Scaling of domain periodicity with thickness measured in BaTiO3 single crystal lamellae and comparison with other ferroics

The focused ion beam microscope has been used to cut parallel-sided {100}-oriented thin lamellae of single crystal barium titanate with controlled thicknesses, ranging from 530 nm to 70 nm. Scanning transmission electron microscopy has been used to examine domain configurations. In all cases, stripe domains were observed with {011}-type domain walls in perovskite unit-cell axes, suggesting 90 degrees domains with polarization in the plane of the lamellae. The domain widths were found to vary as the square root of the lamellar thickness, consistent with Kittel's law, and its later development by Mitsui and Furuichi and by Roytburd. An investigation into the manner in which domain period adapts to thickness gradient was undertaken on both wedge-shaped lamellae and lamellae with discrete terraces. It was found that when the thickness gradient was perpendicular to the domain walls, a continuous change in domain periodicity occurred, but if the thickness gradient was parallel to the domain walls, periodicity changes were accommodated through discrete domain bifurcation. Data were then compared with other work in literature, on both ferroelectric and ferromagnetic systems, from which conclusions on the widespread applicability of Kittel's law in ferroics were made.

Maximum of dielectric permittivity caused by structural transition in ferroelectric BaTiO3-SrTiO3 superlattices

We invoke the onset of dislocations along the BaTiO3-SrTiO3 interface as reported by Wunderlich et al. to explain the non-monotonic behaviour of the dielectric permittivity as a function of superlattice periodicity and the less than four-fold in-plane symmetry at the dielectric maximum. At a periodicity of about 10/10, depending on composition and growth mechanism, several groups report a maximum of dielectric permittivity. In addition to that we observe in-plane symmetry less than tetragonal for 10/10 superlattices by HR-XRD, in contrast to initial low-resolution data from Tabata et al. thus challenging the assumption of unrelaxed strain all the way through the superlattice. The aim of this article is to link both effects to the increasing volume fraction of conducting layers close to the interface in series with the superlattice layers.

Imaging domains in BaTiO3 single crystal nanostructures: comparing information from transmission electron microscopy and piezo-force microscopy

This article compares and contrasts information
obtained, using transmission electron microscopy (TEM)
and piezo-force microscopy (PFM), on domain configurations
adopted in single crystal lamellae of BaTiO3, that had
been cut directly from bulk using a focused ion beam
microscope with top and bottom surfaces parallel to
{100}pseudocubic. Both forms of imaging reveal domain
walls parallel to {110}pseudocubic, consistent with sets of 90
domains with dipoles oriented parallel to the two
\001[pseudocubic directions in the plane of the lamellae.
However, the domain width was observed to be dramatically
larger using PFM than it was using TEM. This suggests
significant differences in the surface energy densities
that drive the domain formation in the first place, that could
relate to differences in the boundary conditions in the two
modes of imaging (TEM samples are imaged under high
vacuum, whereas PFM imaging was performed in air).
Attempts were made to map local dipole orientations
directly, using a form of ‘vector’ PFM. However, information
inferred was largely inconsistent with the known
crystallography of the samples, raising concern about the
levels of care needed for accurate interpretation of PFM
images.

Domain Bundle Boundaries in Single Crystal BaTiO3 Lamellae: Searching for Naturally Forming Dipole Flux-Closure / Quadrupole Chains

Naturally occurring boundaries between bundles of 90o stripe domains, which form in BaTiO3 lamellae on cooling through the Curie Temperature, have been characterised 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 centres of inversion exist at positions where core singularities should have been expected.

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.

Domain annihilation due to temperature and thickness gradients in single-crystal BaTiO3

The manner in which 90? ferroelectric-ferroelastic domains respond to changes in temperature has been mapped in BaTiO3 single crystals using atomic force microscopy. Domain periodicity remains unaltered until approximately 2 ? C below the Curie temperature (TC ), whereupon domains coarsened dramatically. This behavior was successfully rationalized by considering the temperature dependence of the parameters associated with standard models of ferroelastic domain formation. However, while successful in describing the expected radical increase in equilibrium period with temperature, the model did not predict the unusual mechanism by which domain coarsening occurred; this was not continuous at a local level but instead involved discrete domain annihilation events. Subsequent insights from a combination of free energy analysis for the system and further experimental data from an analogous situation, in which domain period increases with increasing crystal thickness, suggested that domain annihilation is inevitable whenever a component of the relevant gradient that affects domain period is orientated parallel to the domain walls. Consistent with this thesis, we note that, for the observations presented herein, the thermal gradient possessed a significant component parallel to the domain walls. We suggest that domain annihilation is a general feature of domain structures in gradient fields.

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 BaTiO3 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.

Morphology dependence of the dielectric properties of epitaxial BaTiO3 films and epitaxial BaTiO3/SrTiO3 multilayers

Epitaxial BaTiO3 films and epitaxial BaTiO3/SrTiO3 multilayers were grown by pulsed laser deposition on vicinal surfaces of (001)-oriented Nb-doped SrTiO3 (SrTiO3:Nb) single-crystal substrates. Atomic force microscopy was used to investigate the surface topography of the deposited films. The morphology of the films, of the BaTiO3/SrTiO3 interfaces, and of the column boundaries was investigated by cross-sectional high-resolution transmission electron microscopy. Measurements of the dielectric properties were performed by comparing BaTiO3 films and BaTiO3/SrTiO3 multilayers of different numbers of individual layers, but equal overall thickness. The dielectric loss saturates for a thickness above 300 nm and linearly decreases with decreasing film thickness below a thickness of 75 nm. At the same thickness of 75 nm, the thickness dependence of the dielectric constant also exhibits a change in the linear slope both for BaTiO3 films and BaTiO3/SrTiO3 multilayers. This behaviour is explained by the change observed in the grain morphology at a thickness of 75 nm. For the thickness dependence of the dielectric constant, two phenomenological models are considered, viz. a 'series-capacitor' model and a 'dead-layer' model.

Initial growth stages of epitaxial BaTiO3 films on vicinal SrTiO3 (001) substrate surfaces

The initial growth mechanism of epitaxial BaTiO3 films is studied by combined application of atomic force microscopy, cross sectional high-resolution transmission electron microscopy, and x-ray diffraction. Epitaxial BaTiO3 thin films were grown by pulsed laser deposition on vicinal Nb-doped SrTiO3 (SrTiO3:Nb) (001) substrates with well-defined terraces. X-ray diffraction and cross sectional high-resolution transmission electron microscopy investigations revealed well-defined epitaxial films and a sharp interface between BaTiO3 films and SrTiO3:Nb substrates. The layer-then-island (Stranski-Krastanov mode) growth mechanism observed by analyzing the morphology of a sequence of films with increasing amount of deposited material has been confirmed by microstructure investigations. (C) 2002 American Institute of Physics.

Formation of epitaxial BaTiO3/SrTiO3 multilayers grown on Nb-doped SrTiO3 (001) substrates

The formation of epitaxial BaTiO3/SrTiO3 multilayers; is studied in terms of the growth mechanism by investigating surface morphologies, crystalline orientations, microstructures, and structures of the interfaces, as well as by determining the dielectric properties. Under specific conditions, the epitaxial BaTiO3 films follow a layer-then-island (Stranski-Krastanov) mechanism on SrTiO3 (001)-oriented substrates. In view of actual efforts made to grow epitaxial superlattices involving very thin individual layers of BaTiO3 and/or SrTiO3, we have determined that the BaTiO3 films Of up to 6,nm thickness do not show any defects and have a sharp BaTiO3-on-SrTiO3 interface. On the contrary, SrTiO3-on-BaTiO3 interfaces within multilayers are rough, probably due to the different growth mechanisms of the two different materials, or due to a difference in the morphological stability of the growth surfaces caused by different surface energies of BaTiO3 and SrTiO3 and by different mobilities of the Ba and Sr atoms reaching the SrTi3 and BaTiO3 layers, respectively.

Microstructure and dielectric properties of epitaxial BaTiO3 films and BaTiO3/SrTiO3 multilayers

Epitaxial BaTiO3 films and BaTiO3/SrTiO3 multilayers were grown by pulsed laser deposition (PLD) on (001)-oriented Nb-doped SrTiO3 (SrTiO3:Nb) substrates. Measurements of the dielectric properties were performed comparing BaTiO3 films and BaTiO3/SrTiO3 multilayers of different number of individual layers, but equal overall thickness. The dielectric loss saturates for a thickness above 300 nm, and linearly decreases with decreasing film thickness below a thickness of 75 nm, and it is independent on the number of multilayers, pointing to some interface effect. The thickness dependence of the dielectric constant of BaTiO3 films and BaTiO3/SrTiO3 multilayers; exhibits a change in the linear slope at a thickness of 75 nm. This behavior is explained by the change observed in the morphology at a thickness of 75 nm. In order to explain the thickness dependence of the dielectric constant, two approaches are considered in this paper, viz. a "series capacitor" model and a "dead layer" model.

Initial growth stages of epitaxial BaTiO3 films on vicinal SrTiO3 : Nb (001) substrates

The growth mechanism of epitaxial BaTiO3 films on vicinal Nb-doped SrTiO3 (srTiO(3):Nb) (001) substrate surfaces was studied in terms of surface morphology, crystalline orientation, microstructure, and film/substrate interface. Well-oriented BaTiO3 thin films were grown on SrTiO3 substrates with well-defined terraces by pulsed laser deposition. The regularly terraced TiO2-terminated surfaces of vicinal SrTiO3:Nb (001) substrates were prepared by a definite chemical and thermal treatment. Under our conditions, BaTiO3 seems to grow with a layer-then-island (Stranski-Krastanov) growth mechanism. In order to investigate the orientation and crystallinity of the BaTiO3 films, x-ray diffraction and high-resolution transmission election microscopy were performed. Ferroelectricity of the BaTiO3 films was proved by electrical measurements performed on Pt/BaTiO3/SrTiO3:Nb heterostructures.