Electro-optic properties of ZrO2 , HfO2 , and LiNbO3 ferroelectric phases: A comparative density functional study

We report the Pockels electro-optic properties of ${\mathrm{ZrO}}_{2}$ and ${\mathrm{HfO}}_{2}$ orthorhombic $Pbc{2}_{1}$ and rhombohedral $R3m$ ferroelectric phases, and we compare them to the well-known rhombohedral $R3c$ ${\mathrm{LiNbO}}_{3}$ Pockels material from density functional theory calculations using the crystal suite of programs. Specifically, three essential processes are explicitly investigated: The electronic, the ionic (or vibrational), and the piezoelectric contributions. Our calculations reveal that the ionic part coming from the low-frequency phonon modes contributes the most to the electro-optic coefficients of rhombohedral ${\mathrm{LiNbO}}_{3}$ and of orthorhombic ${\mathrm{ZrO}}_{2}$ and ${\mathrm{HfO}}_{2}$. Additionally, the low-frequency phonon modes exhibit zero contribution to the Pockels coefficients of ${\mathrm{ZrO}}_{2}$ and ${\mathrm{HfO}}_{2}$ rhombohedral $R3m$ phase.