Phase Transitions and Switching Dynamics of Topological Domains in Hafnium Oxide-Based Cylindrical Ferroelectrics from Three-Dimensional Phase Field Simulation

The phase transitions and switching dynamics of topological polar textures in hafnium oxide (HfO₂)-based cylindrical-shell ferroelectrics are studied using a three-dimensional (3D) phase field model based on the self-consistent solution of the time-dependent Ginzburg-Landau model and Poisson equation. The comprehensive interplays of bulk free energy, gradient energy, depolarization energy, and elastic energy are taken into account. When a cylindrical ferroelectric device is biased under the in-plane radial electric field, there is a size-controlled phase transition between the ferroelectric (FE), antiferroelectric (AFE), and paraelectric (PE) phases, depending on ferroelectric film thickness and cylindrical shell radius. For in-plane polarization textures at the equilibriums, the FE phase has a Néel-like texture with a center-type four-quad domain, the AFE phase has a monodomain texture, and the PE phase has a Bloch-like texture with a vortex four-quad domain. These polarization domain textures are resultant from energy competition and topologically protected by the geometrical confinement. The polarization dynamics from polar states towards equilibriums are analyzed considering the separated contributions of x- and y-components of polarizations that are driven by x-y in-plane electric fields. The emergent topological domains and phase transitions provide guidelines for geometrical engineering of a novel nano-structured ferroelectric device that is different from the planar one, offering new possibilities for multi-functional high-density ferroelectric memory.