Polarization Dependence of Born Effective Charge and Dielectric Constant in KNbO$_3$

TL;DR

This study investigates how the Born effective charge and dielectric constant in KNbO₃ vary significantly with atomic structure across different phases, using ab initio calculations to reveal their sensitivity to atomic geometry and phase transitions.

Contribution

It provides detailed ab initio calculations of Z^{*} and psilon_{ty} across cubic, tetragonal, and rhombohedral phases, highlighting their dependence on atomic geometry and phase stability.

Findings

Z^{*} and psilon_{ty} vary by up to 27% and 50% respectively across phases.

All zone center phonon modes are stable in the rhombohedral phase, matching experimental data.

Soft mode stabilization occurs in the tetragonal phase, indicating phase transition effects.

Abstract

The Born effective charge Z^{*} and dielectric tensor \epsilon_{\infty} of KNbO_3 are found to be very sensitive to the atomic geometry, changing by as much as 27% between the paraelectric cubic and ferroelectric tetragonal and rhombohedral phases. Subtracting the bare ionic contribution reveals changes of the dynamic component of Z^{*} as large as 50%, for atomic displacements that are typically only a few percent of the lattice constant. Z^{*}, \epsilon_{\infty} and all phonon frequencies at the Brillouin zone center were calculated using the {\it ab initio} linearized augmented plane-wave linear response method with respect to the reference cubic, experimental tetragonal, and theoretically determined rhombohedral ground state structures. The ground state rhombohedral structure of KNbO_3 was determined by minimizing the forces on the relaxed atoms. By contrast with the cubic structure, all zone center phonon modes of the rhombohedral structure are stable and their frequencies are in good agreement with experiment. In the tetragonal phase, one of the soft zone center modes in the cubic phase is stablized. In view of the small atomic displacements involved in the ferroelectric transitions, it is evident that not only the soft mode frequencies but also the Born effective charge and dielectric constants are very sensitive to the atomic geometry.