Mapping of the full polarization switching pathways for HfO and its implications.

The discovery of ferroelectric phases in HfO offers insights into ferroelectricity. Its unique fluorite structure and complex polarization switching pathways exhibit distinct characteristics, challenging conventional analysis methods. Combining group theory and first-principles calculations, we identify numerous unconventional electric polarization switching pathways in HfO with energy barriers of 0.32 to 0.57 eV as a function of the different shift in the suboxygen lattices. In total, we identify 47 switching pathways for the orthorhombic phase, corresponding to the left cosets of the [Formula: see text] group with [Formula: see text] group. Contrary to the conception that the tetracoordinated oxygen (O) layers are inactive, our result demonstrates that both the tricoordinated oxygen (O) and O can be displaced, leading to polarization switching along any axial direction. The multiple switching pathways in HfO result in both 180° polarization reversal and the formation of 90° domains observed experimentally. Calculations show that specific switching pathways depend on the orientation of the applied electric field relative to the HfO growth surface. This allows HfO to automatically adjust the in-plane polarization direction under an out-of-plane electric field, thereby maximizing the out-of-plane component and contributing to the wake-up process. These findings redefine the roles of O and O layers, clarify unconventional switching pathways, and enhance our understanding of electric field response mechanisms, wake-up, and fatigue in ferroelectrics.