Direct imaging of the spatial and energy distribution of nucleation centres in ferroelectric materials

Macroscopic ferroelectric polarization switching, similar to other first-order phase transitions, is controlled by nucleation centres. Despite 50 years of extensive theoretical and experimental effort, the microstructural origins of the Landauer paradox, that is, the experimentally observed low values of coercive fields in ferroelectrics corresponding to implausibly large nucleation activation energies, are still a mystery. Here, we develop an approach to visualize the nucleation centres controlling polarization switching processes with nanometre resolution, determine their spatial and energy distribution and correlate them to local microstructure. The random-bond and random-field components of the disorder potential are extracted from positive and negative nucleation biases. Observation of enhanced nucleation activity at the 90 composite function domain wall boundaries and intersections combined with phase-field modelling identifies them as a class of nucleation centres that control switching in structural-defect-free materials.     

Unexpectedly low barrier of ferroelectric switching in HfO2 via topological domain walls

Fluorite-structure ferroelectrics — in particular the orthorhombic phase of HfO₂ — are of paramount interest to academia and industry because they show unprecedented scalability down to 1-nm-thick size and are compatible with Si electronics. However, their polarization switching is believed to be limited by the intrinsically high energy barrier of ferroelectric domain wall (DW) motions. Here, by unveiling a new topological class of DWs, we establish an atomic-scale mechanism of polarization switching in orthorhombic HfO₂ that exhibits unexpectedly low energy barriers of DW motion (up to 35-fold lower than given by previous conjectures). These findings demonstrate that the nucleation-and-growth-based mechanism is feasible, challenging the commonly held view that the rapid growth of the oppositely polarized domain is impossible. Building on this insight, we describe a strategy to substantially reduce the coercive fields in HfO₂-based ferroelectric devices. Our work is a crucial step towards understanding the polarization switching of HfO₂, which could provide a means to solve the key problems associated with operation speed and endurance.     

A COD fracture model of ferroelectric ceramics with applications in electric field induced fatigue crack growth

In this paper, Crack Opening Displacement (COD) is introduced to study the fracture and fatigue of ferroelectrics. A fundamental solution for the COD of ferroelectrics is derived considering both the piezoelectric effect and ferroelectric effect. Bases on this solution, a nonlinear COD fracture model of ferroelectrics, which takes into account the effect of domain switching, is developed and accords well with the experimental results. Furthermore, fatigue crack growth in ferroelectrics is analytically investigated using this COD model. Comparison between the experimental results and the predicted electric-field-induced fatigue crack growth shows the applicability of the proposed COD model.     

A Monte Carlo simulation on domain pattern and ferroelectric behaviors of relaxor ferroelectrics

The domain configuration and ferroelectric property of mode relaxor ferroelectrics (RFEs) are investigated by performing a two-dimensional Monte Carlo simulation based on the Ginzburg-Landau theory on ferroelectric phase transitions and the defect model as an approach to the electric dipole configuration in relaxor ferroelectrics. The evolution of domain pattern and domain wall configuration with lattice defect concentration and temperature is simulated, predicting a typical two-phase coexisted microstructure consisting of ferroelectric regions embedded in the matrix of a paraelectric phase. The diffusive ferroelectric transitions in terms of the spontaneous polarization hysteresis and dielectric susceptibility as a function of temperature and defect concentration are successfully revealed by the simulation, demonstrating the applicability of the defect model and the simulation algorithm. A qualitative consistency between the simulated results and the properties of proton-irradiated ferroelectric copolymer is presented.     

Energy functions and basic equations for ferroelectrics

Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics.     

Phase field modeling of flexoelectric effects in ferroelectric epitaxial thin films

The flexoelectric effect which is defined as the coupling between strain gradient and polarization has long been neglected because it is insignificant in bulk ferroelectrics. However, at nanoscale, the strain gradient can be dramatically increased leading to giant flexoelectric effects. In the present study, the flexoelectric effects in epitaxial nano thin films of a 180° multi-domain structure, which are subjected to a compressive in-plane misfit strain, are investigated by the phase field method. Unlike the case of a single domain structure where the strain gradient is mainly attributed to the formation of dislocation which relaxes the misfit strain, in a multi-domain structure, it is attributed to many factors, such as surface and interface effects, misfit relaxation and domain wall structure. The results obtained show that relatively large flexoelectricity-induced electric fields are produced near the domain wall region. The induced field will not only influence the domain structure of the thin film, but also the hysteresis loops when it is under an applied electric field.     

Analysis of polarization behavior in relaxation of BaTiO₃-based ferroelectrics using wideband dielectric spectroscopy

Wideband dielectric spectra from the kilohertz to terahertz range are discussed for BaTiO?-based ferroelectrics. Ceramics of BaTiO? (BT), Ba(0.6)Sr(0.4)TiO? (BST-0.6), and BaZr(0.25)Ti(0.75)O? (BZT-0.25) were selected as normal ferroelectrics, ferroelectrics with diffuse phase transition (DPT ferroelectrics), and relaxor ferroelectrics, respectively. The variation of ionic polarization in both BT and BST-0.6 ceramics with temperature could be explained by the softening of the soft phonon mode. In BZT-0.25, a permittivity anomaly at the dielectric maximum temperature (T(m)) at low frequencies is not attributed to the softening of the soft phonon mode, but originates from the permittivity derived from the dipole polarization (?(dipole)). Relaxor behavior in BZT-0.25 is derived from the increase in the depression of ?(dipole) on cooling across the T(m) with increasing frequency. In dipole polarization, BT, BST- 0.6, and BZT-0.25 all exhibited a similar tendency of ?(dipole) above the Curie temperature (T(c)) and T(m). However, behavior of ?(dipole) below the T(c) can be explained by the ferroelectric domains in BT, whereas the variation of ?(dipole) below the Tm could be explained by growth process of polar nanoregions (PNRs) in BST-0.6 and BZT-0.25. Regarding this, BT can be distinguished from BST-0.6 and BZT-0.25. Relaxation in BT could be interpreted as successive change in polarization mechanism from normal ferroelectrics to relaxor ferroelectrics via DPT ferroelectrics.     

Electric field gradients and spontaneous quadrupoles in elastic ferroelectrics

A continuum model for the behavior of elastic ferroelectrics is proposed in this work. The electric field and the electric field gradient together with spontaneous dipole and quadrupole polarization are taken as independent variables of the stored energy function. Thus, a theory with reversible and spontaneous polarization is created. The main focus is on the role of the reversible and spontaneous quadrupoles. It is proved, both analytically and numerically, that spontaneous quadrupole polarization is responsible for the geometry of domain walls in the bulk of elastic ferroelectrics. On the other hand, reversible quadrupoles play a prominent role in the size effect of a thin ferroelectric film.     

Microdeformations in ferroelectrics

Ferroelectrics undergo one or more crystallographic phase transitions, which involve lattice distortions. The direction of spontaneous polarization in ferroelectrics can be reoriented by an applied electric field (or mechanical stress). There is a spontaneous strain accompanying spontaneous polarization. Phase transitions and domain reorientations thus result in microdeformations. Many devices such as actuators and transducers are based on this behaviour. The origin of microdeformations in ferroelectrics and their consequences are discussed here.     

Control of coercive field in lithium niobate crystals with repeated polarization reversal

In this study, the amount of decrease in coercive field of congruent lithium niobate during repeated poling and back-poling was measured. The polarization is reversed in 300 ms and then back-poled during the rest period. The coercive field can be decreased around 1 kV/mm with a repeated poling interval of 5 s. As the interval prolonged, the poling field decrease became smaller, and a stretched exponential function is suggested for the experimental fitting resulting in a set of meaningful parameters. These values are essential for the design of high quality domain engineering.     

Atomic Level 1D Structural Modulations at the Negatively Charged Domain Walls in BiFeO3 Films

Charged domain walls (CDWs) show great potentials to mediate the properties of ferroelectrics. Direct mapping of these domain walls at an atomic scale is of critical importance for understanding the domain wall dominated properties. Here, based on aberration‐corrected scanning transmission electron microscopy, tail‐to‐tail CDWs at 71°, 109°, and 180° domains in BiFeO₃ thin films have been identified. 2D mappings demonstrate 1D structural modulations with alternate lattice expansions and clockwise/counterclockwise lattice rotations at these CDWs. Such behaviors of CDWs reveal a remarkable contrast to the uncharged domain walls and imply delicate interactions between bound charges and structural compensations of domain wall. These results are expected to provide new information on domain wall structures and shed some light on the understanding of domain wall properties in ferroelectrics.     

Analysis methods for characterizing ferroelectric/ferroelastic domain reorientation in orthorhombic perovskite materials and application to Li-doped Na0.5K0.5NbO3

Ferroelectric and ferroelastic domains can be reoriented during the application of electric field through domain wall motion. This study develops a method to quantify the domain reorientation in perovskite ferroelectrics with orthorhombic crystal lattices. In situ, high-energy X-ray diffraction was utilized to obtain intensity ratios that are necessary for the calculation. Domain reorientation in orthorhombic Li-doped Na_0.5K_0.5NbO₃ is then quantified using this method. The preference of domain orientations is explained by considering the angle between spontaneous polarization of the respective domains and the applied electric field direction. The extent of domain reorientation increases as the Li substitution increases which additionally correlates to increased piezoelectric coefficient d ₃₃ and field-induced strain. Increased domain wall motion is further proposed to originate due to the increased compositional proximity to the morphotropic phase boundary, a proposed universal behavior in ferroelectric compositions-containing phase boundaries.     

Influence of antiferromagnetic ordering on ferroelectric polarization switching of YMnO3 epitaxial thin films

In this study, the switching behavior of ferroelectric polarization of (0001) YMnO(3) epitaxial films at around Néel temperature was investigated. From the experimental results of the frequency and temperature dependences of coercive electric filed (E(c)) obtained from polarization-electric field (P-E) hysteresis loop, the crosscorrelation phenomena between magnetics and ferroelectrics are discussed in detail. The P-E hysteresis loops of the films were measured in the frequency range from 1 Hz to 10 kHz, and the temperature was varied from 10 to 150 K. Frequency dependence of Ec accorded with Ishibashi-Orihara's theory at the measured temperature range. However, temperature dependence of E(c) disagreed with Devonshire's theory below 120 K, which is close to the Néeel temperature of the YMnO(3) epitaxial film. disagreed with Devonshire's theory below 120 K, which is close to the Neel temperature of the YMnO(3) epitaxial film.     

High-resolution studies of domain switching behavior in nanostructured ferroelectric polymers

We have demonstrated an effective electrical control of polarization in the individual crystalline nanomesas of the ferroelectric polymer, poly(vinylidene fluoride)-trifluoroethylene (PVDF-TrFE) and its relation to the polymer structure. The mechanism of polarization reversal has been investigated via sub-10 nm real space imaging of domain pattern evolution under an applied electric field. The domain switching behavior revealed in PVDF-TrFE nanomesas is drastically different from that observed in inorganic solid-state crystalline ferroelectrics. The nanoscale features of the switching process include remote domain nucleation and spatially nonuniform wall velocity. Local switching spectroscopy and domain dynamics studies relate the observed switching features to a random-bond type disorder associated with defects in conformation and molecular packing.     

Photovoltaics with Ferroelectrics: Current Status and Beyond

Ferroelectrics carry a switchable spontaneous electric polarization. This polarization is usually coupled to strain, making ferroelectrics good piezoelectrics. When coupled to magnetism, they become so‐called multiferroic systems, a field that has been widely investigated since 2003. While ferroelectrics are birefringent and non‐linear optically transparent materials, the coupling of polarization with optical properties has received, since 2009, renewed attention, triggered notably by low‐bandgap ferroelectrics suitable for sunlight spectrum absorption and original photovoltaic effects. Consequently, power conversion efficiencies up to 8.1% were recently achieved and values of 19.5% were predicted, making photoferroelectrics promising photovoltaic alternatives. This article aims at providing an up‐to‐date review on this emerging and rapidly progressing field by highlighting several important issues and parameters, such as the role of domain walls, ways to tune the bandgap, consequences arising from the polarization switchability, and the role of defects and contact electrodes, as well as the downscaling effects. Beyond photovoltaicity, other polarization‐related processes are also described, like light‐induced deformation (photostriction) or light‐assisted chemical reaction (photostriction). It is hoped that this overview will encourage further avenues to be explored and challenged and, as a byproduct, will inspire other research communities in material science, e.g., so‐called hybrid halide perovskites.     

Energetic analysis of ferroelectric domain patterns by equivalent inclusion method

The formation of domain configuration in ferroelectrics is a consequence of energy minimization, and critically depends on their transformation strain and spontaneous polarization. In this article, we develop an energetic analysis on ferroelectric domain patterns using equivalent inclusion method, treating ferroelectric domain as an ellipsoidal inhomogeneous inclusion in a ferroelectric matrix. The potential energy of the domain is calculated in terms of its orientation and shape, and the energy minimizing configurations have been identified. Both tetragonal and rhombohedral crystals have been analyzed, and the lamellar domain configurations as predicted by the compatibility analysis have been recovered. Additional energy minimizing states have also been revealed, including needle type of domains and charged domains. Different contributions of strain compatibility and polarization compatibility have also been analyzed.     

Microstructure,dielectric and ferroelectric properties of barium zirconate titanate ceramics prepared by microwave sintering

Barium zirconate titanate ceramics were fabricated by microwave sintering. Effects of microwave sintering time on microstructure, dielectric and ferroelectric properties of barium zirconate titanate ceramics have been investigated. The result shows that the ceramic samples sintered at 2.5 kW for 15–30 min are single phase perovskite structure and there is no secondary phase observed. As the microwave sintering time extends, barium zirconate titanate ceramics become more uniform and the grain size increases. The data of dielectric properties indicate that the samples prepared by microwave sintering for 15–30 min are the ferroelectrics with diffuse phase transition and the diffuseness of phase transition weakens with the extending of microwave sintering time. As microwave sintering time increases, the remnant polarization increases initially and then decreases. Moreover, the remnant polarization and the coercive field of the samples sintered for 15 and 20 min decrease as measuring frequency increases, but the measuring frequency has little effect on ferroelectricity of the sample sintered for 30 min. The temperature dependences of hysteresis loops further prove that the samples are ferroelectrics with diffuse phase transition.     

Domain wall velocity and interrupted pulse experiments

The velocity of magnetic domain walls in Bloch wall Permalloy thin films excited by interrupted easy axis drive fields is investigated and correlated with the available theory of transient wall contraction. The experimental technique is useful in determining the average wall velocity, and by comparing the velocity-field curves with field duration as a parameter it is possible to infer several features of the transient behavior. It is found that, when the displacement of the wall is of the order of a characteristic distance associated with the wall coercive force interaction, the threshold field for net motion as well as the mobility of the average velocity curves depend on the field duration. The theory together with a breakable-spring model of the coercive force interaction reasonably explain the observed phenomena.     

铁电微分回线谱参数和极化疲劳

用铁电微分回线谱分析方法研究了Ba _0.99 Sr _0.01 TiO ₃陶瓷的极化疲劳效应, 该方法可将线性和非线性电导、非铁电极化电容、以及纯铁电极化信号完全分开. 实验给出各效应对应的微分谱线型参数在疲劳过程中的变化规律, 并据此分出样品中分别由180°畴和90°畴提供的极化, 发现在同等作用下, 180°畴提供的极化更快出现疲劳.