Modeling of Ferroelectric Oxide Perovskites: From First to Second Principles

Abstract

Taking a historical perspective, we provide a brief overview of the first-principles modeling of ferroelectric perovskite oxides over the past 30 years. We emphasize how the work done by a relatively small community on the fundamental understanding of ferroelectricity and related phenomena has been at the origin of consecutive theoretical breakthroughs, with an impact going often well beyond the limit of the ferroelectric community. In this context, we first review key theoretical advances such as the modern theory of polarization, the computation of functional properties as energy derivatives, the explicit treatment of finite fields, or the advent of second-principles methods to extend the length and timescale of the simulations. We then discuss how these have revolutionized our understanding of ferroelectricity and related phenomena in this technologically important class of compounds. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 13 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Ab initio multi-scale modeling of ferroelectrics: The case of PbTiO3

“…We use Eq. ( 6) to compute ∆G f −p (T ) for L ∈ [6,9,12,15] and T ∈ [815, 820, 825, 830]K with P = 1e Å. The results are plotted in Fig.…”

“…The empirical force fields are fitted to a limited set of DFT data, but often fail to describe the ab-initio potential energy surface with uniform accuracy, even after fine tuning [10][11][12][13][14]. These schemes, sometimes dubbed "second principles" in the literature, have been examined in a recent review article [15]. Problems with this methodology originate from the limited representative power of hand-crafted empirical potentials, and from the difficulty of inferring the dpendence of the electronic degrees of freedom on the atomic configurations.…”

The effect of composition on phonon softening in ABO3-type perovskites: DFT modelling

“…As regards temperature (see ref. 2–4 for an overview), a “semi-empirical” strategy commonly used consists of: (i) fixing the lattice parameters to the experimental ones, if known at temperature T (and standard pressure), and optimizing the atomic position only, or, (ii) fixing the volume to the experimental value if known at temperature T (and standard pressure), and optimizing the full structure.…”

“…It is now well established that there is a direct link between the distortion of the unit cell along the polar axis, the spontaneous polarization, the B off-centering, and the increase of the hybridization between the B and O ions (see ref. 3, 4, 26 and 100). Then, the larger the spontaneous polarization, the larger the other mentioned quantities.…”

“…Perovskite crystals are known to present an extremely rich phase diagram and to possess a number of physical properties, such as permittivity and piezoelectric coefficient, that become anomalously large in the vicinity of phase transitions having a ferroelectric character. [1][2][3][4] Many factors such as temperature, pressure, intensity of an external electric field and nanoand micro-structure of the material can influence the value of these properties. 1,5,6 Also, atomic substitution is an efficient way to tune the phase diagram of solid solutions and achieve exceptional performance at close to room temperature and pressure.…”