Properties of (001) NaNbO 3 films under epitaxial strain: A first-principles study

First-principles calculations are performed to investigate and analyze properties of (001) thin films made of the most complex perovskite system, namely, $\mathrm{Na}\mathrm{Nb}{\mathrm{O}}_{3}$ (NNO), and are subject to epitaxial strain. In particular, an energy-versus-misfit strain phase diagram is constructed and reveals the existence of three different ground states for different strain regimes. For large compressive strain and up to moderate tensile strain, a monoclinic $Cc$ phase occurred, with its polarization and axis of antiphase tilting both rotating within a ($\overline{1}10$) plane with the magnitude of the strain. For large tensile strain, a ferroelectric orthorhombic state of $Pmc{2}_{1}$ symmetry emerges with polarization lying along the [110] in-plane direction together with an octahedral tilting adopting the ${a}^{\ensuremath{-}}{a}^{\ensuremath{-}}{c}^{+}$ pattern and an antiferroelectric vector associated with the reciprocal zone-border $X$ point. Finally, in between and for a narrow region of strain, a complex ground state is found. It has orthorhombic $Pca{2}_{1}$ symmetry, for which a complex tilting pattern coexists with polarization pointing along the [001] out-of-plane direction and antiferroelectric displacement associated with the $\mathrm{\ensuremath{\Delta}} k$ point located halfway between the zone-center $\mathrm{\ensuremath{\Gamma}}$ and zone-border $X$ point. Ferroelectric, antiferroelectric, and antiferrodistortive properties are also reported and discussed as a function of misfit strain.