Stacking-tunable multiferroic states in bilayer ScI2

TL;DR

Bilayer ScI2 demonstrates stacking-tunable multiferroicity, where interlayer sliding and rotation switch magnetic coupling between AFM and FM, induce sliding ferroelectricity in AB/BA configurations, and enable valley polarization through SOC when inversion symmetry is broken. First-principles DFT and Heisenberg-model analysis reveal stacking-dependent interlayer exchange: AA stabilizes AFM, AB/BA stabilize FM, with other stackings showing similar switching tendencies; AB/BA stacking yields a measurable out-of-plane polarization of $P = 0.18\times10^{-12}$ C/m. Valley polarization is spin-resolved and valley-contrasting under SOC, with splittings up to about $101$ meV in AB/BA and $99$–$100$ meV in AB*/BA*, while AA* shows no polarization. This work establishes a single-material platform where magnetism, ferroelectricity, and valleytronics can be coherently controlled via stacking, enabling reconfigurable spintronic and valleytronic devices and potentially extending to other 1H vdW bilayers with partially filled $d$ orbitals.

Abstract

Two-dimensional(2D) multiferroic materials hold significant promise for advancing the miniaturization and integration of nanodevices. In this study, we demonstrate that 2D bilayer ScI2, which exhibits ferromagnetic(FM) ordering within each layer, enables the tuning of interlayer magnetic coupling, ferroelectricity, and valley polarization through interlayer sliding and rotation. Our first-principles calculations show that the AA stacking configuration induces antiferromagnetic (AFM) interlayer coupling, while a 180 rotation of one layer (resulting in the antialigned AA stacking) leads to FM interlayer coupling. Moreover, the interlayer magnetic coupling can be switched between AFM and FM by translating the stacking configuration: FM in the aligned AB and BA configurations, and AFM in the antialigned AB and BA configurations. This switching behavior is driven by variations in superexchange interactions due to orbital hopping between layers. Notably, the aligned stacking exhibits ferroelectricity upon sliding, which is induced by interlayer orbital hybridization and the resulting asymmetric charge redistribution, with maximal ferroelectric behavior occurring at the AB and BA stacking configurations. Additionally, for the AB and BA stackings, spontaneous valley polarization emerges from the manipulation of the spin orientation toward the out-of-plane direction. This valley polarization arises due to inversion symmetry breaking, either through ferroelectricity (in the AB and BA stackings) or AFM interlayer coupling , in combination with spin-orbit coupling. These results highlight the intricate interplay between magnetism, ferroelectricity, and valley polarization in bilayer ScI2, with each property being tunable via stacking configuration.

Figures (7)

• Figure 1: Optimized structures of (a) monolayer and (b) bilayer ScI$_2$. For the bilayer ScI$_2$, six stacking configurations are displayed: three aligned stacking configurations (AA, AB, and BA) and three antialigned stacking configurations (AA$^{*}$, AB$^{*}$, and BA$^{*}$). In (a), the lattice parameters $a$ and $b$ represent the primitive unit cell, along with its corresponding Brillouin zone. In (b), $\mathbf{t}_1 = \left( -\frac{1}{3}, -\frac{2}{3} \right)$ and $\mathbf{t}_2 = \left( \frac{1}{3}, \frac{2}{3} \right)$ denote fractional in-plane translations of the upper layer along the $y$-axis.
• Figure 2: Calculated (a) phonon dispersion, (b) total energy variation from ab initio molecular dynamics simulations, and (c) spin-polarized band structure of monolayer ScI$_2$. The inset in (b) shows the structure at the end of the simulation. The PDOS for the Sc 3$d_{z^2}$ and I 5$p$ orbitals is also provided in (c), while that for other orbitals is shown in Supplemental Fig. S1 SM.
• Figure 3: Calculated energy profiles of the interlayer FM and AFM coupling states for the (a) aligned and (b) antialigned stacking configurations as a function of interlayer sliding. The zero energy in (a) and (b) is referenced to the AA and AA$^{*}$ stacking configurations, respectively. The color scale represents the energy difference between the interlayer FM and AFM coupling states, where a positive (negative) value indicates a preference for the FM (AFM) state, with the unit of meV/f.u.
• Figure 4: The NN and NNN Sc atoms for the (a) AA and (b) AB stacking configurations. The solid (dashed) lines represent the connections between NN (NNN) Sc atoms. The schematic diagrams of the orbitals participating in the supersuperexchange mechanism for the AA and AB stacking configurations are displayed in (c) and (d), respectively.
• Figure 5: (a) Calculated planar averages of electrostatic potentials along the $z$ axis for the aligned and antialigned stacking configurations. The charge density differences ${\Delta}{\rho}$ and their planar averages along the $z$ axis for the aligned and antialigned stacking configurations are displayed in (b). The isosurface value in ${\Delta}{\rho}$ is set to 0.6${\times}$10$^{-4}$$e$/Å$^3$.