Mapping of the full polarization switching pathways for HfO₂ and its implications

The discovery of ferroelectric phases in HfO₂ 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 HfO₂ 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_IV) layers are inactive, our result demonstrates that both the tricoordinated oxygen (O_III) and O_IV can be displaced, leading to polarization switching along any axial direction. The multiple switching pathways in HfO₂ 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 HfO₂ growth surface. This allows HfO₂ 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_III and O_IV layers, clarify unconventional switching pathways, and enhance our understanding of electric field response mechanisms, wake-up, and fatigue in ferroelectrics.