Ab initio functional-independent calculations of the clamped Pockels tensor of tetragonal barium titanate

TL;DR

This paper introduces an ab initio method to calculate the Pockels tensor of ferroelectric materials, allowing for functional-independent results and accurate predictions of electro-optical properties in tetragonal barium titanate.

Contribution

The authors develop a novel, functional-independent computational approach to determine the Pockels tensor, enabling analysis beyond LDA and addressing phonon mode stabilization issues.

Findings

Successfully calculated the Pockels tensor of BTO beyond LDA.

Revealed the dependence of $r_{51}$ on titanium off-centering.

Validated the method's ability to recover experimental Pockels coefficients.

Abstract

We present an ab initio method to calculate the clamped Pockels tensor of ferroelectric materials from density-functional theory, the modern theory of polarization exploiting the electric-enthalpy functional, and automated first- and second-order finite-difference derivatives of the polarizations and the Hellmann-Feynman forces. Thanks to the functional-independent capabilities of our approach, we can determine the Pockels tensor of tetragonal barium titanate (BTO) beyond the local density approximation (LDA), with arbitrary exchange-correlation (XC) functionals, for example, PBEsol. The latter, together with RRKJ ultra-soft pseudo-potentials (PP) and a supercell exhibiting local titanium off-centering, enables us to stabilize the negative optical phonon modes encountered in tetragonal BTO when LDA and norm-conserving PP are combined. As a result, the correct value range of $r_{51}$, the largest experimental Pockels coefficient of BTO, is recovered. We also reveal that $r_{51}$ increases with decreasing titanium off-centering for this material. The lessons learned from the structural, dielectric, and vibrational investigations of BTO will be essential to design next-generation electro-optical modulators based on the Pockels effect.