  Intertwined ionic conduction and ferroelectric (FE) switching in HfO2 lead to
extensive focuses. To describe its fundamental phenomena, we present a
free-energy model describing the potential of ferroelectrics with successive FE
switching paths, and extend the domain model of ionic conduction to
ferroelectric domains. Associate theoretical analyses and first-principles
calculations suggest a nesting-domain pattern with opposite piezoelectric loops
during the nucleation-and-growth process in displacive FE-HfO2. A collective
oxygen ion conduction mechanism is also proposed with a field-dependent ionic
conductivity following the Merz's law. We conclude that the ionic
conductibility is concomitant with the ferroelectricity in HfO2, and it may
provide a new venue for pursuing low temperature fast oxide-ion conductors and
artificial synapses.
