Symmetry and three-dimensional anisotropy of polar domain boundaries observed in ferroelastic $\mathrm{LaAl}{\mathrm{O}}_3$ in the complete absence of ferroelectric instability

The domain boundaries of ferroelastic $\mathrm{LaAl}{\mathrm{O}}_3$ (LAO) are examined using a nonlinear optical second harmonic generation (SHG) microscope. Although bulk crystalline LAO possesses centro-symmetry and is inherently non-SH active, our three-dimensional observations reveal that the domain boundaries of LAO exhibit SH activity with almost the same magnitude within a boundary. The polarization dependence of the SH intensities shows strong anisotropy, which is explained by the polar trigonal point group, $3m$. The polar direction is found to be along the ${\left[111\right]}_{pc}$ axis and inclined from the domain boundary plane. It implies that the biquadratic coupling scheme of two order parameters could be the main origin of the emergence of polar nature at the domain boundary. Our experimental results together with those of $\mathrm{CaTi}{\mathrm{O}}_3$ suggest that the polar nature of the domain boundary in ferroelastic materials may be a ubiquitous phenomenon.

Figure 1

(a) Polarization microscope image of $\mathrm{LaAl}{\mathrm{O}}_3$ under a crossed Nicol configuration. (b) 2D image of SH wave distribution. The area by the SHGM is enclosed by the square in (a). On the right, cross-section 1D plot for a dashed line is shown.

Figure 2

Constructed 3D SHG image. White planes correspond to the domain boundaries that are SH active.

Figure 3

(a) Polar diagrams mapping of $\mathrm{LaAl}{\mathrm{O}}_3$. Fitting results using (b) $3m$ and (c) 32 point groups. Blue dots correspond to the experimental data and the red line to the fitting result.

Figure 4

(a) Nonlinear optical surface plot of $\mathrm{LaAl}{\mathrm{O}}_3$ representing the three-fold symmetry along the ${\left[111\right]}_{pc}$ direction. (b) The 3D SH intensity distribution plot constructed from the experimental results. The color code represents the magnitude of the $d$ tensor component and SH intensity.