Order-disorder, ferroelasticity and mobility of domain walls in multiferroic Cu-Cl boracite.

Domain walls in Cu-Cl boracite develop as a consequence of an improper ferroelastic, improper ferroelectric transition, and have attracted close interest because some are conductive and all can be mechanically written and repositioned by application of an electric field. The phase transition and its associated dynamical properties have been analysed here from the perspective of strain and elasticity. Determination of spontaneous strains from published lattice parameter data has allowed the equilibrium long-range order parameter for F [Formula: see text]3c → Pca21 to be modelled simply as being close to the order-disorder limit. High acoustic loss in the cubic phase, revealed by resonant ultrasound spectroscopy, is consistent with the presence of dynamical microdomains of the orthorhombic structure with relaxation times in the vicinity of ∼10-5-10-6 s. Low acoustic loss in the stability field of the orthorhombic structure signifies, on the other hand, that ferroelastic twin walls which develop as a consequence of the order-disorder process are immobile on this time scale. A Debye loss peak accompanied by ∼1% elastic stiffening at ∼40 K is indicative of some freezing of defects which couple with strain or of some more intrinsic freezing process. The activation energy of ⩾∼0.01-0.02 eV implies a mechanism which could involve strain relaxation clouds around local ferroelectric dipoles or freezing of polarons that determine the conductivity of twin walls.

Low-Voltage Domain-Wall LiNbO3 Memristors.

Application of conducting ferroelectric domain walls (DWs) as functional elements may facilitate development of conceptually new resistive switching devices. In a conventional approach, several orders of magnitude change in resistance can be achieved by controlling the DW density using supercoercive voltage. However, a deleterious characteristic of this approach is high-energy cost of polarization reversal due to high leakage current. Here, we demonstrate a new approach based on tuning the conductivity of DWs themselves rather than on domain rearrangement. Using LiNbO3 capacitors with graphene, we show that resistance of a device set to a polydomain state can be continuously tuned by application of subcoercive voltage. The tuning mechanism is based on the reversible transition between the conducting and insulating states of DWs. The developed approach allows an energy-efficient control of resistance without the need for domain structure modification. The developed memristive devices are promising for multilevel memories and neuromorphic computing applications.

Studies of Multiferroic Palladium Perovskites.

We have studied the atomic force microscopy (AFM), X-ray Bragg reflections, X-ray absorption spectra (XAS) of the Pd L-edge, Scanning electron microscopey (SEM) and Raman spectra, and direct magnetoelectric tensor of Pd-substituted lead titanate and lead zirconate-titanate. A primary aim is to determine the percentage of Pd+4 and Pd+2 substitutional at the Ti-sites (we find that it is almost fully substitutional). The atomic force microscopy data uniquely reveal a surprise: both threefold vertical (polarized out-of-plane) and fourfold in-plane domain vertices. This is discussed in terms of the general rules for Voronoi patterns (Dirichlet tessellations) in two and three dimensions. At high pressures Raman soft modes are observed, as in pure lead titanate, and X-ray diffraction (XRD) indicates a nearly second-order displacive phase transition. However, two or three transitions are involved: First, there are anomalies in c/a ratio and Raman spectra at low pressures (P = 1 - 2 GPa); and second, the c/a ratio reaches unity at ca. P = 10 GPa, where a monoclinic (Mc) but metrically cubic transition occurs from the ambient tetragonal P4 mm structure in pure PbTiO3; whereas the Raman lines (forbidden in the cubic phase) remain until ca. 17 GPa, where a monoclinic-cubic transition is known in lead titanate.

Hall effect in charged conducting ferroelectric domain walls.

Enhanced conductivity at specific domain walls in ferroelectrics is now an established phenomenon. Surprisingly, however, little is known about the most fundamental aspects of conduction. Carrier types, densities and mobilities have not been determined and transport mechanisms are still a matter of guesswork. Here we demonstrate that intermittent-contact atomic force microscopy (AFM) can detect the Hall effect in conducting domain walls. Studying YbMnO3 single crystals, we have confirmed that p-type conduction occurs in tail-to-tail charged domain walls. By calibration of the AFM signal, an upper estimate of ∼1 × 1016 cm-3 is calculated for the mobile carrier density in the wall, around four orders of magnitude below that required for complete screening of the polar discontinuity. A carrier mobility of∼50 cm2V-1s-1 is calculated, about an order of magnitude below equivalent carrier mobilities in p-type silicon, but sufficiently high to preclude carrier-lattice coupling associated with small polarons.

A diode for ferroelectric domain-wall motion.

For over a decade, controlling domain-wall injection, motion and annihilation along nanowires has been the preserve of the nanomagnetics research community. Revolutionary technologies have resulted, like racetrack memory and domain-wall logic. Until recently, equivalent research in analogous ferroic materials did not seem important. However, with the discovery of sheet conduction, the control of domain walls in ferroelectrics has become vital for the future of what has been termed 'domain-wall electronics'. Here we report the creation of a ferroelectric domain-wall diode, which allows a single direction of motion for all domain walls, irrespective of their polarity, under a series of alternating electric field pulses. The diode's sawtooth morphology is central to its function. Domain walls can move readily in the direction in which thickness increases gradually, but are prevented from moving in the other direction by the sudden thickness increase at the sawtooth edge.

Switching ferroelectric domain configurations using both electric and magnetic fields in Pb(Zr,Ti)O3-Pb(Fe,Ta)O3 single-crystal lamellae.

Thin single-crystal lamellae cut from Pb(Zr,Ti)O3-Pb(Fe,Ta)O3 ceramic samples have been integrated into simple coplanar capacitor devices. The influence of applied electric and magnetic fields on ferroelectric domain configurations has been mapped, using piezoresponse force microscopy. The extent to which magnetic fields alter the ferroelectric domains was found to be strongly history dependent: after switching had been induced by applying electric fields, the susceptibility of the domains to change under a magnetic field (the effective magnetoelectric coupling parameter) was large. Such large, magnetic field-induced changes resulted in a remanent domain state very similar to the remanent state induced by an electric field. Subsequent magnetic field reversal induced more modest ferroelectric switching.

Studies of the Room-Temperature Multiferroic Pb(Fe0.5Ta0.5)0.4(Zr0.53Ti0.47)0.6O3: Resonant Ultrasound Spectroscopy, Dielectric, and Magnetic Phenomena.

Recently, lead iron tantalate/lead zirconium titanate (PZTFT) was demonstrated to possess large, but unreliable, magnetoelectric coupling at room temperature. Such large coupling would be desirable for device applications but reproducibility would also be critical. To better understand the coupling, the properties of all 3 ferroic order parameters, elastic, electric, and magnetic, believed to be present in the material across a range of temperatures, are investigated. In high temperature elastic data, an anomaly is observed at the orthorhombic mm2 to tetragonal 4mm transition, Tot = 475 K, and a softening trend is observed as the temperature is increased toward 1300 K, where the material is known to become cubic. Thermal degradation makes it impossible to measure elastic behavior up to this temperature, however. In the low temperature region, there are elastic anomalies near ≈40 K and in the range 160-245 K. The former is interpreted as being due to a magnetic ordering transition and the latter is interpreted as a hysteretic regime of mixed rhombohedral and orthorhombic structures. Electrical and magnetic data collected below room temperature show anomalies at remarkably similar temperature ranges to the elastic data. These observations are used to suggest that the three order parameters in PZTFT are strongly coupled.

Manipulating ferroelectric domains in nanostructures under electron beams.

Freestanding BaTiO3 nanodots exhibit domain structures characterized by distinct quadrants of ferroelastic 90° domains in transmission electron microscopy (TEM) observations. These differ significantly from flux-closure domain patterns in the same systems imaged by piezoresponse force microscopy. Based upon a series of phase field simulations of BaTiO3 nanodots, we suggest that the TEM patterns result from a radial electric field arising from electron beam charging of the nanodot. For sufficiently large charging, this converts flux-closure domain patterns to quadrant patterns with radial net polarizations. Not only does this explain the puzzling patterns that have been observed in TEM studies of ferroelectric nanodots, but also suggests how to manipulate ferroelectric domain patterns via electron beams.

Self-similar nested flux closure structures in a tetragonal ferroelectric.

In specific solid-state materials, under the right conditions, collections of magnetic dipoles are known to spontaneously form into a variety of rather complex geometrical patterns, exemplified by vortex and skyrmion structures. While theoretically, similar patterns should be expected to form from electrical dipoles, they have not been clearly observed to date: the need for continued experimental exploration is therefore clear. In this Letter we report the discovery of a rather complex domain arrangement that has spontaneously formed along the edges of a thin single crystal ferroelectric sheet, due to surface-related depolarizing fields. Polarization patterns are such that nanoscale "flux-closure" loops are nested within a larger mesoscale flux closure object. Despite the orders of magnitude differences in size, the geometric forms of the dual-scale flux closure entities are rather similar.

Magnetic switching of ferroelectric domains at room temperature in multiferroic PZTFT.

Single-phase magnetoelectric multiferroics are ferroelectric materials that display some form of magnetism. In addition, magnetic and ferroelectric order parameters are not independent of one another. Thus, the application of either an electric or magnetic field simultaneously alters both the electrical dipole configuration and the magnetic state of the material. The technological possibilities that could arise from magnetoelectric multiferroics are considerable and a range of functional devices has already been envisioned. Realising these devices, however, requires coupling effects to be significant and to occur at room temperature. Although such characteristics can be created in piezoelectric-magnetostrictive composites, to date they have only been weakly evident in single-phase multiferroics. Here in a newly discovered room temperature multiferroic, we demonstrate significant room temperature coupling by monitoring changes in ferroelectric domain patterns induced by magnetic fields. An order of magnitude estimate of the effective coupling coefficient suggests a value of ~1 × 10(-7) sm(-1).

Domain wall propagation in meso- and nanoscale ferroelectrics.

As part of an ongoing programme to evaluate the extent to which external morphology alters domain wall mobility in ferroelectrics, the electrical switching characteristics of single-crystal BaTiO(3) nanorods and thin film plates have been measured and compared. It was found that ferroelectric nanorods were more readily switched than thin plates; increasing the shape constraint therefore appears to enhance switchability. This observation is broadly consistent with previous work, in which local notches patterned along the length of nanorods enhanced switching (McMillen et al 2010 Appl. Phys. Lett. 96 042904), while antinotches had the opposite effect (McQuaid et al 2010 Nano Lett. 10 3566). In this prior work, local enhancement and denudation of the electric field was expected at the notch and antinotch sites, respectively, and this was thought to be the reason for the differences in switching behaviour observed. However, for the simple nanorods and plates investigated here, no differences in the electric field distributions are expected. To rationalise the functional measurements, domain development during switching was imaged directly by piezoresponse force microscopy. A two-stage process was identified, in which narrow needle-like reverse domains initially form across the entire interelectrode gap and then subsequently coarsen through domain wall propagation perpendicular to the applied electric field. To be consistent with the electrical switching data, we suggest that the initial formation of needle domains occurs more readily in the nanorods than in the plates.

Polarization closure in PbZr((0.42))Ti((0.58))O(3) nanodots.

Domain states in PbZr((0.42))Ti((0.58))O(3) single-crystal ferroelectric nanodots, formed on cooling through the Curie temperature, were imaged by transmission electron microscopy. In the majority of cases, 90° stripe domains were found to form into four distinct "bundles" or quadrants. Detailed analysis of the dipole orientations in the system was undertaken, using both dark-field imaging and an assumption that charged domain walls were energetically unfavorable in comparison to uncharged walls. On this basis, we conclude that the dipoles in these nanodots are arranged such that the resultant polarizations, associated with the four quadrant domain bundles, form into a closed loop. This "polarization closure" pattern is reminiscent of the flux-closure already commonly observed in soft ferromagnetic microdots but to date unseen in analogous ferroelectric dots.

Mesoscale flux-closure domain formation in single-crystal BaTiO3.

Over 60 years ago, Charles Kittel predicted that quadrant domains should spontaneously form in small ferromagnetic platelets. He expected that the direction of magnetization within each quadrant should lie parallel to the platelet surface, minimizing demagnetizing fields,and that magnetic moments should be configured into an overall closed loop, or flux-closure arrangement. Although now a ubiquitous observation in ferromagnets, obvious flux-closure patterns have been somewhat elusive in ferroelectric materials. This is despite the analogous behaviour between these two ferroic subgroups and the recent prediction of dipole closure states by atomistic simulations research. Here we show Piezoresponse Force Microscopy images of mesoscopic dipole closure patterns in free-standing, single-crystal lamellae of BaTiO(3). Formation of these patterns is a dynamical process resulting from system relaxation after the BaTiO(3) has been poled with a uniform electric field. The flux-closure states are composed of shape conserving 90° stripe domains which minimize disclination stresses.

Domain bundle boundaries in single crystal BaTiO3 lamellae: searching for naturally forming dipole flux-closure/quadrupole chains.

Naturally occurring boundaries between bundles of 90° stripe domains, which form in BaTiO(3) lamellae on cooling through the Curie Temperature, have been characterized using both piezoresponse force microscopy (PFM) and scanning transmission electron microscopy (STEM). Detailed interpretation of the dipole configurations present at these boundaries (using data taken from PFM) shows that in the vast majority of cases they are composed of simple zigzag 180° domain walls. Topological information from STEM shows that occasionally domain bundle boundaries can support chains of dipole flux closure and quadrupole nanostructures, but these kinds of boundaries are comparatively rare; when such chains do exist, it is notable that singularities at the cores of the dipole structures are avoided. The symmetry of the boundary shows that diads and centers of inversion exist at positions where core singularities should have been expected.

The effect of antinotches on domain wall mobility in single crystal ferroelectric nanowires.

Changes in domain wall mobility, caused by the presence of antinotches in single crystal BaTiO(3) nanowires, have been investigated. While antinotches appeared to cause a slight broadening in the distribution of switching events, observed as a function of applied electric field (inferred from capacitance-voltage measurements), the effect was often subtle. Greater clarity of information was obtained from Rayleigh analysis of the capacitance variation with ac field amplitude. Here the magnitude of the domain wall mobility parameter (alpha) associated with irreversible wall movements was found to be reduced by the presence of antinotches--an effect which became more noticeable on heating toward the Curie temperature. The reduction in this domain wall mobility was contrasted with the noticeable enhancement found previously in ferroelectric wires with notches. Finite element modeling of the electric field, developed in the nanowires during switching, revealed regions of increased and decreased local field at the center of the notch and antinotch structures, respectively; the absolute magnitude of field enhancement in the notch centers was considerably greater than the field reduction in the center of the antinotches and this was commensurate with the manner in, and degree to, which domain wall mobility appeared to be affected. We therefore conclude that the main mechanism by which morphology alters the irreversible component of the domain wall mobility in ferroelectric wire structures is via the manner in which morphological variations alter the spatial distribution of the electric field.

Domains in ferroelectric nanodots.

Almost free-standing single crystal mesoscale and nanoscale dots of ferroelectric BaTiO(3) have been made by direct focused ion beam patterning of bulk single crystal material. The domain structures which appear in these single crystal dots, after cooling through the Curie temperature, were observed to form into quadrants, with each quadrant consisting of fine 90 degrees stripe domains. The reason that these rather complex domain configurations form is uncertain, but we consider and discuss three possibilities for their genesis: first, that the quadrant features initially form to facilitate field-closure, but then develop 90 degrees shape compensating stripe domains in order to accommodate disclination stresses; second, that they are the result of the impingement of domain packets which nucleate at the sidewalls of the dots forming "Forsbergh" patterns (essentially the result of phase transition kinetics); and third, that 90 degrees domains form to conserve the shape of the nanodot as it is cooled through the Curie temperature but arrange into quadrant packets in order to minimize the energy associated with uncompensated surface charges (thus representing an equilibrium state). While the third model is the preferred one, we note that the second and third models are not mutually exclusive.

Ordered arrays of lead zirconium titanate nanorings.

Periodic arrays of nanorings of morphotropic phase boundary lead zirconium titanate (PZT) have been successfully fabricated using a novel self-assembly technique: close-packed monolayers of latex nanospheres were deposited onto Pt-coated silicon substrates, and then plasma cleaned to form ordered arrays of isolated nanospheres, not in contact with each other. Subsequent pulsed laser deposition of PZT, high angle argon ion etching and thermal annealing created the arrays of isolated nanorings, with diameters of ∼100 nm and wall thicknesses of ∼10 nm. Energy dispersive x-ray analysis confirms that the rings are compositionally morphotropic phase boundary PZT, and high resolution transmission electron microscopy imaging of lattice fringes demonstrates some periodicities consistent with perovskite rather than pyrochlore material. The dimensions of these nanorings, and the expected 'soft' behaviour of the ferroelectric material from which they are made, means that they offer the most likely opportunity to date for observing whether or not vortex arrangements of electrical dipoles, analogous to those seen in ferromagnetic nanostructures, actually exist.

Creation of damage-free ferroelectric nanostructures via focused ion beam milling.

We present a novel method for creating damage-free ferroelectric nanostructures with a focused ion beam milling machine. Using a standard e-beam photoresist followed by a dilute acid wash, nanostructures ranging in size from 1 µm down to 250 nm were created in a 90 nm thick lead zirconate titanate (PZT) wafer. Transmission electron microscopy and piezoresponse force microscopy (PFM) confirmed that the surfaces of the nanostructures remained damage free during fabrication, and showed no gallium implantation, and that there was no degradation of ferroelectric properties. In fact DC strain loops, obtained using PFM, demonstrated that the nanostructures have a higher piezoresponse than unmilled films. As the samples did not have any top hard mask, the method presented is unique as it allows for imaging of the top surface to understand edge effects in well-defined nanostructures. In addition, as no post-mill annealing was necessary, it facilitates investigation of nanoscale domain mechanisms without process-induced artefacts.

Strategies for gallium removal after focused ion beam patterning of ferroelectric oxide nanostructures.

As part of a study into the properties of ferroelectric single crystals at nanoscale dimensions, the effects that focused ion beam (FIB) processing can have, in terms of structural damage and ion implantation, on perovskite oxide materials has been examined, and a post-processing procedure developed to remove such effects. Single crystal material of the perovskite ferroelectric barium titanate (BaTiO(3)) has been patterned into thin film lamellae structures using a FIB microscope. Previous work had shown that FIB patterning induced gallium impregnation and associated creation of amorphous layers in a surface region of the single crystal material some 20 nm thick, but that both recrystallization and expulsion of gallium could be achieved through thermal annealing in air. Here we confirm this observation, but find that thermally induced gallium expulsion is associated with the formation of gallium-rich platelets on the surface of the annealed material. These platelets are thought to be gallium oxide. Etching using nitric and hydrochloric acids had no effect on the gallium-rich platelets. Effective platelet removal involved thermal annealing at 700 degrees C for 1 h in a vacuum followed by 1 h in oxygen, and then a post-annealing low-power plasma clean in an Ar/O atmosphere. Similar processing is likely to be necessary for the full recovery of post FIB-milled nanostructures in oxide ceramic systems in general.