Enhanced Piezoelectricity in PbTiO$_3$/BaTiO$_3$ Superlattices

First-principles calculations by Cooper and Rabe predict an enhancement of the piezoelectric coefficient ($d_{33}$) in PbTiO$_3$/BaTiO$_3$ (PTO/BTO) superlattices for intermediate values of PTO concentration. PTO/BTO superlattices have been fabricated using an off-axis RF magnetron sputtering technique, enabling x-ray diffraction, electrical measurements and atomic force microscopy on this system. The experimental results agree with the calculated polarization, tetragonality and enhanced piezoelectricity as a function of PTO concentration. Additional first-principles calculations indicate that the enhancement in $d_{33}$ is more pronounced in shorter-period superlattices. By applying a Landau-Devonshire model to this system, we find that the enhanced piezoelectricity is due to the combination of a bulk effect associated with the presence of finite electric fields in each layer and interfacial effects. Implications of our results for future experiments are discussed.