  Ferroelectric hafnia exhibits promising robust polarization and silicon
compatibility for ferroelectric devices. Unfortunately, it suffers from
difficult polarization switching. Methods to enable easier polarization
switching are needed, and the underlying reason for this switching difficulty
is not understood. Here, we investigated the 180$^\circ$ domain walls of hafnia
and their motion through nucleation. We found that the domains of
multiple-order parameter hafnia possess complicated three-dimensional dipole
patterns and lead to domain walls of different symmetry. The most common domain
wall type is a complex domain wall involving reversal of both polarization and
tetragonality order parameters. This domain wall symmetry ensures a good
matching of the dipoles perpendicular to the domain wall, which leads to low
domain wall energy. However, this ensures a sharp, high energy, charged domain
wall on the edges of nuclei that results in difficult nucleation. Thus, this
domain wall is too stable to move, which explains the switching difficulty of
hafnia. By contrast, another simple domain wall, involving only polarization
reversal, has a poor matching of dipoles perpendicular to the domain wall. This
leads to higher domain wall energy and ensures a diffusive and low energy
charged domain wall that enables easier nucleation. This simple domain wall is
thus not too stable and easier to move. Our theory advances domain wall
nucleation theory from the field of conventional single-order parameter to
multiple-order parameters. We propose controlling the populations of different
domain wall types in hafnia as a way to enable fast polarization switching and
lower coercive fields.
