Atomic-scale mapping of dipole frustration at 90° charged domain walls in ferroelectric PbTiO3 films

The atomic-scale structural and electric parameters of the 90° domain-walls in tetragonal ferroelectrics are of technological importance for exploring the ferroelectric switching behaviors and various domain-wall-related novel functions. We have grown epitaxial PbTiO3/SrTiO3 multilayer films in which the electric dipoles at 90° domain-walls of ferroelectric PbTiO3 are characterized by means of aberration-corrected scanning transmission electron microscopy. Besides the well-accepted head-to-tail 90° uncharged domain-walls, we have identified not only head-to-head positively charged but also tail-to-tail negatively charged domain-walls. The widths, polarization distributions, and strains across these charged domain-walls are mapped quantitatively at atomic scale, where remarkable difference between these domain-walls is presented. This study is expected to provide fundamental information for understanding numerous novel domain-wall phenomena in ferroelectrics.

The atomic-scale structural and electric parameters of the 906 domain-walls in tetragonal ferroelectrics are of technological importance for exploring the ferroelectric switching behaviors and various domain-wall-related novel functions. We have grown epitaxial PbTiO 3 /SrTiO 3 multilayer films in which the electric dipoles at 906 domain-walls of ferroelectric PbTiO 3 are characterized by means of aberration-corrected scanning transmission electron microscopy. Besides the well-accepted head-to-tail 906 uncharged domain-walls, we have identified not only head-to-head positively charged but also tail-to-tail negatively charged domain-walls. The widths, polarization distributions, and strains across these charged domain-walls are mapped quantitatively at atomic scale, where remarkable difference between these domain-walls is presented. This study is expected to provide fundamental information for understanding numerous novel domain-wall phenomena in ferroelectrics. F erroelectrics possess controllable polar states and electromechanical couplings, they were found extensive applications as high-density memories, thin-film capacitors and actuators as well as sensors [1][2][3] . In addition, they are showing multifunctional capabilities, as seen the finding of domain-wall conductivity [3][4][5][6] in ferroelectrics. Domain-walls in ferroelectrics are topological interfaces that separate domains with different orientations of polarizations. Historically, the domain-walls in ferroelectrics were thought to be simple, but their physical nature is found to be quite complicated in the past decade 3 . The local structural, chemical, and electric features as well as the dipole-defect interactions of domain-walls are of great importance and the macroscopic physical properties of ferroelectrics are strongly associated with these microstructural characteristics [7][8][9][10][11][12] .
Tetragonal ferroelectrics generally exhibit two types of domain-walls: 90u and 180u domain-walls, which have dipoles across the domain-walls arranged as 90u (nearly) and 180u configurations, respectively [7][8][9][10][11][12][13][14] . The 180u domains have the same strain, and hence are easy to switch 8,10-12 . However, the strong coupling of the polarization to the elastic strain of 90u domains limits the poling and piezoelectric ability of tetragonal ferroelectrics, which is a large obstacle for their potentials [7][8][9][10][11][12] . To understand the atomistic mechanisms involved during 90u domains switching, it is highly essential to figure out the structural and electric behaviors of 90u domain-walls on the atomic-scale which is known little up to date. Previously, the width of 90u domain-walls was studied by conventional transmission electron microscopy (TEM), and was 20 nm for BaTiO 3 (ref. 15), then 4-15 nm for BaTiO 3 , (Ba, Pb)TiO 3 and Pb(Zr 0.52 Ti 0.48 )O 3 (refs. [16][17][18]. These measurements might be overestimated due to the limitation of instrument resolution, since the width of 90u domain-walls in PbTiO 3 were later found to be atomically sharp as 1.0-2.8 nm, determined by high resolution transmission electron microscopy (HRTEM) and weak beam transmission electron microscopy [19][20][21][22] . In the meanwhile, more and more theoretical works have proposed the presence of atomically sharp 90u domain-walls in tetragonal ferroelectrics [22][23][24] . Nevertheless, the dipoles across the 90u domain-walls were almost ignored in previous experiments, although the appearance of 'head-to-head' domain-walls was inferred in some modified rhombohedral PZT ceramics by the diffraction contrast analysis in a TEM 25 . Generally, the dipole configurations across the 90u domain-walls were arbitrarily treated as 'head-to-tail' arrangement in theoretical simulations based on the consideration of the electrostatic energy [15][16][17][18][19][20][21][22][23][24] . The newly developed scanning probe microscopy (SPM) based instruments show great potential to map the polarization distribution at ferroelectric surfaces, but its lateral resolution is about 5-30 nm, which is far from atomic-scale 3,26,27 .
The atomic and electronic behaviors of ferroelectrics have become readily accessible through aberrationcorrected scanning transmission electron microscopy (STEM) 28 [35][36][37] has recently become feasible. In this study, we have grown PbTiO 3 / SrTiO 3 multilayer films and mapped atomic details and polarization distributions across the 90u domain-walls in an aberration-corrected STEM at high angle annular dark field (HAADF) mode. We have directly observed not only positively charged but also negatively charged 90u domain-walls at atomic scale.

Results
PbTiO 3 /SrTiO 3 multilayer films were prepared by pulsed laser deposition (PLD). The films were deposited on GdScO 3 (GSO) substrate, which exert tensile strain on the epitaxial PbTiO 3 /SrTiO 3 superlattices 38 . Such ferroelectric/paraelectric heterostructures have attracted lots of interests because they offer a huge space for exploring the subtle interplay between their multiple order parameters [39][40][41] .
Identification of 906 positively-charged-domain-wall. Figure 1a shows an atomic resolution HAADF image of a  (Fig. 1d). The Ps direction (yellow arrow in Fig. 1d, colored arrows in Fig. 1a) of  Such a 90u CDW is actually a broad area (labeled area I, as will be specified in the following) and thus is marked by two white dotted lines (Fig. 1a). Nominally, the 'headto-head' arrangement of Ps produces positive bound charges near the CDW 42 , so here we name it in terms of 90u positively-chargeddomain-wall (PCDW). Similarly, the 90u uncharged-domain-wall is short-written as 90u UCDW. A careful observation indicates that, on both structural and electric level, the 90u PCDW is rather wider than the 90u UCDW. According the famous Kittel's law, the DW width is a crucial factor for determining the DW patterns and thus the properties such as nonlinear electro-optics 3 . The local behaviors of the present 90u PCDW (rhombus-highlighted area labeled '2' in the lower left of figure 1a) are comparatively studied with the 90u UCDW (rhombus-highlighted area labeled '1' in the upper left of figure 1a), and the average data are obtained along PTO{110} p (subscript p denotes pseudo-cubic), which is generally thought to be the location of 90u DWs in tetragonal ferroelectrics [22][23][24] . The magnitudes of Ps vectors are determined by corresponding d Ti because the relationship between the d Ti and the Ps is well-known 33 Fig. 2e). The ratio of c B /a B indicates a slow changing of tetragonality, from 1.075 to 1.01 (Fig. 2f). There is no inter-section of c B and a B lattice, and thus no sudden jump of tetragonality, which displays some unusual features of the 90u PCDW compared with the uncharged domain-walls. Generally, the Ps and strain in ferroelectric materials are coupled 8,33 , as a result, the Ps Y also changes slowly from domain B (about 80-100 mCcm 22 ) to area I (0) (olive-circle curve in Fig. 2h). However, Ps X almost keeps almost a constant value of about 40 mCcm 22 (red-circle curve in Fig. 2h). It is proposed that the accumulated bound charges induced by the 90u PCDW might be responsible for the invariable Ps X . The continuous and slow changing of lattice and Ps indicate that there is no obvious DW across the domain B and area I (violet gradual shadows in Fig. 2e-h). In other words, here the 90u PCDW is a broad area where the Ps vectors are disordered.
To directly gain insight into the polarization distributions, the Ps vectors of each unit-cell near the 90u PCDW were mapped and superimposed on the HAADF image (Fig. 3). The arrows located at the Ti 41 column positions indicate the directions and modulus of the Ps vectors. For most PTO cells, the Ps values are in the range of 70-100 mCcm 22 . Unlike the 90u UCDW, where the directions of the Ps vectors changed rapidly, the Ps is strongly restricted and disordered at the 90uPCDW. According to the disorder of the Ps vectors, no obvious 'domain-wall' could be identified, which is consistent with its lattice behavior (Fig. 2e, f). Bound charges produced by the 'head-to-head' dipole arrangement may be responsible for the restriction and disorder of the 90uPCDW.
Identification of 906 negatively-charged-domain-wall. In addition to the 90u PCDW, 90u Ps vectors configured as 'tail-to-tail' CDW is also identified in the present films. Since the 'tail-to-tail' Ps arrangement may nominally induce negative bound charges near the CDW 42 , here we name it as 90u negatively-charged-domainwalls (90u NCDW). We will see that the structural and electric parameters of 90u NCDW are remarkably different from those of 90u PCDW. Figure 4a shows an atomic resolution HAADF image of a PTO layer containing twin structures. Using the same methodology as that in figure 1, the position of 90u UCDWs is outlined, as marked by the blue dotted lines in the upper left part of figure 4a. By mapping the d Ti vectors of each PTO unit-cell, 90u DW with 'tail-to-tail' arrangement of Ps vectors is identified, as traced by the red (upper segment) and light red (lower segment near the PTO/STO interface) dotted lines. The 90u NCDW separates domain A and B in figure 4a, with Ps directions pointing to left and top, respectively (magnified insets in Fig. 4a). Different from the 90u PCDW, the upper segment of the 90u NCDW is much narrower like that of the uncharged ones, while the lower segment is broadened similar to that of the 90u PCDW. The local behaviors of the two segments of the 90u NCDW are comparatively analyzed with the 90u UCDWs. In figure 5, the upper 90u NCDW (rhombus-highlighted area labeled '2' in Fig. 4a) is compared with the left 90u UCDW (rhombus-highlighted area labeled '1' in Fig. 4a), while the lower 90u NCDW (rhombus-highlighted area labeled '3' in Fig. 4a) is compared with a 90u UCDW which is also near the PTO/STO interface neighboring with the 90u NCDW, seen in figure 4b. Here this 90u UCDW is the connection between domain A and a c domain, which was located at the left side of domain A. The lattice and Ps characters of the left 90u UCDW (Fig. 4a) as well as the 90u UCDW near the PTO/STO interface (Fig. 4b) are shown in figure 5a-d and figure 5e-h. We can see that the width of 90u UCDW was not disturbed by the PTO/STO interface (Fig. 5e-h), since both the structural and electric parameters changed rapidly across these 90u UCDWs. However, the lattice parameters of these two 90u UCDW are different: the c-axis in domain A and B in figure 5a (0.415-0.42 nm) are bigger than those in domain C and A in figure 5e (about 0.41 nm). These differences were probably induced by the complex strains near the PTO/STO interface 33 . According to the sharp change of lattice and Ps vectors, both the 90u UCDWs possess the same width about 4 unit-cells, which is qualitatively the same as the 90u UCDW in figure 2a.
The structural and electric parameters of the upper and lower segments of the 90u NCDW were analyzed (Fig. 5i-l and Fig. 5mp). The lattice and polarization also change rapidly across the upper 90u NCDW. This DW width is about 5 unit-cells, almost the same as the 90u UCDW, shadowed in light blue in figure 5i-l. However, for the lower segment of the 90u NCDW, the corresponding parameter slopes are obviously abated. The width of this DW is about 10 unitcells (gradually shadowed in red in Fig. 5m-p), which is much bigger than that of the 90u UCDW. Nevertheless, like the 90u UCDW, the location of the 90u NCDW is still along {110} PTO.
The Ps vectors of each unit-cell near the 90u NCDW are also mapped and superimposed on the HAADF image (Fig. 6a, b). The 90u UCDW and the upper segment of the 90u NCDW are shown in figure 6a. Unlike the 90u UCDW, where the Ps directions rotate sharply with 90u at the DW, the Ps is almost maintained and rotates inchmeal at the 90u NCDW. The Ps vectors, in one or two units away from the 90u NCDW, are somewhat inclined to the NCDW both in domain A and B. And this trend is most obvious at the 90u NCDW because the Ps vectors rotate about 45u respective to horizontal or vertical plane (marked with red arrows in Fig. 6a), which produces diagonal Ps directions along the 90u NCDW. This inclination of Ps vectors along the 90u NCDW may help to relieve the bound charges and thus lower the depolarization field 3 , and to stabilize the narrow 90u NCDW. In contrast, the Ps vectors seem to be strongly disturbed at the lower segment of the 90u NCDW near the PTO/STO interface, as shown in figure 6b. According to the diffusion of the Ps vectors, no obvious 'domain-wall' could be identified. Instead, it is more like a 'domain-wall-band' with a thickness about 10 unit-cells, which is consistent with the lattice behaviors (Fig. 5m, n). Except for the bound charges, the PTO/STO interface may also be responsible for the diffusion of the lower segment of the 90u NCDW because of the interface-induced depolarization field which is very common in thin film ferroelectrics 3 .
To directly visualize the 2D structural parameters and Ps angles, unit-cell-wise structure and Ps angle mapping are displayed. The lattice parameter, gradient of the lattice parameter and Ps angles of the PTO unit-cells near the 90u PCDW and NCDW are mapped unit-cell by unit-cell, as shown in Figure 7. The out-of-plane lattice spacing mapping results clearly exhibit the 90u UCDWs, since there is sudden jump of the lattice spacing (blue to green, presumably corresponds to 0.39-0.42 nm, Fig. 7a, b). Although the 90u PCDW is diffused since the lattice spacing slowly changes from 0.395 to 0.42 nm (light blue to white then to green) with a width about several tens unit-cells (Fig. 7a, which is consistent with Fig. 2e), we note that the 90u NCDW is much sharper (Fig. 7b). To visually show the differences among the uncharged, positively and negatively-charged 90u DWs, in-plane lattice gradient of the out-of-plane lattice spacing are mapped. The lattice gradient is defined as jc x11 2 c x j/1U.C., where c x denotes an out-of-plane lattice spacing and c x11 denotes the out-of-plane lattice spacing of the right neighbor unit-cell of c x , and 'unit-cell' is abbreviated as 'U.C.', (Fig. 7c, d). The uniform dark blue means there is no in-plane lattice gradient since there is no lattice change in a single domain. The sudden change of lattice c to a (or a to c) across the 90u UCDWs makes obvious contrast in figure 7c, d. The maximum of the lattice gradient is about 0.01 to 0.015 nm/U.C. across the 90u UCDWs. It is clear that the left 90u UCDW in figure 7c terminates in the matrix, which results in the formation of the 90u PCDW. Compared with the uncharged DWs, the lattice gradient of the 90u PCDW is invisible (Fig. 7c), this means the lattice change across the 90u PCDW is much slower. Such a status is also seen in figure 2e. However, the 90u NCDW possesses visible lattice gradient (Fig. 7d). Moreover, the lattice gradient of the upper segment is comparable to the 90u UCDW (note that their color-scales are almost the same). Nevertheless, as seen in figure 7d, the colorscale of the 90u NCDW changes gradually from green to light blue as the DW tracing from top to bottom. This indicates that when the 90u NCDW reaches the PTO/STO interface, the lattice gradient is continuously relieved. In addition, the DW is broadened simultaneously with relief of the lattice gradient, as marked with the violet dotted lines (Fig. 7d). Such a status is also seen in figure 5m.
The Ps angles of each unit-cell near the 90u PCDW and 90u NCDW are also mapped (Fig. 7e, f). It is seen that the Ps directions change rapidly across the 90u UCDWs, behaving like their lattice gradient. However, the Ps directions at the 90u PCDW are strongly disordered (see the color fluctuation in Fig 7e). Moreover, this wedgy disordered area is much broader than the uncharged ones with tens of unit-cells at the bottom. For the 90u NCDW, the change of Ps angles are much sharper than those of the 90u PCDW. This is almost comparable to the 90u UCDWs for the upper segment and just somewhat relieved for the lower segment (Fig. 7f).

Discussion
Although the 180u CDWs are common in uniaxial 42,44 and possible in multiaxial ferroelectrics 14,45 , the 90u CDW in tetragonal ferroelectrics in our experiments is the first direct atomic-scale observation. Generally, it is proposed that internal charge carriers, for example, oxygen vacancies or electron holes, can screen the bound charges accompanying with the CDW 3,42,45,46 , thus the CDW could be stabilized. In the case of present PTO/STO films, it is proposed that the charge carriers are probably oxygen vacancies (Vo 21 ), which possess positive charges screening the negative bound charges induced by the 90u NCDW. This inference is constant with our observation because the 90u NCDW is less disturbed compared with the 90u PCDW, and the later probably deserved a depletion layer of Vo 21 , which was repulsed by the positive bound charges 44 . In addition, for ferroelectrics with a specific charge carriers (positive, such as Vo 21 and electron holes, or negative, such as electrons), only one kind of CDW can be effectively screened 42,44 . On this condition, if a ferroelectric possesses both PCDW and NCDW simultaneously, only one kind of CDW could be neutralized, that is probably the situations of our present observation, which was proposed in theoretical work 42 . Our results suggest the lattice and polarization are coupled ideally for all kinds of 90u DWs in PTO. This is remarkably different from the decoupling observed by AFM and PFM in BaTiO 3 (Refs. 47) which showed the polarization distribution is much wider than that of lattice.
The charge carrier accumulation was hypothesized to be a cause for the increased conductivity at the CDWs in ferroelectrics 3,44 . In hexagonal ferroelectric HoMnO 3 , the widths of 180u PCDW and NCDW were also found to be different, based on the conductive atomic force microscopy (cAFM) observation where the DW width was absent from atomic-scale information limited by the AFM tip radius. In tetragonal PbTiO 3 films of the present study, the difference between the 90u PCDW (carrier depletion) and NCDW (carrier accumulation) at atomic scale may qualitatively explain the different conduction behaviors between 'head-to-head' and 'tail-to-tail' 180u DWs in HoMnO 3 (ref. 44). In addition, the coupling of Ps and elastic strain for the 90u DWs is much stronger than the 180u DWs 8,10-12 . This implies that, during the 180u switching the 90u CDWs may generally exist, at least in a dynamical style. Earlier PFM studies showed that this kind of 90u CDWs may play an important role for the retention failure of the PZT memories because the switched 180u domains could be reversed by the 90u CDW as time elapses 48,49 .
In summary, by using aberration-corrected STEM, the unusual frustration of dipole arrangements and strain behaviors of 90u  CDWs in PTO/STO multilayer films are identified on the atomicscale, where the widths, polarization distributions, and strains across these charged domain walls are mapped quantitatively. ''Glass-like'' dipole behaviors are observed at the 90u CDWs. We anticipate the present atomic-scale investigations of the uncharged and charged 90u DWs may help to interpret the switching behaviors, the newly realized domain-wall functions, and the retention failure mechanism in ferroelectrics. Moreover, the present study is expected to clarify the long-standing argument about the width of the 90u DWs in tetragonal ferroelectrics. During the review stage of this paper, a research group in Michigan University reported an occurrence of 90u charged domain walls in Pb(Zr 0.2 Ti 0.8 )O 3 thin films formed by in-situ electric response 50 .

Methods
Thin-film synthesis and STEM sample preparations. The PbTiO 3 /SrTiO 3 thin films were deposited on GdScO 3 substrates by pulsed laser deposition (PLD), using a Lambda Physik LPX 305i KrF (l 5 248 nm) excimer laser. The PbTiO 3 targets were 3 mol% Pb-enriched sintered ceramics. The target-substrate distance was 40 mm. The background pressure was 10 25 Pa. During the growth of PbTiO 3 , the substrate temperature was kept at 650uC, with a laser energy density of 2 Jcm 22 , a laser repetition rate of 5 Hz and under an oxygen pressure of 20 Pa. For the growth of SrTiO 3 layers, the substrate temperature was also 650uC, with a laser energy density of 1 Jcm 22 , a laser repetition rate of 2 Hz and under an oxygen pressure of 8 Pa. Before deposition, the GdScO 3 substrate was pre-heated at 750uC for 5 min to clean the substrate surface and then cooled down to the growth temperature (10uC/min). The laser was focused on the ceramic target for 30 min pre-sputtering to clean the target surface. After deposition, the film was in-situ-annealed at 650uC in an oxygen pressure of 5 3 10 4 Pa for 10 min, and then cooled down to room temperature at a cooling rate of about 5uC/min. The samples for the STEM experiments were prepared by slicing, gluing, grinding, dimpling, and finally ion milling. A Gatan PIPS was used for the final ion milling.
STEM imaging and analysis. One of the great advantages of HAADF-HRSTEM imaging mode is that it is not sensitive to the variety of local specimen thickness, and therefore, it is quite suitable for large-scale imaging. The finding of the novel domain configurations in the relatively large scale in this work is believed to benefit from the HAADF imaging mode. In addition, the aberration-corrected TEM used in this study features very little drift; for example, the STEM spot drift and specimen drift are 0.14 nm/min and 0.16 nm/min, respectively. HAADF images in this study were recorded using aberration-corrected scanning transmission electron microscopes (Titan Cubed 60-300 kV microscope (FEI) fitted with a high-brightness fieldemission gun (X-FEG) and double Cs correctors from CEOS, and a monochromator operating at 300 kV). The convergence angle of the electron beam is 25 mrad, yields a probe size of less than 0.10 nm. The determination of the atom coordinates in the HAADF-STEM images were carried out by fast Fourier transform (FFT) filtering the images using only a low-pass annular mask restricted slightly more than the resolution limit of the image, thus the lattice spacing and Ti 41 shifts (d Ti ) were deduced. The atom positions were determined accurately by fitting them as 2D Gaussian peaks by using Matlab 14,33,34,51 . The d Ti were calculated as a vector between each Ti 41 and the center of mass of its four nearest A-site neighbor Pb 21 . The Ps vectors were deduced by the d Ti . The visualization of the 2D Ps vectors (Fig. 3 and Fig. 6) was carried out using Matlab. The visualization of the lattice, lattice gradient and Ps angles (Fig. 7) was carried out using the combination of Matlab and ImageJ software 34 .