Polar and toroidal electromechanical properties designed by ferroelectric nano-metamaterials

Abstract The recent advance in metamaterials provides a promising route to efficiently tailor and design a variety of material properties through rationally engineered building blocks. To further exploit the metamaterial concept with respect to electromechanical properties, we investigate electromechanical responses in ferroelectric nano-metamaterials using a phase field model based on Ginzburg-Landau theory. A wide magnitude range for apparent piezoelectric coefficients, which are strongly dependent on the internal structure, are obtained in ferroelectric nano-metamaterials, manifesting ferroelectric nano-metamaterials possess great versatility for tailoring the piezoelectricity. Unusual positive transverse piezoelectric coefficients, and consequently positive piezoelectric anisotropy can be achieved in ferroelectric nano-metamaterials. These unusual coefficients go beyond those which typically occur in homogenous ferroelectrics. We further introduce and demonstrate a new functionality of piezotoroidicity, which represents a new type of electromechanical coupling between ferrotoroidic ordering and mechanical excitation, emerging in ferroelectric nano-metamaterials. The present study thus opens exciting opportunities for the tailoring and design of electromechanical properties through deliberate control of the internal structure of ferroelectric nano-metamaterials by further extension of the metamaterial concept to electromechanical nano-metamaterials.