Strain-Gradient-Induced Polarization in ${\mathrm{SrTiO}}_3$ Single Crystals

Piezoelectricity is inherent only in noncentrosymmetric materials, but a piezoelectric response can also be obtained in centrosymmetric crystals if subjected to inhomogeneous deformation. This phenomenon, known as flexoelectricity, can significantly affect the functional properties of insulators, particularly thin films of high permittivity materials. We have measured strain-gradient-induced polarization in single crystals of paraelectric ${\mathrm{SrTiO}}_3$ as a function of temperature and orientation down to and below the 105 K phase transition. Estimates were obtained for all the components of the flexoelectric tensor, and calculations based on these indicate that local polarization around defects in ${\mathrm{SrTiO}}_3$ may exceed the largest ferroelectric polarizations. A sign reversal of the flexoelectric response detected below the phase transition suggests that the ferroelastic domain walls of ${\mathrm{SrTiO}}_3$ may be polar.

Figure 1

Experimental setup for flexoelectric measurements.

Figure 2

Temperature dependence of the ratio $I/z_0$ (which is proportional to $\mu$) and of the capacitance for a sample polished down to $100\mu \mathrm{m}$ using diamond impregnated lapping film. The flexoelectric response increases with the dielectric constant, showing an anomaly at the ferroelastic phase transition. The absolute temperature values shown may be a few degrees too low due to some thermal lag between the thermocouple and the sample. The inset shows the linear dependence of flexoelectric polarization on strain gradient for $300\mu \mathrm{m}$ thick STO crystals of different orientations at room temperature.

Figure 3

Temperature and static force dependence of the flexoelectric current for the $100\mu \mathrm{m}$ sample in Fig. 2. As the static force is increased, the domain walls become less mobile due to impingement and a recovery of the positive flexoelectric current is observed. Similar behavior was observed for the original thicker crystals. Domains with the $c$ axes along ${\mathbf{x}}_1$ and ${\mathbf{x}}_3$ are labeled $+$ and $-$, respectively.