Tetrahedral rotations in alkaline-earth metal orthovanadates

The alkaline-earth orthovanadate Sr${}_3$V${}_2$O${}_8$ with the palmierite structure is reported to host a dielectric anomaly as well as a structural phase transition above the room temperature. With 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${}_3$V${}_2$O${}_8$ ($\text{M}=\text{Ca, Sr, Ba}$) 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 $R\bar{3}m$ to $C2\mathrm{/}c$ emerges. This change is accompanied with a rotation of the oxygen tetrahedra. Our calculations also indicate that the polar instability in these compounds are suppressed by these tetrahedral rotations.