Ab Initio bulk free energy surface of proper ferroelectrics

TL;DR

This paper introduces a systematic first-principles method using metadynamics and molecular dynamics to accurately derive the bulk free energy surface of proper ferroelectrics, exemplified by lead titanate.

Contribution

It presents a novel approach combining DFT, metadynamics, and all-atom MD to compute the free energy surface without prior assumptions.

Findings

Errors are systematically controlled and are around 1meV/atom.

The method accurately captures phase transition behavior.

The accuracy depends primarily on the DFT functional used.

Abstract

We report a systematic and accurate approach for deriving the bulk free energy surface (FES), a function of temperature, polarization, and strain, from the first-principles density functional theory (DFT) of proper ferroelectrics. The core of our approach is the metadynamics algorithm that extracts the polarization dependence of the FES from all-atom molecular dynamics simulations without an a priori ansatz. The rest of the FES is derived from the metadynamics trajectories that span the relevant phase space. We demonstrate our approach in the case of lead titanate. The errors across the phase transition, due to DFT numerics, all-atom molecular dynamics, and free energy evaluation by enhanced sampling, can be systematically controlled and are of the order of 1meV/atom. The accuracy of the resulting ab initio FES is only limited by the adopted functional approximation of DFT.