Tunable and parabolic piezoelectricity in hafnia under epitaxial strain

Piezoelectrics are a class of functional materials that have been extensively used for application in modern electro-mechanical and mechatronics technologies. The sign of longitudinal piezoelectric coefficients is typically positive but recently a few ferroelectrics, such as ferroelectric polymer poly(vinylidene fluoride) and van der Waals ferroelectric CuInP₂S₆, were experimentally found to have negative piezoelectricity. Here, using first-principles calculation and measurements, we show that the sign of the longitudinal linear piezoelectric coefficient of HfO₂ can be tuned from positive to negative via epitaxial strain. Nonlinear and even parabolic piezoelectric behaviors are further found at tensile epitaxial strain. This parabolic piezoelectric behavior implies that the polarization decreases when increasing the magnitude of either compressive or tensile longitudinal strain, or, equivalently, that the strain increases when increasing the magnitude of electric field being either parallel or antiparallel to the direction of polarization. The unusual piezoelectric effects are from the chemical coordination of the active oxygen atoms. These striking piezoelectric features of positive and negative sign, as well as linear and parabolical behaviors, expand the current knowledge in piezoelectricity and broaden the potential of piezoelectric applications towards electro-mechanical and communications technology.