Separating different contributions to the crystal-field parameters using Wannier functions

Abstract

We discuss the calculation of crystal-field splittings using Wannier functions and show how contributions to the crystal-field splitting that are due to hybridization with different ligand states can be separated from the bare Coulomb contribution by constructing sets of Wannier functions incorporating different levels of hybridization. We demonstrate this method using SrVO3 as a generic example of a transition metal oxide. We then calculate trends in the crystal-field splitting for two series of hypothetical tetragonally distorted perovskite oxides and discuss the relation between the calculated 'electrostatic' contribution to the crystal field and the simple point charge model. Finally, we apply our method to the charge disproportionated 5d electron system CsAuCl3. The proposed procedure elucidates the way in which the negative charge transfer energy in this material leads to a reversal of the p-d ligand contribution to the crystal-field splitting such that the eg states of the nominally Au(3+) cation are energetically lower than the corresponding t2g states.

Crystal field, ligand field, and interorbital effects in two-dimensional transition metal dichalcogenides across the periodic table

“…In Ref. [20], it was suggested to use this freedom to estimate different contributions to the ligand field splitting of a given set of orbitals. For instance, if one is interested in the splitting of the valence d orbitals of…”

“…Indeed, the on-site energies of some of the d WFs are shifted upward in energy compared to the spd model, as we summarize in Table II. The differences of on-site energies between the spd and pd models can be interpreted as the hybridization energy between s and d orbitals [20].…”

Pressure induced Lifshitz transition and anomalous crystal field splitting in AFeAs (A=Li/Na) Fe-based superconducting compounds: A first principles study

“…Bloch states in the periodic solids are characterized by a band index m and a wave vector k in the first Brillouin zone (FBZ). The many body Hamiltonian is diagonal in this basis [33]:…”

“…Using this feature we can construct three different sets of Wannier functions (TB models) corresponding to : (i) 'd-model'-only effective Fe-d orbitals, (ii) 'dp-model' containing Fe-d orbitals and Asp orbitals, and (iii) 'dps-model' containing Fe-d orbitals, As-p orbitals, Li/Na-s orbitals. The onsite energy difference, obtained using different orbital projections, can be interpreted as decomposition of the total crystal field splitting [33].…”

“…Hydrostatic pressure can further modify this degree of hybridization, hence the corresponding crystal field splitting. Therefore, we have employed the maximally localized Wannier function (MLWF) formalism to analyze the effect of d − p hy-bridization due to applied pressure on crystal field splitting [33,34].…”