Anomalous Piezoelectricity from Polarization-Dependent Electrostriction in Wurtzites

The piezoelectric coefficient is a third-rank tensor connecting the strain or stress with the electric field or polarization, whereas the electrostriction coefficient is a fourth-rank tensor relating the strain to the square of electric polarization. The electrostriction tensor components in the current literature are often treated as constants independent of polarization, resulting in piezoelectric tensor components that are linearly proportional to polarization and the dielectric susceptibility tensor. Here, we study the electrostriction and piezoelectricity in strongly polar wurtzites, including AlN, Al$_{1-x}$Sc$_x$N, Al$_{1-x}$B$_x$N, GaN, and ZnO. We discover that electrostriction and the elastic modulus in wurtzites are both strongly polarization-dependent, and the piezoelectric coefficient is highly nonlinear with respect to polarization, including the anomalous possibility that decreasing polarization increases the electromechanical strain response. These unusual dependencies of electrostriction and piezoelectric effects on polarization arise from the evolution of a layered reference nonpolar structure toward a tetrahedrally coordinated wurtzite network structure as the polarization increases. The findings have important implications in understanding the thermodynamics of the general class of wurtzite ferroelectrics and in manipulating their piezoelectric and ferroelectric behaviors.