Effect of covalency and interactions on the trigonal splitting in NaxCoO2

TL;DR

This study investigates how covalency and electron interactions influence the trigonal splitting in NaxCoO2 by calculating the crystal field splitting through a detailed cluster model, revealing sensitivity to Coulomb parameters.

Contribution

The paper introduces a numerical cluster model that accurately computes the trigonal crystal field splitting, highlighting discrepancies with LDA calculations and emphasizing the role of Coulomb interactions.

Findings

Trigonal splitting Delta is approximately 130 meV.

Delta's sign agrees with quantum chemistry but not with LDA.

Splitting is highly sensitive to Coulomb parameters.

Abstract

We calculate the effective trigonal crystal field Delta which splits the t2g levels of effective models for NaxCoO2 as the local symmetry around a Co ion is reduced from Oh to D3d. To this end we solve numerically a CoO6 cluster containing a Co ion with all 3d states and their interactions included, and its six nearest-neighbor O atoms, with the geometry of the system, in which the CoO6 octahedron is compressed along a C3 axis. We obtain Delta near 130 meV, with the sign that agrees with previous quantum chemistry calculations, but disagrees with first-principles results in the local density approximation (LDA). We find that Delta is very sensitive to a Coulomb parameter which controls the Hund coupling and charge distribution among the d orbitals. The origin of the discrepancy with LDA results is discussed.