Spontaneous polarization in NaNbO${}_3$ film on NdGaO${}_3$ and DyScO${}_3$ substrates

Pure NaNbO${}_3$ is an antiferroelectric material at room temperature that irreversibly transforms to a ferroelectric polar state when subjected to an external electrical field or lattice strain. Experimentally, it has been observed that NaNbO${}_3$ films grown on NdGaO${}_3$ exhibit an electrical polarization along the [001]${}_{\mathrm{P}\mathrm{C}}$ direction, whereas films on DyScO${}_3$ substrates exhibit a polarization along the [011]${}_{\mathrm{P}\mathrm{C}}$ direction. These effects have been attributed to the realization of different lattice symmetries in the films due to the incorporation of lattice strain imposed by the use of oxide substrates with different lattice parameters. However, the underlying atomistic mechanisms of the resulting phase symmetry in the films are hardly clear, given that NaNbO${}_3$ features a diverse and complex phase diagram. In turn, these also impede a straightforward tailoring and optimization of the resulting macroscopic properties on different substrates. To clarify this issue, we perform all-electron first-principles calculations for several potential NaNbO${}_3$ polymorphs under stress and strain. The computed properties, including the ferroelectric polarization, reveal that an orthorhombic $Pmc{2}_1$ phase is realized on NdGaO${}_3$ substrates since this is the only phase with an out-of-plane polarization under a compressive strain. Conversely, the monoclinic $Pm$ phase is consistent for the samples grown on DyScO${}_3$ substrate, since this phase exhibits a spontaneous in-plane polarization along [011]${}_{\mathrm{P}\mathrm{C}}$ under tensile strain.