Direct observation of rotation of polarization at 90-degree domain walls in BaTiO3

The rotation of polarization at 90-degree domain walls in tetragonal BaTiO3 was directly observed by the STEM-CBED method, which combines scanning transmission electron microscopy and convergent-beam electron diffraction (CBED). The CBED patterns in the domain wall region exhibit continuous changes in intensity distribution within disks and specific features corresponding to the direction of the rotation of polarization. Simulations were performed using hypothetical superstructures created by continuously connecting Ti displacement with a 90-degree rotation and showed good qualitative agreement with the experimental patterns. The quantitative evaluation of the mirror symmetries existing in the tetragonal structure in bulk form revealed the width of the domain wall is approximately 9 nm. While distorted regions with slightly broken symmetry in CBED disks were found to extend further on both sides of the domain wall region in 6–7 nm. This finding can explain the discrepancy in the domain wall widths reported in previous studies.


Introduction
Ferroelectric materials have found widespread use in everyday life due to their versatile applications, including capacitors, which are among the most indispensable devices. The principle of operation of ferroelectric devices is based on the response of the polarized domain to an applied voltage, and also on the response of the domain wall. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] So far, there have been many reports on ferroelectric domains, and many of them only describe the domain distribution and its change with the application of an electric field. [17][18][19][20][21][22][23][24][25][26][27][28] On the other hand, there have been a limited number of reports on ferroelectric domain walls, and the width of the domain wall varies depending on techniques, such as transmission electron microscopy (TEM) image, [29][30][31][32] electron holography, 33) X-ray scattering, 34) DFT calculation, [35][36][37][38][39] and so on. Hence, for the further development of ferroelectric devices and new ferroelectrics, detailed discussions of domain walls including observation and analysis of rotation of polarization at the domain wall are crucial.
The convergent-beam electron diffraction (CBED) method, which utilizes nanometer-sized electron probes, can be combined with the TEM method to obtain experimental data from any local area. 40) The CBED method is particularly useful for analyzing ferroelectrics, due to its capability to examine non-centrosymmetric structures through dynamical diffraction. Compared to the widely used scanning transmission electron microscopy (STEM) method, the CBED method uses diffraction patterns, which provide information in reciprocal space and are not affected by the spherical aberration of magnetic objective lenses. The high achievable resolution allows for exceptional sensitivity to sub-picometer atomic displacements, resulting in superior detection of ionic polarization. 41) The intensity distribution of CBED patterns is also sensitive to changes in the distribution of valence electrons, allowing the CBED method to detect and analyze electronic polarization. 42) STEM-CBED, also known as 4D-STEM, involves scanning an electron probe over a specimen to obtain CBED patterns at each probe position. This enables mapping of changes in the CBED pattern in real space, facilitating the analysis of non-uniform distributions, such as interface and nanodomain distributions. Previous studies have successfully utilized this method to observe the temperature dependence or electric field response of nanodomains in BaTiO 3 and other ferroelectric materials, [43][44][45][46][47][48][49] as well as interface-induced polarization structures. 50) In BaTiO 3 , it was found that the orthorhombic, tetragonal and cubic phases are formed as the average structures of the variants of the rhombohedral nanostructures. 45,48) In this study, we aim to directly observe rotations of polarization in ferroelectric domain walls using the STEM-CBED method.

Experimental methods
The 90-degree domains of ferroelectric BaTiO 3 were chosen for observation of domain walls. Detailed observation of nondoped BaTiO 3 domain walls is challenging because they are easily moved by electron beam irradiation. Therefore, we used BaTiO 3 doped with 0.3% V to Ti sites. The doping of small amounts of transition metal elements suppresses domain wall movement, enabling detailed experiments using nano-electron probes. Single crystals of V-doped BaTiO 3 were grown according to previously described methods. 51) For TEM observation, several tens of microns of crushed single crystals were glued onto copper grids, and a few nanometers of carbon coating were applied to prevent chargeup during observation and suppress domain wall motion. CBED patterns were acquired using an energy-filter transmission electron microscope (JEM-2010FEF) operated at an accelerating voltage of 100 kV and RT. The size of the experimental electron probe was approximately 1 nm and the energy filtering was set to an acceptance energy width of approximately 0 ± 15 eV to remove the inelastically scattered background intensities. The intensity distributions of the CBED patterns were recorded using a 4k × 4k pixel CMOS camera (Gatan RIO16). A Bloch-wave dynamical diffraction simulation code MBFIT was used to calculate intensity distributions of CBED patterns. 41,[52][53][54][55][56] 3. Results and discussion Figure 1(a) presents a TEM image containing 90-degree domain walls, where almost no contrast was observed at [100] incidence. The contrast of the domain walls become visible upon tilting the TEM specimen, as indicated by the red arrowheads. Figure 1(b) shows a selected area electron diffraction pattern taken from the region containing the polarized domains, where splitting of diffraction spots due to the 90-degree rotated structure is observed (indicated by red circles). The CBED pattern taken from a single domain is shown in Fig. 1(c). The symmetry of the CBED pattern displays a single vertical mirror parallel to the c*-axis, while the horizontal mirror symmetry is broken, indicating a polar structure. The presence of polar structures can be detected from the mirror symmetry appearing in CBED patterns. This is a powerful and unique advantage of the CBED method for examining ferroelectric materials. Figure 2(a), which is the same region as Fig. 1(a), shows the positions of the 90-degree domain walls indicated by dashed lines and the direction of polarization for each domain. The direction of polarization for each domain was determined by comparing experimental and simulated CBED patterns. STEM-CBED data were obtained from areas (b) and (f) depicted with yellow and green squares, respectively in Fig. 2(a). For the STEM-CBED experiment, the electron probe was scanned to collect data points in a grid of 60 × 60, with a step size of 0.5 nm. A CBED pattern at each probe position was taken with 512 × 512 pixels and an exposure time of 0.1 s.
The CBED patterns shown in Figs. 2(c)-2(e) and 2(g)-2(i) were obtained from the positions of (c)-(e) and (g)-(i) shown in Figs. 2(b) and 2(f), respectively. The CBED patterns in Figs. 2(c) and 2(e) correspond to data from neighboring polarization domains, showing 90-degree rotation of mirror symmetry and the polarization direction. It is noteworthy here that this mirror symmetry arises from the averaging of the local rhombohedral structure in the direction of thickness (the direction in which the electron beam propagates). The direction of polarization averaged in the thickness direction is parallel to [001] because the sizes of the rhombohedral nanodomains are less than several nanometers. The CBED pattern of Fig. 2(d) corresponds to data taken at the domain wall, showing an incomplete diagonal mirror symmetry. The intensity distributions of the reflections indicated by white and yellow circles are seen to be not perfectly symmetrical, indicating pseudo-mirror symmetry. A similar tendency is also seen in Fig. 2(f).
The CBED patterns of Figs. 2(c) and 2(g) were taken from the same domain, and both patterns, showing the same polarization direction. The CBED patterns of Figs. 2(e) and 2(i) also exhibit the same polarization direction. It should be noted that the CBED pattern of Fig. 2(h) taken at the domain wall shows a left-right reversal intensity distributions compared to the pattern of Fig. 2(d) with respect to the pseudo diagonal mirror operation indicated by white dotted lines. This intensity reversal is attributed to the inverted rotational direction of the polarization. It is seen that the intensity distribution of the CBED patterns contains information on the continuous change of polarization direction. Moreover, a symmetry change, and a continuous change of the intensity distribution were observed in the CBED patterns using the STEM-CBED method across the domain wall region.
We attempted to reproduce the experimental results through simulation using a Bloch-wave dynamical diffraction simulation code MBFIT, 41,[52][53][54][55][56] which recently implemented a function to calculate CBED patterns from a supercell with a coherent nano probe. Figure 3(a) illustrates the hypothetical superstructure used for the simulations, which consists of a bulk structure at both ends and is continuously connected to form a Neel-type 90-degree polarization domain. 36) In this simple model, the displacements of Ti and O atoms are opposite to each other, as indicated by the blue and red arrows, respectively. Consequently, the direction of Ti displacement aligns with the direction of polarization (Ps), represented by the yellow arrows, demonstrating a gradual change in the polarization direction. Here, the direction of polarization of the bulk form is set to [001], which is the averaged polarization direction of the rhombohedral nanodomains in the thickness direction. This is because the thickness of the area at which the CBED patterns were obtained was more than 100 nm and the sizes of the rhombohedral nanodomains are less than several nanometers. The probe size, determined by the convergence angle, is approximately (a) (a) Next, we attempted to quantitatively evaluate the symmetry change in the CBED patterns occurring at the polarization domain wall. A 40 nm wide region across the domain wall was evaluated. Figure 4(a) shows a TEM image showing the STEM-CBED data acquisition region indicated by a red rectangle and the directions of polarization. Figure 4(b) shows the STEM image. The CBED patterns shown in Figs. 4(c) and 4(d) were taken from the probe positions of (c) and (d) in Fig. 4(b), respectively. The symmetry breaking index was used for quantitative analysis of symmetry change in CBED patterns. The symmetry breaking index is evaluated from the intensity difference between the symmetry-operated CBED pattern and the original one. 57) In Figs. 4(e) and 4(f), horizontal and vertical mirror symmetries were evaluated, respectively. The symmetry breaking index is expressed as a percentage, where 0% indicates perfect symmetry. The color display is shown in the range of 20%-60%. Figures 4(g) and 4(h) are the average line profiles of symmetry breaking index for the horizontal and vertical mirror symmetries, respectively, across the domain wall. It can be seen that the mirror symmetry of the bulk structure is broken when the probe position is closer to the domain wall from the positions of (c) or (d) in Fig. 4(b). The threshold value of 30% was used to define the width of the rotation of polarization direction, or domain wall, which was evaluated to be 8.8 nm. The red framed region in the Figs. 3(e)-3(h) corresponds to the domain wall, where a significant change of the direction of mirror symmetry is clearly seen. On the other hand, the yellow framed region is located outside the domain wall with a width of 6-7 nm, where the mirror symmetry of the bulk is slightly broken. This region can be attributed to the influence of the domain boundary.
These experimental results are consistent with a theoretical calculation reported by Zhang and Goddard. 58) In the theoretical calculation, the lattice parameter variation was calculated over a length of 74 nm using 5120 atoms, and the domain wall thickness is 21 nm in which the polarization switches over a 5 nm central layer surrounded by two transition layers each 8 nm wide. They pointed out that a sufficiently large supercell is necessary for the stability of the domain wall, resulting in the presence of a distorted region in its vicinity.

Conclusions
The local structure analysis of the 90-degree polarization domain in BaTiO 3 was performed using the STEM-CBED method, which involves scanning nanoelectron probes across the specimen and recording CBED patterns at each position. The experimental patterns and the simulated patterns with gradual changes of Ti displacement showed good qualitative agreement. The rotation of polarization was successfully observed directly from the intensity distributions of CBED patterns. The STEM-CBED method enabled the detection of the effect even in non-localized cases where the rotation of polarization causes a gradual change in the electrostatic potential field, such as the rotation of polarization.
The rotation of polarization has a width of approximately 9 nm, and the intermediate region of 6-7 nm away from the polarization domain wall shows a distinct state compared to the bulk form. The discrepancy in domain widths observed in different measurement methods could potentially arise from variations in the outer region of the polarization domain wall, where a different state from the bulk form was detected. As a future prospect, it is intriguing to compare different compositions, crystal structures, and geometries.
The zeroth-order Laue zone reflections shown in this paper exhibit greater sensitivity to changes in the valence electron density distribution compared to changes in atomic positions. The observed larger breaking of mirror symmetry in experimental CBED patterns than in simulated ones suggests that the valence electron density distribution differs from the isolated atom model used in the present simulation. To further analyze the electronic polarization, we plan to refine the crystal structure factors of the superstructure. However, the use of superstructure can result in a significant increase in the number of atomic positions and crystal structure factors to be determined. Therefore, we plan to the use of Bayesian optimization in conjunction with complementary first-principles calculations. It is noted that in the present structure model of the domain wall, the polarization direction at the bulk region was set to the thickness-averaged [001]. For quantitative analysis of the CBED patterns, the distributions of the rhombohedral nanodomains should be taken into account. 57) The STEM-CBED analysis described here is not limited to ferroelectric domain walls but can be other kinds of interfaces, such as antiphase boundaries, twin boundaries, pn-junctions, two-dimensional electron gas, and other areas of study.