Polarization description of successive ferroelectric switching in hafnia

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.