Complex Domain Patterns Research Articles

Identifying ferroelectric phase and domain structure using angle-resolved piezoresponse force microscopy

We used angle-resolved piezoresponse force microscopy (AR-PFM), vertical PFM (VPFM), and electron backscatter diffraction (EBSD) to provide a systematic interpretation of domain patterns in polycrystalline, near-morphotropic lead zirconate titanate. This material was used to illustrate the power of AR-PFM methods in resolving complex domain patterns where multiple phases may be present. AR-PFM was carried out with a 30° rotation interval, and the resulting data were analysed to identify the orientation of the underlying axis of piezoelectricity. The additional information provided by AR-PFM was studied, comparing its capabilities to those of 3-dimensional PFM, consisting of one VPFM image and two orthogonal lateral PFM (LPFM) images. We show that, in certain conditions, using AR-PFM can identify the phases present at the sub-grain scale. This was confirmed using VPFM and EBSD data. Furthermore, the method can discriminate laminated domain patterns that appear similar in VPFM and can reliably expose domain patterns that may not be seen in LPFM data from a single orientation, or even in 3D PFM data.

Domain evolution processes during poling of a near-morphotropic Pb(Zr, Ti)O3 ceramic

Domain wall motion during the poling of near-morphotropic Pb(Zr,Ti)O3 PZT was observed using Piezoresponse Force Microscopy (PFM). Poling was conducted on bulk polycrystalline PZT in a series of steps, interrupted by vertical PFM scans, which were used to identify the domain evolution processes. The mechanisms of evolution in complex domain patterns such as herringbone and checkerboard structures are revealed. Of interest, in the case of a herringbone pattern consisting of two sets of lamellae angled to each other, one set of lamellae expands and is observed to overwrite the other, transforming the herringbone structure into a single lamination. Also, lengthening without broadening, and simultaneous lengthening and broadening of lamellar domain bands in checkerboard structures are observed. The observations show that 180° and non-180° domain switching can occur simultaneously in complex domain patterns. Methods are developed for identifying the polarization directions of the individual domains in near-morphotropic PZT. The methods combine a knowledge of the compatible domain configurations with crystallographic data from electron backscatter diffraction and PFM data. The resulting map of polarization directions enables clear identification of the polarization switching mechanisms.

Influence of strain on space-charge distribution at ferroelectric thin-film free surfaces

Ferroelectric perovskites are wide-bandgap semiconductors and therefore are often modeled as perfect dielectrics. However, space charges can play an important role in regions with large electric fields, such as at domain walls, free surfaces, near electrodes, etc. In this paper, we apply a mesoscale model to examine the space-charge distribution at free-surface closure domain patterns in a ferroelectric thin film. The model uses a conventional electromechanical phase-field approach for ferroelectric domain patterns in combination with drift–diffusion based equations to model space-charge distribution. We additionally apply a boundary element method to compute the stray electric fields outside the ferroelectric free surface. We probe the influence of mechanical strain, such as would be applied through a substrate, on the distribution of space charge. We find an indirect, but strong, coupling between mechanics and space-charge distribution. The physical mechanism of this coupling is as follows: the mechanical strain induces changes in the domain patterns and polarization distribution; this in turn changes the local electric fields sufficiently that space charges are redistributed on the free surface rather than moving towards the bottom electrode. We note two interesting features of this coupling: first, the coupling mechanism is operative only at free surfaces due to the complex domain patterns in these regions, and would not occur in the bulk; second, although domain patterns are visually only marginally changed by the presence of space charges, the changes in electric field due to these seemingly small changes is significant and this provides the coupling with space charge.

Demonstration of laser induced magnetization reversal in GdFeCo nanostructures

Magnetization switching by a single femtosecond laser heat pulse is demonstrated for out-of-plane domains with sizes down to 200 nm in GdFeCo nanostructures. A complex magnetic domain configuration was revealed with a photoemission electron microscope employing x-ray magnetic circular dichroism at the Fe L3 edge and consisted of in-plane magnetized rims and out-of-plane domains, which results from the structuring process. No influence of this complex domain pattern on the switching efficiency of the structures was detected, constituting an important step towards the application of laser induced magnetization switching in storage devices.

Free surface domain nucleation in a ferroelectric under an electrically charged tip

This paper examines the process of domain nucleation in ferroelectric perovskites at a free surface due to electrical fields applied through a charged tip above the surface. We use a real-space phase-field model to model the ferroelectric, and apply a boundary element-based numerical method that enables us to accurately account for the stray electric fields outside the ferroelectric and the interactions through electric fields between the external tip and ferroelectric. We calculate the induced domain patterns, the stress and internal electric fields, and the induced surface displacement for various relative orientations of the crystal lattice with respect to the free surface. The effect of the external spatially inhomogeneous electric field leads to the formation of complex domain patterns and nominally incompatible microstructures. Two key findings are: first, in c axis films, a new domain forms beneath the tip through 180° switching and this new domain has the opposite piezo-response as the original domain, leading to a distinct displacement signature on the surface; and second, in a axis films, domain nucleation occurs at lower applied field because polarization rotates to align with the applied field, whereas in c axis films, the polarization magnitude reduces until 180° switching occurs at a higher applied field. We also see that the calculated domain patterns differ significantly from analytical approximations that are often used.

Local domain engineering in relaxor 0.77PbMg1/3Nb2/3O3-0.23PbSc1/2Nb1/2O3 single crystals

We used piezoresponse force microscopy (PFM) to study the dc bias field-induced domain structure of the (001) oriented single crystals of 0.77PbMg1/3Nb2/3O3-0.23PbSc1/2Nb1/2O3 relaxor. In the as-grown state, no polarization contrast was observed due to the average cubic symmetry of the crystal. Upon application of a dc bias applied via a PFM tip, a stable complex domain pattern, corresponding to a hedgehog-type topological defect, appeared on the surface of the crystal. The shape of these domains depended on the magnitude of the field. If the field was below a threshold, the domains possessed a cylindrical form. Above the threshold, the border between domains became close to a straight line. At high biases and large separation between the pulses, the development of the domains obeyed an avalanche-type dynamics.

Magnetic disparities at the interfaces of Co–pentacene–Co hybrid structures

We investigated two series of ultrathin ferromagnet-organic semiconductor (FM-OSC) hybrid structures fabricated with reversed layer orders in ultra-high vacuum conditions to emulate the interfaces of FM/OSC/FM organic spin-valves. Using X-ray photoemission electron microscopy (PEEM), the magnetic responses of the cobalt (Co) layer in contact with the pentacene (Pc) film were investigated on a microscopic scale. According to the PEEM images acquired on Pc (1.8 nm)/Co bilayers, the Co top layer was found to turn on its ferromagnetic order after its thickness reaches 2.2 nm. Also, upon the onset of magnetic contrast, the element-specific images revealed that the Pc/Co bilayers exhibit a complex domain pattern whose average dimension is at least two orders of magnitude smaller than that of the pattern found in Co (2.4 nm)/Pc bilayers. Further X-ray photoelectron spectroscopy investigations suggest that the magnetic disparities observed between Co/Pc and Pc/Co bilayers are correlated with the different chemistries occurred at their interfaces.

Domain Engineering for Enhanced Ferroelectric Properties of Epitaxial (001) BiFeO Thin Films

Adv. Mater. 2009, 21, 817–823 2009 WILEY-VCH Verlag Gm Multiferroic BiFeO3 has attracted great interest due to its promising application tomagnetoelectric devices. In addition, the high remanent polarization and piezoelectric response of BiFeO3 thin films, which are comparable to those of conventional Ti-rich lead zirconia titanate, suggested BiFeO3 as a strong candidate for lead-free nonvolatile memories. BiFeO3 has a rhombohedral perovskite structure with pseudocubic lattice parameters ar1⁄4 3.96 A and ar1⁄4 0.68. Due to this low symmetry, (001)-oriented epitaxial BiFeO3 films possess the rhombohedral distortion along one of the four (111) crystallographic directions of the pseudocubic perovskite unit cell. Thus, eight possible polarization (ferroelectric) variants, which correspond to four structural (ferroelastic) domains, may form in the films, leading to complex domain patterns with both {100} and {101} twin boundaries. Such a complex domain structure can deteriorate the ferroelectric response of the system by external electric field, and complicates the examination of the coupling between magnetic and ferroelectric order parameters in BiFeO3. [3]

Indentation plasticity of barium titanate single crystals: Dislocation influence on ferroelectric domain walls

The plastic behaviors of barium titanate (0 0 1) and (1 1 0) single crystals are studied with atomic force microscopy and piezoresponse force microscopy (PFM) following nanoindendation damage. Plastic deformation mechanisms of ferroelectric barium titanate single crystals are discussed with a focus on the interaction between PFM response and dislocation activities. Nanoindentation tests indicate that the theoretical strength is approached prior to the first pop-in event, consistent with the creation of dislocation nucleation sites required for the onset of plasticity. Surface topographic and piezoelectric analyses indicate that pile-ups around indents result from dislocation activities on the primary slip system, { 1 1 0 } pc 〈 1 1 ¯ 0 〉 pc . The more complex indentation-induced domain patterns observed on (1 1 0) barium titanate are also discussed.

Diffuse phase transition in BaTi1−xSnxO3 ceramics: An intermediate state between ferroelectric and relaxor behavior

Dielectric relaxation and polar structures of BaTi1−xSnxO3 ceramics, x=0.10–0.20, are investigated by means of dielectric spectroscopy and piezoresponse force microscopy. A transition regime between “normal” ferroelectric and relaxor behaviors is encountered. In the compositions with x=0.10, a complex domain pattern confirming the ferroelectric state is observed. Strong dielectric relaxation around Tm is attributed to domain wall motion. On the other hand, the dielectric spectra in the sample with x=0.20 are very similar to those observed in relaxor ferroelectrics. Analysis of the relaxation spectra at the intermediate concentration, x=0.15, reveals both domain wall response and an additional contribution related to mesoscale polar structures. The appearance of relaxor behavior in BaTi1−xSnxO3 is discussed within the framework of the random field model.

Ferroelectric domains and twinning in high-quality SrBi2Ta2O9 single crystals

The domain structure of high-quality SrBi2Ta2O9 (SBT) single crystals is investigated by x-ray diffraction and piezoelectric force microscopy. Both ferroelectric 180° domains and ferroelastic 90° domains (twins) are revealed at room temperature. Remarkably, coexisting domains of two types form a well-defined “herringbone” structure with mostly flat 90° walls. Formation of the observed complex domain pattern is attributed to a two-stage process associated with the presence of separate ferroelastic and ferroelectric phase transitions in SBT.

Turing Patterns, Spatial Bistability, and Front Instabilities in a Reaction−Diffusion System

The chlorine dioxide−iodine−malonic acid oscillating reaction produces Turing patterns when operated in open spatial reactors. In the same operating conditions, the chlorine dioxide−iodide bistable reaction leads to spatial bistability between two steady states that do not break the symmetry of boundary conditions. We develop a system combining these two properties. Phase diagram studies show that the Turing pattern region cannot be generically made to interact with the phenomenon of spatial bistability. In the spatial bistability region, stationary pulses and complex transient domain patterns are observed, a new phenomenon for the chlorite−iodide driven systems. These have no connection with the previously observed Turing patterns. We propose a systematic design method to produce permanent domain patterns in systems exhibiting spatial bistability.

Understanding the submicron domain structure of MnAs thin films on GaAs(001): Magnetic force microscopy measurements and simulations

Over a wide temperature range of 30 °C around room temperature, MnAs films on GaAs(001) semiconductor substrates break up into ordered arrays of submicron-sized ferromagnetic α and paramagnetic β wires. Both the hard and the easy axis of magnetization (perpendicular to the wires) lie in the film plane and a large variety of complex domain patterns are found in micromagnetic investigations with magnetic force microscopy (MFM). A systematic analysis of the domain configurations is given and the most likely configurations are identified through MFM contrast simulations.

Investigation of Domain Structure of SrBi2Ta2O9 Single Crystals via Polarized Optical and Piezoelectric Force Microscopy

High-quality SrBi2Ta2O9 (SBT) single crystals were grown via high-temperature self-flux solution method. The crystals had a shape of platelets with c-axis normal to the major face according to x-ray diffraction. The optical observations with polarized light revealed complex domain patterns with mutually orthogonal domains in (a, b)-plane. The twin boundaries with rounded borders may correspond to microtwinning at the scale of the size of the elementary cell. Piezoelectric force microscopy revealed an irregular domain configuration consisting of fine antiparallel domains oriented along [100] direction.

Scanning electron microscope with polarization analysis: Micromagnetic structures in ultrathin films

The basics of the scanning electron microscope with polarization analysis are presented and special features of the microscope are discussed. The spin polarization of the secondary electrons allows for a high contrast as the topography of the sample is strongly suppressed. The feature of the method is that the orientation of the magnetization is measured and used for domain imaging. For complex domain patterns that makes the interpretation easy and direct. Examples are shown how the high surface sensitivity is used for the investigation of all kind of samples. The decoration by a thin ferromagnetic film makes even contaminated and samples with strongly spoiled surfaces accessible for scanning electron microscope with polarization analysis (SEMPA) investigation. Recently, the magnetic resolution of SEMPA has been pushed into the range of a few nm.

Improvements and actual problems in domain imaging by type-I magnetic contrast in SEM

Improvements in domain observation by the scanning electron microscope (SEM) type-I magnetic contrast have been achieved thanks to the use of digital image processing (DIP) system. Domain images with considerably enhanced contrast and reduced noise can be obtained. By combining image alignment with image subtraction and summation techniques, it is possible at present to separate superimposed magnetic and non-magnetic features in the images taken with a single secondary electron detector. As a consequence, detailed studies of domain structures in the cases of very weak type-I contrast and complex domain patterns, which were not possible before, can now be made. The actual problems related to the complicated mechanism of type-I magnetic contrast and its relatively low resolution are also discussed.

Micromagnetic disorder in antiparallel biased spin valves

The reorientation of antiferromagnetically coupled Co layers comprising the pinned layers of an antiparallel biased spin valve is reported. Initially, the lower Co layer is saturated in the growth field in the deposition chamber, but it reorients as the upper Co layer grows to be thicker than the lower one. We have investigated the nature of this reorientation by ex situ transport measurements and Lorentz microscopy, and found it highly inhomogeneous, leading to a complex in-plane domain pattern. This results in a reduction of the giant magnetoresistance of the spin valves close to the balance point, where the benefits of the antiparallel biasing are greatest.

Imaging magnetic domain structure in sub-500 nm thin film elements

Magnetic imaging in the transmission electron microscope (TEM) has been used to examine submicron elements with the aim of discovering down to what element size complex domain patterns can form. The elements were squares, circles, triangles, and pentagons in the size range 100–500 nm and were made from 36 nm Co films or 8 nm Ni80Fe20 (NiFe) with in-plane magnetization. The magnetic domain structures in these elements were imaged at high resolution using the differential phase contrast imaging mode in a TEM. Nonuniform magnetization structures were seen in the images. Vortices were present at remanence in all shapes of 36-nm-thick Co elements down to 100 nm size and in circular NiFe elements down to 116 nm diameter. Triangular NiFe elements did not have a vortex state at remanence, instead the magnetization curved round within the element but did not achieve complete flux closure. In simulations of square and circular NiFe elements, it was found that defects at the edges of the elements encouraged reversal by a vortex mechanism, whereas for simulated elements with no defects, reversal was by rotation and occurred at much lower fields.

Magnetic microstructure of the spin reorientation transition: a computer experiment.

The scenario of the spin reorientation in two-dimensional films within first-order anisotropy approximation is theoretically studied by means of Monte Carlo simulations. The magnetic microstructure is investigated as a function of the ratio of the perpendicular anisotropy energy to the dipolar one. If the anisotropy dominates, out-of-plane domains will be found while in-plane vortices appear for a vanishing anisotropy. In the range of comparable anisotropy and dipolar energies a complex domain pattern evolves yielding a continuous transition between the two structures. The structure with equally distributed magnetic moment orientations is stable at the point where anisotropy and dipolar energies cancel each other.

Magnetic domain structure of multidomain magnetite as a function of temperature: observation by Kerr microscopy

This study presents magnetic domain observations of the crystallographic (110)- and (111)-planes of various monocrystalline multidomain (MD) magnetites (Fe 3O 4) using the magneto-optical Kerr effect (MOKE). At room temperature (RT), lamellar domains separated by 180°-, and closure domains with 71°-, and 109°-walls have been observed on the (110)-plane due to the two easy directions of magnetization within this plane. Domain structure observations on the (111)-plane reveal more complex domain patterns, which are formed by arrays of closure domains. Furthermore, in this study, the behaviour of the domain structure as a function of temperature has been observed. For high temperature domain observations, a special furnace has been developed which allows domain observations using the MOKE between room temperature and Curie-point (575°C). During observation, the furnace is evacuated to 10 −3 Pa in order to prevent chemical alteration effects of the sample. The temperature dependence of the domain structure on the (110)-plane has been observed for various (MD) magnetites from Minais Gerais (Brazil) and the Zillertal (Austria). Magneto-optical domain contrasts could be observed up to 555°C. During heating and cooling, the domain structure proved to be reversible. The mean domain width at each temperature step was determined by two methods in order to obtain an improved approximation. At RT, the mean domain width for different crystals varies between 40 and 90 μm. The heating experiments on Brazilian magnetites show that the mean domain width is relatively stable from RT up to 350–400°C; it then increases significantly at higher temperatures up to the Curie-point of magnetite. The experimental results are in good agreement with theoretical calculations of the absolute domain width in MD magnetite for a large range of grain sizes and varying temperatures.