Supplementary Material

The supplementary material covers the microfabrication of cantilevers and clamped-clamped beams, X-ray diffraction and SEM analyses to confirm the amorphous nature and thickness of the HfO2 layer, and P-E loop measurements to determine the material's relative permittivity. Methods for isolating and measuring the flexoelectric coefficient using a Laser Doppler Vibrometer are explained, along with a full derivation of the curvature formula and a comprehensive theoretical expression for the flexoelectric coefficient. Additionally, calculations for determining the detection limit of our method are provided. The material also presents simulations comparing resonance frequency shifts in cantilevers and clamped-clamped beams to elucidate flexoelectric effects.