  Flexoelectricity, inherent in all materials, offers a promising alternative
to piezoelectricity for nanoscale actuation and sensing. However, its
widespread application faces significant challenges: differentiating
flexoelectric effects from those of piezoelectricity and other phenomena,
verifying its universality across all material structures and thicknesses, and
establishing a comprehensive database of flexoelectric coefficients across
different materials. This work introduces a groundbreaking methodology that
accurately isolates flexoelectricity from piezoelectric, electrostrictive and
electrostatic effects, with a detection threshold extending below 1 fC/m. The
robustness of this method is demonstrated through its application to amorphous
hafnium oxide (HfO$_2$), successfully measuring a flexoelectric coefficient of
105 $\pm$ 10 pC/m. This measurement signifies the first measurement of
flexoelectricity in hafnia, as well as in any amorphous material. Additionally,
the study compiles a list of published flexoelectric coefficients, revealing an
important insight. The relationship between the flexoelectric coefficient and
the material's relative permittivity is better approximated by a quadratic
proportionality. This challenges the traditional linear assumption proposed in
Kogan's work and opens new avenues for future research in flexoelectric
materials.
