Atomic-Scale Measurement of Flexoelectric Polarization at ${\mathrm{SrTiO}}_3$ Dislocations

Owing to the broken translational symmetry at dislocations, a strain gradient naturally exists around the dislocation cores and can significantly influence the electrical and mechanical properties. We use aberration corrected scanning transmission electron microscopy to directly measure the flexoelectric polarization ($\sim 28\mu \mathrm{C}{\mathrm{cm}}^{-2}$) at dislocation cores in ${\mathrm{SrTiO}}_3$. The polarization charges can interact with the nonstoichiometric dislocation cores and thus impact the electrical activities. Our findings can help us to understand the properties of dislocations in perovskite, providing new insights into the design of new devices via defect engineering such as bicrystal fabrication and thin film growth.

Figure 1

Strain distribution at a 10° ${\mathrm{SrTiO}}_3$ grain boundary. (a) HAADF image. GPA showing strain distributions (b) $e_{xx}$ nearly parallel to the grain boundary plane and (c) $e_{zz}$ nearly perpendicular to the grain boundary plane. Calculated strength of strain gradients from (d) $e_{xx}$ and (e) $e_{zz}$.

Figure 2

PFM measurement. (a) Topography. (b) Schematic illustration showing the electric dipole component perpendicular to the grain boundary plane. In-plane PFM measurements from (c) a left-to-right scan (trace) and (d) a right-to-left scan (retrace), respectively. The measured signal is amplitude $\times \cos$ (phase).

Figure 3

Polarization at the dislocations in ${\mathrm{SrTiO}}_3$. (a) Near the dislocation cores, oxygen octahedron distortion is visible with the naked eye. The contrast of the ABF image is inverted and colored for clarity. (b) The vector map of displacement between the Sr and TiO columns. Orange vectors, $<7.5\mathrm{pm}$; yellow, 7.5–20 pm; green, $>20\mathrm{pm}$. The unit cell scale mapping of (c) strain and (d) the corresponding strain gradient perpendicular to the grain boundary plane. The dislocation cores are highlighted by the white trapezoids.

Figure 4

Electronic structures and elemental distribution in ${\mathrm{SrTiO}}_3$ dislocations. (a) The Ti-$L$ edges across the grain boundary. The blue spectra are from the grain boundary plane. (Inset) The recorded spectra region. (b) The plot of the average Ti valence across the grain boundary plane. (c) Atomically resolved EDS measurement.