Electronic structure, magnetism and exchange integrals in transition metal oxides: role of the spin polarization of the functional in DFT+$U$ calculations

TL;DR

This study examines how the choice of spin polarization in DFT+$U$ calculations affects the accuracy of magnetic exchange interactions in transition metal oxides, highlighting the superiority of LDA+$U$ over LSDA+$U$ for this purpose.

Contribution

It systematically compares LDA+$U$ and LSDA+$U$ methods, revealing that LDA+$U$ provides more consistent exchange interactions and better aligns with the Heisenberg model.

Findings

LDA+$U$ yields more consistent exchange constants than LSDA+$U$.

Band gap dependence on magnetic configuration is stronger in LDA+$U$.

LDA+$U$ shows better agreement with the Heisenberg model.

Abstract

Density functional theory augmented with Hubbard-$U$ corrections (DFT+$U$) is currently one of the widely used methods for first-principles electronic structure modeling of insulating transition metal oxides (TMOs). Since $U$ is relatively large compared to band widths, the magnetic excitations in TMOs are expected to be well described by a Heisenberg model. However, in practice the calculated exchange parameters $J_{ij}$ depend on the magnetic configuration from which they are extracted and on the functional used to compute them. In this work we investigate how the spin polarization dependence of the underlying exchange-correlation functional influences the calculated magnetic exchange constants of TMOs. We perform a systematic study of the predictions of calculations based on the local density approximation plus $U$ (LDA+$U$) and the local spin density approximation plus $U$ (LSDA+$U$) for the electronic structures, total energies and magnetic exchange interactions $J_{ij}$'s extracted from ferromagnetic (FM) and antiferromagnetic (AFM) configurations of several transition metal oxide materials. We report that, for realistic choices of Hubbard $U$ and Hund's $J$ parameters, LSDA+$U$ and LDA+$U$ calculations result in different values of the magnetic exchange constants and band gap. The dependence of the band gap on the magnetic configuration is stronger in LDA+$U$ than in LSDA+$U$ and we argue that this is the main reason why the configuration dependence of the $J_{ij}$'s is found to be systematically more pronounced in LDA+$U$ than in LSDA+$U$ calculations. We report a very good correspondence between the computed total energies and the parameterized Heisenberg model for LDA+$U$ calculations, but not for LSDA+$U$, suggesting that LDA+$U$ is a more appropriate method for estimating exchange interactions.