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

Sohan Lal; Sudhir K. Pandey

doi:10.1016/j.physleta.2017.04.026

paper

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

arXiv:1611.02028 · doi:10.1016/j.physleta.2017.04.026

Abstract

In present work, we try to understand the importance of effective Coulomb interaction ( $U_{e f}$ ) 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 $U_{e f}$ 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 $U_{L S D A}$ ( $U_{P B E so l}$ ) 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 $\frac{t}{U _{e f}}$ ( $t$ 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 $\frac{t}{U _{e f}}$ 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) $\frac{t}{U _{e f}}$ (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 $a_{L S D S}$ ( $a_{P B E so l}$ ) 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 $a_{e x p}$ 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.

16 pages, 3 figures, 2 tables

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

Abstract

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