Domain wall formation and migration in ferroelectric hafnium oxide.

Orthorhombic hafnium oxide (HfO₂) is predicted to exhibit multiple domain walls (DWs): the pbca-like DW with the lowest energy but hindered migration, and higher-energy pbcn-like and t-like DWs. However, which of these DWs most readily appears during polarization switching has yet to be determined. We adopt machine-learning interatomic-potentials and molecular dynamics simulations to investigate the dynamic processes of ferroelectric HfO₂ under an electric field. The simulation shows that a local electric field above 5 MV cm^-1 within a domain can induce local polarization switching, forming the t-like DW. This DW exhibits facile migration, requiring a critical field of only 1.2 MV cm^-1. The pbca-like DW emerges only when the applied electric field exceeds 6 MV cm^-1. The pbcn-like DW is not identified, although its energy is comparable to that of t-like DW. During a migration cycle of the t-like DW, an intermediate state resembling the pbcn-like DW appears, but this intermediate state cannot be stably maintained. Room-temperature phonon calculations show that the pbcn-like DW possesses an imaginary frequency mode, preventing stabilization, while the t-like DW is dynamically stable. This work sheds light on the room-temperature instability of the pbcn-like DW and highlights the crucial role of the mobile t-like DW in polarization switching of HfO₂.