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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., Comment: 26 pages

Hafnium dioxide (HfO2) is a promising ferroelectric (FE) material for achieving high-density nonvolatile memory and neuromorphic computing, due to its compatibility with the mainstream integrated circuit technology and the surprisingly enhanced ferroelectricity by reduced thickness. The FE switching dynamics is essential to the device performance, but the complexity of HfO2 atomic structure causes unknown of various FE switching paths and domain wall configurations. Here, we demonstrate that its low-barrier paths and domain walls can be comprehensively found and understood from a perspective of topological symmetry. By discussing pseudo-chirality and equivalent transformation relations in crystal with first principles and lattice modes, we classify and analyze 4 low-barrier FE switching paths and 93 irreducible topology domain wall configurations in HfO2. Anisotropic switching mechanism is found based on the mobility investigation for 12 types of 180{\deg} side domain walls. This methodology is expected to be generally applicable to displacive ferroelectrics with low unit cell point group symmetries, and lay a foundation for mechanism study of the switching dynamics.