Tetrahedral rotations in the alkaline-earth metal orthovanadates

The alkaline-earth metal orthovanadate ${\mathrm{Sr}}_{3}{({\mathrm{VO}}_{4})}_{2}$ with the palmierite structure is reported to host a dielectric anomaly as well as a structural phase transition above the room temperature. With ${\mathrm{V}}^{5+}$ ions and tetrahedral oxygen coordination, the crystal structure of this compound is not studied in detail from first principles yet. In this work, we perform a detailed analysis of the crystal structure and instabilities of ${M}_{3}{({\mathrm{VO}}_{4})}_{2}$ ($M=\text{Ca,}\phantom{\rule{4.pt}{0ex}}\text{Sr,}\phantom{\rule{4.pt}{0ex}}\text{Ba}$) orthovanadates with the palmierite structure using first-principles density functional theory. We find that as the ${M}^{2+}$ cation size decreases, a significant structural distortion that changes the symmetry from $R\overline{3}m$ to $C2/c$ emerges. This change is accompanied with a rotation of the oxygen tetrahedra. Our calculations also indicate that the polar instability in these compounds is suppressed by these tetrahedral rotations.