Landau free energy of ferroelectric crystals by thermodynamic integration

Abstract

Using Molecular Dynamics simulations based on the effective hamiltonian developed by Zhong, Vanderbilt and Rabe [Phys. Rev. Lett. {\bf 73}, 1861 (1994)] (and fitted on first-principles calculations only), the technique of the thermodynamic integration is applied to barium titanate. It allows to compute the difference of free energy between macroscopic states with different polarizations, from the thermal averages of the forces acting on the local modes. This is achieved by performing molecular dynamics under the constraint of fixed polarization. The Landau free energy is thus interpreted as a potential of mean force. The thermodynamic integration directly gives access (numerically) to the Landau free energy of barium titanate as a function of $\vec{P}$, without any assumption on its analytical form. This technique, mainly used in computational chemistry, allows to make a direct connection between phenomenological theories and atomic-scale simulations. It is applied and validated to the case of BaTiO${}_3$ under fixed volume. The results are compared to available phenomenological potentials of the litterature.

arXiv commentsubmitted to Phys. Rev. B

References in corpus (6)

• First-principles theory of ferroelectric phase transitions for perovskites: The case of BaTiO3
• Phase transitions in BaTiO${}_3$ from first principles
• Landau thermodynamic potential for BaTiO_3
• Phenomenological theory of phase transitions in epitaxial BaTiO3 thin films
• Devonshire-Landau free energy of BaTiO3 from first principles
• Anharmonicity of BaTiO_3 single crystals

Cited by in corpus (3)

• Simulating the radiofrequency dielectric response of relaxor ferroelectrics: Combination of Coarse-Grained Hamiltonians and Kinetic Monte Carlo
• Free energies of ferroelectric crystals from a microscopic approach
• Ab Initio bulk free energy surface of proper ferroelectrics