This study investigates the tunable and parabolic piezoelectricity in hafnium (HfO₂) under epitaxial strain. Using first-principles calculations and measurements, the researchers demonstrate that the longitudinal linear piezoelectric coefficient of HfO₂ can be tuned from positive to negative via epitaxial strain. Nonlinear and parabolic piezoelectric behaviors are observed at tensile epitaxial strain, where the polarization decreases with increasing strain magnitude, either compressive or tensile. This behavior is attributed to the chemical coordination of oxygen atoms. The unusual piezoelectric effects, including both positive and negative signs and linear and parabolic behaviors, expand the current understanding of piezoelectricity and broaden its potential applications in electro-mechanical and communications technology. The study also confirms the experimental results using piezoresponse force microscopy and molecular dynamics simulations, highlighting the potential for frequency conversion in communications technology.This study investigates the tunable and parabolic piezoelectricity in hafnium (HfO₂) under epitaxial strain. Using first-principles calculations and measurements, the researchers demonstrate that the longitudinal linear piezoelectric coefficient of HfO₂ can be tuned from positive to negative via epitaxial strain. Nonlinear and parabolic piezoelectric behaviors are observed at tensile epitaxial strain, where the polarization decreases with increasing strain magnitude, either compressive or tensile. This behavior is attributed to the chemical coordination of oxygen atoms. The unusual piezoelectric effects, including both positive and negative signs and linear and parabolic behaviors, expand the current understanding of piezoelectricity and broaden its potential applications in electro-mechanical and communications technology. The study also confirms the experimental results using piezoresponse force microscopy and molecular dynamics simulations, highlighting the potential for frequency conversion in communications technology.