Electro-optic effects in some sliding ferroelectrics

Abstract

Sliding ferroelectrics, which exhibit out-of-plane polarization arising from specific stacking rather than conventional ionic displacements, are new types of ferroelectrics whose underdeveloped physics needs to be explored. Here, we investigate the electro-optic (EO) response of these materials using first-principles calculations, focusing on ZrI$_{2}$ as a prototype. We reveal that, contrary to conventional ferroelectrics, the EO effect in ZrI$_{2}$ is dominated by its electronic contribution rather than the ionic one, which promises faster EO responses. Furthermore, both biaxial and uniaxial strains significantly enhance this response, and a universal-like linear relationship between the band gap and such response is discovered. We also report a large elasto-optic coefficient that is independent of biaxial strain. Similar large linear EO coefficients and properties are found in other sliding ferroelectrics, including different zirconium dihalides, as well as BN and BP bilayers. These findings highlight sliding ferroelectrics as highly promising candidates for ultrafast nonlinear optical devices and reveal unusual mechanisms.

Figures (4)

• Figure 1: The crystal structures of (a) $\beta$-ZrI$_{2}$ ($Pmn2_1$), (b) s-ZrI$_{2}$ ($Pnma$), and (c) $\alpha$-ZrI$_{2}$ ($P2_1/m$), respectively; (d) two possible polarization switching paths of ZrI$_{2}$ bulk. The s-ZrI$_{2}$ and $\alpha$-ZrI$_{2}$ are the intermediate states of path I and path II, respectively; (e) clamped EO tensor and polarization ($P$) as a function of the sliding path II; and (f) clamped EO tensor versus biaxial strain in $\beta$-ZrI$_{2}$.
• Figure 2: (a) The polarization, band gap, and (b) clamped EO coefficient $r_{33}^{\eta}$ as a function of biaxial strain. The clamped EO coefficient $r_{33}^{\eta}$ as a function of (c) polarization, (d) band gap, (e) $\kappa$ (the product between the polarization $P_\text{s}$ and $E_{0}$), and (f) $\gamma$ (the ratio between $P_\text{s}$ and $E_{0}$) under biaxial strain.
• Figure 3: (a) Piezoelectric coefficient $d_{33}$ and elasto-optic coefficient $p_{33}$, and (b) clamped $r_{33}^{\eta}$ and unclamped $r_{33}^{\sigma}$ EO coefficients of $\beta$-ZrI$_2$ as a function of biaxial strain.
• Figure 4: Same as Fig. \ref{['fig2']} but under uniaxial strain.