  Spontaneous polarization is essential for ferroelectric functionality in
non-centrosymmetric crystals. High-integration-density ferroelectric devices
require the stabilization of ferroelectric polarization in small volumes. Here,
atomic-resolution transmission electron microscopy imaging reveals that
twinning-induced symmetry breaking in colloidal nanocrystals of centrosymmetric
HfO2 leads to the formation of multiple polarization orders, which are
associated with sub-nanometer ferroelectric and antiferroelectric phases. The
minimum size limit of the ferroelectric phase is found to be ~4 nm3. Density
functional theory calculations indicate that transformations between the
ferroelectric and antiferroelectric phases can be modulated by lattice strain
and are energetically possible in either direction. The results of this work
provide a route towards applications of HfO2 nanocrystals in information
storage at densities that are more than an order of magnitude higher than the
scaling limit defined by the nanocrystal size.
