Domains in three-dimensional ferroelectric nanostructures

We report the experimental measurement of domains in single- crystal nanocolumns of ferroelectric BaTiO3, together with a theory of domain size scaling in three- dimensional structures which explains the observations.

Nanoscale ferroelectrics machined from single crystals

This paper summarises some of the most recent work that has been done on nanoscale ferroelectrics as a result of a joint collaborative research effort involving groups in Queen's University Belfast, the University of Cambridge and the University of St. Andrews. Attempts have been made to observe fundamental effects of reduced size, and increasing morphological complexity, on ferroelectric behaviour by studying the functional response and domain characteristics in nanoscale single crystal material, whose size and morphology have been defined by Focused Ion Beam (FIB) patterning. This approach to nanoshape fabrication has allowed the following broad statements to be made: (i) in single crystal BaTiO3 sheets, permittivity and phase transition behaviour is not altered from that of bulk material down to a thickness of similar to 75 nm; (ii) in single crystal BaTiO3 sheets and nanowires changes in observed domain morphologies are consistent with large scale continuum modeling.

Thin film capacitor cut from single crystals using focused ion beam milling

The focused ion beam microscope (FIB) has been used to fabricate thin parallel-sided ferroelectric capacitors from single crystals of BaTiO3 and SrTiO3. A series of nano-sized capacitors ranging in thickness from similar to660 nm to similar to300 nm were made. Cross-sectional high resolution transmission electron microscopy (HRTEM) revealed that during capacitor fabrication, the FIB rendered around 20 nm of dielectric at the electrode-dielectric interface amorphous, associated with local gallium impregnation. Such a region would act electrically in series with the single crystal and would presumably have a considerable negative influence on the dielectric properties. However, thermal annealing prior to gold electrodes deposition was found to fully recover the single crystal capacitors and homogenise the gallium profile. The dielectric testing of the STO ultra-thin single crystal capacitors was performed yielding a room temperature dielectric constant of similar to300, as is the case in bulk. Therefore, there was no evidence of a collapse in dielectric constant associated with thin film dimensions.

Size Effects on Thin Film Ferroelectrics: Experiments on Isolated Single Crystal Sheets

Thin lamellae were cut from bulk single crystal BaTiO3 using a Focused Ion Beam Microscope. They were then removed and transferred onto single crystal MgO substrates, so that their functional properties could be measured independent of the original host bulk ferroelectric. The temperature dependence of the capacitance of these isolated single crystal films was found to be strongly bulk-like, demonstrating a sharp Curie anomaly, as well as Curie-Weiss behaviour. In addition, the sudden change in the remanent polarisation as a function of temperature at TC was characteristic of a first order phase change. The work represents a dramatic improvement on that previously published by M. M. Saad, P. Baxter, R. M. Bowman, J. M. Gregg, F. D. Morrison & J. F. Scott, J. Phys: Cond. Matt., 16 L451-L456 (2004), as critical shortcomings in the original specimen geometry, involving potential signal contributions from bulk BaTiO3, have now been obviated. That the functional properties of single crystal thin film lamellae are comparable to bulk, and not like those of conventionally deposited heteroegenous thin film systems, has therefore been confirmed.

Origin of Ferroelastic domains in Free-Standing Single Crystal Ferroelectric Films

The origin of the unusual 90 degrees ferroelectric/ferroelastic domains, consistently observed in recent studies on mesoscale and nanoscale free-standing single crystals of BaTiO3 [Schilling , Phys. Rev. B 74, 024115 (2006); Schilling , Nano Lett. 7, 3787 (2007)], has been considered. A model has been developed which postulates that the domains form as a response to elastic stress induced by a surface layer which does not undergo the paraelectric-ferroelectric cubic-tetragonal phase transition. This model was found to accurately account for the changes in domain periodicity as a function of size that had been observed experimentally. The physical origin of the surface layer might readily be associated with patterning damage, seen in experiment; however, when all evidence of physical damage is removed from the BaTiO3 surfaces by thermal annealing, the domain configuration remains practically unchanged. This suggests a more intrinsic origin, such as the increased importance of surface tension at small dimensions. The effect of surface tension is also shown to be proportional to the difference in hardness between the surface and the interior of the ferroelectric. The present model for surface-tension induced twinning should also be relevant for finely grained or core-shell structured ceramics.

The Influence of Point Defects and Inhomogeneous Strain on the Functional Behaviour of Thin film Ferroelectrics

An attempt has been made to unequivocally identify the influence that inhomogeneous strain fields, surrounding point defects, have on the functional properties of thin film ferroelectrics. Single crystal thin film lamellae of BaTiO3 have been integrated into capacitor structures, and the functional differences between those annealed in oxygen and those annealed in nitrogen have been mapped. Key features, such as the change in the paraelectric-ferroelectric phase transition from first to second order were noted and found to be consistent with mean field modeling predictions for the effects of inhomogeneous strain. Switching characteristics appeared to be unaffected, suggesting that point defects have a low efficacy in domain wall pinning.

Effect of wall thickness on the ferroelastic domain size of BaTiO3

Extremely regular self-organized patterns of 90^o ferroelastic domains have been reported in freestanding single crystal thin films of ferroelectric BaTiO₃. Lukyanchuk et al. [Phys Rev B 79, 144111 (2009)] have recently shown that the domain size as a function of thickness for such free standing films can be well described assuming that the domains are due to stress caused by a surface tension layer that does not undergo the paraelectric–ferroelectric transition. From the starting point of Lukyanchuk’s model, it is shown here that the ‘‘universal’’relationship between domain size and domain wall thickness previously observed in ferroelectrics, ferromagnets and multiferroics is also valid for ferroelastic domains.Further analysis of experimental data also shows that the domain wall thickness can vary considerably (an order of magnitude) from sample to sample even for the same material (BaTiO₃), in spite of which the domain size scaling model is still valid, provided that the correct,sample dependent, domain wall thickness is used.

Domains in Ferroelectric Nanodots

Almost free-standing single crystal mesoscale and nanoscale dots of ferroelectric BaTiO3 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° 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° 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° 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.

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 BaTiO3 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 (R) 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.

Scaling of Superdomain Bands in Ferroelectric Dots

Bundles of 90° stripe domains have been observed to form into distinct groups, or bands, in mesoscale BaTiO3 single crystal dots. Vector piezoresponse force microscopy (PFM) shows that each band region, when considered as a single entity, possesses a resolved polarization that lies approximately along the pseudocubic direction; antiparallel alignment of this resultant polarization in adjacent bands means that these regions can be considered as 180° “superdomains.” For dots with sidewall dimensions below ~2 microns, Landau–Kittel like scaling in the width of these superdomains was observed, strongly suggesting that they form in response to lateral depolarizing fields. In larger dot structures, scaling laws break down. We have rationalized these observations by considering changes in the driving force for the adoption of equilibrium superdomain periodicities implied by Landau–Kittel-free energy models; we conclude that the formation of ordered bands of superdomains is a uniquely meso/nanoscale phenomenon. We also note that the superdomain bands found by PFM imaging in air contrast with the quadrant arrangements seen previously by Schilling et al. (Nano Lett., 9, 3359 (2009)) through transmission electron microscopy imaging in vacuum. The importance of the exact nature of the boundary conditions in determining the domain patterns that spontaneously form in nanostructures is therefore clearly implied.

Shape-induced phase transition of domain patterns in ferroelectric platelets

Using a combination of experimental and computational techniques, changes in the domain structures seen infreestanding single-crystal platelets of BaTiO3 have been described in terms of a second-order phase transition.The transition is driven by the change in the length-to-width ratio of the platelet sidewalls and results in a symmetrybreaking of a complex, quadrant domain pattern. The phenomenon can be described by a Landau formalism inwhich (1) the order parameter is not the polarization but rather is the degree to which the domain pattern becomesoff-centered, and (2) the shape anisotropy of the platelet substitutes for temperature in the conventional Landauexpansion as the controlling thermodynamic variable. Bistability, in terms of the direction in which the domainpattern moves off center, coupled with the spontaneous macroscopic polarization and toroidal moment that resultfrom this off-centering, prompt the possibility of a new form of memory storage.

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 BaTiO3 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.

Room-temperature single phase multiferroic magnetoelectrics: Pb(Fe,M)x(Zr,Ti)(1−x)O3 [M=Ta, Nb]

We describe extensive studies on a family of perovskite oxides that are ferroelectric and ferromagnetic at ambient temperatures. The data include x-ray diffraction, Raman spectroscopy, measurements of ferroelectric and magnetic hysteresis, dielectric constants, Curie temperatures, electron microscopy
(both scanning electron microscope and transmission electron microscopy (TEM)) studies, and both longitudinal and transverse magnetoelectric constants a33 and a31. The study extends earlier work to lower Fe, Ta, and Nb concentrations at the B-site (from 15%–20% down to 5%). The magnetoelectric
constants increase supralinearly with Fe concentrations, supporting the earlier conclusions of a key role for Fe spin clustering. The room-temperature orthorhombic C2v point group symmetry inferred from earlier x-ray diffraction studies is confirmed via TEM, and the primitive unit cell size is found to be the basic perovskite Z¼1 structure of BaTiO3, also the sequence of phase transitions with increasing temperature from rhombohedral to orthorhombic to tetragonal to cubic mimics barium titanate.

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.

Nucleation-Induced Self-Assembly of Multiferroic BiFeO3-CoFe2O4 Nanocomposites

Large areas of perfectly ordered magnetic CoFe2O4 nanopillars embedded in a ferroelectric BiFeO3 matrix were successfully fabricated via a novel nucleation-induced self-assembly process. The nucleation centers of the magnetic pillars are induced before the growth of the composite structure using anodic aluminum oxide (AAO) and lithography-defined gold membranes as hard mask. High structural quality and good functional properties were obtained. Magneto-capacitance data revealed extremely low losses and magneto-electric coupling of about 0.9 mu C/cmOe. The present fabrication process might be relevant for inducing ordering in systems based on phase separation, as the nucleation and growth is a rather general feature of these systems.