LETTER pubs.acs.org/NanoLett
Polarization Closure in PbZr(0.42)Ti(0.58)O3 Nanodots L. J. McGilly and J. M. Gregg* Centre for Nanostructured Media, School of Maths and Physics, Queen’s University Belfast, University Road, Belfast, BT7 1NN. United Kingdom ABSTRACT: Domain states in PbZr(0.42)Ti(0.58)O3 single-crystal ferroelectric nanodots, formed on cooling through the Curie temperature, were imaged by transmission electron microscopy. In the majority of cases, 90 stripe domains were found to form into four distinct “bundles” or quadrants. Detailed analysis of the dipole orientations in the system was undertaken, using both dark-field imaging and an assumption that charged domain walls were energetically unfavorable in comparison to uncharged walls. On this basis, we conclude that the dipoles in these nanodots are arranged such that the resultant polarizations, associated with the four quadrant domain bundles, form into a closed loop. This “polarization closure” pattern is reminiscent of the flux-closure already commonly observed in soft ferromagnetic microdots but to date unseen in analogous ferroelectric dots. KEYWORDS: Ferroelectrics, domains, flux closure, nanodots, transmission electron microscopy, needle domains he driving force behind the formation of flux-closure states in ferroics is the minimization of demagnetizing or depolarizing fields, achieved through the creation of head-to-tail magnetic or dipolar loops. If spatially continuous rotation of the vector orientation of local magnetization or polarization about a core occurs, then a vortex state develops. However, a less exotic fluxclosure arrangement can also be realized through formation of domain quadrants, in which the magnetization or polarization step-rotates from one quadrant to the next.1 5 While these kinds of domain patterns are commonly observed in ferromagnetics, the existence of dipole closure states in ferroelectrics is not yet well established or understood. Indeed, until recently, it was not a topic of great research activity. This changed within the past decade when Bellaiche and co-workers predicted a range of complex domain patterns in nanoscale ferroelectrics in which flux-closure was a central driving theme.6,7 Since then a burgeoning interest in ferroelectric as well as multiferroic closure domain states has developed, leading to a profusion of both theoretical and experimental studies.8 19 If anything, this theme is currently expanding to potentially include all forms of domain topologies associated with cores or central singularities,20 gaining inspiration from the detailed theoretical descriptions made earlier by Mermin.21 For many of the exotic domain topologies to exist in ferroelectrics, dipoles must be able to rotate away from their crystallographically constrained orientations. Malleability of polar orientation has been inferred from several piezoresponse force microscopy (PFM) studies,12,13 but direct imaging of polar rotation using aberration-corrected transmission electron microscopy (TEM)17,18 has generated unequivocal confirmation of the phenomenon. For pure ferroelectric materials, obvious polar rotation is perhaps most likely to occur in systems such as PbZr(1-x)Ti(x)O3 (PZT) where a morphotropic phase boundary (MPB) exists:22,23 anisotropy near the MPB is expected to be lowered allowing for greater polar malleability.24 26 Indeed, it is perhaps no coincidence that the polar rotation observations made
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by Jia et al.18 were on thin film cross sections of PZT. While polar rotation in ferroelectrics has been established in principle, entire flux-closure, or vortex states that form in response to depolarizing fields, have rarely been directly observed.17,19 In the current study, we present an investigation into the domain configurations that develop in single-crystal PbZr(0.42)Ti(0.58)O3 nanodots machined from coarse-grained bulk ceramic. Fine-scale 90 stripe domains were found to spontaneously form into quadrant bundles on cooling through the Curie temperature. Careful analysis of domain orientations using dark-field TEM and consideration of the electrostatic nature of boundaries between quadrant domain bundles allowed for a full rationalization of the dipole orientations within the nanodots. While polar rotation was not probed, it was clear that the domains formed into a complex dipolar loop structure on length scales of the order of ∼100 nm. Such a polarization pattern is in direct contrast with the quadrupole states observed previously in BaTiO3 dots.27,28 In addition, while nanostructures of PZT have previously been fabricated, these have either been polycrystalline in nature29 33 or required epitaxial growth conditions;34 of the single-crystalline structures reported,35 39 few explicitly investigated domain states.37 39 Hence the approach outlined in this study represents an advance in domain state investigation in PZT nanostructures. A coarse-grained bulk ceramic PbZr(0.42)Ti(0.58)O3 pellet was fabricated using standard mixed oxide methods (using high purity PbO, ZrO2 & TiO powders): constituent powders were mixed by ball-milling for several hours then thermally treated at 800 C for 2 h before being remilled and pressed into a 30 mm diameter pellet and sintered at 1200 C for 1 h. Adjustment of the sinter heating and cooling rates helped produce ceramics with predominately large grains of approximately 10 20 μm in diameter, as can be seen in Figure 1a. Energy dispersive X-ray analysis on thin sections taken from the ceramic confirmed the Received: September 7, 2011 Published: September 08, 2011 4490
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Figure 1. Piezoresponse force microscopy image overlay on 3D topography of bulk ceramic PZT (a) showing a rich domain structure within large grains. Secondary electron image (b) showing an individual grain from which a lamella will be milled in a site between the two crosses. The schematic in (c) shows a lamella lifted out of the bulk ceramic onto a 100 nm thin Si3N4 membrane receiving additional FIB milling with the beam perpendicular to the lamellar face to pattern free-standing, isolated nanostructures similar to that seen in the secondary electron image in (d). AFM topography (e) before (left) and after etching (right) in 3 M HCl for several minutes is evidently sufficient to remove gallium oxide islands from the surfaces of the lamella after the annealing step. Note that in (c e) the color coding helps distinguish between PbZr(0.42)Ti(0.58)O3 lamellae (orange) and the 100 nm Si3N4 membranes (green).
cation stoichiometry of Pb(0.99 ( 0.02), Zr(0.42 ( 0.01), and Ti(0.58 ( 0.01), while X-ray diffraction (data not shown) was employed to check that the ferroelectric perovskite phase had been formed; no traces of pyrochlore were detected either through X-ray or through electron diffraction. The use of a FEI200TEM focused ion beam (FIB) microscope enabled thin sections or “lamellae” to be cut from individual grains (using the milling steps typically used for preparing samples for TEM), as demonstrated in Figure 1b. Effectively such sectioning produced small single-crystal PZT sheets; however prior to TEM investigation, the crystallographic orientation of each lamella had yet to be determined. The lamella was then lifted from the bulk ceramic onto a 3 mm diameter Si3N4 TEM substrate with 100 nm thin membrane regions; further FIB milling, perpendicular to the surface of the lamellae, was used to pattern almost free-standing, isolated nanodots as shown in the schematic in Figure 1c and in the secondary electron image of the nanostructures in Figure 1d. Subsequent annealing to 500 C for 1 h allowed implanted Ga+ from FIB processing to be expelled to the nanostructure surface where gallium oxide islands readily formed; these islands could be removed by etching in 3 M HCl for several minutes. The annealing stage allowed domains to form in response to the nanostructure morphology (and associated depolarizing fields) upon cooling through the Curie temperature. A Dimension 3100 atomic force microscope (AFM) was used in order to check surface topography quality before and after etching as seen in the example in Figure 1e. TEM (Tecnai F20) was used to determine the approximate orientation of the bounding surfaces of the nanodots and to visualize the domain structure present. Selected area diffraction patterns confirmed crystallographic directions and were used to ascertain the tetragonality of the system. For the composition of PZT used in this study the tetragonality was determined to be 3.4 ( 0.5%. In Figure 2, bright-field TEM imaging shows the domain structures typically observed in PbZr(0.42)Ti(0.58)O3 nanodots cut from approximately {100}pseudocubic (pc) oriented lamellae. As
can be seen, fine-scale 90 stripe domains (with domain walls parallel to {110}pc) occur in distinct “bundles”. A striking resemblance in domain structure was seen across a series of similarly oriented nanodots (illustrated by the images in Figure 2a c) suggesting this is an energetically favorable domain configuration. An electron diffraction pattern, representative of that obtained from a set of parallel stripe domains, can be seen in Figure 2d. The type of diffraction spot splitting displayed is a signature of a 90 a-a domain structure in which polarization is found to lie within the plane of the sample;40 this, along with the crystallography of the domain walls allowed unambiguous designation of domains in Figure 2a c as being of this 90 a-a type with all dipole orientations contained within the plane of the images presented. The origin of the observed spot splitting can be understood by referring to the schematic illustration shown in Figure 2e, which shows the nature of the tetragonal unit cells either side of a domain wall. Note that the {110}pc planes parallel to the domain wall itself in both of the domains are necessarily parallel to each other and of equal periodicity. The diffraction spots associated with these {110}pc planes either side of the domain wall therefore superpose (see Figure 2f,d). On the other hand, the {110}pc planes that lie approximately perpendicular to the domain wall in each of the domain variants are not parallel to each other (although they do have the same periodicity). In the diffraction pattern, the orientation of the reciprocal lattice vectors perpendicular to these planes do not superpose and hence splitting is observed (Figure 2f). This analysis will be of use in the dark-field imaging discussion below. In attempting to understand the nature and genesis of the domain patterns, we first considered the broad-brush polarization pattern created by the bundles of stripe domains arranged into four quadrants. Polarization within each stripe domain locally lies along the Æ100æpc directions; however, the component of polarization parallel to the {110}pc domain walls switches orientation by 180 across each domain wall. The sum of all the 4491
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Figure 2. Bright-field TEM images (a c) show the domain structure within free-standing isolated nanodots of PbZr(0.42)Ti(0.58)O3 while (d) shows an electron diffraction pattern representative of the region highlighted in (c) by the white circle. The type of diffraction spot splitting is indicative of the 90 a-a domain structure found in the circled region and depicted in the schematic diagram in (e) where a single domain wall (yellow) separates regions where the unit cell and therefore polarization are apart by 90-θ. This θ deviation from 90 is manifest in the simulated diffraction pattern in (f) by splitting of the 011 reflection associated with the lower left domain in (e) and 101 reflection associated with the upper right domain in (e). However, the real-space vectors separating (011) planes in the lower domain and (101) planes in the upper domain in the schematic illustration are parallel across the domain wall and therefore in (f) the corresponding reciprocal lattice vectors (orange) are parallel resulting in superposing diffraction spots.
Figure 3. Color-coded representations of the 16 possible distinct and equivalent domain configurations for a square geometry displaying quadrants. Distinct states can be transformed to equivalent states via one of two possible symmetry operations: either rotation by 90, 180, or 270 clockwise about an axis out of the page at the center of the square or through charge inversion in which all dipoles (red arrows) have their orientation reversed. The restriction of the allowed polar directions for each quadrant is displayed in the box along with the color legend corresponding to each polar direction.
polarizations, or resultant polarization, in each quadrant of stripe domains is therefore oriented perpendicular to the 90 domain walls (components parallel to the walls resolve to give no net contribution). Since this resultant polarization must adopt one of only two Æ110æpc directions, there are only 16 possible configurations that could be present in the nanodots, as depicted in Figure 3. Many of these configurations are degenerate or equivalent by symmetry; we have grouped them into five families of equivalent states. The challenge in subsequent analysis was to identify the family to which the polarization patterns observed in the nanodots belonged. With this in mind, two further aspects of analysis were employed: first, dark-field TEM was used to unequivocally identify the c-axis orientation in each of the 90 stripe domains; second, electrostatic conditions at the boundaries between quadrants were considered.
In dark-field TEM,41 selection of individual diffraction spots by aperture positioning allows only those electrons diffracted from the associated crystallographic planes to be used to form the image. Thus the resulting electron intensity shows regions in the same crystallographic orientations. The enlargement of Figure 4a shows a split diffraction spot labeled as 303 and 033 reciprocal vectors according to the two domain variants considered in Figure 2. By selecting the upper spot of this split pair (the 303 spot), domains with their c-axes approximately horizontal in Figure 4 will be imaged. Equally, by selecting the lower spot (the 033 spot), those domains with c-axes vertical in Figure 4 will be imaged (see Figure 4c e). This dark-field structural information can be easily correlated with the corresponding bright-field image from Figure 4b so that pale or dull contrast can be ascribed a particular unit cell orientation and accordingly extended to all domains of similar contrast under the same imaging conditions. 4492
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Figure 4. Comparison between bright-field and dark-field TEM of domains in a nanodot. Selected area diffraction pattern obtained for the nanodot seen in Figure 2a and an enlargement showing splitting of the 033 and 303 spots from two domain variants (a). A bright-field TEM image (b) of the right portion of the nanodot in Figure 2a showing domain structure and corresponding dark-field images of the same area formed using the 303 spot (c) and 033 spot (d). The insets to (c,d) show the respective apertured diffraction spots. In (e), a color overlay of the two dark-field images demonstrates the interlinking nature of high intensity regions/domains from each image. The 303 diffraction spot originates from unit cells that possess the c-axis horizontal to the page and the 033 spot stems from unit cells with c-axis vertical so that brightfield image contrast can be compared to this data; pale contrast corresponds to unit cells with c-axis vertical and dull contrast to unit cells with c-axis horizontal as shown by the schematics. The white pointer in (b,c) identifies the same domain in both images.
Knowledge of unit cell orientation for particular domains becomes significant when noting that at each boundary between quadrants, in the studied nanodots, the ferroelastic domains form needlelike “points” and associated “flares” (the complementary shape associated with a needle point).42 Useful information regarding the dipole nature of the quadrant boundary is contained within this asymmetric fine structure. From the dark-field TEM analysis of Figure 4, the unit cell orientation of particular points and flares is now known and one of two possible local polarization directions can be assigned (charge symmetry will of course produce an equivalent state with all dipoles reversed). In Figure 5, a schematic representation of a domain bundle boundary is shown for two cases: one for which electrostatic boundary conditions are generally favorable and one where the head-tohead dipole arrangement produces charged domain walls for the same domain pattern/topology. It is worth noting that the resultant polarizations in both cases seem on first inspection to be similar and it is only from closer scrutiny of the fine structure of the domain topology that the charge disparity becomes apparent. We assume that preferable electrostatic conditions similar to that in Figure 5a will be prevalent over those in Figure 5b; this assumption was used to assign the dipole directions within all domains, given the c-axis unit cell orientation information that had already been obtained from dark-field imaging. Analysis of domain topology fine structure can be seen in Figure 6, using the electrostatic considerations outlined above to determine dipole orientation within each quadrant. In order to ascribe polarization orientation for individual domains, first a domain with known unit cell orientation is chosen and second a selection is made on the direction of the polarization from the two antiparallel possibilities available. This choice then determines
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Figure 5. Schematic representations of bundle boundary with domain needle points and flares that invariably exist upon impingement onto a domain running along a perpendicular direction. In (a) dipoles within the domains are such that electrostatically unfavorable “head-to-head” configurations are mostly avoided and the boundary region is almost entirely a simple 90 a-a domain wall. In direct contrast, the case in (b) shows a highly unfavorable configuration of dipoles where a large area of the quadrant boundary region will accumulate charge through head-tohead arrangements. The resultant polarizations (red double-body arrows) for (a,b), seen in (c,d), respectively, are largely equivalent and only differ in the bundle boundary fine structure of the domain topology.
the surrounding adjacent domain polarizations, given that they are established to be 90 a-a domains. In this way, a resultant polarization is decided for the entire quadrant. Domain orientations in the next quadrant can be established via the assumed electrostatic considerations outlined in Figure 5. In this manner once an initial assumption is made about the orientation of one domain, all other domain orientations are propagated; as a result the broad-brush net polarizations associated with the quadrants can be determined. It can now clearly be seen that the resultant polarization for each quadrant leads onto the next such that a continuous loop is found as shown in Figure 7. The yellow area is a region in which 180 domain walls must exist as demanded by the assignment of dipoles in each quadrant (but these have not been imaged directly on TEM, as 180 domains do not show strong contrast in bright-field imaging). The existence of a 180 domain wall connecting two 3-fold wall junctions or “vertices” has already been inferred in BaTiO3;14 its presence in PZT nanodots may extend the applicability of Potts’ over Clock models in describing ferroelectric domain wall junctions, as discussed by Srolovitz and Scott.43 Comparing this determined domain pattern to those in Figure 3 shows that the nanodot has adopted one of the distinct states with only a single equivalent state. Of the other four distinct states, each would produce highly unfavorable electrostatic conditions at several or all of the quadrant boundaries. It is only the high tetragonality-produced spot splitting and successful aperture selection of individual split spots for dark-field TEM that allowed this ‘”point-flare” electrostatic argument to be effectively used. Such arguments would not be practical in lower tetragonality ferroelectrics such as BaTiO3. In addition, this type of quadrant domain structure (with macroscopic polarization closure) was seen repeatedly in different nanodots of the same morphology and was found to be considerably stable over a period of several months. This strongly indicates that the polarization closure configuration adopted on cooling through 4493
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Figure 6. A bright-field TEM image (left) and the corresponding electron diffraction pattern of the same nanodot from Figure 2a shows the locations of the magnified images a d. To the right of images a d are the associated schematic representations of the local domain configurations. The gray area in c designates a region for which it is difficult to define domain topology.
’ ACKNOWLEDGMENT The authors acknowledge financial support from the Engineering and Physical Sciences Research Council (Grant EP/ F004869/1), The Department for Employment and Learning in Northern Ireland, and The Leverhulme Trust (F/00 203/V). Constructive relevant discussions with J. F. Scott, G. Catalan, I. Luk’yanchuk, and N. Valanoor are also acknowledged. ’ REFERENCES
Figure 7. A bright-field TEM image (a) of the center region of the nanodot from Figure 2a and the associated schematic representation of the domain configuration (b). The gray area is a region for which it is difficult to define domain topology while the yellow area is one in which 180 domain walls must exist as demanded from the dipole configuration as determined from the quadrant boundary electrostatic conditions. Resultant polarization (red double-body arrows) is constructed such that each polarization leads to the next in a “loop” fashion.
the Curie temperature is a low energy state for the system. It should be noted that while prior observations of flux-closure required the application of an electric field12,15,16,19 in this study we have shown that single-crystal free-standing nanostructures can spontaneously form such domain patterns on cooling through the Curie temperature under boundary-related depolarizing fields alone. In conclusion the domain states in single-crystal free-standing isolated nanodots of PbZr(0.42)Ti(0.58)O3, produced by means of FIB milling of lamellae from large-grained bulk ceramic, have been investigated. Using bright- and dark-field TEM, combined with electrostatic considerations at boundaries between bundles of 90 stripe domains, resultant polarization structures were revealed. These structures were found to consist of large-scale closed loops in polarization, very similar to the flux-closure patterns already known in ferromagnets, but scarcely observed in ferroelectrics.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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