Correlations and local order parameter in the paraelectric phase of barium titanate

Abstract

General features of the order parameter distribution in barium titanate in its paraelectric phase and in its ferroelectric phases (tetragonal and orthorhombic) are presented. The density of probability of the polarization [Formula: see text], defined by an average of the local order parameters over regions of various sizes and shapes (L(x) × L(y) × L(z)), is examined by molecular dynamics simulations using a first-principles derived effective Hamiltonian. The free energies [Formula: see text] associated with these probabilities are computed by thermodynamic integration. The evolution of these quantities are explained through the computation of pair correlations, which are found, as stated in several previous works, very anisotropic, 'needle-like', with longitudinal correlations ([Formula: see text]) having much longer range than transverse ones ([Formula: see text]). The correlations explain why the density of probability of the order parameter evolves from a multiple-peaked distribution with maxima along [111] (in the single cell), along [100] for small needle-like regions, towards a single-peaked distribution for larger regions. A useful expression in which the shape-dependence of the free energy is manifest is provided.

Surface polarization, rumpling, and domain ordering of strained ultrathinBaTiO3(001) films with in-plane and out-of-plane polarization

“…by considering the basic contributions to the energy of a ferroelectric in terms of short/long-range interactions and longitudinal/lateral correlations [11]: Extending the domain width l adds destabilizing (lateral) electrostatic contributions. Thus maintaining the ferroelectric state requires elongating the domain in the direction of the polarization (increase L), adding stabilizing (longitudinal) electrostatic contributions.…”

Low temperature ferroelectric behavior in morphotropic Pb (Zr1−xTix)O3

“…A reverse field of magnitude 30 MV/m was applied along [00] to facilitate picosecond switching at the start of the production run. To characterize the switching dynamics we register the time evolution of the free energy, following the definition given in ref . The free energy expressed as a Density of Probability (DoP) is defined as the mean of the order parameter, which here returns the averaged local polarization (Figure ).…”

Dielectric relaxation in Li-doped KTaO3studied by kinetic Monte Carlo

“…We believe that this approach, although not directly transferable to other relaxor materials, such as PMN or PSN, opens a promising way to study such complex systems, in which long characteristic times associated with relaxation of polar nanoregions govern the physics, while a model derived from first principles remains mandatory to successfully capture the microscopic scale. [2][3][4][5]26 Extending the method to these "classical" relaxors should require a spatial coarse graining to extract the surface free energy seen by the macrodipoles associated with polar nanoregions, [27][28][29] before applying the KMC method to these coarse-grained degrees of freedom.…”