Effective-Hamiltonian modeling of external pressures in ferroelectric perovskites

TL;DR

This paper investigates the validity of modeling external pressure effects in ferroelectric perovskites using effective Hamiltonians derived from first-principles calculations, addressing key assumptions and providing illustrative results for BaTiO3.

Contribution

It critically examines the assumptions underlying effective Hamiltonian modeling of pressure effects and offers guidance for constructing more accurate models when these assumptions fail.

Findings

Validated the assumptions for BaTiO3 under pressure

Identified limitations of the Taylor expansion truncation at finite pressures

Provided methods to construct effective Hamiltonians beyond standard assumptions

Abstract

The phase-transition sequence of a ferroelectric perovskite such as BaTiO_3 can be simulated by computing the statistical mechanics of a first-principles derived effective Hamiltonian [Zhong, Vanderbilt and Rabe, Phys. Rev. Lett. 73, 1861 (1994)]. Within this method, the effect of an external pressure (in general, of any external field) can be studied by considering the appropriate "enthalpy" instead of the effective Hamiltonian itself. The legitimacy of this approach relies on two critical assumptions that, to the best of our knowledge, have not been adequately discussed in the literature to date: (i) that the zero-pressure relevant degrees of freedom are still the only relevant degrees of freedom at finite pressures, and (ii) that the truncation of the Taylor expansion of the energy considered in the effective Hamiltonian remains a good approximation at finite pressures. Here we address these issues in detail and present illustrative first-principles results for BaTiO_3. We also discuss how to construct effective Hamiltonians in cases in which these assumptions do not hold.