compounds are found to be $\geq$44.89 eV above the Fermi level. Corresponding to these values of $E_{d}$, the self-consistently calculated values of effective $U_{LSDA}$ ($U_{PBEsol}$) for ZnV$_{2}$O$_{4}$, MgV$_{2}$O$_{4}$ and CdV$_{2}$O$_{4}$ are $\sim$5.73 ($\sim$5.92), $\sim$6.06 ($\sim$6.22) and $\sim$5.59 ($\sim$5.71) eV, respectively. The calculated values of $\frac{t}{U_{ef}}$ ($t$ is the transfer integral between neighbouring sites) increases with decreasing V-V distance from CdV$_{2}$O$_{4}$ to MgV$_{2}$O$_{4}$ to ZnV$_{2}$O$_{4}$ and are found to be consistent with experimentally reported band gap. The values of $\frac{t}{U_{ef}}$ for ZnV$_{2}$O$_{4}$, MgV$_{2}$O$_{4}$ and CdV$_{2}$O$_{4}$ are found to be $\sim$0.023, $\sim$0.020 and $\sim$0.018, respectively. Hence, CdV$_{2}$O$_{4}$ with small (large) $\frac{t}{U_{ef}}$ (experimental band gap) as compared to ZnV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$ is found to be in localized-electron regime, while ZnV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$ are intermediate between localized and an itinerant-electron regime. The calculated values of lattice parameters $a_{LSDS}$ ($a_{PBEsol}$) are found to be $\sim$1.7\%, $\sim$2.0\% and $\sim$2.4\% ($\sim$0.6\%, $\sim$0.7\% and $\sim$0.7\%) smaller than $a_{exp}$ for CdV$_{2}$O$_{4}$, MgV$_{2}$O$_{4}$ and ZnV$_{2}$O$_{4}$, respectively, which indicates that the PBEsol functional predicts the lattice parameters in good agreement with the experimental data.