Raymond G. P. McQuaid

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 BaTiO3. Formation of these patterns is a dynamical process resulting from system relaxation after the BaTiO3 has been poled with a uniform electric field. The flux-closure states are composed of shape conserving 90° stripe domains which minimize disclination stresses.

Ferroelectric Domain Wall Injection

Ferroelectric domain wall injection has been demonstrated by engineering of the local electric field, using focused ion beam milled defects in thin single crystal lamellae of KTiOPO4 (KTP). The electric field distribution (top) displays localized field hot-spots, which correlate with nucleation events (bottom). Designed local field variations can also dictate subsequent domain wall mobility, demonstrating a new paradigm in ferroelectric domain wall control.

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.

Exploring Vertex Interactions in Ferroelectric Flux-Closure Domains

Using piezoresponse force microscopy, we have observed the progressive development of ferroelectric flux-closure domain structures and Landau-Kittel-type domain patterns, in 300 nm thick single-crystal BaTiO3 platelets. As the microstructural development proceeds, the rate of change of the domain configuration is seen to decrease exponentially. Nevertheless, domain wall velocities throughout are commensurate with creep processes in oxide ferroelectrics. Progressive screening of macroscopic destabilizing fields, primarily the surface-related depolarizing field, successfully describes the main features of the observed kinetics. Changes in the separation of domain-wall vertex junctions prompt a consideration that vertex-vertex interactions could be influencing the measured kinetics. However, the expected dynamic signatures associated with direct vertex-vertex interactions are not resolved. If present, our measurements confine the length scale for interaction between vertices to the order of a few hundred nanometers.

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.

Sequential injection of domain walls into ferroelectrics at different bias voltages: Paving the way for “domain wall memristors”

Simple meso-scale capacitor structures have been made by incorporating thin (∼300 nm) single crystal lamellae of KTiOPO4 (KTP) between two coplanar Pt electrodes. The influence that either patterned protrusions in the electrodes or focused ion beam milled holes in the KTP have on the nucleation of reverse domains during switching was mapped using piezoresponse force microscopy imaging. The objective was to assess whether or not variations in the magnitude of field enhancement at localised “hot-spots,” caused by such patterning, could be used to both control the exact locations and bias voltages at which nucleation events occurred. It was found that both the patterning of electrodes and the milling of various hole geometries into the KTP could allow controlled sequential injection of domain wall pairs at different bias voltages; this capability could have implications for the design and operation of domain wall electronic devices, such as memristors, in the future.

The influence of notches on domain dynamics in ferroelectric nanowires

The extent to which notches inhibit axial switching of polarization in ferroelectric nanowires was investigated by monitoring the switching behavior of single crystal BaTiO3 wires before and after patterning triangular notches along their lengths. Static zero-field domain patterns suggested a strong domain-notch interaction, implying that notches should act as pinning sites for domain wall propagation. Surprisingly though, notches appeared to assist, rather than inhibit, polar switching. The origin of this effect was rationalized using finite element modeling of the electric field distribution along the notched wire; it was found that the air gap associated with the notch acted to enhance the local field, both in the air, and in the adjacent region of the ferroelectric. It seems that this local field enhancement outweighs any pinning interactions.

Injection and controlled motion of conductingdomain walls in improper ferroelectric Cu-Clboracite

Ferroelectric domain walls constitute a completely new class of sheet-like functional material. Moreover, since domain walls are generally writable, erasable and mobile, they could be useful in functionally agile devices: for example, creating and moving conducting walls could make or break electrical connections in new forms of reconfigurable nanocircuitry. However, significant challenges exist: site-specific injection and annihilation of planar walls, which show robust conductivity, has not been easy to achieve. Here, we report the observation, mechanical writing and controlled movement of charged conducting domain walls in the improper-ferroelectric Cu3B7O13Cl. Walls are straight, tens of microns long and exist as a consequence of elastic compatibility conditions between specific domain pairs. We show that site-specific injection of conducting walls of up to hundreds of microns in length can be achieved through locally applied point-stress and, once created, that they can be moved and repositioned using applied electric fields.

Large Carrier Mobilities in ErMnO3 Conducting Domain Walls Revealed by Quantitative Hall-Effect Measurements

Kelvin probe force microscopy (KPFM) has been used to directly and quantitatively measure Hall voltages, developed at conducting tail-to-tail domain walls in ErMnO3 single crystals, when current is driven in the presence of an approximately perpendicular magnetic field. Measurements across a number of walls, taken using two different atomic force microscope platforms, consistently suggest that the active p-type carriers have unusually large room temperature mobilities of the order of hundreds of square centimeters per volt second. Associated carrier densities were estimated to be of the order of 1013 cm-3. Such mobilities, at room temperature, are high in comparison with both bulk oxide conductors and LaAlO3-SrTiO3 sheet conductors. High carrier mobilities are encouraging for the future of domain-wall nanoelectronics and, significantly, also suggest the feasibility of meaningful investigations into dimensional confinement effects in these novel domain-wall systems.