Negative longitudinal piezoelectric effect and electric auxetic effect in ferroelectric HfO2 and related fluorite-structure ferroelectrics

Unusual negative longitudinal piezoelectric effect (NLPE) and electric auxetic effect (EAE) have essential implications for designs of piezoelectric sensors and actuators. The emerging ferroelectric HfO2 is recently discovered to have both effects, while the underlying physical mechanisms remain elusive. To understand and regulate these intriguing effects, it is crucial to investigate the piezoelectricity in ferroelectric HfO2 and related fluorite-structure ferroelectrics. Here, we corroborate using first-principles calculations that all twelve fluorite-structure ferroelectrics covered in this study possess the NLPE. A chemical tendency of piezoelectricity is demonstrated, i.e., the larger the "iconicity," the stronger the NLPE. The structural origin is attributed to the predominant influence of the triple-coordinated anion displacement, namely, the more "ionic" fluorite-structure ferroelectrics exhibit larger anion displacement under a pressure or strain, which gives rise to a more negative internal-strain contribution dominating over the positive clamped-ion contribution and hence a stronger NLPE. Moreover, we confirm several electric auxetic materials in fluorite-structure ferroelectrics with finite electric field calculations. We find that the piezoelectricity of electric auxetic materials is suppressed by the external electric field along the polar direction, since it weakens the bonding heterogeneity. The unraveled fundamental understanding of the NLPE and EAE in this study may profoundly benefit the design and application of fluorite-structure ferroelectrics.