Understanding the role of Hubbard corrections in the rhombohedral phase of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>BaTiO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>

Abstract

We present a first-principles study of the low-temperature rhombohedral phase of ${\mathrm{BaTiO}}_{3}$ using Hubbard-corrected density-functional theory. By employing density-functional perturbation theory, we compute the onsite Hubbard $U$ for $\mathrm{Ti}(3d)$ states and the intersite Hubbard $V$ between $\mathrm{Ti}(3d)$ and $\mathrm{O}(2p)$ states. We show that applying the onsite Hubbard $U$ correction alone to $\mathrm{Ti}(3d)$ states proves detrimental, as it suppresses the $\mathrm{Ti}(3d)--\mathrm{O}(2p)$ hybridization and drives the system towards a cubic phase. Conversely, when both onsite $U$ and intersite $V$ are considered, the localized character of the $\mathrm{Ti}(3d)$ states is maintained, while also preserving the $\mathrm{Ti}(3d)--\mathrm{O}(2p)$ hybridization, restoring the rhombohedral phase of ${\mathrm{BaTiO}}_{3}$. The generalized $\text{PBEsol}+U+V$ 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 $\text{PBEsol}+U+V$ provide satisfactory agreement with the experimental Raman spectrum when the PBEsol geometry is used, while $\mathrm{PBEsol}\text{+}U$ Raman spectrum diverges strongly from experimental data highlighting the adverse impact of the $U$ correction alone in ${\mathrm{BaTiO}}_{3}$. Our findings underscore the promise of the extended Hubbard $\text{PBEsol}+U+V$ functional with first-principles $U$ and $V$ for the investigation of other ferroelectric perovskites with mixed ionic-covalent interactions.

Topics & Concepts