Understanding the role of Hubbard corrections in the rhombohedral phase of BaTiO$_3$

TL;DR

This study demonstrates that including both onsite and intersite Hubbard corrections in density-functional theory accurately captures the rhombohedral phase of BaTiO$_3$, improving agreement with experimental properties and highlighting the importance of intersite interactions.

Contribution

It introduces a first-principles method to compute onsite and intersite Hubbard parameters, showing that combined U and V corrections better preserve the ferroelectric phase of BaTiO$_3$ than onsite U alone.

Findings

Including both U and V maintains Ti 3d–O 2p hybridization.

PBEsol+U+V yields accurate band gap and dielectric constant.

U correction alone suppresses hybridization and favors cubic phase.

Abstract

We present a first-principles study of the low-temperature rhombohedral phase of BaTiO$_3$ using Hubbard-corrected density-functional theory. By employing density-functional perturbation theory, we compute the onsite Hubbard $U$ for Ti($3d$) states and the intersite Hubbard $V$ between Ti($3d$) and O($2p$) states. We show that applying the onsite Hubbard $U$ correction alone to Ti($3d$) states proves detrimental, as it suppresses the Ti($3d$)-O($2p$) hybridization and drives the system towards a cubic phase. Conversely, when both onsite $U$ and intersite $V$ are considered, the localized character of the Ti($3d$) states is maintained, while also preserving the Ti($3d$)-O($2p$) hybridization, restoring the rhombohedral phase of BaTiO$_3$. The generalized PBEsol+$U$+$V$ functional yields good agreement with experimental results for the band gap and dielectric constant, while the optimized geometry is slightly less accurate compared to PBEsol. Zone-center phonon frequencies and Raman spectra are found to be significantly influenced by the underlying geometry. PBEsol and PBEsol+$U$+$V$ provide satisfactory agreement with the experimental Raman spectrum when the PBEsol geometry is used, while PBEsol+$U$ Raman spectrum diverges strongly from experimental data highlighting the adverse impact of the $U$ correction alone in BaTiO$_3$. Our findings underscore the promise of the extended Hubbard PBEsol+$U$+$V$ functional with first-principles $U$ and $V$ for the investigation of other ferroelectric perovskites with mixed ionic-covalent interactions.