Theory and simulations

####
Spatio-temporal distribution of relative Ti-O_{6} displacements in cubic BaTiO_{3}

BaTiO_{3} is often considered a model ferroelectric material in which
the dielectric properties are defined by the displacements of Ti ions
with respect to surrounding oxygen atoms.
However, despite the decades of a dedicated research,
certain controversies have remained as to the description of collective movements
of the Ti ions. We approached this problem using nonoscale-oriented
X-ray scattering methods and large-scale atomistic simulations
[1].
Together these allowed us to show that the Ti dynamics can be exhaustively
explained by phonons excited on a timescale of picoseconds.

The three-dimensional distribution of the x-ray diffuse scattering intensity of
BaTiO_{3} has been recorded in a synchrotron experiment and simultaneously
computed using molecular dynamics simulations of a shell model.
Together, these have allowed the details of the disorder in paraelectric BaTiO_{3}
to be clarified. The narrow sheets of diffuse scattering, related
to the famous anisotropic longitudinal correlations of Ti ions,
are shown to be caused by the overdamped anharmonic soft phonon branch.
This finding demonstrates that the occurrence of narrow sheets
of diffuse scattering agrees with a displacive picture of the cubic phase
of this textbook ferroelectric material. The presented methodology allows
one to go beyond the harmonic approximation in the analysis of phonons and phonon-related scattering.

**Reference:**

[1] M. Paściak, T. R. Welberry, J. Kulda, S. Leoni, and J. Hlinka, Dynamic Displacement Disorder of Cubic BaTiO

_{3}, Phys. Rev. Lett.

**120**, 167601 (2018).

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#### Domain wall contribution to lattice dynamics and permittivity of BiFeO_{3}

Ferroelectric materials are known for their exceptionally high dielectric permittivity. It turns out, that important part of it originates from a material's complicated microstructure and in particular from interfaces between ferroelectric domains.

In this study we investigate different types of interfaces in a multiferroic BiFeO_{3}.
By means of atomistic modelling we show that some configurations of interfaces can
greatly enhance the permittivity by hosting terahertz-range collective polar fluctuations.
The key result is that the permittivity is modified in the THz range.
This fundamental finding and its understanding can be used in a design of new materials
[
J. Hlinka, M. Pasciak, S. Körbel, and P. Márton, Phys. Rev. Lett. **119**, 057604 (2017)
].

#### First-principles-based Landau-Devonshire potential for BiFeO_{3}

We describe a first-principles-based computational strategy for determination of the Landau-Devonshire potential.

It exploits the configuration space attached to the eigenvectors of the modes frozen in the ground state.
This allows to probe the energy surface in the vicinity of the ground state,
which is most relevant for the properties of the ordered phase.
We apply this procedure to BiFeO_{3} in order to determine potential energy associated with strain,
polarization, and oxygen octahedra tilt.
[
P. Marton, A. Klíč, M. Paściak, and J. Hlinka, Phys. Rev. B **96**, 174110 (2017)
].

#### Existence conditions for ferroaxial materials

All 212 species of structural phase transitions with a macroscopic symmetry breaking were inspected with respect to the simultaneous occurrence of the ferroelastic, ferroelectric, and ferroaxial properties.

For each species, a matrix of representative equilibrium property tensors in both high-symmetry and low-symmetry phases, showing emergence of spontaneous components, were explicitly worked out [http://palata.fzu.cz/species/13x13axial]. Results can serve as a useful tool in search of fundamentally new material properties [J. Hlinka et al., Phys. Rev. Lett. 116, 177602 (2016)].

#### Ising lines: Natural topological defects within ferroelectric Bloch walls

Phase-field simulations demonstrate that the polarization order-parameter field
in the Ginzburg-Landau-Devonshire model of rhombohedral ferroelectric BaTiO_{3} allows
for an interesting linear defect, stable under simple periodic boundary conditions.
This linear defect, here called the Ising line, can be described as an about 2-nm-thick
intrinsic paraelectric nanorod acting as a highly mobile borderline between finite portions
of Bloch-like domain walls of opposite helicity.

These Ising lines play the role of domain boundaries associated with the Ising-to-Bloch domain-wall phase transition. Therefore, the electric field parallel to the Ising line can be used to induce the Ising line motion, which mediates the switching of both polarization and chirality of the Bloch wall without changing the bulk domain polarization. Detailed description of this study can be found in the paper [ V. Stepkova, P. Marton, and J. Hlinka, Phys. Rev. B 92, 094106 (2015)]

####
Phase transition in ferroelectric domain walls of BaTiO_{3}

The seminal paper by Zhirnov (1958 Zh. Eksp. Teor. Fiz. 35 1175–80) explained why the structure of domain walls
in ferroelectrics and ferromagnets is so different. We have recently realized that the antiparallel
ferroelectric walls in rhombohedral ferroelectric BaTiO_{3} can be switched between the Ising-like state
(typical for ferroelectrics) and a Bloch-like state (unusual for ferroelectric walls but
typical for magnetic ones) [see Figure 1] by a compressive epitaxial stress.

Phase-field simulations using a Ginzburg–Landau–Devonshire model allows to explore this strain-induced phase transition within the domain wall in detail [Figure 2]. Strain-tunable chiral properties of ferroelectric Bloch walls promise a range of novel phenomena in epitaxial ferroelectric thin films. Results are published in JPCM [ V. Stepkova et al., J. Phys.: Condens. Matter 24, 212201 (2012)].

#### Dielectric response of a phase transition in domain wall

Computer simulations based on Ginzburg-Landau-Devonshire theory was used to study details of a phase-transition between Ising and Bloch type of a domain wall.

Such transition was predicted to appear for 180 degree domain wall in the rhombohedral ferroelectric phase
of BaTiO_{3} close to 2GPa compressive stress
[
V. Stepkova et al., J. Phys.: Condens. Matter **24**, 212201 (2012)].
We confirm the hypothesis that the phase transition is of the first-order and predict corresponding
divergent increase of the dielectric permittivity in the vicinity of the transition.
In case of dense domain-wall pattern it can represent a substantial part of the dielectric response of the material
[
P. Marton et al., Phase Transitions **86**, 103 (2012)].

#### Piezoelectric response of nanotwinned ferroelectric perovskites

Computer simulations based on Ginzburg-Landau-Devonshire theory has benn used to investigate
piezoelectric properties of tetragonal BaTiO_{3} crystals. We have shown that piezoelectric response
of twinned BaTiO_{3} increases with increasing density of 90-degree domain walls.

A considerable enhancement of piezoelectric coefficients
is predicted below 50 nm. We have also shown that main contribution to the longitudinal piezoelectric coefficient comes
from volume of domain, rather than from the domain wall region. Nevertheless, the experimentally reported impact of
domain wall density is even stronger than in our simulations. Our most recent theoretical investigations
[P. Marton et al, Physical Review B 81, 144125 (2010)]
suggest that ferroelectric perovskites
such as BaTiO_{3} most likely support also more exotic domain walls, resembling Bloch walls known
from ferromagnetism. This kind of domain walls might account for additional enhancement of the electromechanical
material response.