Ferroelectric properties in PbZrO$_{3}$/BaZrO$_{3}$ superlattices: an \textit{ab-initio} study

Properties of tetragonal (BaZrO$_{3})_{1}$/(PbZrO$_{3})_{\mathrm{n}}$ ferroelectric superlattices with n $=$ 1--3 are calculated from first principles within the density functional theory. We show that an antiferroelectric PbZrO$_{3}$ displays ferroelectric behavior if deposited on a paraelectric substrate (BaZrO$_{3})$. We have performed total energy calculations to investigate the origins of the ferroelectricity and analyze the polarization of BaZrO$_{3}$/(PbZrO$_{3})_{\mathrm{n}}$ superlattices as function of PbZrO$_{3}$ thickness. The densities of states (DOS) show that there is a strong hybridization between Zr/Pb and O atoms which play important role in stabilizing the ferroelectric ground state in the superlattices. Our calculations show that the polarization and tetragonality ($c/a$ ratio) are reduced in the BaZrO$_{3}$/PbZrO$_{3}$ superlattices with respect to bulk tetragonal PbZrO$_{3}$. Moreover, the tetragonality and polarizations of superlattices increase with increasing the fraction of PbZrO$_{3}$ in the superlattices. The estimated polarization of the (BaZrO$_{3})_{1}$/(PbZrO$_{3})_{1}$ superlattice is (38.46 $\mu $C/cm$^{2})$, while it is (56.82$\mu $C/cm$^{2})$ for the (BaZrO$_{3})_{1}$/(PbZrO$_{3})_{3}$ superlattice and (74.22$\mu $C/cm$^{2})$ for bulk tetragonal PbZrO$_{3}$ These ferroelectric superlattices have good lattice matching with shape-memory NiMnIn Heusler alloys and could be very useful as a ferroelectric substrate to systems.