Direct evidence of polar nature of ferroelastic twin boundaries in ${\mathrm{CaTiO}}_3$ obtained by second harmonic generation microscope

The polar nature of twin boundaries (TBs) of inherently nonpolar ferroelastic ${\mathrm{CaTiO}}_3$ is examined by the confocal second harmonic generation (SHG) microscope. Three-dimensional SHG images of samples with the pseudocubic (110) and (1-11) planes confirm that both crystallographically prominent TB ($W$ plane) and nonprominent TB ($W^{\prime }$ plane) are SHG active and consequently polar. The directions of the electric polarization $P_S$ are determined from the anisotropy of SHG intensities. In the $W^{\prime }$ plane, the SHG polar diagrams are well fitted using the point-group symmetry 2, which reveals that the $P_S$ directions parallel to the twofold axis do not lie in the $W^{\prime }$ plane but are tilted from it. In the $W$ plane, the $P_S$ direction lies in the mirror plane of the point-group symmetry $m$.

Figure 1

The relation between the orthorhombic axes $a_o$, $b_o$, $c_o$, and the pseudocubic axes a//x, b//y, c//z. The suffix $O$ indicates the orthorhombic coordinate.

Figure 2

Optical set-up of the confocal SHG microscope used in the present experiment.

Figure 3

(a) Polarization microscope image of CTO-1 taken in the crossed Nicol configuration. (b–d) SHG section images at different depths ($Z$) from the surface. The observed area is the enclosed square in (a). A zoom-in picture of the enclosed region is also shown in an inserted figure. Here $X$ and $Y$ axes with capital letters indicate the scanning axes of the SHG microscope, which varied for observation experiments. The coordinate should be discriminated from x, y, z with small letters.

Figure 4

SHG images of another area of CTO-1. (a–c) show the X-Y section images at different $Z$. (d–f) show the Y-Z section images of the same area. (g) 3D schematic images of TBs of type A ($W^{\prime }$) and type B ($W$) in CTO-1.

Figure 5

(a) SHG image of an area that contains three SHG active TBs of type A. The corresponding polar diagrams mapping is shown in (b). (c–e) Fitting results for TB1, TB2, and TB3, respectively.

Figure 6

(a) and (b) SHG image and the corresponding polar diagrams mapping of type B, respectively. The fitting result is indicated in (c).

Figure 7

The polarization microscope image of CTO-2 taken in the crossed Nicol configuration. White cross ($X^{\prime }$ and $Y^{\prime }$ axes) indicates the extinction angle of the area where type D is observed. The black lines are added for making clear the locations of TBs. Three bright regions correspond to type C. Arrows in Fig. 5 show the projection of the electric polarization onto the section plane.

Figure 8

(a) and (b) SHG X-Y section images of type C in CTO-2 with different depths ($Z$) along the [1-11] axis, and (c) shows to the X-Z section image of the same area.

Figure 9

(a) and (b) SHG X-Y section SHG image of type D in CTO-2 with different $Z$. (c) Schematic 3D image of type D.