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 $C2/c$ 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.