Twin-boundary-mediated flexoelectricity in ${\mathrm{LaAlO}}_3$

Flexoelectricity has garnered much attention owing to its ability to bring electromechanical functionality to nonpiezoelectric materials and its nanoscale significance. In order to move towards a more complete understanding of this phenomenon and improve the efficacy of flexoelectric-based devices, it is necessary to quantify microstructural contributions to flexoelectricity. Here we directly measure the flexoelectric response of bulk centrosymmetric ${\mathrm{LaAlO}}_3$ crystals with different twin-boundary microstructures. We show that twin-boundary flexoelectric contributions are comparable to intrinsic contributions at room temperature and enhance the flexoelectric response by $\sim 4\times$ at elevated temperatures. Additionally, we observe time-dependent and nonlinear flexoelectric responses associated with strain-gradient-induced twin-boundary polarization. These results are explained by considering the interplay between twin-boundary orientation, beam-bending strain fields, and pinning site interactions, and directly demonstrate that macroscopic flexoelectric responses are very sensitive to structural defects.

Figure 1

(a) Overview of experimental flexoelectric characterization. The short-circuit current induced by low-frequency three-point bending is measured for a sample cut into a beam geometry. (b) Flexoelectric characterization of a ${\mathrm{LaAlO}}_3$ crystal with no twin boundaries. The strain-gradient-induced polarization in this sample is linear, with an effective flexoelectric coefficient of $3.2\pm 0.3\mathrm{nC}/\mathrm{m}$ (flexocoupling voltage of $14.5\pm 1.4\mathrm{V}$). The linear fit is shown as a dashed line. The uncertainty corresponds to the 95% confidence interval of the fit.

Figure 2

Flexoelectric characterization of ${\mathrm{LaAlO}}_3$ crystals with uniform, lamellar twin-boundary microstructures. (a) Type I boundaries have normals ($\widehat{n}$) perpendicular to the long axis of the sample ($\widehat{x}$) as shown by reflection polarized optical microscopy. The flexoelectric response of the Type I sample was linear and increased to an effective steady-state flexoelectric coefficient of $4.8\pm 0.3\mathrm{nC}/\mathrm{m}$ (flexocoupling voltage of $21.7\pm 1.4\mathrm{V}$) after strain gradient cycling. (b) Type II boundaries have normals parallel to the long axis of the sample as shown by reflection polarized optical microscopy. The flexoelectric response of the Type II sample was linear and increased to an effective steady-state flexoelectric coefficient of $3.5\pm 0.2\mathrm{nC}/\mathrm{m}$ (flexocoupling voltage of $15.8\pm 0.9\mathrm{V}$) after strain gradient cycling. In both plots, lines are linear fits with circles/dashed lines indicating initial measurements and squares/solid lines indicating steady-state measurements after strain gradient cycling. Uncertainties correspond to the 95% confidence interval of the fit. Images are false-colored for clarity.

Figure 3

Flexoelectric measurements in ${\mathrm{LaAlO}}_3$ crystals with a mixture of twin-boundary orientations. (a) The temperature dependence of the flexoelectric coefficient correlates with the known temperature dependence of twin-boundary motion. Dashed lines are visual guides. (b) Flexoelectric polarization at room temperature and fixed dynamic force decreases with increasing static force because of the nonlinear elastic response of twin boundaries. Solid line is a fit using a catenary cable model.

Figure 4

Flexoelectric characterization of a ${\mathrm{LaAlO}}_3$ crystal with a mixture of Type I and II twin-boundary orientations. (a) The initial flexoelectric response is linear at low strain gradients with an effective flexoelectric coefficient of $3.6\pm 0.1\mathrm{nC}/\mathrm{m}$ (flexocoupling voltage of $16.3\pm 0.5\mathrm{V}$), and nonlinear above a strain gradient of $\sim 0.25{\mathrm{m}}^{–1}$. (b) The steady-state flexoelectric response after strain gradient cycling remains linear at low strain gradients with an increased effective flexoelectric coefficient of $4.0\pm 0.2\mathrm{nC}/\mathrm{m}$ (flexocoupling voltage of $18.1\pm 0.9\mathrm{V}$). There is pronounced nonlinear behavior above $\sim 0.25{\mathrm{m}}^{–1}$.