Giant Flexoelectric Effect in Ferroelectric Epitaxial Thin Films

We report on nanoscale strain gradients in ferroelectric ${\mathrm{HoMnO}}_3$ epitaxial thin films, resulting in a giant flexoelectric effect. Using grazing-incidence in-plane x-ray diffraction, we measured strain gradients in the films, which were 6 or 7 orders of magnitude larger than typical values reported for bulk oxides. The combination of transmission electron microscopy, electrical measurements, and electrostatic calculations showed that flexoelectricity provides a means of tuning the physical properties of ferroelectric epitaxial thin films, such as domain configurations and hysteresis curves.

Figure 1

(a) XRD $\theta \mathrm{\text{−}}2\theta$ scans of ${\mathrm{HoMnO}}_3$ films. The gray solid vertical line indicates the position of the (0004) diffraction peak of bulk ${\mathrm{HoMnO}}_3$. Schematic diagrams show tensile-strain relaxation (b) for typical growth conditions and (c) for a film with more oxygen vacancies, which induced crystal-volume expansion. Because of various relaxation mechanisms, we represent the strain-relaxation process by dashed guidelines.

Figure 2

(a) Variation in the averaged in-plane strain $\overline{u}$ as a function of penetration depth $L$ in HMO10 and HMO350. The solid curves are fitted results. (b) Estimated strain gradient in HMO10 and HMO350 as a function of the distance from the film surface $z$.

Figure 3

(a) Schematic diagram showing how $E_S$ can affect domain configuration, which depends on $P_{\mathrm{O}2}$ during the growth process. (b) At high growth temperatures, defect dipoles can align along the polarization of each domain. (c) Expected variations in the $P\mathrm{\text{−}}E$ hysteresis loops according to the alignment of the defect dipoles, which can depend on $P_{\mathrm{O}2}$.

Figure 4

Ferroelectric domain images, measured by using dark-field TEM imaging, of the as-grown film deposited at a $P_{\mathrm{O}2}$ of (a) 20 and (c) 300 mTorr. The bright and dark regions are attributed to the up- and down-polarization domains, respectively. (b) and (d) show intensity profiles of the TEM images, from which the averaged width $\overline{\alpha }$ ($\overline{\beta }$) of the up-polarization (down-polarization) domains were estimated.

Figure 5

Systematic variation in (a) the $P\mathrm{\text{−}}E$ and (b) $I_{\mathrm{SW}}$ hysteresis loops from double loops to biased single loops for different $P_{\mathrm{O}2}$ during the growth process. $I_{\mathrm{SW}}$ was measured during the polarization-switching process from down to up domains, and the $I_{\mathrm{SW}}$ data were well fitted by the sum (gray solid line) of two Lorentzian curves (black solid lines).