Strain gradients cause spontaneous polarization in all dielectric materials, a universal property known as flexoelectricity. In a recent issue of Applied Physics Letters, an international team of researchers report on the flexoelectricity of two key antiferroelectric materials as a function of temperature. Their work revealed that antiferroelectricity is most likely not caused by flexoelectricity, as some researchers have proposed.

In contrast to ferroelectric materials that exhibit spontaneous electric polarization, the electric dipoles in antiferroelectric materials are aligned antiparallel to their nearest neighbors—analogous to the magnetic moments in antiferromagnetic materials. The strength of a material’s antiferroelectric property is a function of temperature, among other variables, and disappears above the Curie temperature.

“Antiferroelectrics are much less studied than most other families of functional materials,” says Pablo Vales-Castro, lead author of the new research and a doctoral student at Universitat Autonoma de Barcelona, working with Gustau Catalán at Institut Català de Nanociència i Nanotecnologia (ICN2). “There is much yet to learn about antiferroelectrics—not least [of which is] the origin of antiferroelectricity,” he says.

Researchers have hypothesized that flexoelectricity may be closely linked to antiferroelectricity, and could even drive the antiparallel dipole arrangement. If this is the case, antiferroelectrics should display an anomalously large change in polarization for a given change in strain gradient. This would be reflected in a material’s flexoelectric coefficient,  the change in polarization per strain gradient as calculated from the linear fit to experimental data.

To explore whether this is the case, Vales-Castro and Catalán worked with colleagues from the University of Silesia in Katowice, Poland and Tsinghua University, China to determine the flexoelectric coefficients of two materials, the archetype antiferroelectric PbZrO₃ and the lead-free antiferroelectric AgNbO₃. Using a dynamic mechanical analyzer, the researchers applied periodic bending stresses to samples of each material while recording the elastic response and displacement current. They collected data over a temperature range that extended beyond the Curie temperature of each material, from room temperature to 250°C for PbZrO₃ and up to 400°C for AgNbO₃.

Surprisingly, the data revealed unexceptional flexoelectric behavior. The team measured room-temperature flexoelectric coefficients of 2-6 nC/m for all samples; these values are smaller than those reported for ferroelectrics and relaxors (on the order of units or tens of μC/m) and comparable to those of the non-polar perovskite SrTiO₃ (1-10 nC/m). The flexocoupling constants, related coefficients that eliminate most of the temperature dependence, also fell within the standard range (~1-10 V) reported for non-antiferroelectric materials. Since the flexoelectric coefficients of antiferroelectrics are identical to or smaller than the coefficients of non-antiferroelectrics, the research team concluded that flexoelectricity does not drive antiferroelectricity or, at a minimum, that the picture is incomplete.

On the other hand, some additional intriguing results related to the flexocoupling emerged. AgNbO₃ undergoes a number of phase changes over the temperature range of the experiment and at each of these points, flexoelectric anomalies arose as discontinuities in the flexocoupling value. In addition, both materials showed a sharp peak in flexocoupling at the Curie temperature—an unexpected result given that the flexocoupling coefficient is independent of the dielectric permittivity.

“As our work shows, the existing hypothesis regarding the origin of antiferroelectricity as being linked to flexoelectricity is either wrong or else more nuanced than previously thought. It certainly is not caused by an anomalously large flexocoupling,” Catalán says. Expanding on this, Vales-Castro says, “We have not yet found a way to reconcile these results with the theoretical expectation. That, we hope, is something that theoreticians are going to look into now.”

Flexoelectricity has only recently become an active area of experimental research. Exciting discoveries are emerging, but there is still plenty of room for fundamental research. “There are entire families of materials for which flexoelectricity is yet to be characterized, despite the fact that it is a universal property,” say the researchers.

Xiaoning Jiang leads the Micro/Nano Engineering Lab at North Carolina State University and is not affiliated with this research. His research team explores how flexoelectricity can be used to monitor structural health and in sensing applications. The lack of information about flexoelectricity in materials limits options for designing flexoelectric structures and devices, according to Jiang, so he finds this research encouraging. “Considering the favorable scaling effect in flexoelectricity, antiferroelectric, and other solid dielectric films or nanostructures are of particular interest,” he says.

Read the abstract in Applied Physics Letters.