Cubic interaction parameters for t2g Wannier orbitals

TL;DR

This paper calculates the actual cubic interaction parameters for t2g orbitals in transition metal oxides, revealing significant deviations from the commonly assumed spherical symmetry interactions, especially in 5d orbitals.

Contribution

It provides a detailed method to determine cubic interaction parameters for t2g orbitals, highlighting deviations from standard models in real materials.

Findings

Deviations from spherical symmetry are significant in 5d orbitals (~25%)

Deviations are less pronounced in 3d orbitals (~6%)

Screening reduces the deviations in interaction parameters

Abstract

Many-body calculations for multi-orbital systems at present typically employ Slater or Kanamori interactions which implicitly assume a full rotational invariance of the orbitals, whereas the real crystal has a lower symmetry. In cubic symmetry, the low-energy $t_{2g}$ orbitals have an on-site Kanamori interaction, albeit without the constraint $U = U' + 2J$ implied by spherical symmetry ($U$: intra-orbital interaction, $U'$: inter-orbital interaction, $J$: Hund's exchange). Using maximally localized Wannier functions we show that deviations from the standard, spherically symmetric interactions are indeed significant for $5d$ orbitals ($\sim25%$ for BaOsO$_3$ ; $\sim12%$ if screening is included), but less important for $3d$ orbitals ($\sim6\%$ for SrVO$_3$; $\sim1\%$ if screened).