Room-temperature ferroelectricity in CuInP2S6 ultrathin flakes

Two-dimensional (2D) materials have emerged as promising candidates for various optoelectronic applications based on their diverse electronic properties, ranging from insulating to superconducting. However, cooperative phenomena such as ferroelectricity in the 2D limit have not been well explored. Here, we report room-temperature ferroelectricity in 2D CuInP2S6 (CIPS) with a transition temperature of ∼320 K. Switchable polarization is observed in thin CIPS of ∼4 nm. To demonstrate the potential of this 2D ferroelectric material, we prepare a van der Waals (vdW) ferroelectric diode formed by CIPS/Si heterostructure, which shows good memory behaviour with on/off ratio of ∼100. The addition of ferroelectricity to the 2D family opens up possibilities for numerous novel applications, including sensors, actuators, non-volatile memory devices, and various vdW heterostructures based on 2D ferroelectricity.

). Because the high ionic conductivity of the CIPS has a sizable contribution to its dielectric response at room temperature 2 , this asymmetric behavior could originate from the diode-like transport characteristic due to the asymmetric top and bottom electrical contacts (highly-doped Si versus Au). Moreover, the polarization switching is correlated with more than one bump in each branch of the hysteresis loops, suggesting a multistep switching process, which, again, is possibly related to the competition between the stable ferrielectric order and the metastable ferroelectric order. Although the experimental observation suggests a ferrielectric ground state 1 , a ferroelectric one may be stabilized by the cation disorders in the crystal 3,4 .

Supplementary Note 2: Vector PFM study of the CIPS flakes to determine the polarization direction.
To verify that the polarization of CIPS is completely perpendicular to the layer plane with no inplane component, concerted vertical (out-of-plane, OP) and lateral (in-plane, IP) PFM are carried out under off-resonance mode, which is beneficial for quantitative piezoresponse evaluation. The results are summarized in Supplementary Fig. 5 and 6. When the azimuth angle between AFM tip and the sample is 0° (starting reference), we observed clear piezoresponse signal and domain pattern in the OP-PFM amplitude and phase images. In contrast, IP-PFM images showed noiselevel amplitude signal, and no distinguishable domain pattern could be resolved in the phase channel. Because the in-plane piezoresponse is proportional to the in-plane polarization component, perpendicular to the cantilever of the AFM tip, we rotated the sample for 90° to further rule out the possibility that the in-plane polarization vector happens to lie parallel to the cantilever. The OP-PFM images were well reproduced as they were not affected by the in-plane orientation of the sample. The slightly reduced amplitude signal was probably attributed to the tip wear-out. Again, no detectable signal was found in the IP-PFM images.
Finally, to rule out residual charging effect on the PFM, we have written a box-in-box pattern in the center of the scanned area and recorded down the resulting PFM images (Supplementary Fig.   5c, f, i, l). Once again, no piezoresponse signal can be detected in the IP-PFM images. These findings clearly support that the polarization vector is perpendicular to the layer plane/substrate surface.

Supplementary Note 3: DFT calculation of the ferroelectricity in bilayer CIPS.
The supercell of 40 atoms for bilayer of CIPS was used in this calculation. The structure was first fully relaxed until the force on each atom is below 0.001 Ry/Angstrom. The relaxed in-plane lattice constants were found to be 6.096 and 10.564 Angstroms, which are consistent with other reported values 5,6 . The relaxed structure, based on which the polarization is calculated, is shown in Supplementary Fig. 7. In our calculations, we find that the Cu atom is shifted 1.57 Angstrom above the middle layer of S-S layer and the In atom is shifted 0.26 Angstrom below the middle layer of S-S. This is consistent with the prior works which indicate a ferroelectric phase 1 . It is found that the phase transition between paraelectric and ferroelectric is accompanied by the hopping of Cu (upper/down, center and interlayer as clearly described by others 1,6,7 ). With the relaxed supercell in hand, we first performed a self-consistent calculation and then an estimation of the polarization. The polarization is determined in the out-of-plane (z) direction to be 0.57 C/m 2 . This value is much larger than the value measured by experiments, however, qualitatively it is clear that both computation and experiments show a clear ferroelectric behavior. There are several possible reasons for the discrepancy in the quantitative value of the spontaneous polarization. We approximate the original system by CuInP 2 S 6 other than the actual chemical constitute Cu 0.975 InP 2 S 6 6 , because it is computationally (nearly) impossibly to model the exact material system. Since the polarization is mainly contributed by the displaced Cu and In ions, the larger polarization might be due to the high density of Cu used in the calculations. The other factor is the temperature effect since it was found that decrease of temperature may enhance the polarity of Cu and In 1 . The experiment is done at room temperature but the calculation is done at 0 K.

Supplementary Note 4: Ferroelectric switching of CIPS flakes with different thicknesses.
Supplementary Fig. 8 to 12 demonstrate the detailed evolutions of topography and correlated PFM images of CIPS flakes with thickness ranging from 4 nm to 400 nm before and after polarization switching using AFM tip on heavily-doped Si substrate. Special care was taken to ensure the applied bias was just above the coercive voltage, because higher bias would lead to the irreversible modification of the CIPS surface due to its high ionic conductivity 8 . Besides, compared with conventional oxide ferroelectrics, the written patterns in CIPS were usually worse defined. The switched domains can extend far beyond the area as defined by the AFM tip, especially in thicker films. This finding implies high domain wall energy in CIPS crystal, and similar behavior has been reported in organic molecular ferroelectric 9 . Whether it is a common characteristic in weakly-bonded ferroelectrics requires further investigations.
The ferroelectric retention behavior of the CIPS flakes was illustrated in Supplementary Fig. 13.
The switched pattern was still discernible after two-month time in the 30-nm-thick CIPS flake.
Surprisingly, the domain pattern in the unswitched area was greatly changed. Similar behavior was also observed in other unswitched CIPS flakes, which could be due to the internal field at the CIPS/Si interface. This magnitude of the piezoelectric response was further confirmed by laser scanning vibrometer 13 , suggesting negligible electrostatic contribution thanks to the large stiffness of the AFM tip.

Supplementary
The quantitative measurements of the switching hysteresis loops showed similar behavior as those presented in Fig. 3, with larger piezoresponse observed in thicker flakes ( Supplementary   Fig. 15). The effective longitudinal piezoelectric coefficient d 33 of a 200-nm-thick CIPS flake was calculated to be around 12 pm/V, about half the value of a single-domain BiFeO 3 (BFO) thin film with comparable thickness (Supplementary Fig. 15). Given that the dielectric permittivities of CIPS and BFO are comparable and the spontaneous polarization of BFO is at least one order of magnitude higher, the electrostrictive coefficient Q 33 of CIPS should be much larger than BFO since d 33 ~ Q 33 Pε r , where P, polarization; ε r , dielectric constant 14 . This is understandable considering the much higher elastic compliance of vdW crystals perpendicular to the layer direction compared to the in-plane one 14 . Interestingly, the phase loops of CIPS and BFO are 180° out-of-phase, meaning the piezoelectric coefficient of CIPS is negative (Supplementary Fig. 16).
Negative piezoelectricity has been observed in hydrogen-bonded organic molecular ferroelectrics and polymer ferroelectrics such as PVDF, the common feature of which is the loose packing structure 9,16 . CIPS probably falls into the same category due to the compressibility of the vdW gap.

Supplementary Note 6: Second-harmonic generation characterization of CIPS
Optical methods such as second-harmonic generation (SHG) have proven to be extremely sensitive to changes in the crystal structure symmetry 17 , which allows for detection of the ferrielectric to paraelectric transition as shown in Fig. 4b. Here we present a symmetry analysis showing the correlation between the ferrielectric phase and non-zero second-order susceptibility tensor components. We first investigate the excitation power dependence of the SHG in CIPS.
The SHG intensity scales quadratically with excitation power as expected ( Supplementary Fig.   17a), and indicates that the ultrathin samples are undamaged under the 5-10 mW of average power used in Fig. 4. In the paraelectric phase, CIPS is in the centrosymmetric crystal class 2/m.
When the temperature decreases below T c (~315 K), the Cu and In sublattices displace antiparallel to each other along the z-axis, breaking the two-fold rotational symmetry about the y axis. Thus, the crystal class becomes m, which is noncentrosymmetric. Since our excitation and collection is at normal incidence (along z axis of the crystal), the allowed second-order susceptibility tensor components simplify to , , . With these four components, we achieve a good fit to the experimental data in Fig. 4a. To gain a better intuition for the origin of