# Effects of the Hubbard U on density functional-based predictions of BiFeO$_3$ properties

## TL;DR

This study systematically examines how the Hubbard U parameter influences the structural, ferroelectric, and electronic properties of BiFeO$_3$, highlighting significant effects on electronic structure and recommending a U value of at most 4 eV for accurate predictions.

## Contribution

The paper provides a comprehensive analysis of the impact of the U parameter on BiFeO$_3$, emphasizing the importance of systematic U selection for electronic structure accuracy.

## Key findings

- Structural and ferroelectric properties are minimally affected by U in the typical range.
- Electronic structure shows significant U-dependent changes, including band gap increase.
- Inversion of $t_{2g}$/$e_{g}$ ordering occurs for U > 4 eV.

## Abstract

First principles studies of multiferroic materials, such as bismuth ferrite (BFO), require methods that extend beyond standard density functional theory (DFT). The DFT+U method is one such extension that is widely used in the study of BFO. We present a systematic study of the effects of the U parameter on the structural, ferroelectric and electronic properties of BFO. We find that the structural and ferroelectric properties change negligibly in the range of U typically considered for BFO (3-5 eV). In contrast, the electronic structure varies significantly with U. In particular, we see large changes to the character and curvature of the valence band maximum and conduction band minimum, in addition to the expected increase in band gap, as U increases. Most significantly, we find that the $t_{2g}$/$e_{g}$ ordering, expected from crystal field theory, is inverted for U values larger than 4 eV. We therefore recommend a U value of at most 4 eV to be applied to the Fe $d$ orbitals in BFO. More generally, this study emphasises the need for systematic investigations of the effects of the U parameter not merely on band gaps but on the electronic structure as a whole, especially for strongly correlated materials.