Properties of (001) ${\mathrm{NaNbO}}_3$ 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 $a^{-}{a}^{-}{c}^{+}$ 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 $\mathrm{\Delta } k$ point located halfway between the zone-center $\mathrm{\Gamma }$ and zone-border $X$ point. Ferroelectric, antiferroelectric, and antiferrodistortive properties are also reported and discussed as a function of misfit strain.

Figure 1

Total energy versus misfit strain curves for the three presently considered phases of epitaxial (001) $\mathrm{Na}\mathrm{Nb}{\mathrm{O}}_3$ thin films. The zero of the energy corresponds to the minimal energy, which is associated with the $Pmc{2}_1$ phase at an epitaxial strain of $+1.78$%.

Figure 2

Misfit strain dependence of (a) the polarization and (b) quantities related to oxygen octahedral tilting (see text) for the three presently considered phases of epitaxial (001) $\mathrm{Na}\mathrm{Nb}{\mathrm{O}}_3$ thin films

Figure 3

Misfit strain dependence of a quantity related to antipolar displacements (see text) associated with (a) the $\mathrm{\Delta }$ and (b) $X$ points of the cubic first Brillouin zone for the three presently considered phases of epitaxial (001) $\mathrm{Na}\mathrm{Nb}{\mathrm{O}}_3$ thin films