Interplay of electrostatic screening and crystallographic orientation governing domain wall morphology in ferroelectric nanodots

Flux-closure domain is a prototypical chiral topological structure in ferroelectric square nanodots, distinguished by its characteristic cross-shaped 90\ifmmode^\circ\else\textdegree\fi{} domain walls, in stark contrast to the continuous polarization rotation observed in vortex domain. In recent years, several studies have predominantly focused on the chiral switching of flux-closure domain, the feasibility of domain wall rotation has received comparatively little attention. However, the rotation mechanism of the 90\ifmmode^\circ\else\textdegree\fi{} domain walls in flux-closure domain represents a critical yet unresolved issue in the broader context of domain wall dynamics. In this paper, the polarization configurations in ferroelectric nanodots under varying distinct depolarization fields and crystallographic orientations are systematically investigated via phase-field simulations. The results demonstrate that the formation and transformation of 90\ifmmode^\circ\else\textdegree\fi{} domain walls of flux-closure domain in the nanodots are governed by the interplay between surface screening conditions and crystallographic orientation. Under weak screening (i.e., near open-circuit conditions), the domain walls remain pinned at a fixed 45\ifmmode^\circ\else\textdegree\fi{} relative to the global geometric coordinates as a Saltire-cross shape, irrespective of the variation in crystallographic orientation. With increasing screening, a competitive balance arises between the depolarization field and crystallographic anisotropy, leading to the destabilization of the 90\ifmmode^\circ\else\textdegree\fi{} domain walls and driving the transition from a flux-closure domain state to an ideal vortex domain state. Under strong screening (i.e., near short-circuit conditions), crystallographic orientation becomes dominant, driving the continuous reorientation of domain walls from a Saltire-cross shape to a Greek-cross shape with respect to the global coordinates. This work elucidates the coupled influence of electrostatic boundary screening and crystallographic anisotropy on domain morphology, emphasizing the competitive interplay between electrostatic, gradient, and elastic energy contributions. These findings elucidate the coupled electrostatic and crystallographic mechanisms underlying domain wall rotation, advance the fundamental understanding of topological polar structures, and offer new insights for domain-wall-based nanoelectronic applications.