Effect of covalency and interactions on the trigonal splitting in Na x CoO2

Abstract

We calculate the effective trigonal crystal field Delta that splits the t2g levels of effective models for Nax CoO2 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≈ 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 that controls the Hund coupling and charge distribution among the d orbitals. The origin of the discrepancy with LDA results is discussed.