Sliding multiferroicity in hexagonal stacked CrI3

Abstract

Developing new multiferroics at the two-dimensional (2D) limit with energy-efficient magnetoelectric coupling can inform the interplay physics of novel orders and advance on-chip high-performance computing applications. Here we apply stacking order engineering to create a new type of 2D multiferroics, namely sliding multiferroics, based on polar hexagonal stacked (H-stacked) CrI3. This new stacking order removes structural inversion symmetry and gives rise to room temperature sliding ferroelectricity, as confirmed by Raman spectroscopy, second harmonic generation spectroscopy and electrical transport measurements. Building upon the gate-dependent reflective magnetic circular dichroism, first-principles calculations, and modeling, sliding ferroelectricity is shown to interplay with an emergent interfacial ferromagnetism via interlayer spin-polarized charge transfer. This coupling mechanism results in non-volatile magnetic switching by as low as 0.4V across the H-stacked CrI3. Our demonstration introduces polar stacking order engineering of 2D magnets as a general approach to create non-volatile 2D multiferroics with efficient magnetoelectric coupling, paving the way for low-power electronics and spintronics at the atomically thin limit.

Figures (13)

• Figure 1: Polar stacking order engineering of CrI3. a, Side view of the four-layer (4L) natural monoclinic CrI3 with an inversion center ($\bar{1}$) located between the middle layers. Blue balls represent Cr atoms while purple balls represent I atoms. b, Side view of the crystal structure of a 2L+2L hexagonal stacked CrI3 (H-CrI3). In this stacking, the top two layers have been twisted by $180^\circ$, breaking $\mathcal{P}$ and allowing for a vertical electric dipole $P_z$ pointing upward (left) or downward (right panel). The two energy-degenerate configurations are switchable by an interlayer sliding displacement between the top and bottom bilayers. c, Optical image of a typical 2L+2L H-CrI3 sample, where the two bilayer flakes are outlined in purple and blue. The inset shows the original flake for "tear-and-stack," where the bilayer is outlined in purple and the dashed line marks the approximate tearing location. d, Ultralow-frequency Raman spectrum of 2L+2L H-CrI3 (blue) compared to a natural monoclinic 2L sample (purple) at 295 K. The two emergent interlayer phonon modes with strong Raman activity are attributed to the symmetry reduction in the polar H-CrI3.
• Figure 2: Stacking order asymmetry and sliding ferroelectricity in hexagonal-stacked CrI3. a, Temperature dependence of the second harmonic generation (SHG) intensity (in log scale) excited by linear polarized light for 2L+2L H-CrI3 and 2L natural monoclinic CrI3 samples. Both samples are paramagnetic above $T_N\sim$45 K (light blue shaded temperature regime) and a negligible SHG is found in the natural monoclinic CrI3 flake due to its centrosymmetric crystal structure. In contrast, the H-CrI3 sample shows a much stronger SHG that persists up to room temperature, resulting from its polar stacking order. Below $T_N\sim$45 K (light yellow shaded regime), the long-range spin order in both samples breaks $\mathcal{P}$ and dominates the SHG contribution. b,c, Polarization-resolved SHG intensity as a function of the incident polarization angle below (b, at 2 K) and above (c, at 80 K) the magnetic transition temperature for the same 2L+2L H-CrI3 and 2L natural monoclinic CrI3 samples in (a). The distinct SHG patterns observed for H-CrI3 reflect a different space group arising from its polar stacking order (see Supplementary Note 1 for more details). Data for 2L+2L, 2L, and the substrate are in red, black and grey, respectively. Solid lines in subplots (b) and (c) are SHG fits from the appropriate (magnetic or nonmagnetic) point group. d, Schematic of a device in which the resistance of the top few-layer graphene senses the local electric field change induced by the out-of-plane dipole switching in H-CrI3. e, Resistance of the top few-layer graphene ($R_{Gr}$) as the vertical electric field ($E=V_b/d$) is swept up and down in a loop for a 2L+2L stacked device at 295 K, showing hysteretic behavior indicative of sliding ferroelectricity.
• Figure 3: Observation of interfacial ferromagnetism in hexagonal-stacked CrI3.a,b, Reflective magnetic circular dichroism (RMCD) as a function of the applied out-of-plane $B$ for (a) natural monoclinic 4L CrI3 and (b) 2L+2L H-CrI3. c, Energy differences from first-pinciples calculations as the middle interface in 1L+1L (left) and 2L+2L H-CrI3 (right) are set to have AFM or FM order. $\Delta E$ denotes the change in energy relative to the AFM order in the middle interface. An FM order between the two layers in the middle of the polar stack is energetically preferred. d,e, RMCD as a function of out-of-plane $B$ for (d) 6L and (e) 3L+3L CrI3. Insets in (a,b,d,e) show the simulated magnetization evolution based on an Ising model ( Supplementary Note 3) with emergent interfacial ferromagnetism, which agrees with the experimental observations. Orange and green arrows in subplots (a-e) denote the spin alignment in each layer. f, RMCD spatial mapping of a 3L+3L H-CrI3 sample, showing uniform interfacial ferromagnetism at $B=0$ T. The two trilayer flakes are outlined in red and black dashed lines.
• Figure 4: Efficient non-volatile magnetoelectric coupling in hexagonal-stacked CrI3 sliding multiferroics.a, Schematics of a dual-gate device based on H-CrI3, which can independently control the external electron doping ($n_e$) and out-of-plane electric field ($E$) experienced by the H-CrI3. b,$n_e$-assisted switching of the magnetic state of a 3L+3L H-CrI3 device at $B=0.30$ T, just below the coercive field. c, Out-of-plane electric field $E$-assisted switching of a 3L+2L H-CrI3 at $B=0.34$ T, just below the coercive field. d, Pure out-of-plane electric field control of magnetism at $B=0$ T for a 2L+2L H-CrI3. The non-volatile RMCD hysteresis suggests a nontrivial ME coupling in H-CrI3. The left vertical axis shows the raw RMCD change relative to the RMCD of state $A$, whereas the right vertical axis shows the fractional change relative to state $A$. The top horizontal axis shows the estimated voltage across the CrI3. e, Top graphene resistance ($R_{Gr}$) as a function of $E$ in the same device as in subplot (d). The $R_{Gr}$ hysteresis is indicative of sliding ferroelectricity. Insets highlight where the forward and backward sweeps merge, indicating a hysteresis window similar to that of the magnetization in d. Measurements in subplots (e) and (d) proceeded at $B=0$ T after ramping the magnetic field to $-2.2$ T and back to 0 T. f, Illustration of the proposed ME coupling mechanism in 2L+2L H-CrI3. The non-volatile magnetism change is attributed to the interlayer spin-polarized charge transfer via the $E$-driven sliding ferroelectric transition in H-CrI3.
• Figure S1: Identifying the layer number of CrI3 flakes.a, Optical contrast vs. number of layers, based on several flakes of different thicknesses. The contrast is defined as $C = \frac{I_s-I_f}{I_s+I_f}$, where $I_s$ and $I_f$ are the intensities of the substrate and flake, respectively. b, Optical image of a flake, with the line cut showing a $8.2\%$ contrast, consistent with a bilayer. c, Atomic force microscopy image of a stack made from the flake in b. The inset shows a height of 1.4 nm, consistent with that of a bilayer (a layer has a thickness of 0.7 nm).