Distinguish the Orientation of Sliding Ferroelectricity by Second-Harmonic Generation

Abstract

As the emerging ferroelectric (FE) materials, the ultrathin two-dimensional (2D) sliding ferroelectrics without phase-matching bottleneck, usually exhibit the pronounced second harmonic generation (SHG) responses. Despite the structural polarity of sliding ferroelectrics can be precisely detected via SHG characterizations, distinguishing the orientations of sliding ferroelectricity based on SHG responses has rarely been realized, as SHG intensities for upward and downward polarization states are supposed to be same. In current work, combining computational simulations and experimental characterizations, the orientation of sliding ferroelectricity is demonstrated to be readily distinguishable via SHG responses in 2D SnP2S6 (SnP2Se6), a new sliding FE material. Specifically, owing to the unique symmetry operation within FE-SnP2S6 (SnP2Se6), the intersection between \c{hi}xxx and \c{hi}yyy SHG susceptibility coefficients with opposite signs leads to the effective rotation of SHG polar directions upon switching of sliding ferroelectricity. Moreover, the remarkable dependence of SHG polar directions on the orientation of sliding ferroelectricity is further validated by experimental characterizations performed on SnP2S6 crystal in a single FE domain structural form. This work opens up the avenue for in-situ detecting the ferroelectricity orientation of 2D sliding ferroelectrics based on SHG nonlinear optical responses, and also demonstrates the controllable optical nonlinearly for new "slidetronics" applications.

Figures (5)

• Figure 1: (a) Atomic structure for vdW layered SnP$_2$S$_6$, composed of three monolayers in $ABC$ stacking sequence. Both top and side views are provided. (b) Top: simulated interlayer charge density of raw SnP$_2$S$_6$ trilayer “exfoliated” from the bulk phase, SnP$_2$S$_6$ trilayer in $ABC$ stacking but without cation polar displacement and trilayer with cation polar displacement and $ABA$ stacking sequence. Charge accumulation and depletion of the as-formed interlayer dipoles are indicated by yellow and cyan isosurface plots with the isovalue of $\pm 1.8 \times 10^{-4} \, \text{e}/\text{Å}^3$, respectively. Bottom: the planar-averaged electrostatic potential profiles for SnP$_2$S$_6$ trilayers, where the out-of-plane polarizations create the non-zero potential offsets between two ends.
• Figure 2: (a) Our simulated PES associated with the sliding between two SnP$_2$S$_6$ monolayers. The unit cell of SnP$_2$S$_6$ is marked by a black diamond, the red arrow indicates the direction for optimal interlayer sliding pathway along [$\overline{1}$10] direction, and the yellow arrow is the lattice vector. (b) The optimal polarization switching pathway via consecutive sliding of individual monolayers between trilayer structures with $ABC$ and $CBA$ stacking sequences. The solid and dashed rectangles indicate the stationary and sliding monolayers, respectively. Solid blue arrows mark the sliding directions of monolayers. The interlayer dipoles between adjacent monolayers are represented by red arrows. (c) The simulated planar-averaged screening charge $\Delta \rho$ along the out-of-plane direction for +$P$ state of SnP$_2$S$_6$ trilayer, where $\Delta \rho$ from interlayer and intralayer areas are in red and blue colors, respectively. (d) Along the optimal interlayer slidng pathway, variation of system energy and polarization magnitude $P$ during the polarization switching between $\pm$$P$ states of SnP$_{2}$S$_{6}$ trilayer.
• Figure 3: (a) Illustration of the SHG polarimetry geometry, where the linearly-polarized light with the frequency $\omega$ and polarization angle $\theta$ propagating along out-of-plane $z$ axis is incident on FE SnP$_2$S$_6$ among $xy$ Cartesian plane. (b) $\pm$$P$ states of SnP$_2$S$_6$ with opposite FE polarizations are interconnected by $C_2$ rotation operation applied along [$\overline1$10] direction. (c) The simulated real parts of six independent SHG susceptibility coefficients for FE SnP$_2$S$_6$ bulk. Blue and red lines represent $\chi(\omega)$ for $\pm$$P$ states, respectively. Except for $\chi _{xyz}$ and $\chi _{yyy}$, other coefficients reverse their signs upon polarizations switching.
• Figure 4: (a) Illustration of polarization switching in FE SnP$_2$S$_6$ via rotation operation performed in real space (black) and reciprocal space (blue). (b) The simulated real parts of $\chi_{xxx}$ and $\chi_{yyy}$ coefficients among the reciprocal space for $\pm$$P$ states of FE SnP$_{2}$S$_{6}$. The inset indicates how SHG susceptibility coefficients transform upon polarization switching and associated $C_2$ rotation operation. (c) The simulated SHG polar plots for $\pm$$P$ states of FE SnP$_2$S$_6$, where red and blue lines represent SHG responses perpendicular and parallel to $E(\omega)$ of the incident linearly polarized light. At the characteristic frequency of $\hbar\omega = 0.94$ eV, the patterns of $I_\parallel$ and $I_\bot$ are nearly swapped between $\pm$$P$ states.
• Figure 5: (a) Schematic diagram and optical morphologies for ferroelectricity switching of SnP$_2$S$_6$ through performing 180$^\circ$ flipping along the diagonal $[\overline110]$ direction. Pink dot represents the laser spot. (b) The measured polarization angle dependent SHG spectrum (containing only the parallel component $I_\parallel$) of SnP$_2$S$_6$ crystal incident by 1064 nm laser. After performing 180$^\circ$ flipping, about 6$^\circ$ rotation of SHG polar direction for SnP$_2$S$_6$ is detected. (c) The simulated SHG polar plots ($I_\parallel$ component only) for $\pm$$P$ states of FE SnP$_2$S$_6$ bulk under the photon energy of $\hbar\omega = 0.74$ eV ($\approx$ 1/2 theoretical $E_g$), where the net rotation of SHG polar direction by 4.6$^\circ$ is predicted.