Construction of First Principle Based Adiabatic and Diabatic Hamiltonian for TiO$_6^{8-}$ unit of BaTiO$_3$ Crystal: Photoemission Spectra and Ferroelectricity

TL;DR

This paper develops a first-principles method to construct adiabatic and diabatic Hamiltonians for the TiO$_6^{8-}$ unit in BaTiO$_3$, linking electronic structure, photoemission spectra, and ferroelectricity.

Contribution

It introduces a novel ab initio approach to compute PESs and NACTs for the TiO$_6^{8-}$ unit, advancing understanding of ferroelectricity in BaTiO$_3$.

Findings

Theoretical photoemission spectra match experimental data.

Diabatic PESs reveal key electronic interactions.

Order parameter predictions align with experiments.

Abstract

The ferroelectric property of BaTiO$_3$ crystal arises from the strong Pseudo Jahn-Teller (PJT) interactions between the non-degenerate ground electronic state, $^1A_{1g}$ and the degenerate $^1T_{1u}$ symmetry states through the nuclear distortions of $t_{1u}$ modes in TiO$_6^{8-}$ unit. In a $d^0$ electronic configuration of $Ti^{4+}$ ion, the PJT interaction leads to a stabilization effect, which has been explored using Beyond Born-Oppenheimer (BBO) theory. The $^1T_{1u}$ excited states form a three-state degeneracy, exhibiting feeble Jahn-Teller (JT) distortions over the $t_{2g}$ planes. For the first time, we compute \textit{ab initio} adiabatic potential energy surfaces (PESs) and non-adiabatic coupling terms (NACTs), and thereafter, diabatic PESs and couplings for the perovskite unit, TiO$_6^{8-}$. Using a Time-Dependent Discrete Variable Representation (TDDVR) approach, the theoretical photoemission spectra exhibit good agreement with the experimental ones. Moreover, the experimental observation on order parameter associated with ferroelectric properties of BaTiO$_3$ crystal show close resemblance with present and other theoretical predictions.