Macroscopic descriptions of ferroelectrics have an obvious appeal in terms of efficiency and physical intuition. Their predictive power, however, has often been thwarted by the lack of a systematicp rocedure to extract the relevant materials parameters from the microscopics. Here we address this limitation by establishing an unambiguous two-way mapping between spatially inhomogeneous fields and discrete lattice modes. This yields a natural treatment of gradient couplings in the macroscopic regime via a long-wavelength expansion of the crystal Hamiltonian. Our analysis reveals an inherent arbitrariness in both the flexoelectric and polarization gradient coefficients, which we ascribe to a translational freedom in the definition of the polar distortion pattern. Remarkably, such arbitrariness cancels out in all physically measurable properties (relaxed atomic structure and energetics) derived from the model, pointing to a generalized translational covariance in the continuum description of inhomogeneous ferroelectric structures. We demonstrate our claims with extensive numerical tests on 180-degree domain walls in common ferroelectric perovskites, finding excellent agreement between the continuum model and direct first-principles calculations.
We have measured the bending-induced polarization of Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals with compositions at the relaxor-ferroelectric phase boundary. The crystals display very large flexoelectricity, with flexocoupling coefficients an order of magnitude bigger than the theoretical upper limit set by the theories of Kogan and Tagantsev. This enhancement persists in the paraphrase up to a temperature T* that coincides with the start of elastic softening in the crystals. Analysis of the temperature dependence and cross-correlation between flexoelectric, dielectric and elastic properties ind…
Flexoelectricity describes the coupling between polarization and strain/stress gradients in insulating crystals. In this paper, using the Landau-Ginsburg-Devonshire phenomenological approach, we found that flexoelectricity could increase the theoretical critical thickness in epitaxial BaTiO3 thin films, below which the switchable spontaneous polarization vanishes. This increase is remarkable in tensile films while trivial in compressive films due to the electrostriction caused decrease of potential barrier, which can be easily destroyed by the flexoelectricity, between the ferroelectric state …
A centrosymmetric stress cannot induce a polar response in centric materials, piezoelectricity is, for example, possible only in non-centrosymmetric structures. An exception is meta-materials with shape asymmetry, which may be polarized by stress even when the material is centric. In this case the mechanism is flexoelectricity, which relates polarization to a strain gradient. The flexoelectric response scales inversely with size, thus a large effect is expected in nanoscale materials. Recent experiments in polycrystalline, centrosymmetric perovskites [e.g., (Ba,Sr)TiO3] have indicated values o…
Domain walls (DWs) are ubiquitous in ferroelectric materials. Ferroelastic DWs refer to those who separate two domains with unparalleled polarizations (or two different ferroelastic variants). It is long believed that the structures of ferroelastic DWs can be simply explained from the perspective of mechanical and electric compatibilities in the framework of the Landau-Ginzburg-Devonshire (LGD) theory. Here we show that the converse flexoelectricity must be taken into account for fully describing the nature of ferroelastic DWs. In our work, an unexpected asymmetric structure is identified, whi…
The propagation front of a crack generates large strain gradients and it is therefore a strong source of gradient-induced polarization (flexoelectricity). Herein, we demonstrate that, in piezoelectric materials, a consequence of flexoelectricity is that crack propagation will be helped or hindered depending on whether it is parallel or antiparallel to the piezoelectric polar axis. This means that the theory of fracture physics can no longer assume mechanical symmetry in polar materials. The discovery of fracture asymmetry also has practical repercussions for the electromechanical fatigue of fe…
The theories of flexoelectricity and that of nonlocal elasticity are closely related, and are often considered together when modeling strain-gradient effects in solids. Here I show, based on a first-principles lattice-dynamical analysis, that their relationship is much more intimate than previously thought, and their consistent simultaneous treatment is crucial for obtaining correct physical answers. In particular, I identify a gauge invariance in the theory, whereby the energies associated to strain-gradient elasticity and flexoelectrically induced electric fields are individually reference-d…
Using the self-consistent Landau-Ginzburg-Devonshire approach we simulate and analyze the spontaneous formation of the domain structure in thin ferroelectric films covered with the surface screening charge of the specific nature (Bardeen-type surface states). Hence we consider the competition between the screening and the domain formation as alternative ways to reduce the electrostatic energy and reveal unusual peculiarities of distributions of polarization, electric and elastic fields conditioned by the surface screening length and the flexocoupling strength. We have established that the crit…
Abstract: In this paper we show that experimentally realizable apparently piezoelectric thin-film super-lattices can be created from non-piezoelectric materials provided an odd-order (e.g. trilayer) stacking sequence is used. The size-dependent mechanism of flexoelectricity, which couples gradients of strain to polarization, allows such a possibility. We present closed-form analytical expressions for the response of various thin-film and super-lattice configurations. We also clarify some of the subtleties that arise in considering interface boundary conditions in the theory of flexoelectricity…
The influence of flexoelectric coupling on the internal structure of neutral domain walls in tetragonal phase of perovskite ferroelectrics is studied. The effect is shown to lower the symmetry of 180-degree walls which are oblique with respect to the cubic crystallographic axes, while {100} and {110} walls stay "untouched". Being of the Ising type in the absence of the flexoelectric interaction, the oblique domain walls acquire a new polarization component with a structure qualitatively different from the classical Bloch-wall structure. In contrast to the Bloch-type walls, where the polarizati…
Pressure-induced polarization switching in ferroelectric thin films has emerged as a powerful method for domain patterning, allowing to create predefined domain patterns on free surfaces and under thin conductive top electrodes. However, the mechanisms for pressure induced polarization switching in ferroelectrics remain highly controversial, with flexoelectricity, polarization rotation and suppression, and bulk and surface electrochemical processes all being potentially relevant. Here we classify possible pressure induced switching mechanisms, perform elementary estimates, and study in depth u…
Ferroelectric materials are characterized by the presence of an electric dipole that can be reversed by application of an external electric field, a feature that is exploited in ferroelectric memories. All ferroelectrics are piezoelectric, and therefore exhibit a strong intrinsic coupling between polarization and elastic deformation - a feature widely used in piezoelectric transducers and high-displacement actuators. A less explored and exploited property is flexoelectricity, i.e. the coupling between polarization and a strain gradient. Though flexoelectricity is an old concept (it was discove…
Various phenomena related to inhomogeneous magnetoelectric interaction are considered. The interrelation between spatial modulation of order parameter and electric polarization, known as flexoelectric effect in liquid crystals, in the case of magnetic media appears in a form of electric polarization induced by spin modulation and vice versa. This flexomagnetoelectric interaction is also related to the influence of ferroelectric domain structure on antiferromagnetic vector distribution, and to the magnetoelectric properties of micromagnetic structures. The influence of inhomogeneous magnetoelec…
The sensitivity of ferroelectric domain walls to external stimuli makes them functional entities in nanoelectronic devices. Specifically, optically driven domain reconfiguration with in-plane polarization is advantageous and thus highly sought. Here, we show the existence of in-plane polarized sub-domains imitating a single domain state and reversible optical control of its domain wall movement in a single-crystal of ferroelectric BaTiO3. Similar optical control in the domain configuration of non-polar ferroelastic material indicates long-range ferroelectric polarization is not essential for t…
The coupling of translational modes to the reorientational motion is an essential property of systems with internal orientational degrees of freedom. Due to their high complexity most of those systems (molecular crystals, glasses...) present a major puzzle for scientists. In this paper we analyze the Raman scattering of a relatively simple ferroelectric system, KTa(1-x)Nb(x)O(3), which may serve as a model for more complicated cases. We are showing that there is a strong coupling between translational and reorientational motion in the crystal. Our data suggest that this coupling is the main re…
Charged domain walls and boundaries in ferroelectric materials display distinct phenomena, such as an increased conductivity due to the accumulation of bound charges. Here, we report the electron microscopy observations of atomic-scale arrangements at charged domain boundaries in the hybrid improper ferroelectric Ca$_{2.46}$Sr$_{0.54}$Ti$_2$O$_7$. Like in the prototype improper ferroelectric YMnO$_3$, we find that charged domain boundaries in Ca$_{2.46}$Sr$_{0.54}$Ti$_2$O$_7$ correspond to out-of-phase boundaries, which separate adjacent domains with a fractional translational shift of the uni…
Using the modified Landau-Ginsburg-Devonshire thermodynamic theory, it is found that the coupling between stress gradient and polarization, or flexoelectricity, has significant effect on ferroelectric properties of epitaxial thin films, such as polarization, free energy profile and hysteresis loop. However, this effect can be completely eliminated by applying an optimized external, uniform electric field. The role of such uniform electric field is shown to be the same as that of an ideal gradient electric field which can suppress the flexoelectricty effect completely based on the present theor…
We report on nanoscale strain gradients in ferroelectric HoMnO3 epitaxial thin films, resulting in a giant flexoelectric effect. Using grazing-incidence in-plane X-ray diffraction, we measured strain gradients in the films, which were 6 or 7 orders of magnitude larger than typical values reported for bulk oxides. The combination of transmission electron microscopy, electrical measurements, and electrostatic calculations showed that flexoelectricity provides a means of tuning the physical properties of ferroelectric epitaxial thin films, such as domain configurations and hysteresis curves.
A phenomenological model on the relationship between viscoelasticity and flexoelectricity is proposed to address the electromechanical coupling under rheological processes in viscoelastic materials. Our theoretical studies show that some observed ferroelectric phenomena in certain viscoelastic materials, like polymer films, may not be intrinsic material behavior.
The coupling between strain gradients and polarization, known as flexoelectricity, offers a new mechanism to control the functionality of dielectric materials. However, for the effect to be practically attractive, dynamic control of the strain gradient with magnitudes far exceeding those achievable via mechanical deformation (~10 $m^{-1}$) is needed. Strain-engineered thin films exhibit extraordinary strain gradients of $10^5-10^6 m{-1}$ arising from structural relaxation within a short space range that greatly enhances the steady-state flexoelectric effect. Here we report a giant, optically i…
Mechanical restoring forces acting on ferroelastic domain walls displaced from the equilibrium positions in epitaxial films are calculated for various modes of their cooperative translational oscillations. For vibrations of the domain-wall superlattice with the wave vectors corresponding to the center and boundaries of the first Brillouin zone, the soft modes are singled out that are distinguished by a minimum magnitude of the restoring force. It is shown that, in polydomain ferroelectric thin films, the soft modes of wall vibrations may create enormously large contribution to the film permitt…
Evolution of a stripe array of polarization domains triggered by the oxygen vacancy migration in an acceptor doped ferroelectric is investigated in a self-consistent manner. A comprehensive model based on the Landau-Ginzburg-Devonshire approach includes semiconductor features due to the presence of electrons and holes, and effects of electrostriction and flexoelectricity especially significant near the free surface and domain walls. A domain array spontaneously formed in the absence of an external field is shown to undergo a reconstruction in the course of the gradual oxygen vacancy migration …
We report first-principle atomistic simulations on the effect of local strain gradients on the nanoscale domain morphology of free-standing PbTiO$_3$ ultrathin films. First, the ferroelectric properties of free films at the atomic level are reviewed. For the explored thicknesses (10 to 23 unit cells), we find flux-closure domain structures whose morphology is thickness dependent. A critical value of 20 unit cells is observed: thinner films show structures with 90$^\circ$ domain loops, whereas thicker ones develop, in addition, 180$^\circ$ domain walls, giving rise to structures of the Landau-L…
In numerous functional materials, such as steels, ferroelectrics and magnets, new functionalities can be achieved through the engineering of the domain structures, which are associated with the ordering of certain parameters within the material. The recent progress in imaging techniques with atomic-scale spatial resolution transformed our understanding of domain topology revealing that, along with simple stripe-like or irregularly shaped domains, intriguing vortex-type topological domain configurations also exist. In this Review, we present a new classification scheme of "ZmxZn domains with Zl…
The orientational and translational order of a thermotropic ferroelectric liquid crystal (2MBOCBC) imbibed in self-organized, parallel, cylindrical pores with radii of 10, 15, or 20 nm in anodic aluminium oxide monoliths (AAO) are explored by high-resolution linear and circular optical birefringence as well as neutron diffraction texture analysis. The results are compared to experiments on the bulk system. The native oxidic pore walls do not provide a stable smectogen wall anchoring. By contrast, a polymeric wall grafting enforcing planar molecular anchoring results in a thermal-history indepe…
