Hubbard U and Hund's Exchange J in Transition Metal Oxides: Screening vs. Localization Trends from Constrained Random Phase Approximation

TL;DR

This paper calculates the effective Coulomb interactions in transition metal oxides using constrained RPA, revealing how screening and localization trends vary with model choice and across different series of compounds.

Contribution

It implements cRPA within a LAPW framework and compares two low-energy Hamiltonians, showing how U and J depend on the model and material series.

Findings

U decreases along the 3d series due to screening

U is larger in 4d oxides compared to 3d for the t2g model

Trends depend on the choice of low-energy Hamiltonian

Abstract

In this work, we address the question of calculating the local effective Coulomb interaction matrix in materials with strong electronic Coulomb interactions from first principles. To this purpose, we implement the constrained random phase approximation (cRPA) into a density functional code within the linearized augmented plane wave (LAPW) framework. We apply our approach to the 3d and 4d early transition metal oxides SrMO3 (M=V, Cr, Mn) and (M=Nb, Mo, Tc) in their paramagnetic phases. For these systems, we explicitly assess the differences between two physically motivated low-energy Hamiltonians: The first is the three-orbital model comprising the t2g states only, that is often used for early transition metal oxides. The second choice is a model where both, metal d- and oxygen p-states are retained in the construction of Wannier functions, but the Hubbard interactions are applied to the d-states only ("d-dp Hamiltonian"). Interestingly, since -- for a given compound -- both U and J depend on the choice of the model, so do their trends within a family of these compounds. In the 3d perovskite series SrMO3 the effective Coulomb interactions in the t2g Hamiltonian decrease along the series, due to the more efficient screening. The inverse -- generally expected -- trend, increasing interactions with increasing atomic number, is however recovered within the more localized "d-dp Hamiltonian". Similar conclusions are established in the layered 4d perovskites series Sr2MO4 (M=Mo, Tc, Ru, Rh). Compared to their isoelectronic and isostructural 3d analogues, the 4d 113 perovskite oxides SrMO3 (M=Nb, Mo, Tc) exhibit weaker screening effects. Interestingly, this leads to an effectively larger U on 4d shells than on 3d when a t2g model is constructed.