A compressive uniaxial mechanical stress is applied on ferroelastic CaTiO3 (CTO), and a change in the domain structure is observed under a polarization microscope and a second harmonic generation (SHG) microscope. New twin walls (TWs) appear perpendicular to the original TWs under stress. The SHG microscope observations and analyses confirm that this type of stress-induced TWs is polar, similar to the original TWs, and is crystallographically prominent with monoclinic symmetry m. A quantitative estimation of this stress-induced effect reveals that CTO is hard ferroelastic in the sense that the TW movement requires a large stress. A possible application of this phenomenon is discussed.
The continual demands for the miniaturization of electronic devices have directed us towards finding new approaches over the last several decades. “Domain boundary engineering”1–3 is one of the most promising candidates, and research in this field has accelerated since the late 2000s. Historically, domain boundaries have been considered an obstacle for research and applications, and much effort has been devoted to obtaining a single domain state. However, theoretical and experimental evidences of the functionality of the domain boundaries of ferroic materials, such as superconductivity,4 high defect mobility,5–8 the photovoltaic effect,9–11 unusual vortices,12 and ferroelectricity,13,14 have completely revised our traditional impressions of domain boundaries. Twin walls (TWs) in ferroelastic materials have attracted special attention for several reasons. First, TWs are mobile15,16 and controllable under stress, which can avoid the serious difficulties connected with the electric conductivity on manipulating ferroelectric domains. The mobile TWs could have large responses in physical properties. Second, the typical wall thickness is much thinner than a magnetic domain wall, because polar TWs of the Ising type are the most preferable due to the nonpolar nature of adjacent domains. The stress-induced domain boundary effects are thus promising for application to high-density memory devices.
The functionality of the TWs of some ferroelastics such as CaTiO3 (CTO) and SrTiO3 was theoretically predicted.17–19 In particular, numerical simulations of CTO showed that the displacement of Ti atoms causes local polarizations at and close to the TWs.17,18 Aberration-correcting transmission electron microscope (TEM) observations combined with the statistical parameter estimation theory20–23 revealed that Ti atoms shift approximately 6 pm along the TWs and that the TWs exhibit ferroelectricity.13 Recently, we conducted second harmonic generation microscope (SHGM) observations on CTO and confirmed that the TWs are SH-active and consequently polar.14 These results indicate a possibility to realize memory devices with a density higher than the racetrack memory that uses a magnetic domain wall in information storage.24 For this purpose, it is fundamentally necessary to manipulate TWs under stress. However, no research has grappled with this issue yet, mainly because of the difficulty of obtaining single crystals of good quality and the complex nature of CTO twins. In the present work, we apply a uniaxial mechanical stress to change the twin structures and investigate the changes in TWs and their polar nature using the SHGM. The SHGM is a powerful technique for observing some ferroic materials due to its high sensitivity to breaks in the spatial and/or time inversions.25–32 In this research, we prove for the first time that the external stress can create new TWs and that these are also polar, as in the natural TW states. We think that this is not self-evident because the polarity of the TWs is induced by the shift of Ti atoms,13 which could depend on the TW direction. It is also important for applications to quantitatively determine the threshold stress that can move the TWs. Based on these experimental results, we discuss the possibility of application to memory devices.
CTO single crystals were grown by an optical floating-zone method. The details of the sample preparation are described in Ref.14 and 33. X-ray diffraction confirms that the samples contain neither impurities nor secondary phases. The specimens are cut into rectangular shapes (1.2 x 2 mm2) with a thickness of 350 μm along the pseudo-cubic (001) pc and both surfaces were optically polished. SHGM observations were carried out at room temperature. We used an Nd:YVO4 laser (NL640, EKSPLA) with a wavelength of 1064 nm, a repetition frequency of 40 kHz, and a pulse width of 10 ns as a light source. A fundamental wave passes through a half-wave plate that controls the polarization direction and is focused on the sample by an objective of 100 magnifications. SH waves generated from the specimen are collected by a rear objective of the same magnification, and its polarization direction is selected by an analyzer. Light with a wavelength of 532 nm is chosen by a spectrometer, and the SH intensities are detected by a photomultiplier tube. Two-dimensional (2D) and three-dimensional (3D) images of the SH wave distributions are obtained by scanning the specimen using piezo actuators along the lateral (XY) directions and a stepping motor along the depth (Z) direction. The spatial resolutions of our microscope system are determined to be 0.5 μm for the lateral and 1.5 μm for the depth directions using the numerical aperture (NA = 0.7) of the objective. SHGM can determine the point symmetry of the sample, since the anisotropy of the SHG intensity directly reflects the symmetric nature of the third-rank tensor components d.
Figure 1 (a) presents a polarization microscope image of an as-grown CTO specimen under the crossed nicols condition. There is only one type of TWs aligned along the  pc direction. Figure 1 (b) shows a 2D SHGM image of the area shown in (a), obtained with a 0.50 μm scanning step. The polarization directions of the polarizer and an analyzer were fixed along the Y axis in the figure. It is noted that the SH intensities from the sample are extremely weak, being an order of magnitude less than 10-8 compared to that of a LiNbO3 single crystal. Two SH-active lines parallel to the X axis are observed as bright areas. By comparison with Fig. 1 (a), these SH-active lines are identified as TWs. On the other hand, no SH intensity signal is detected from the domain itself, and it is always dark, as shown in Fig. 1(b). Figure 1 (c) exhibits a 3D SHGM image of the CTO sample. Even inside the specimen, the TWs are polar, keeping the same magnitudes of the SH intensity. The positions of the SH-active lines do not change along the sample depth direction, which indicates that these TWs are almost perpendicular to the sample surface. The anisotropy of the SH intensity was measured at an angular step of 6 of the pair of the polarizer and analyzer. The polarization directions of the fundamental and SH waves were kept parallel. The whole 2D SHGM image was divided into small regions, and the polarization dependence of the SH intensity was plotted for each area to obtain the 2D mapping of the SH intensities in the polar diagram. Figure 1 (d) presents a polar diagram map of the area enclosed by the red lines in Fig. 1(b). The TWs exhibit SH anisotropy with a two-wing pattern. Fig. 1 (e) and (f) show typical examples picked up from Fig. 1 (d). Detailed analyses of the polar diagram are provided later.
In the case of ferroelastic materials, an appropriate application of stress changes the domain structures. To observe the change in the domain structure under stress, we developed an apparatus for applying a uniaxial stress under a microscope. Using this apparatus, a stress-induced strain is produced in the sample by driving in a screw. Figure 2 presents the polarization microscope images of the CTO sample under different stresses applied parallel to the pc direction. We simply estimate the magnitude of the stress from the strain by multiplying it by the elastic stiffness c. In this calculation, we use the elastic stiffness of BaTiO3 at room temperature (c66 = 1.34*1011 [N/m2])34 because we did not find any report on the c value of CTO and the values of c in the perovskite oxide family are almost identical. Before applying a stress, a stripe domain pattern parallel to the pc direction was observed, as shown in Fig. 2 (a). When the stress exceeds 5.4*108 N/m2, new TWs perpendicular to the original ones suddenly appear from the sample edge (Fig. 2(b)). Upon increasing the stress, these new TWs start to propagate towards the middle of the specimen, as shown in Fig. 2 (c). In spite of that, the original TWs do not show an obvious change under the stress. Figure 2 (d) shows an enlarged image of the new TWs observed in Fig. 2 (c). Even after removing the stress, these newly appeared TWs remain unchanged, which indicates that the applied stress and the induced strain are conjugate. We selected an enclosed square region in Fig. 2 (d) and performed the SHGM observation, as shown in Fig. 2 (e). The polarization directions of the fundamental and SH waves were fixed parallel to the X axis. Eight narrow SH-active lines were observed as bridging the wide SH-active lines. Compared with the polarization microscope image, these newly appeared SH-active lines are the stress-induced TWs. Figure 2 (f) shows the changes in the SH intensities along the dashed line in Fig. 2 (e). No SH-active area was observed except the new TWs, which indicates that the domains themselves remain nonpolar under and after applying stress. 2D SHGM images of the new TWs were taken at different depths, and the results are shown in Fig. 3 (a) and (b). Figure 3 (c) shows the 3D SHGM image constructed from the 2D scans, with two SH-active lines observed through the specimen. This result suggests that the newly appeared TWs are SH-active and polar. The positions of the SH-active lines do not change along the axial direction, which means that these TWs are perpendicular to the sample surface. The polarization dependence of the SH intensity was measured in the same region, and the SHG polar diagrams on the two lines in Fig. 3 (a) are shown in Fig. 3 (d) and (e). The anisotropy of the SH intensity exhibits a similar tendency to that of the original TWs. The maximum SH intensity can be observed along a line perpendicular to the TW. With a further application of stress (above 2.0*109 N/m2), another type of TW parallel to the original ones starts to appear, as shown in Fig. 4. This is probably due to other elastic stiffness components caused by a small mis-orientation of the sample edges. Figures 4 (a) and (b) show polarization microscope and SHGM observation images, respectively. The SHG image was taken with 0.2 μm steps along the X and Y axes. This TW was generated at the edge of the specimen and extends its length with the increasing stress. SHG microscope observation reveals that these TWs are also polar. The newly appeared TW has a needle shape with an apex of a sharp opening angle of 2 ∼ 3 towards the growing direction.
It is worth discussing here the different types of ferroelectric domain boundaries: Ising, Bloch and Néel types. In particular, recent theoretical works claim the possibility of Bloch- or Néel-type domain boundaries in addition to the traditional Ising type in the prototype ferroelectrics PbTiO3, LiNbO3, BaTiO3 and PbZr1-xTixO3.35–42 Since the spatial resolution of our SHGM is much greater than the unit cell scale, it is difficult to quantitatively determine the boundary type only from the present experimental data. Nevertheless, from the viewpoint of the electrostatic energy, the Ising-type TWs are most preferable in ferroelastics because the adjacent domains are nonpolar.
In ferroelastics, there are two different types of TW called W and W’ walls.43 The W wall is crystallographically prominent, whereas the W’ wall is crystallographically non-prominent. According to Sapriel,44 21 different TWs can be formed as the result of m3mFmmm structural phase transitions, and the plane equations of these TWs are calculated based on the symmetry change at the ferroelastic phase transition. Among them, 9 TWs belong to the W walls and the rest to the W’ walls. To verify which types the observed TWs belong to, the angles between the TWs and the crystallographic axes are calculated. Before applying stresses, they align parallel to the  pc direction. 3D SHGM observation confirms that the TW is almost perpendicular to the (001) surface. Compared with the calculation, the equation of the original TWs is expressed as x = y belonging to the W walls. The stress-induced TW is investigated in the similar way, and it is determined as x = -y, which is also the W wall. Our SHG microscope observation reveals that the W wall is more preferable than the W’ wall under a uniaxial stress, since there is no sign of the appearance of W’ walls.
From the structural point of view, all W walls are mirror planes. Additionally, our previous SHG microscope observations determined that the symmetry of the W wall is determined as monoclinic m.14 Therefore, we assumed the symmetry of the observed TWs to be m to explain the polarization dependence of the SH intensity. In the case of m whose mirror plane is laid on the xz plane, the symmetry-permitted SHG dijk tensor components are expressed as
Here, the Voigt notation is adopted. Since the plane equations of the observed TWs are x = y and x = -y, the rotation matrix operation is necessary to obtain the proper SHG d’ijk tensors. The transformed SHG tensor components are tabulated in the following matrix.
Using these tensor components, the obtained SH intensity can be expressed as
where P1(2ω) and P2(2ω) are defined as
Here, θ is the polarization angle of the fundamental and SH waves from the X axis. The fitting results are shown in Fig. 1 (e), (f) and Fig. 3 (d), (e) by the red lines. The calculation results coincide well with the experimental data. Therefore, we can conclude that both the original and stress-induced TWs possess monoclinic m symmetry.
In summary, a uniaxial stress was applied to a CTO single crystal, and a change in the domain structure was observed. With the application of the stress, new TWs appear perpendicular to the original TWs. These newly appeared TWs are also SH-active with monoclinic symmetry m.
Although our experimental evidence suggests the possibility of controlling the functional TWs, it is relatively difficult to apply directly this technique to memory devices since CTO has rather hard TWs compared with other ferroelastics (the coercive stress of Pb3(PO4)2 is 1.5*105N/m2). However, it would be possible to change the ferroelectric domains inside the TWs and use them for information storage. In this case, the robust nature of the TWs in CTO would be advantageous to this application field. Additionally, the Ising type of TWs is much more favorable compared with the Bloch- or Néel-type domain walls. We are planning to perform this type of research using observations of the interference SHGM technique.29
It would be also noticed that the layered structure of non-polar domains and polar TWs could be a possible candidate of the negative capacitance material, which is very important for MOS-FET applications with a small driving voltage.45 On this line of research, we are also going to investigate temperature dependences of the polar nature of TWs and their over-all and local dielectric responses.
This work is partly supported by a Grant-in-Aid for Young Scientists (B) from the Ministry of Education, Culture, Sports, Science and Technology in Japan (Grants No. 15K1764). H. Y. is grateful for financial supports from the Shimazu Sci. Foundation and the Murata Science Foundation in Japan.