Electro-optic properties of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>ZrO</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>HfO</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>LiNbO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> ferroelectric phases: A comparative density functional study
Ali El Boutaybi, Panaghiotis Karamanis, Thomas Maroutian, Sylvia Matzen, Laurent Vivien, Philippe Lecoeur, Michel Rérat
Abstract
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.