Structure of Weiss domains in ferroelectric crystals

The structure of Weiss domains in ferroelectric crystals in each of which the polarization vector is constant, is investigated through a new variational principle. The general field equations are obtained and it is shown that in the presence of external electric field the total electric field is also constant in Weiss domains but is usually different from that of the polarization field. Moreover, it is proved that domain walls can only be planar surfaces. Finally the case corresponding to pure polarization fields is also treated and an illustrative problem is considered.     

Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces

The polarization of the ferroelectric BiFeO(3) sub-jected to different electrical boundary conditions by heterointerfaces is imaged with atomic resolution using a spherical aberration-corrected transmission electron microscope. Unusual triangular-shaped nanodomains are seen, and their role in providing polarization closure is understood through phase-field simulations. Heterointerfaces are key to the performance of ferroelectric devices, and this first observation of spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces reveals properties unlike the surrounding film including mixed Ising-Ne?el domain walls, which will affect switching behavior, and a drastic increase of in-plane polarization. The importance of magnetization closure has long been appreciated in multidomain ferromagnetic systems; imaging this analogous effect with atomic resolution at ferroelectric heterointerfaces provides the ability to see device-relevant interface issues. Extension of this technique to visualize domain dynamics is envisioned.     

Atomic-scale study of electric dipoles near charged and uncharged domain walls in ferroelectric films

Ferroelectrics are materials exhibiting spontaneous electric polarization due to dipoles formed by displacements of charged ions inside the crystal unit cell. Their exceptional properties are exploited in a variety of microelectronic applications. As ferroelectricity is strongly influenced by surfaces, interfaces and domain boundaries, there is great interest in exploring how the local atomic structure affects the electric properties. Here, using the negative spherical-aberration imaging technique in an aberration-corrected transmission electron microscope, we investigate the cation-oxygen dipoles near 180 degrees domain walls in epitaxial PbZr(0.2)Ti(0.8)O(3) thin films on the atomic scale. The width and dipole distortion across a transversal wall and a longitudinal wall are measured, and on this basis the local polarization is calculated. For the first time, a large difference in atomic details between charged and uncharged domain walls is reported.     

Structure of weiss domains in elastic ferroelectric crystals

In this work a variational principle is proposed to study the existence and structure of Weiss domains in elastic ferroelectric crystals. Weiss domains are defined as certain subregions of the crystal in each of which the polarization vector is uniform and has a constant magnitude which is equal to the saturation polarization per unit mass for the crystal. The variational principle differs from previous ones in that the variations of the domain walls are also taken into account and it is a direct generalization of the one corresponding to the rigid crystals which we have proposed earlier. In deriving the general theory the dependence on the polarization gradients are also considered and the effect of this dependence when passing from one domain to another is represented by an appropriately chosen surface energy on domain walls. The domain structure is studied under homogeneous deformation. The effect of a small deformation field on the shape of domains is illustrated in the case of a rectangular uniaxial crystal which has initially no electric field inside. It is shown that the deformation creates a small electric field in the crystal and domain walls change slightly.     

Tunable metallic conductance in ferroelectric nanodomains

Metallic conductance in charged ferroelectric domain walls was predicted more than 40 years ago as the first example of an electronically active homointerface in a nonconductive material. Despite decades of research on oxide interfaces and ferroic systems, the metal-insulator transition induced solely by polarization charges without any additional chemical modification has consistently eluded the experimental realm. Here we show that a localized insulator-metal transition can be repeatedly induced within an insulating ferroelectric lead-zirconate titanate, merely by switching its polarization at the nanoscale. This surprising effect is traced to tilted boundaries of ferroelectric nanodomains, that act as localized homointerfaces within the perovskite lattice, with inherently tunable carrier density. Metallic conductance is unique to nanodomains, while the conductivity of extended domain walls and domain surfaces is thermally activated. Foreseeing future applications, we demonstrate that a continuum of nonvolatile metallic states across decades of conductance can be encoded in the size of ferroelectric nanodomains using electric field.     

Dynamics of ferroelastic domains in ferroelectric thin films

Dynamics of domain interfaces in a broad range of functional thin-film materials is an area of great current interest. In ferroelectric thin films, a significantly enhanced piezoelectric response should be observed if non-180 degrees domain walls were to switch under electric field excitation. However, in continuous thin films they are clamped by the substrate, and therefore their contribution to the piezoelectric response is limited. In this paper we show that when the ferroelectric layer is patterned into discrete islands using a focused ion beam, the clamping effect is significantly reduced, thereby facilitating the movement of ferroelastic walls. Piezo-response scanning force microscopy images of such islands in PbZr0.2Ti0.8O3 thin films clearly point out that the 90 degrees domain walls can move. Capacitors 1 microm2 show a doubling of the remanent polarization at voltages higher than approximately 15 V, associated with 90 degrees domain switching, coupled with a d33 piezoelectric coefficient of approximately 250 pm V-1 at remanence, which is approximately three times the predicted value of 87 pm V-1 for a single domain single crystal.     

Modeling of ferroelectric domains in thin films and superlattices

We have developed the set of numerical (finite-element) and analytical tools that are based on the self-consistent solution of the electrostatic equations coupled with material Ginzburg–Landau equations with an objective to model the profile of domain textures in the entire temperature region. We calculated the evolution of principal parameters of domain texture: modulation vector, distribution of polarization, renormalization of critical temperature etc. In contrast to the Kittel approximation we conclude that the profile of polarization across domains in nanometric ferroelectric thin films is highly nonuniform.     

Structural visualization of polarization fatigue in epitaxial ferroelectric oxide devices

Ferroelectric oxides, such as Pb(Zr,Ti)O(3), are useful for electronic and photonic devices because of their ability to retain two stable polarization states, which can form the basis for memory and logic circuitry. Requirements for long-term operation of practical devices such as non-volatile RAM (random access memory) include consistent polarization switching over many (more than 10(12)) cycles of the applied electric field, which represents a major challenge. As switching is largely controlled by the motion and pinning of domain walls, it is necessary to develop suitable tools that can directly probe the ferroelectric domain structures in operating devices-thin-film structures with electrical contacts. A recently developed synchrotron X-ray microdiffraction technique complements existing microscopic probes, and allows us to visualize directly the evolution of polarization domains in ferroelectric devices, through metal or oxide electrodes, and with submicrometre spatial resolution. The images reveal two regimes of fatigue, depending on the magnitude of the electric field pulses driving the device: a low-field regime in which fatigue can be reversed with higher electric field pulses, and a regime at very high electric fields in which there is a non-reversible crystallographic relaxation of the epitaxial ferroelectric film.     

Surface-stabilized ferroelectric liquid-crystal diffraction gratings with micrometer-scale pitches

The first-order diffraction efficiency eta1 of surface-stabilized ferroelectric liquid-crystal (SSFLC) phase gratings is calculated for device thicknesses in the range d = 1 to 5 microm and for pitches p of 5 to 20 microm assuming incident light at 633 nm. The peak value of eta1 as a function of d has negligible dependence on the incoming polarization when p = 20 microm. For smaller pitch values the peak value of eta1 decreases and becomes increasingly dependent on the orientation of the incoming polarization owing to the influence of the domain walls that occur between the SSFLC pixels.     

Complementary characterization techniques for identification of ferroelectric domains in KNbO3 single crystals

KNbO₃ single crystals are often utilized for their piezoelectric and optical properties. In this study the domain configurations in as-grown single crystals were investigated using reflected light microscopy, scanning electron microscopy and atomic force microscopy. Using atomic force microscopy it was possible to image the distortion induced on the crystal surface by the domain walls and to quantify the predicted angle between (001)_pc planes across these walls for the cases of both 90° domain walls and S walls. These features can also be imaged using the other two techniques. This direct measurement of surface distortion verifies the geometrical model of domain structures, and suggests that any possible strain energy considerations are minor in predicting the surface topography in the material after phase changes from the growth temperature.     

A threshold electric field for acoustic emission from ferroelectric Rochelle salt

As Rochelle salt is cycled around its ferroelectric loop, copious acoustic emission (AE) is produced, predominantly as the regions of saturation polarisation at the loop extremities are approached. A threshold field for AE has been found, which has been measured throughout the temperature range (?18° to +24°C) in which Rochelle salt is in its ferroelectric state. Near both the lower and upper Curie points the threshold field becomes larger, a finding which is attributed to the higher voltage required to induce the acoustic noise generating processes, namely domain wall nucleation and annihilation, because as each Curie point is approached the domain walls become more mobile.     

Electrostatic coupling and local structural distortions at interfaces in ferroelectric/paraelectric superlattices

The performance of ferroelectric devices is intimately entwined with the structure and dynamics of ferroelectric domains. In ultrathin ferroelectrics, ordered nanodomains arise naturally in response to the presence of a depolarizing field and give rise to highly inhomogeneous polarization and structural profiles. Ferroelectric superlattices offer a unique way of engineering the desired nanodomain structure by modifying the strength of the electrostatic interactions between different ferroelectric layers. Through a combination of X-ray diffraction, transmission electron microscopy, and first-principles calculations, the electrostatic coupling between ferroelectric layers is studied, revealing the existence of interfacial layers of reduced tetragonality attributed to inhomogeneous strain and polarization profiles associated with the domain structure.     

Abnormal C–V curve and clockwise hysteresis loop in ferroelectric barium stannate titanate ceramics

Reversible hysteresis loop, defined as integral of small signal dielectric constant with electrical field, represents the contribution of the reversible part of polarization. In barium stannate titanate ceramics, field dependence of small signal dielectric constant was abnormal. The subsequent mathematical integral showed an abnormal clockwise hysteresis loop in the temperature range of 10–40 °C. The ferroelectric hysteresis loop measured by Sawyer–Tower circuit showed slim-waist or pinched shape. This phenomenon may reveal abnormal domain switching mechanism and is believed to be related with the strong interaction between point defects and domain walls.     

Structural consequences of ferroelectric nanolithography

Domains of remnant polarization can be written into ferroelectrics with nanoscale precision using scanning probe nanolithography techniques such as piezoresponse force microscopy (PFM). Understanding the structural effects accompanying this process has been challenging due to the lack of appropriate structural characterization tools. Synchrotron X-ray nanodiffraction provides images of the domain structure written by PFM into an epitaxial Pb(Zr,Ti)O(3) thin film and simultaneously reveals structural effects arising from the writing process. A coherent scattering simulation including the superposition of the beams simultaneously diffracted by multiple mosaic blocks provides an excellent fit to the observed diffraction patterns. Domains in which the polarization is reversed from the as-grown state have a strain of up to 0.1% representing the piezoelectric response to unscreened surface charges. An additional X-ray microdiffraction study of the photon-energy dependence of the difference in diffracted intensity between opposite polarization states shows that this contrast has a crystallographic origin. The sign and magnitude of the intensity contrast between domains of opposite polarization are consistent with the polarization expected from PFM images and with the writing of domains through the entire thickness of the ferroelectric layer. The strain induced by writing provides a significant additional contribution to the increased free energy of the written domain state with respect to a uniformly polarized state.     

铁电阴极电子发射研究进展

铁电发射是一种新型强流受激电子发射，本文综述了铁电弱发射和强发射的研究现状及其发射机理，重点分析了不同的铁电体相结构、电压脉冲激励波形、铁电发射结构以及萃取电压的波形等对铁电阴极电子发射特性和工作机理的影响，总结了目前铁电阴极等离子体辅助电子发射机理和模型，最后介绍了铁电阴极的应用前景。     

Strong ultrasonic microwaves in ferroelectric ceramics

It is well known that ferroelectric materials have piezoelectric properties which allow the transformation of electrical signals into mechanical signals and vice versa. The transducer action normally is restricted to frequencies up to the mechanical resonance frequency of the sample. There are, however, two mechanisms which allow transducer action in ferroelectric ceramics at much higher frequencies: one is the normal piezoelectric effect in a ferroelectric ceramic in which the crystallites have periodic domain structures, the other is a domain wall effect in which ferroelastic domain walls in a periodic domain structure are powerful shear wave emitters. Both mechanisms give rise to extensive dielectric losses in ceramics at microwave frequencies.     

Electroacoustic waves of a moving domain wall superlattice in a ferroelectric crystal

The dispersion properties of electroacoustic wave modes confined by a superlattice of 180° domain walls uniformly moving in a tetragonal ferroelectric crystal are considered. It is shown that the manifold of partial electroacoustic interfacial waves in the superlattice is restricted to the first allowed band, the configuration of which in the plane of spectral variables can significantly vary under the action of moving domain walls. For the partial electroacoustic interfacial waves with the Bloch wavenumbers χ π/d (where d is the lattice half-period), the motion of domain walls is predicted to result in splitting of the modes of a static superlattice into pairs, which is invariant with respect to reversal of the direction of motion.     

Anisotropic conductance at improper ferroelectric domain walls

Transition metal oxides hold great potential for the development of new device paradigms because of the field-tunable functionalities driven by their strong electronic correlations, combined with their earth abundance and environmental friendliness. Recently, the interfaces between transition-metal oxides have revealed striking phenomena, such as insulator-metal transitions, magnetism, magnetoresistance and superconductivity. Such oxide interfaces are usually produced by sophisticated layer-by-layer growth techniques, which can yield high-quality, epitaxial interfaces with almost monolayer control of atomic positions. The resulting interfaces, however, are fixed in space by the arrangement of the atoms. Here we demonstrate a route to overcoming this geometric limitation. We show that the electrical conductance at the interfacial ferroelectric domain walls in hexagonal ErMnO(3) is a continuous function of the domain wall orientation, with a range of an order of magnitude. We explain the observed behaviour using first-principles density functional and phenomenological theories, and relate it to the unexpected stability of head-to-head and tail-to-tail domain walls in ErMnO(3) and related hexagonal manganites. As the domain wall orientation in ferroelectrics is tunable using modest external electric fields, our finding opens a degree of freedom that is not accessible to spatially fixed interfaces.     

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.     

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.