Electro-optic effects in ferroelectrics from first principles

This review summarizes recent first-principles studies on electro-optic (EO) effects in ferroelectric materials, focusing on linear and nonlinear EO responses, strain engineering of EO coefficients in three-dimensional (3D) and two-dimensional (2D) ferroelectrics. The linear and nonlinear EO effects are predicted in Pb(Zr,Ti)O$_3$ and BaTiO$_3$ ferroelectric oxides, respectively, which is in good agreement with the previous experimental findings. The origin of such different responses can be understood by the electric-field-induced behavior of some specific phonon frequencies and some force constants. The large linear and nonlinear EO responses are also predicted in 2D ferroelectric SnS monolayer. Furthermore, it is demonstrated that the EO responses of AlN/ScN superlattices, NbOI$_{2}$, and sliding ferroelectrics can be significantly enhanced under epitaxial strain. In particular, in AlN/ScN superlattices and NbOI$_{2}$ systems, a strain-induced phase transition has been discovered, driven by the softening of the lowest phonon modes, which results in large linear EO responses. Additionally, a detailed study on the EO effect in the prototype sliding ferroelectric ZrI$_{2}$ revealed a fundamental discovery: the EO effect in this material is predominantly electronic in origin. It is further shown that both biaxial and uniaxial strains significantly enhance this electronic EO response, and a universal linear relationship between the EO coefficient and the band gap is uncovered. The investigation is further extended to the temperature and frequency dependence of EO responses in BaTiO$_3$, identifying the dominant physical contributions across different frequency ranges. This review represents a significant and general advance that is expected to stimulate substantial future theoretical and experimental exploration in the field.