Crossover of polar and toroidal orders in ferroelectric nanodots with a morphotropic phase boundary and nonvolatile polar-vortex transformations

Ferroelectric vortices are promising candidates for developing high-capacity memory devices and discovery of intriguing electromechanical properties. It is well known that the ferroelectric vortex state tends to stabilize at poor screening conditions and a relatively good screening condition would give rise to a polar state. However, what happens at the intermediate screening condition remains unclear. In this work, by including a Bardeen screening model into phase-field simulations, we explore the screening-mediated state stabilization in ferroelectric nanodots. A state coexistence regime where the polar and toroidal orders can both stabilize in a ferroelectric nanodot is found at certain range of screening (that is, screening length from 0.011 to 0.022 nm at room temperature). The mechanism of state coexistence is analyzed by construction of the input-dependent free-energy profile according to the energy minimum principle. The coexistence regime is further revealed to be tunable by geometrical parameters. Importantly, the polar and vortex states can be readily switched between each other via electrical and mechanical loads, paving the way towards a type of nonvolatile multilevel memory. Moreover, a screening-mediated morphotropic phase boundary (MPB) with strong dielectric and piezoelectric responses is demonstrated. Our study thus discovers a stability crossover of polar and toroidal orders in ferroelectric nanodots at intermediate screening condition accompanied with superior electromechanical properties and the feasibility in multilevel memory application.