Flexo-Ferroelectricity and a Work Cycle of a Two-Dimensional-Monolayer Actuator.

Well recognized mechanical flexibility of two-dimensional (2D) materials is shown to bring about unexpected behaviors to the recently discovered monolayer ferroelectrics, especially those displaying normal, off-plane polarization. A "ferro-flexo" coupling term is introduced into the energy expression, to account for the connection of ferroelectricity and bending (strain gradient) of the layer, to predict and quantify its spontaneous curvature and how it affects the phase transitions. With InP as a chemically specific representative example, the first-principles calculations indeed reveal strong coupling ∼ P ·ϰ between the ferroelectric polarization ( P ) and the curvature of the layer (ϰ ≡ 1/ r ), having profound consequences for both mechanics and ferroelectricity of the material. Due to flexural relaxation, the spontaneous polarization and the transition barrier rise significantly, leading to large changes in the Curie temperature, coercive field, and domain wall width and energy, based on Monte Carlo simulations. On the other hand, the polarization switching, characteristic to ferroelectrics, does induce an overall layer bending, enabling a conversion of electrical signal to movement as an actuator; its possible work-cycles and maximum work-efficiency are briefly discussed.