Molecular Dynamics Study of Ferroelectric Perovskites based on Effective Hamiltonians: implementation of Nose-Hoover and Parinello-Rahman algorithms

TL;DR

This paper applies molecular dynamics simulations using effective Hamiltonians to study ferroelectric perovskites, implementing Nose-Hoover and Parinello-Rahman algorithms to analyze phase transitions and thermodynamic properties.

Contribution

It introduces the implementation of Nose-Hoover and Parinello-Rahman algorithms within molecular dynamics for ferroelectric perovskites based on first-principles effective Hamiltonians.

Findings

Successfully reproduces Monte Carlo results on phase transitions

Analyzes polarization and strain evolution with temperature

Studies thermodynamics of BaTiO3

Abstract

Molecular Dynamics is applied to Ferroelectric Perovskites in the framework of a first-principles derived effective Hamiltonian (Zhong, Vanderbilt, Rabe, Phys. Rev. Lett. {\bf 73} (1994), 1861). The degrees of freedom, that obey the Newton equations of motion, are the local modes and the displacement modes. The Nose-Hoover method is implemented, as well as the Parinello-Rahman scheme to perform fixed temperature and fixed stress tensor simulations. This allows to study the thermodynamics of ferroelectric perovskites and to reproduce successfully the Monte Carlo results on phase transitions, polarization and homogeneous strain evolution with temperature of BaTiO$_3$, taken as an example.