Enhanced piezoelectricity in PbTiO$_{3}$/BaTiO$_{3}$ superlattices

Short period ferroelectric/ferroelectric PbTiO$_{\rm 3}$ (PTO)/BaTiO$_{\rm 3}$ (BTO) superlattices are studied using density functional theory. Contrary to the trends in paraelectric/ferroelectric superlattices the polarization remains nearly constant for PTO concentrations below 50\%. In addition, a significant decrease in the $c/a$ ratio below the PTO values is observed. We predict an enhancement in the $d_ {33}$ piezoelectric coefficient peaking at $\sim$75\% PTO concentration due to the different polarization-strain coupling in PTO and BTO layers. Further analysis with a superlattice effective Hamiltonian reveals that these trends are bulk properties which are a consequence of the reduced $P$ brought about by the polarization saturation in the BTO layers.