Complex Domain Patterns Research Articles

Growth of ferroelectric domain nuclei: Insight from a sharp-interface model

We present an analytical framework to study the impact of electromechanical properties on the growth of a ferroelectric nucleus. Ferroelectric domain evolution is typically simulated by phase-field models, which have shown that nuclei evolve from needle-like structures into complex domain patterns. However, there has been limited in-depth analysis of the interplay between electrostatics, mechanics and piezoelectricity and their effect on nucleus growth because of the complexity involved in the phase-field description. In this study, we describe the ferroelectric domain wall as a sharp interface and solve for the fields inside an elliptic ferroelectric nucleus via Eshelby’s inclusion problem. We analytically determine the driving traction profile around the nucleus to gain insight into the movement of the domain wall with and without applied electromechanical loading. We analyze how the growth is affected by the permittivity, elasticity, and piezoelectricity as well as the nucleus’ eccentricity. We further demonstrate that applied loads do not significantly affect nucleus growth, which is primarily determined by the self-equilibrated mechanical and electric field, and that the anisotropy in material properties is essential in determining the growth of a ferroelectric nucleus.

Formation of self-assembled nanodomain structure as a result of motion of oriented planar phase boundary in single crystals of tetragonal PMN-PT

We studied the formation of the domain structure as a result of the motion of a planar interphase boundary in the {001}-cut tetragonal PMN-PT crystals during cooling with oriented temperature gradient. The specialized heating/cooling stage was assembled for this purpose. Piezoresponse force microscopy was used to image the domain structure at the (001) and (010) surfaces of the samples with high spatial resolution, revealing a complex quasi-periodic domain pattern with a periodicity from 300 to 400 nm.

Exploring the effect of low concentration of stannum in lead-free BCT-BZT piezoelectric compositions for energy related applications

Piezoelectric, ferroelectric and electromechanical properties were studied at macroscopic and local scale level in stannum doped (Ba0.88Ca0.12)(SnxZr0.1-xTi0.9)O3 ceramics, with an objective to explore the effect of low content (0 ≤ x ≤ 0.5 at%) of the substituent (Sn) on the functional properties. The results exemplified that the substitution had an influence on the crystal lattice and microstructure that affected the dielectric, ferroelectric, and electromechanical properties. Enhancement in electrical/electromechanical properties were observed with stannum substitution. Optimal electrical properties were obtained in the composition with Sn = 0.3 at% that exhibited maximum piezoelectric constant d33 = 405 pC/N, planar electromechanical coupling factor kp ∼0.41, and saturation polarization Ps=12.1 μC/cm2. The same composition showed an electric-field strain response, Smax ∼0.08% and a converse piezoelectric coefficient, d33* of ∼525 pm/V. Local scale characterization via piezoresponse force microscopy technique revealed complex domain patterns comprising stripe-like macro-domains and featureless nano-sized domains. Energy harvesting and energy storage performance were evaluated for exploring their suitability in energy applications.

Evolution of domain structure in 0.96(K0.48Na0.52)(Nb0.96Sb0.04)O30.04(Bi0.50Na0.50)ZrO3 ceramics with poling and temperature

Domain structure often has significant influences on both piezoelectric properties and piezoelectric temperature stability of a ferroelectric ceramic. In-depth studies on the characters of domain structure should be helpful for the better understanding of piezoelectric performance. In this work, the evolution of domain structure in large-d33 0.96(K0.48Na0.52)(Nb0.96Sb0.04)O3−0.04(Bi0.50Na0.50)ZrO3 ceramics with poling and temperature was systematically investigated via comparing the various domain patterns that are obtained by acid-etching. It was found that domain structure changes greatly upon poling and varies largely with temperature. Complex domain patterns consisting of long narrow parallel stripes or herringbone structure separated by 180°-domain boundaries are observed in the unpoled ceramics at room temperature. Domain patterns become less complicated upon poling, due to the collective polarization reversals of parallel-stripe domain clusters and banded fine-stripe domain segments. Parallel stripes and herringbone bands become much wider upon poling, as some narrow stripes and herringbone bands coalesce into broad ones, respectively. Hierarchical domain structure is commonly seen in the domain patterns acid-etched at room temperature, but is less frequently recognized at elevated temperatures. Schematic models of domain configurations were proposed to explain the domain structure and its evolution with poling.

Piezoelectric properties, phase transitions and domain structure of (Bi,Na)HfO3−modified (K,Na)(Nb,Sb)O3 ceramics

Piezoelectric performances of (K,Na)NbO3-based ceramics are often greatly affected by phase transitions and domain structure, which are in turn substantially determined by chemical compositions. Systematical studies from this perspective are important for the good understanding about piezoelectric characters. Further, whether rhombohedral-tetragonal (R-T) or rhombohedral-orthorhombic-tetragonal (R-O-T) phase coexistence is really the essential precondition for obtaining high piezoelectric coefficient d33 is also a fundamental issue. A series of (1-x)(K0.48Na0.52)Nb0.955Sb0.045O3–x(Bi0.50Na0.50)HfO3 ceramics with 0.01≦x≦0.04 were chosen in this work to examine the compositional effects on piezoelectric properties, phase transitions and domain structure. It was found that piezoelectric coefficient d33, orthorhombic-tetragonal (O-T) phase transition and domain structure are sensitive to the chemical composition. The d33 increases first, reaches a maximum of 512 pC/N at x = 0.037 and then decreases with x. Dielectric measurement showed that the O-T phase transition temperature TO-T decreases monotonically with x while the rhombohedral-orthorhombic phase transition temperature TR-O remains almost unchanged when x ≥ 0.03. Domain structure was investigated by acid etching. All the compositional ceramics exhibit quite complex domain patterns consisting of long parallel stripes and irregularly-shaped domain boundaries before poling. Domain patterns become less complicated upon poling due to the collective polarization reversals of domain clusters. The ceramic with x = 0.037 differs significantly from the others, showing its TO-T close to room temperature and possessing the unique domain structure that contains a large amount of hierarchical nanodomain structure. Its outstanding piezoelectric properties should be ascribed to the O-T phase coexistence and the characteristic domain structure.

First-principles study of topologically protected vortices and ferroelectric domain walls in hexagonal YGaO3

Ferroelectric behavior on the meso- and macroscopic scale depends on the formation and dynamics of domains and controlling the domain patterns is imperative to device performance. While density functional theory (DFT) calculations have successfully described the basic properties of ferroelectric domain walls, the necessarily small cell sizes used for the calculations hampers DFT studies of complex domain patterns. Here, we simulate large-scale complex ferroelectric domain patterns in ferroelectric ${\mathrm{YGaO}}_{3}$ using multisite local orbitals as implemented in the DFT code conquest. The multisite local orbital basis set gives similar bulk structural and electronic properties, and atomic domain wall structures and energetics as those obtained with conventional plane-wave DFT. With this basis set model, 3600-atom cells are used to simulate topologically protected vortices. The local atomic structure at the vortex cores is subtly different from the domain walls, with a lower electronic band gap suggesting enhanced local conductance at these cores.

Monolayer behavior of pure F-DPPC and mixed films with DPPC studied by epifluorescence microscopy and infrared reflection absorption spectroscopy

The monolayer behavior of a l-DPPC derivative with a single fluorination in one of its terminal methyl groups (F-DPPC) at air-water interface was investigated by epifluorescence microscopy and infrared reflection absorption spectroscopy (IRRAS). Epifluorescence microscopy was utilized to study the shape and morphology of liquid-condensed (LC) domains observed upon compression of the film. IRRAS was employed for the determination of chain order and orientation. The shapes of LC-domains in a monolayer of F-DPPC are more dependent on the rate of compression than those of DPPC. The LC domains of F-DPPC display pronounced fractal growth patterns depending on the compression speed. The evolution of LC domain occurs under dominating electrostatic dipolar forces in F-DPPC. IRRAS measurements with the analysis of the frequency of the methylene stretching vibrations as a function of film compression show that the acyl chains in an F-DPPC monolayer in the LE-phase are more disordered than those in a DPPC film. The reason for the higher chain disorder in LE phase F-DPPC monolayers is a back folding of the fluorinated sn-2 chain terminus towards the air-water interface leading to larger molecular area requirement. Angular dependent IRRA spectra of monolayers at a surface pressure of 30 mN m−1 show that in the LC phase DPPC and F-DPPC exhibit a similar tilt of the acyl chains of ca. 28−30 ° relative to the surface normal. F-DPPC is ideally miscible with l-DPPC-d62 having the same chirality, as indicated by epifluorescence images and by IRRAS. However, the LC domains in an equimolar mixture of d-DPPC and F-DPPC having opposite chirality show multi-lobed complex domain patterns indicating chiral phase separation within LC domains.

Giant electrocaloric effect at the antiferroelectric-to-ferroelectric phase boundary in Pb(ZrxTi1–x)O3

Molecular dynamics simulations predict a giant electrocaloric effect at the ferroelectric-antiferroelectric phase boundary in PZT (PbTiO3-PbZrO3). These large-scale simulations also give insights into the atomistic mechanisms of the electrocaloric effect in Pb(ZrxTi1–x)O3. We predict a positive electrocaloric effect in ferroelectric PZT, but antiferroelectric PZT exhibits a negative-to-positive crossover with the increasing temperature or electric field. At the antiferroelectric-to-ferroelectric phase boundary, we find complex domain patterns. We demonstrate that the origin of the giant electrocaloric change of temperature is related to the easy structural response of the dipolar system to external stimuli in the transition region.

Ferroelectric monoclinic phases in strained K0.70Na0.30NbO3 thin films promoting selective surface acoustic wave propagation

We present a detailed analysis of the ferroelectric domain structure of K0.70Na0.30NbO3 thin films on (110) TbScO3 grown by metal–organic chemical vapor deposition. Upon piezoresponse force microscopy and nanofocus x-ray diffraction measurements we derive a domain model revealing monoclinic MC domains. The complex domain pattern is formed out of four co-existing in-plane orientations of the shearing direction of the monoclinic unit cell resulting in four types of superdomains each being composed of well-ordered stripe domains. Finally, we present surface acoustic wave (SAW) experiments that exhibit extraordinary signal intensities given the low thickness of the tested film. Moreover, the SAW propagation is found to occur selectively along the identified shearing directions.

Memory effect and magnetocrystalline anisotropy impact on the surface magnetic domains of magnetite(001)

The structure of magnetic domains, i.e. regions of uniform magnetization separated by domain walls, depends on the balance of competing interactions present in ferromagnetic (or ferrimagnetic) materials. When these interactions change then domain configurations also change as a result. Magnetite provides a good test bench to study these effects, as its magnetocrystalline anisotropy varies significantly with temperature. Using spin-polarized electron microscopy to map the micromagnetic domain structure in the (001) surface of a macroscopic magnetite crystal (~1 cm size) shows complex domain patterns with characteristic length-scales in the micrometer range and highly temperature dependent domain geometries. Although heating above the Curie temperature erases the domain patterns completely, cooling down reproduces domain patterns not only in terms of general characteristics: instead, complex microscopic domain geometries are reproduced in almost perfect fidelity between heating cycles. A possible explanation of the origin of the high-fidelity reproducibility is suggested to be a combination of the presence of hematite inclusions that lock bulk domains, together with the strong effect of the first order magnetocrystalline anisotropy which competes with the shape anisotropy to give rise to the observed complex patterns.

Probing Ferroic States in Oxide Thin Films Using Optical Second Harmonic Generation

Forthcoming low-energy consumption oxide electronics rely on the deterministic control of ferroelectric and multiferroic domain states at the nanoscale. In this review, we address the recent progress in the field of investigation of ferroic order in thin films and heterostructures, with a focus on non-invasive optical second harmonic generation (SHG). For more than 50 years, SHG has served as an established technique for probing ferroic order in bulk materials. Here, we will survey the specific new aspects introduced to SHG investigation of ferroelectrics and multiferroics by working with thin film structures. We show how SHG can probe complex ferroic domain patterns non-invasively and even if the lateral domain size is below the optical resolution limit or buried beneath an otherwise impenetrable cap layer. We emphasize the potential of SHG to distinguish contributions from individual (multi-) ferroic films or interfaces buried in a device or multilayer architecture. Special attention is given to monitoring switching events in buried ferroic domain- and domain-wall distributions by SHG, thus opening new avenues towards the determination of the domain dynamics. Another aspect studied by SHG is the role of strain. We will finally show that by integrating SHG into the ongoing thin film deposition process, we can monitor the emergence of ferroic order and properties in situ, while they emerge during growth. Our review closes with an outlook, emphasizing the present underrepresentation of ferroic switching dynamics in the study of ferroic oxide heterostructures.

Probing Ferroic States in Oxide Thin Films Using Optical Second Harmonic Generation

Forthcoming low-energy consumption oxide electronics rely on the deterministic control of ferroelectric and multiferroic domain states at the nanoscale. In this review, we address the recent progress in the field of investigation of ferroic order in thin films and heterostructures, with a focus on non-invasive optical second harmonic generation (SHG). For more than 50 years, SHG has served as an established technique for probing ferroic order in bulk materials. Here, we will survey the specific new aspects introduced to SHG investigation of ferroelectrics and multiferroics by working with thin film structures. We show how SHG can probe complex ferroic domain patterns non-invasively and even if the lateral domain size is below the optical resolution limit or buried beneath an otherwise impenetrable cap layer. We emphasize the potential of SHG to distinguish contributions from individual (multi-) ferroic films or interfaces buried in a device or multilayer architecture. Special attention is given to monitoring switching events in buried ferroic domain- and domain-wall distributions by SHG, thus opening new avenues towards the determination of the domain dynamics. Another aspect studied by SHG is the role of strain. We will finally show that by integrating SHG into the ongoing thin film deposition process, we can monitor the emergence of ferroic order and properties in situ, while they emerge during growth. Our review closes with an outlook, emphasizing the present underrepresentation of ferroic switching dynamics in the study of ferroic oxide heterostructures.

Strain engineering of monoclinic domains in KxNa1−xNbO3 epitaxial layers: a pathway to enhanced piezoelectric properties

A novel concept to obtain a ferroelectric material with enhanced piezoelectric properties is proposed. This approach is based on the combination of two pathways: (i) the evolution of a ferroelectric monoclinic phase and, (ii) the coexistence of different types of ferroelectric domains leading to polarization discontinuities at the domain walls. Each of these pathways enables polarization rotation in the material which is responsible for giant piezoelectricity. Targeted incorporation of anisotropic epitaxial lattice strain is used to implement this approach. The feasibility of our concept is demonstrated for K0.9Na0.1NbO3 epitaxial layers grown on NdScO3 substrates where the coexistence of (100)pc and (001)pc pseudocubic oriented monoclinic domains is experimentally verified. This coexistence results in a complex periodic domain pattern with alternating emergence of ferroelectric in-plane a1a2 and inclined MC monoclinic phases, which differ in the direction of the electrical polarization vector. Our approach opens the possibility to exploit ferroelectric properties in both vertical and lateral directions and to achieve enhanced piezoelectric properties in lead-free material caused by singularities at the domains walls.

Magnetic stripes and holes: Complex domain patterns in perforated films with weak perpendicular anisotropy

Hexagonal antidot arrays have been patterned on weak perpendicular magnetic anisotropy NdCo films by e-beam lithography and lift off. Domain structure has been characterized by Magnetic Force Microscopy at remanence. On a local length scale, of the order of stripe pattern period, domain configuration is controlled by edge effects within the stripe pattern: stripe domains meet the hole boundary at either perpendicular or parallel orientation. On a longer length scale, in-plane magnetostatic effects dominate the system: clear superdomains are observed in the patterned film with average in-plane magnetization along the easy directions of the antidot array, correlated over several antidot array cells.

Ferroelastic Domain Boundary-Based Multiferroicity

Domain boundary engineering endeavors to develop materials that contain localized functionalities inside domain walls, which do not exist in the bulk. Here we review multiferroic devices that are based on ferroelectricity inside ferroelastic domain boundaries. The discovery of polarity in CaTiO3 and SrTiO3 leads to new directions to produce complex domain patterns as templates for ferroic devices.

Hierarchical ferroelectric and ferrotoroidic polarizations coexistent in nano-metamaterials.

Tailoring materials to obtain unique, or significantly enhanced material properties through rationally designed structures rather than chemical constituents is principle of metamaterial concept, which leads to the realization of remarkable optical and mechanical properties. Inspired by the recent progress in electromagnetic and mechanical metamaterials, here we introduce the concept of ferroelectric nano-metamaterials, and demonstrate through an experiment in silico with hierarchical nanostructures of ferroelectrics using sophisticated real-space phase-field techniques. This new concept enables variety of unusual and complex yet controllable domain patterns to be achieved, where the coexistence between hierarchical ferroelectric and ferrotoroidic polarizations establishes a new benchmark for exploration of complexity in spontaneous polarization ordering. The concept opens a novel route to effectively tailor domain configurations through the control of internal structure, facilitating access to stabilization and control of complex domain patterns that provide high potential for novel functionalities. A key design parameter to achieve such complex patterns is explored based on the parity of junctions that connect constituent nanostructures. We further highlight the variety of additional functionalities that are potentially obtained from ferroelectric nano-metamaterials, and provide promising perspectives for novel multifunctional devices. This study proposes an entirely new discipline of ferroelectric nano-metamaterials, further driving advances in metamaterials research.

Scale effects and the formation of polarization vortices in tetragonal ferroelectrics

Vortices consisting of 90° quadrant domains are rarely observed in ferroelectrics. Although experiments show polarization flux closures with stripe domains, it is as yet unclear why pure single vortices are not commonly observed. Here, we model and explore the energy of polarization patterns with vortex and stripe domains, formed on the square cross-section of a barium titanate nanowire. Using phase-field simulations, we calculate the associated energy of polarization patterns as a function of nanowire width. Further, we demonstrate the effects of surface energy and electrical boundary conditions on equilibrium polarization patterns. The minimum energy equilibrium polarization pattern for each combination of surface energy and nanowire width is mapped for both open- and short-circuit boundary conditions. The results indicate a narrow range of conditions where single vortices are energetically favorable: nanowire widths less than about 30 nm, open-circuit boundary condition, and surface energy of less than 4 N/m. Short-circuit boundary conditions tend to favor the formation of a monodomain, while surface energy greater than 4 N/m can lead to the formation of complex domain patterns or loss of ferroelectricity. The length scale at which a polarization vortex is energetically favorable is smaller than the typical size of nanoparticle in recent experimental studies. The present work provides insight into the effects of scaling, surface energy, and electrical boundary conditions on the formation of polarization patterns.

Simulating acoustic emission: The noise of collapsing domains

Microstructural changes during mechanical shear of a ferroelastic or martensitic material and their signature in acoustic emission (AE) spectroscopy during strain-induced yield and detwinning are investigated by computer simulation. Complex domain patterns are generated during the main yield event, which leads to large displacements of surface atoms and emission of acoustic waves. Loading beyond the yield point leads, eventually, to a simplification of the domain patterns by local movements of needle domains, the nucleation and movement of kinks in domain walls, and the collapse of domains spanning the entire sample (from surface to surface). These microstructural changes lead to much weaker acoustic emissions than those near the yield point. Nucleation/collapse during a yield event involves an energy drop of some 3.7 meV/atom; the collapse of spanning domains releases 0.56 meV/atom, a kink crashing into the surface changes the energy by 0.017 meV/atom, and the collapsing vertical needle changes the energy by 0.017 meV/atom. All these energy bursts can, in principle, be seen by AE. The large energy spread means that AE spectroscopy measures a mixture of events whereby weak and strong signals may signify smaller and bigger events of the same kind or different microstructural changes with intrinsically different signal strengths. In order to disentangle the various contributions, other observables are needed, such as the time-dependent strain matrix of the deformed sample.

Color theorems, chiral domain topology, and magnetic properties of Fe(x)TaS2.

Common mathematical theories can have profound applications in understanding real materials. The intrinsic connection between aperiodic orders observed in the Fibonacci sequence, Penrose tiling, and quasicrystals is a well-known example. Another example is the self-similarity in fractals and dendrites. From transmission electron microscopy experiments, we found that FexTaS2 crystals with x = 1/4 and 1/3 exhibit complicated antiphase and chiral domain structures related to ordering of intercalated Fe ions with 2a × 2a and √3a × √3a superstructures, respectively. These complex domain patterns are found to be deeply related with the four color theorem, stating that four colors are sufficient to identify the countries on a planar map with proper coloring and its variations for two-step proper coloring. Furthermore, the domain topology is closely relevant to their magnetic properties. Our discovery unveils the importance of understanding the global topology of domain configurations in functional materials.

Nanopaleomagnetism of meteoritic Fe–Ni studied using X-ray photoemission electron microscopy

X-ray photoemission electron microscopy (XPEEM) enables natural remanent magnetisation to be imaged with ∼30 nm resolution across a field of view of 5–20 μm. The method is applied to structural features typical of the Widmanstätten microstructure (kamacite – tetrataenite rim – cloudy zone – plessite) in the Tazewell IIICD iron meteorite. Kamacite lamellae and the tetrataenite rim are multidomain, whereas plessite consists of laths of different phases displaying a range of stable magnetisation directions. The cloudy zone (CZ) displays a complex interlocking domain pattern resulting from nanoscale islands of tetrataenite with easy axes distributed along three possible crystallographic directions. Quantitative analysis of the coarse and intermediate CZ was achieved using a combination of image simulations and histogram profile matching. Remanence information was extracted from individual regions of interest ∼400 nm wide, demonstrating for the first time the capability of XPEEM to perform quantitative paleomagnetic analysis at sub-micron length scales. The three tetrataenite easy axis orientations occur with equal probability in the coarse and intermediate CZ, suggesting that spinodal decomposition in these regions was not strongly influenced by internal interaction fields, and that they are suitable candidates for future paleomagnetic studies. The fine CZ shows a strong dominance of one easy axis. This effect is attributed to island–island exchange interactions that render the fine CZ unsuitable for paleomagnetic study. Variations in the relative strength (proportion of dominant easy axis) and direction (direction of dominant easy axis) of a paleomagnetic field can be resolved from different regions of the CZ using XPEEM, raising the prospect of obtaining a time-resolved measurement of the active dynamo period in meteorites originating from the upper unmelted regions of differentiated asteroids (e.g. chondrites, pallasites, mesosiderites).