Atomically resolved structure of step-like uncharged and charged domain walls in polycrystalline BiFeO₃

Domain walls (DWs) in ferroelectrics are nanoscale topological features that mark the transition between regions with homogeneous orientations of the polarization. DWs can have different properties than the domains themselves;^1,2 furthermore, they are dynamic interfaces as they can be moved, erased, and thus manipulated by means of external electric or mechanical fields. There are two strong motivations to study the complexity of the physics and chemistry of DWs in ferroelectrics at the atomic scale. First, the unique electrical properties that the walls can possess, in combination with their dynamic nature under an applied electric field, provide to the DWs with the potential to become “the device.”³ New applications have been proposed for so-called “non-volatile, ferroelectric, domain-wall memories,” where the memory binary state, rather than relying on the conventional polarization state during domain switching, is determined by writing and erasing a particular conductive DW in BiFeO₃ (BFO).⁴ Second, the interphases in ferroelectrics together with the intrinsic lattice distortion can significantly affect the macroscopic electromechanical response of the material.^5–8 For example, in (K,Na)NbO₃-based ceramics, it has been shown that up to 80% of the electric-field-induced macroscopic strain, which is important in, e.g., piezoelectric actuators, can originate from a non-180° DW-switching contribution.⁹ 

The dynamics of DWs is directly influenced by their structure and morphology. Several studies have shown that DWs are not simple, straight interfaces, but that their morphology and structure can be rather complex.^9–14 For example, Lubk et al. showed that DWs in BFO thin films can be rough and produce lattice-wise steps at the atomic level.¹¹ In contrast, no such reports exist for polycrystalline BFO. Reports of morphological features are of particular importance as theoretical studies have shown that steps at the DWs increase their mobility and should thus strongly affect the DW dynamics.^11,15

Studies of DWs are further complicated by the presence of walls that carry an internal bound charge due to there being a nonzero component of polarization that is perpendicular to the domain-wall plane. These walls are usually referred to as charged walls. Depending on the direction of the polarization vector on either side of the wall, DWs are formally referred to as uncharged DWs (UDWs) if they have a “tail-to-head” or “head-to-tail” configuration, or charged DWs (CDWs) if they have a negative “tail-to-tail” or a positive “head-to-head” configuration. A “tail-to-tail” or “head-to-head” DW is often considered “strongly” charged as opposed to a “weakly” charged DW (which is a “tail-to-head” or a “head-to-tail” but the electro-neutrality is broken locally in the DW region).¹⁶ In this paper, by CDWs we will refer only to “tail-to-tail”- or “head-to-head”-type DWs. Despite their obvious energetic cost of formation, “strongly” charged DWs have been experimentally observed in different systems.¹⁶ It is not yet clear how the intrinsic charge state of the DW determines its structure and morphology because comparative studies between CDWs and UDWs that are present in the same ferroelectric system remain scarce. As an illustration, for an epitaxial PbZr_0.2Ti_0.8O₃ thin film, it was shown that the charged DWs can be thicker than the uncharged ones.¹⁷ A comparative study at the atomic level of the structure of charged and uncharged DWs in BFO thin films was performed by Wang et al.,¹⁸ which showed a one-dimensional lattice-strain modulation for charged DWs, that is otherwise not present for the uncharged DWs. In the case of BFO, charged DWs are often ignored in calculations,^19–21 but they are more often reported in experimental studies of BFO thin films.^22,23 To the best of our knowledge, the presence of “tail-to-tail”- or “head-to-head”-type CDWs in polycrystalline BFO has not yet been reported.

It cannot be argued that studies of BFO thin films provide an important insight into various phenomena related to DWs. However, it must be emphasized that in thin-film structures, either polycrystalline or single crystalline (epitaxial), the electric, and elastic constraints (e.g., the presence of epitaxial strain or the unique size-effect phenomena) are different from those in the bulk. Furthermore, it was shown in a number of studies how the domain pattern in epitaxial thin films can be strongly controlled and depends on growth parameters such as growth rate,²⁴ oxygen partial pressure during growth,²⁵ thickness,²⁶ or the choice of the substrate.²⁷ Consequently, it is reasonable to assume that the properties of the DWs in thin films differ from those in a conventionally sintered polycrystalline system. Although one could expect that the local properties in a polycrystalline material with randomly oriented grains would average and give a small overall contribution, it has been shown that the local properties of DWs in BiFeO₃ ceramic, such as the elevated electrical conductivity, interfere with their mobility, resulting in a considerable effect on the macroscopic properties.²⁸ 

In this study, we investigate the morphology and structure of uncharged and “tail-to-tail”-charged step-like ferroelastic DWs in polycrystalline BFO using the high-angle annular-dark-field scanning-transmission electron microscopy (HAADF-STEM) technique with atomic resolution. The aim was to understand the local structural differences between the uncharged and charged DWs. We found that both types of DWs can form step-like kinks. In contrast to CDWs, the uncharged walls have a higher and more concentrated strain, coupled with a narrower transition region and an abrupt change in the displacement vector across the wall. We were thus able to show directly that CDWs and UDWs have different structural properties. The results help us in understanding the so far unrevealed local structural and chemical aspects of the rather unusual CDWs and more conventional UDWs in polycrystalline BFO.

BiFeO₃ ceramics were synthesized using a mechanochemically activation preparation technique. Mechanochemically activated powders were compacted and sintered for 6 h at 760 °C using a heating and cooling rate of 5 °C/min. Details of the synthesis procedure are given elsewhere.²⁸ Atomic-scale investigations of the DWs were performed using a Cs-corrected scanning-transmission electron microscope (STEM) from Jeol Ltd., a Jeol ARM 200CF, operating at 200 kV. The collection semi-angle of the high-angle annular-dark-field (HAADF) detector was 68–180 mrad. The coordinates of the intensity maxima of the atomic columns were determined from HAADF images using a 2D Gaussian fit. The normalized Bi-column intensities were determined using a previously reported method,^29,30 in which the detector's background intensity is subtracted from the intensity of each pixel in the raw HAADF image. The intensities of the atomic columns were extracted by the integration of the pixel values within one sigma, approximating a Gaussian-type intensity distribution. For further details about this analysis, see Refs. 30 and 31. The samples for the STEM analysis were prepared using a conventional method: the sample was ground down to 100 μm, dimpled to 12 μm and, finally, thinned to electron transparency using a Gatan PIPS ion-milling system. The thickness of the analyzed areas was between 30 and 50 nm.

We commence by showing three different regions in the sample, each containing a {100}_pc-type DW (pc refers to pseudo-cubic). We describe a DW as being {100}_pc type if it lies in the {100}_pc family of planes. The atomic-level structure of the DW was extracted from HAADF-STEM images [Figs. 1(a)–1(c)], acquired in the [100]_pc zone axis by measuring the direction and magnitude of the projected Fe displacements from the center of the Bi sublattice for each projected unit cell.

We present three kinds of {100}_pc-type DWs: (1) an UDW having step-like features [DW1 in Fig. 1(d)]; (2) a CDW that has similar steps to DW1 [DW2 in Fig. 1(e)] and (3) a wall that has a quasi-rectangular step, having charged/uncharged segments [DW3 in Fig. 1(f)].

We found that DW1 and DW2 have a staircase-like morphology. DW1 has fine steps of 1–2 unit cells, while DW2 has a larger step-height range of 1–3 unit cells. Roughness in the form of step-like kinks was previously reported for La-doped BiFeO₃ thin films,¹¹ and their presence was linked to the enhanced mobility of DWs when switching under an electric field.^11,15 On the other hand, DW3 has a different morphology consisting of a sharp, quasi-rectangular step, forming relatively large (at least 10 unit cells) charged/uncharged segments. A similar step-like morphology was seen to occur when the DW is pinned on edge dislocations;³² however, as seen from the HAADF image, DW3 appears to be free of any other visible crystallographic defects, except the wall itself [Fig. 1(c)].

We went on and evaluated the charge state of the analyzed DWs considering the Fe-displacement vector maps [Figs. 1(d)–1(f)] and taking into account that the projected Fe-displacement vector has an opposite orientation to that of the projected polarization vector.³³ We found that DW1 is overall a {100}_pc-type UDW [Fig. 1(d)], DW2 is a “tail-to-tail” CDW [Fig. 1(e)] and DW3 represents uncharged and “tail-to-tail”-charged segments [Fig. 1(f)]. Note that DW1 has an overall “head-to-tail” configuration even if locally (at the step) the “head-to-tail” configuration is disrupted; likewise, in DW2, the “tail-to-tail” configuration is locally disrupted.

We must point out that the CDWs (i.e., DW2 or the charged segment of DW3) are observed without a particular treatment, i.e., after a conventional sintering process, and, thus, were formed spontaneously despite the high electrostatic energy requirements.³⁴ While reported in BFO thin films^18,22 and in BFO single crystal,¹² CDWs formed spontaneously have not yet been observed directly in polycrystalline BFO.

In rhombohedral symmetry of BFO (space group R3c¹⁸), the spontaneous polarization can lie along one of the four diagonals in the pseudocubic perovskite unit cell (along the [111]_pc direction) which leads to three different types of DWs: 71°, 109°, and 180°. These DW types are distinguished depending on the number of the reversed sign of the polarization components (x,y,z) of a given domain with respect to the polarization components of the adjacent domain. In the case of 71°, 109°, and 180° DW, either one, two or all the three signs of the polarization components are reversed, respectively.¹⁸ Based on the assumptions that we present in supplementary material 1, we were able to conclude that DW1 is a 109° UDW, DW2 can be either a 109° CDW of {100}_pc type or a 71° CDW of {100}_pc type, and DW3 presents charged/uncharged segment of a 109° DW on {100}_pc. A detailed explanation of the DW-type identification together with a three-dimensional representation of the possible polarization configuration on either side of DW1, DW2, and DW3 is shown in supplementary material 1.

Previous studies^30,31 revealed the segregation of Bi vacancies at UDWs in BFO ceramics, owing to the electrostatic and elastic forces driving the defect diffusion at the walls. Motivated by these studies, in the next step, we probed the presence of Bi vacancies by mapping locally the intensities of the Bi atomic columns [Figs. 1(g)–1(i)]. As seen in Fig. 1(g), the variation in intensity of the Bi columns across the DW1 (uncharged 109° DW) is around 5%–10%, indicating the presence of Bi vacancies. Considering that DWs are strained crystallographic defects, the intensity of the atomic columns in the STEM can undergo fluctuations due to the presence of the associated strain fields. These fluctuations are usually below 5%:^35,36 therefore, we can link the 5%–10% drop in the intensity at DW1 to the presence of Bi vacancies segregating at this DW. Using the same intensity-evaluation methodology, a much prominent intensity drop (∼20% relative) for the Bi columns in straight 109° UDWs (i.e., without the step features as shown here for DW1) have been previously reported for BFO ceramics.

A similar drop in the Bi atomic column intensity (5%–10%) was found for DW2 [Fig. 1(h)]. Since the orientation of the projected polarization vector is opposed to that of the projected Fe displacement,³³ DW2 is a “tail-to-tail” wall [Fig. 1(e)] and consequently, it should be negatively charged. Since Bi vacancies are also expected to be negatively charged (i.e., V_Bi‴ in the Vink Kroger notation), their presence at the negatively charged “tail-to-tail” DW2 is unexpected. While this situation would need further investigation, the compensation of the “tail-to-tail” DW is probably driven by a complex interplay between the strain relaxation, which is provided by Bi vacancies,³¹ and screening by positively charged defects, e.g., Fe^4+30,31 or O vacancies.²² 

In the case of DW3, we confirm for the uncharged segment an intensity drop of 5%–10% for the Bi atomic columns [Fig. 1(i), upper map] and for the charged segment we found close to the tip of the step that the intensity of the Bi atomic columns drops by ∼20% relative to the average intensity measured inside the domain itself [Fig. 1(i), bottom map], suggesting a concentrated segregation of Bi-vacancy defects at the corner of the rectangular step.

We discuss next how the lattice strain and the local atomic off-center displacements at the {100}_pc-type DWs depend on the charged state of the wall. We remind the reader that we cannot identify the exact type of DW2: it can be either a 71° “tail-to-tail” CDW on {100}_pc, or a 109° “tail-to-tail” CDW on {100}_pc. However, according to Wang et al.,¹⁸ it is the plane in which DW lie rather than their angle labelled type that dictates the structure of charged DWs. Wang et al.¹⁸ showed that charged 71° DWs on {100}_pc and charged 109° DWs on {100}_pc present similar structural characteristics. In contrast, charged 109° DWs on {100}_pc are considerably different than charged 109° DWs that lie on {110}_pc. Thus, we believe that not knowing whether DW2 is a 71° DW or a 109° DW does not restrict a valuable comparison between the uncharged and charged {100}_pc-type DWs.

The comparison between the charged and uncharged ferroelastic DWs in BiFeO₃ is particularly relevant for understanding the differences between the functional behavior of this type of DWs (such as the switching mechanism and the interaction with point defects), since the analysis is performed in the same experiment, with the same specimen and for DWs that have a similar morphology (i.e., step-like morphology).

Figure 2 shows the distortion of the unit cell perpendicular to the wall plane for DW1 [Fig. 2(b)], DW2 [Fig. 2(c)], and DW3 [Figs. 2(d) and 2(e)]. The lattice at the DW is distorted mainly in the direction perpendicular to the DW plane, as shown in a previous study.³¹ In supplementary material 2, the lattice distortion parallel to DW1 and DW2 is also presented. We calculated the lattice strain in the form of the unit-cell distortion [as schematically presented in Fig. 2(a)] using the Bi sublattice from the same area of the HAADF images shown in Fig. 1.

In the case of uncharged {100}_pc-type walls [DW1, Fig. 2(b), and the uncharged segment of DW3, Fig. 2(d)], we found experimentally that the lattice distortion is located in the middle of the wall with a distortion angle of 3.0°–4.5°. On the other hand, in the case of charged {100}_pc-type walls [DW2, Fig. 2(c), and the charged segment of DW3, Fig. 2(e)], the strain in the wall area is much lower (a distortion angle smaller than 3°) and more diffuse. Previous atomic-structure analyses²⁰ showed that DWs in BFO are strained such that the Bi sublattice exhibits shearing, while the Fe sublattice is practically unaffected when crossing the DW. This intrinsic Bi shear strain can be largely affected by the presence of Bi vacancies accumulated at the walls.³¹ Here, we show that the relative intensity decrease of the Bi atomic columns in the wall region is comparable for the charged and uncharged regions (∼10%, as shown in Fig. 1). Thus, the data suggest that there is no significant difference in the Bi-vacancies concentration between the CDWs and UDWs, meaning that the difference in the Bi-lattice shear values for the charged and uncharged {100}_pc-type walls can be explained as a pure, intrinsic lattice mismatch. The lattice mismatch is higher in the case of uncharged {100}_pc-type walls than in the case of charged {100}_pc-type walls, as confirmed by the analysis shown in supplementary material 3, where the theoretical unit-cell distortion for uncharged-, charged-“tail-to-tail”- and charged-“head-to-head” {100}_pc-type walls was evaluated from a simulated HAADF-STEM image. The results in supplementary material 3 show that the intrinsic shear is much higher at the uncharged wall. Therefore, even though the formation of CDWs is energetically unfavorable from an electrostatic point of view, these DWs are elastically more compatible than the UDWs, resulting in a lower elastic cost during their formation.²⁰ 

We further investigated how the structure of the DW depends on its charge state. For the sake of a comparison, we analyzed the average projected Fe-displacement evolution across the DW from one domain to the other in DW1 and DW2 (Fig. 3).

We analyzed, in the first place, the decomposition of the Fe-displacement vectors into in-plane and out-of-plane components [Figs. 3(a) and 3(b)], followed by the total off-centric Fe-displacement magnitude and angle [Figs. 3(c)–3(f)]. The basic geometrical relationships used in the analysis are schematically explained in Fig. 3(g). Based on our experimental observation, the Fe-displacement vector across the DW evolves differently in UDWs and CDWs.

In Figs. 3(a) and 3(b), we present the decomposed Fe displacements parallel and perpendicular to the plane of the DW. The displacement component that is parallel to the wall has a significant change for the uncharged DW [Fig. 3(a), black data] and the displacement component perpendicular to the wall has a significant change for the charged DW [Fig. 3(b), red data]. The variations in the displacement components support the uncharged and charged configurations of DW1 and DW2, respectively.

A further observation is that the transition region in which the Fe-displacement vector changes in magnitude and orientation is wider for the CDW than for the UDW [∼5 unit cells for DW1, Fig. 3(e), vs ∼10 unit cells for DW2, Fig. 3(f)]. Additionally, we made a statistical analysis considering the different locations across the charged/uncharged step-like DWs. We found that the DW width is greater in the case of the charged DWs (∼10 uc) than for the uncharged DWs (∼6 uc), which confirms our conclusions (see supplementary material 4). This is consistent with a previous report showing that CDWs in epitaxial PbZr_0.2Ti_0.8O₃ thin films are wider than the UDWs.¹⁶ We can link a more abrupt Fe-displacement transition for the UDW [Fig. 3(e)] to a more concentrated strain in the middle of the wall [Fig. 2(b)]. Conversely, a smaller and more dispersed strain for the CDW [Fig. 2(c)] can be associated with a more diffuse transition of the displacement from one domain area to another [Fig. 3(f)].

Second, in both cases, the displacement vector reduces its magnitude and it also rotates through the DW, revealing a non-Ising behavior [see angle evolution in Figs. 3(e) and 3(f)]. Non-Ising behavior was previously theoretically predicted for 109° uncharged DWs in BFO¹⁹ and experimentally shown for charged 109° DWs in BFO thin films.²² Significant differences in their structure, suggest that CDWs and UCDs might have a different role in the switching mechanism; however, further studies are required.

The focus of this study was on the morphology and structure of charged and uncharged {100}_pc-type DWs in polycrystalline BFO. We have shown that the morphology of both types of {100}_pc-type DWs can be complex and form step-like kinks. We found DWs that have different roughness, such as charged-“tail-to-tail” and uncharged DWs that have small steps with a width of ∼1–4 units cells, and a DW that has a sharp, rectangular step that forms charged/uncharged segments of at least ∼10 unit cells. Bi vacancies were found to segregate at the analyzed step-like DWs, regardless of their intrinsic charge nature; a higher degree of Bi-vacancies accumulation was found at the large sharp step. In addition, we structurally compared the charged “tail-to-tail” and the uncharged {100}_pc-type DWs. We show that the uncharged {100}_pc-type DWs have a larger associated lattice strain than the charged-“tail-to-tail” {100}_pc-type DWs, and we were able to explain the result as a pure intrinsic lattice mismatch. This result is an indication that the formation of charged DWs is energetically costly from an electrostatic point of view, compared to the formation of uncharged DWs, but at the same time, it is energetically favorable from the point of view of lattice compatibility. We associate a higher and more concentrated strain for the uncharged {100}_pc type to a more abrupt and narrower transition of the Fe-displacement vector through the DW. In addition, both charged and uncharged DWs exhibit a non-Ising behavior, i.e., they exhibit the simultaneous rotation and reduction of the Fe-displacement vector across the DW. Since the {100}_pc-type DWs have been experimentally shown to be intrinsically different in strain distribution and structure, we assume that their role in the switching mechanism will be different, depending on their particular strain and charged state, as indicated by this study. We hope that these results will generate interest in future studies, theoretical or experimental, aimed at understanding the influence of the structural differences of DWs on their mobility in polycrystalline BFO.

See the supplementary material for schematics of possible polarization configurations on either side of DW1, DW2, and DW3 (supplementary material 1); representation of unit-cell distortion of the Bi-sublattice parallel to the DW1 and DW2 planes (supplementary material 2); the simulated projected unit-cell distortion for uncharged, charged-“tail-to-tail” and charged-“head-to-head” {100}_pc-type DW (supplementary material 3); and statistics on different locations of the DW width for charged and uncharged step-like DWs (supplementary material 4).

The work was carried out within the Research Program P2-0105, Project Nos. J2-2497 and PR-08978 (Slovenian Research Agency). Part of this work was carried out under the Cooperative Research Project Program of Research Institute of Electronics, Shizuoka University. Part of this research was also supported by the Collaborative Research Project of Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology. Ms. Maja Makarovič is acknowledged for the BFO sample preparation. Ms. Brigita Kmet is acknowledged for the TEM sample preparation.

The data that support the findings of this study are available within the article and its supplementary material.