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Organometallic lead halide perovskites are highly efficient materials for solar cells and other optoelectronic applications due to their high quantum efficiency and exceptional semiconducting properties. A peculiarity of these perovskites is the substantial ionic motion under external forces. Here, we reveal that electric field-and light-induced ionic motion in MAPbX3 crystals (X=Cl, Br, I and MA=CH3NH3) leads to unexpected piezoelectric-like response, an order of magnitude larger than in ferroelectric perovskite oxides. The nominal macroscopic symmetry of the crystals is broken by redistribution of ionic species, which can be controlled deterministically by light and electric field. The revealed piezoelectric response is possibly present in other materials with significant ionic activity but the unique feature of organometallic perovskites is the strong effect on the piezoelectric response of interplay of ionic motion (MA+ and X-1) and photoelectrons generated with illumination.

The polarization and strain response of ferroelectric materials at fields below the macroscopic coercive field is of a paramount importance for the operation of many electronic devices. The response of real ferroelectric and related materials is in general complex and difficult to interpret. The reason for this is that many processes in a ferroelectric material contribute to its properties, often concurrently. Examples include motion of ferroelectric and ferroelastic domains, presence of domains within domains, dynamics of different types of polar nano-entities, interaction of polar nano-entities (e.g., polar nanoregions in relaxors) with the strain and polarization within domains, motion of defects and rearrangement of defect clusters and their interaction with polarization and strain. One signature of these processes is nonlinearity of the strain and polarization. Most ferroelectrics exhibit nonlinear response at all practical field levels meaning that the apparent material coefficients depend on the amplitude of the driving excitation. In this paper we show that an investigation of nonlinear behavior is a sensitive way to study various mechanisms operating in dielectric and piezoelectric materials. We review the basic formalism of the nonlinear description of polarization and strain, give a physical interpretation of different terms and illustrate this approach on numerous examples of relaxors, relaxor ferroelectrics, hard and soft ferroelectrics, and morphotropic phase boundary compositions. An experimental approach based on a lock-in technique that is well-suited for such studies is also discussed., Comment: main text 35 pages, 8 figures; supplementary material 3 pages and 5 figures

Ferroelectric materials, upon electric field biasing, display polarization discontinuities known as Barkhausen jumps, a subclass of a more general phenomenon known as crackling noise. Herein, we follow at the nanoscale the motion of 90 degree needle domains induced by an electric field applied in the polarization direction of the prototypical ferroelectric BaTiO3, inside a transmission electron microscope. The nature of motion and periodicity of Barkhausen pulses leads to real-time visualization of distinctive interaction mechanisms of the domains with each other but without coming into contact, a mechanism that has not been observed before, or/and with the lattice where the domain walls appear to be moving through the dielectric medium relatively freely, experiencing weak Peierls-like potentials. Control over the kinetics of ferroelastic domain wall motion can lead to novel nanoelectronic devices pertinent to computing and storage applications.

Macroscopic polarity and its dynamic response to external electric fields and temperature in the nominally ergodic relaxor phase of pristine lead magnesium niobate crystals and ceramics, Pb(Mg1/3Nb2/3)O3 (PMN), were investigated. Dynamic pyroelectric measurements provide evidence for persistent macroscopic polarity of the samples. Annealing experiments below and above Burns temperature of polarized samples relate this polarity to the presence of polar nano entities and their dynamics. The dc electric field strength required for macroscopic polarization reversal is similar to the amplitude of the ac field where dynamic nonlinear dielectric permittivity reaches maximum. Consequently, the aforementioned maximum is related to the reorientation of polar nano entities. The results question the existence of an ergodic state in PMN below Burns temperature., Comment: 14 pages main text, 5 pages supplementary information

We report on the electric field response of 180 degree nanodomain walls in BaTiO$_3$ using in situ electrical biasing in transmission electron microscopy (TEM). The sample is biased on a micro-device designed for reliable testing whose key attributes are confirmed by finite element calculations. The presence of weakly charged zig-zag domain walls at room temperature is attributed to the geometric confinement of the device. The motion of the domain walls under the applied electric field allows to extract local P-E loops where distinct domain wall pinning in deep and random energy potential profiles, characteristic for hard and soft ferroelectrics, respectively, are observed. Hard domain wall pinning results in asymmetrical loops typical for "hard" ferroelectrics while the soft domain wall pinning follows Rayleigh-like behaviour. All effects are measured locally and directly from the imaged domain structure.

The nature of the "forbidden" local- and long-range polar order in nominally nonpolar paraelectric phases of ferroelectric materials has been an open question since the discovery of ferroelectricity in oxide perovskites (ABO3). A currently considered model suggests locally correlated displacements of B-site atoms along a subset of <111> cubic directions. Such offsite displacements have been confirmed experimentally, however, being essentially dynamic in nature they cannot account for the static nature of the symmetry-forbidden polarization implied by the macroscopic experiments. Here, in an atomically resolved study by aberration corrected scanning transmission electron microscopy (STEM) complemented by Raman spectroscopy, we reveal, directly visualize and quantitatively describe static, 2-4 nm large polar nanoclusters in the nominally nonpolar cubic phases of (Ba,Sr)TiO3 and BaTiO3. These results have implications on understanding of the atomic-scale structure of disordered materials, the origin of precursor states in ferroelectrics, and may help answering ambiguities on the dynamic-versus-static nature of nano-sized clusters., Comment: the main text and supplementary information

The dynamic dielectric nonlinearity of barium strontium titanate (Ba1-x,Srx)TiO3 ceramics is investigated in their paraelectric phase. With the goal to contribute to the identification of the mechanisms that govern the dielectric nonlinearity in this family, we analyze the amplitude and the phase angles of the first and the third harmonics of polarization. Our study shows that an interpretation of the field-dependent polarization in paraelectric (Ba1-x,Srx)TiO3 ceramics in terms of the Rayleigh-type dynamics is inadequate for our samples and that their nonlinear response rather resembles that observed in canonical relaxor Pb(Mg1/3Nb2/3)O3., Comment: published in: Sina Hashemizadeh and Dragan Damjanovic, Applied Physics Letters 110 (19), 192905 (2017)

BaTiO3 appears in cubic and hexagonal variants, both of which are centrosymmetric. Samples of cubic BaTiO3 are known to exhibit breaking of the centric symmetry locally and globally. It has been proposed that the local symmetry breaking originates in polar regions, the precursors of the ferroelectric phase. Origins of the macroscopic symmetry breaking, which are not well understood, have been previously tentatively correlated with inhomogeneities in the samples, such as strain gradients that may align or redistribute objects such as charged point defects or polar regions making material macroscopically polar. No such data are available for BaTiO3 with hexagonal symmetry. We compare dielectric, elastic, and pyroelectric properties of the two materials in polycrystalline form. In contrast to cubic BaTiO3, hexagonal BaTiO3 does not exhibit macroscopic pyroelectric response at room temperature. This is consistent with apparent absence of polar regions in the hexagonal material and the fact that in hexagonal BaTiO3 strain rather then polarization is the order parameter for the phase transition into ferroelectric-ferroelastic phase. The thermally stimulated currents measured in hexagonal and cubic BaTiO3, however, show that both materials exhibit noncentric macroscopic symmetry. This result supports the idea that extrinsic factors such as strain gradients, which are apparently common for both materials, may break the macroscopic symmetry, which may then lead to alignment and redistribution of polar regions or charged defects., Comment: accepted in Journal of Applied Physics

Oxygen octahedra tilting is a common structural phenomenon in perovskites and has been subject of intensive studies, particularly in rhombohedral Pb(Zr,Ti)O3 (PZT). Early reports suggest that the tilted octahedra may strongly affect the domain switching behavior, dielectric and piezoelectric properties of PZT ceramics. In a way similar to that proposed for tilts, however, charged defects, associated with oxygen vacancies, may also inhibit the motion of the domain walls, resulting macroscopically in pinched hysteresis loops and reduced piezoelectric response. Here, we revisit the early studies on rhombohedral PZT ceramics with tilted octahedra by considering a possible role of both tilts and charged defects on domain-wall motion. We show that the observed pinched hysteresis loops are likely associated with the presence of defect complexes containing charged oxygen vacancies, and not tilts as suggested in some cases. Regardless of the presence or absence of long-range ordered tilts in rhombohedral PZT, the effect of charged defects is also prominent in weak-field permittivity and piezoelectric properties, particularly at sub-Hz driving conditions where the conductivity, related to the motion of oxygen vacancies, gives rise to strong frequency dispersion., Comment: 8 figures

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 of flexoelectric coefficients that are orders of magnitude higher than theoretically predicted, promising practical applications based on bulk materials. We show that materials with unexpectedly large flexoelectric response exhibit breaking of the macroscopic centric symmetry through inhomogeneity induced by the high temperature processing. The emerging electro-mechanical coupling is significant and may help to resolve the controversy surrounding the large apparent flexoelectric coefficients in this class of materials., Comment: typo corrected

The properties of ferroelectric materials, such as lead zirconate titanate (PZT), are heavily influenced by the interaction of defects with domain walls. These defects are either intrinsic, or are induced by the addition of dopants. We study here PbTiO$_3$ (the end member of a key family of solid solutions) in the presence of acceptor (Fe) and donor (Nb) dopants, and the interactions of the different defects and defect associates with the domain walls. For the case iron acceptors, the calculations point to the formation of defect associates involving an iron substitutional defect and a charged oxygen vacancy (Fe$^{'}_{Ti}$-V$^{^{\textbf{..}}}_O$). This associate exhibits a strong tendency to align in the direction of the bulk polarization; in fact, ordering of defects is also observed in pure PbTiO$_3$ in the form of lead-oxygen divacancies. Conversely, calculations on donor-doped PbTiO$_3$ do not indicate the formation of polar defect complexes involving donor substitutions. Last, it is observed that both isolated defects in donor-doped materials and defect associates in acceptor-doped materials are more stable at 180$^o$ domain walls. However, polar defect complexes lead to asymmetric potentials at domain walls due to the interaction of the defect polarization with the bulk polarization. The relative pinning characteristics of different defects are then compared, to develop an understanding of defect-domain wall interactions in both doped and pure PbTiO$_3$. These results may also help understanding hardening and softening mechanisms in PZT., Comment: 10 pages, 14 figures, accepted by Phys Rev B on December 2013

Elastic storage modulus and loss of relaxor lead magnesium niobate ceramics, Pb(Mg1/3Nb2/3)O3, have been measured with dynamic mechanical analyzer in single cantilever mode in the temperature range from 170 K to 320 K and at frequencies from 0.1 Hz to 50 Hz. The dependence of the elastic susceptibility (inverse modulus) on temperature and frequency of the driving force has characteristics of typical relaxor behavior that can be well described with the Vogel-Fulcher law. The parameters of the Vogel-Fulcher relation exhibit similar values for the dielectric and anelastic relaxations. Similarities and differences between anelastic and dielectric relaxor behaviors are identified., Comment: accepted in Applied Physics Letters

We report on the frequency and stress dependence of the direct piezoelectric d33 coefficient in BiFeO3 ceramics. The measurements reveal considerable piezoelectric nonlinearity, i.e., dependence of d33 on the amplitude of the dynamic stress. The nonlinear response suggests a large irreversible contribution of non-180{\deg} domain walls to the piezoelectric response of the ferrite, which, at present measurement conditions, reached a maximum of 38% of the total measured d33. In agreement with this interpretation, both types of non-180{\deg} domain walls, characteristic for the rhombohedral BiFeO3, i.e., 71{\deg} and 109{\deg}, were identified in the poled ceramics using transmission electron microscopy (TEM). In support to the link between nonlinearity and non-180{\deg} domain wall contribution, we found a correlation between nonlinearity and processes leading to deppining of domain walls from defects, such as quenching from above the Curie temperature and high-temperature sintering. In addition, the nonlinear piezoelectric response of BiFeO3 showed a frequency dependence that is qualitatively different from that measured in other nonlinear ferroelectric ceramics, such as "soft" (donor-doped) Pb(Zr,Ti)O3 (PZT); possible origins of this dispersion are discussed. Finally, we show that, once released from pinning centers, the domain walls can contribute extensively to the electromechanical response of BiFeO3; in fact, the extrinsic domain-wall contribution is relatively as large as in Pb-based ferroelectric ceramics with morphotropic phase boundary (MPB) composition, such as PZT. This finding might be important in the search of new lead-free MPB compositions based on BiFeO3 as it suggests that such compositions might also exhibit large extrinsic domain-wall contribution to the piezoelectric response., Comment: 38 pages, 11 figures

The solid solution 0.5Ba(Ti0.8Zr0.2)O3-0.5(Ba0.7Ca0.3)TiO3 (BCZT) is a promising lead-free piezoelectric material with exceptionally high piezoelectric coefficients. The strong response is related to structural instabilities close to ambient temperature. We report here on temperature-induced anomalies in the dielectric, piezoelectric, and elastic coefficients and Raman spectroscopy of ceramic BCZT. The data indicate ferroelectric-ferroelectric structural phase transitions in this material in addition to those previously reported. An anomaly is also observed above the Curie temperature TC and is associated with the loss of polar structure that persists thirty degrees above TC.

Large bipolar strain of up to 0.36% (peak-to-peak value) was measured in BiFeO3 ceramics at low frequency (0.1 Hz) and large amplitude (140 kV/cm) of the driving field. This strain is comparable to that achievable in highly efficient Pb-based perovskite ceramics, such as Pb(Zr,Ti)O3 and Pb(Mg,Nb)O3-PbTiO3. The strain showed a strong dependence on the field frequency and is likely largely associated with domain switching involving predominantly non-180{\deg} domain walls. In addition, rearrangement of charged defects by applying electric field of low frequency depins these domain walls, resulting in a more efficient switching and, consequently, an increased response.

Many ferroelectric solid solutions exhibit enhanced electro-mechanical properties at the morphotropic boundary separating two phases with different orientations of polarization. The mechanism of properties enhancement is associated with easy paths for polarization rotation in anisotropically flattened free energy profile. Another mechanism of properties enhancement related to free energy flattening is polarization extension. It is best known at temperature-driven ferroelectric-paraelectric phase transitions and may lead to exceedingly large properties. Its disadvantage is temperature instability of the enhancement. In this paper a temperature-composition phase diagram is proposed that exhibits compositionally driven-phase transitions with easy paths for both polarization rotation and polarization extension., Comment: accepted in Appl. Phys. Lett./ presented at APS 2010 March meeting

The structural phase diagram of the Pb-free ferroelectric (Na1/2Bi1/2)1-xBaxTiO3 (NBT-BT), x<0.1, has been explored by Raman spectroscopy at temperatures from 10 to 470 K. The data provide clear evidence for a proposed temperature-independent morphotropic phase boundary at x \approx 0.055. However, there is no evidence for a structural phase transition across T \approx 370 K for x > 0.055, where bulk-property anomalies appear to signal a transition to a nonpolar or antiferroelectric phase. The results identify that the phase above 370 K shows short-range ionic displacements that are identical to those in the long-range-ordered phase below 370 K. These conclusions provide a natural interpretation of the weak piezoelectric response in this system and have important implications for the search for Pb-free piezoelectrics., Comment: 21 pages, 5 figures

We report on the experimental investigation of a high-frequency (1MHz - 1.8GHz) dielectric dispersion in unpoled and poled Pb(Zr,Ti)O3 ceramics. Two overlapping loss peaks could be revealed in the dielectric spectrum. The linear dependence between the lower-frequency peak position and average grain size D, which holds for D< 10mkm, indicates that the corresponding polarization mechanism originates from piezoelectric resonances of grains. The intensity of the higher-frequency peak is drastically reduced by poling. It is thus proposed that this loss peak is related to domain-wall contribution to the dielectric dispersion., Comment: 8 pages, 3 figures

An evidence that the dielectric ageing in the polydomain Pb(Zr0.45Ti0.55)O3 thin films is controlled by progressive pinning of 180 domain walls is presented. To provide such a conclusion, we use a general method, which is based on the study of the time evolution of the nonlinear, but anhysteretic, dielectric response of the ferroelectric to a weak electric field. A thermodynamic model of the ferroelectric system where the dielectric response is controlled by bending movements of pinned 180 domain walls is developed. Within this model, the nonlinear permittivity of the ferroelectric is expressed as a function of the microstructural parameters of the domain pattern. It is shown that using the analysis of the time evolution of the nonlinear permittivity, it is possible to estimate changes in the concentration of the pinning centers that block the movements of the 180 domain walls during aging in polydomain perovskite ferroelectrics., Comment: This version is modifed and corrected according to recently published Erratum: Phys. Rev. B 79, 219903(E) (2009). 21 pages, 3 figures

It is shown that the phase angle of the third harmonic of polarization response (delta3) is very sensitive to the ageing state of hard, Fe-doped lead zirconate titanate [Pb(Zr,Ti)O3 or PZT] ceramics and may thus provide rich information on processes responsible for ageing in hard ferroelectrics. When hard PZT ceramics experience hardening (aged state) - softening (deaged state) transition, delta3 changes by about 90 degrees at subswitching fields and by about 180 degrees at switching conditions. Evolution of delta3 with time, temperature and electric field amplitude during deageing suggests that at least two mechanisms of charge migration, one short-range and one long-range, may participate in the deageing process., Comment: accepted in Journal of Applied Physics

The importance of a high shear coefficient d15 (or d24) to the piezoelectric properties of domain-engineered and polycrystalline ferroelectrics is discussed. The extent of polarization rotation, as a mechanism of piezoelectric response, is directly correlated to the shear coefficient. The terms "rotator" and "extender" are introduced to distinguish the contrasting behaviors of crystals such as 4mm BaTiO3 and PbTiO3. In "rotator" ferroelectrics, where d15 is high relative to the longitudinal coefficient d33, polarization rotation is the dominant mechanism of piezoelectric response; the maximum longitudinal piezoelectric response is found away from the polar axis. In "extender" ferroelectrics, d15 is low and the collinear effect dominates; the maximum piezoelectric response is found along the polar axis. A variety of 3m, mm2 and 4mm ferroelectrics, with various crystal structures based on oxygen octahedra, are classified in this way. It is shown that the largest piezoelectric anisotropies d15/d33 are always found in 3m crystals; this is a result of the intrinsic electrostrictive anisotropy of the constituent oxygen octahedra. Finally, for a given symmetry, the piezoelectric anisotropy increases close to ferroelectric-ferroelectric phase transitions; this includes morphotropic phase boundaries and temperature induced polymorphic transitions., Comment: accepted in J. Appl. Phys

The question of the origin of the piezoelectric properties enhancement in perovskite ferroelectrics is approached by analyzing the Gibbs free energy of tetragonal BaTiO3, PbTiO3 and Pb(Zr,Ti)O3 in the framework of the Landau-Ginzburg-Devonshire theory. The flattening of the Gibbs free energy profile appears as a fundamental thermodynamic process behind the piezoelectric enhancement. The generality of the approach is demonstrated by examining the free energy flattening and piezoelectric enhancement as a function of composition, temperature, electric field and mechanical stress. It is shown that the anisotropy of the free energy flattening is the origin of the anisotropic enhancement of the piezoelectric response, which can occur either by polarization rotation or by polarization contraction. Giant enhancement of the longitudinal piezoelectric response (on the order of 1000 pC/N) is predicted in PbTiO3 under uniaxial compression., Comment: 19 pages, 4 Figures, accepted in Phys. Rev. B