First-principles study of structural and vibrational properties of SrZrO${}_3$

Using first-principles calculations, we investigate the electronic, structural, and vibrational properties of SrZrO${}_3$. We start from the high-symmetry cubic perovskite phase, for which the phonon dispersion curves are reported. We point out the coexistence of structural antiferrodistortive instabilities at the R and M zone-boundary points and a ferroelectric instability at the zone center. We show that the strong antiferrodistortive motions suppress ferroelectricity and are responsible for the orthorhombic ground state as in CaTiO${}_3$. The structural properties of possible intermediate phases and of the orthorhombic $Pnma$ ground state are reported. For the latter, an assignment of IR and Raman zone-center phonon modes is proposed. The main features of the ferroelectric instability are also discussed, and we show that a ferroelectric ground state can even be induced in SrZrO${}_3$ by strain engineering.

Figure 1

Schematic view of the structure of SrZrO${}_3$ (Zr, big green balls; Sr, medium black balls; O, small red balls). Thick black lines show the 20-atom supercell, and thin blue lines show the 40-atom supercell.

Figure 2

Calculated phonon dispersion curves of cubic (a) SrZrO${}_3$, and (b) CaTiO${}_3$ at the GGA-WC volume along the path $\Gamma$-X-M-R-$\Gamma$-M of the cubic Brillouin zone.

Figure 3

Energies (in meV/f.u.) of different phases of SrZrO${}_3$ after full structural relaxations in comparison to that of the cubic phase taken as reference. One formula unit (f.u.) consists in a five-atom $AB$O${}_3$ unit. Arrows indicate the type of additional tilt component ($R_5^{-}$ or $M_3^{+}$) appearing from one structure to another. Glazer's notations clarify along which direction this tilt component appears.