Effect of epitaxial strain on the spontaneous polarization of thin film ferroelectrics

We investigate the variation of the spontaneous ferroelectric polarization with epitaxial strain for BaTiO$_3$, PbTiO$_3$, LiNbO$_3$, and BiFeO$_3$ using first principles calculations. We find that while the strain dependence of the polarization is very strong in the simple perovskite systems BaTiO$_3$ and PbTiO$_3$ it is only weak in LiNbO$_3$ and BiFeO$_3$. We show that this different behavior can be understood purely in terms of the piezoelectric and elastic constants of the unstrained bulk material, and we discuss several factors that determine the strain behavior of a certain material.