Large-scale Domain Engineering in Two-Dimensional Ferroelectric CuInP2S6 via Giant Flexoelectric Effect

: Room-temperature ferroelectricity in two-dimensional materials offer a potential route for developing atomic-scale functional devices beyond Moore’s law. However, as a key for the technology implementations of ferroelectrics in electronics, the controllable generation of uniform domains remains challenging in two-dimensional ferroelectrics at current stage because domain engineering through an external electric field at 2D limit inevitably leads to large leakage current and material break-down. Here, we demonstrate a voltage-free method, the flexoelectric effect, to artificially generate large-scale stripe domains in two-dimensional ferroelectric CuInP 2 S 6 with single domain lateral size at the scale of several hundred microns. With giant strain gradients (~10 6 m -1 ) at nanoscale, we mechanically switch the out-of-plane polarization in ultrathin CuInP 2 S 6 . The flexoelectric control of ferroelectric polarization is understood with a distorted Landau-Ginzburg-Devonshire double well model as evidenced by the shifted ferroelectric hysteresis loops and the first-principle calculations. Through substrate mechanical strain engineering, the stripe domain density is controllable. Our results not only highlight the potential of developing van der Waals ferroelectrics-based memories but also offer the opportunity to study ferroelectric domain physics in two-dimensional materials.


Introduction
Atomically thin van der Waals (vdW) crystals provide the opportunity to explore ferroelectricity at two-dimensional (2D) limit which is a long-sought goal in conventional bulk ferroelectrics due to the constrain of critical size effect 1 . Experimentally, a series of 2D ferroelectrics with intrinsic either in-plane or out-of-plane electric polarization have been verified, such as the SnTe family 2-4 , CuInP2S6 5-10 , α-In2Se3 11-16 , Bi2O2Se 17,18 , and d1T-MoTe2 19 . Besides the atomic thickness, vdW material also offers the layer degree of freedom that leads to the emergence of sliding ferroelectricity induced by interlayer translation [20][21][22] . The rich 2D ferroelectricity found in vdW crystals therefore provide the potential to revolutionize future electronic applications with exotic functions [23][24][25][26] .
For the integration of 2D ferroelectrics in electronics, how to effectively control the polarization state or ferroelectric domains is the central concern because it fundamentally determines the technical practicability. In bulk ferroelectric perovskite oxides, it can be simply realized by applying an external voltage 27,28 . For example, reliable domain structure can be artificially created with the aid of a conductive tip in a scanning probe microscope (SPM) [29][30][31] . Nevertheless, for vdW ferroelectrics with atomic thickness, the out-of-plane switching electric field at 2D limit inevitably results in large leakage current and even material breakdown. As a result, the polarization control and especially the large-scale domain generation is relatively challenging in 2D ferroelectrics. Therefore, an alternative method which is free of external voltage is highly in demand for domain manipulation in vdW ferroelectrics.
Here, to address the above issue, we utilize the flexoelectric effect, a voltage-free mechanical method, to switch the electric polarization and generate artificial domains at large-scale in ultrathin vdW ferroelectrics. The flexoelectric effect (or flexoelectricity) refers to the formation of net electric polarization inside a crystal when an inhomogeneous strain is applied 32,33 . This effect is universal for all materials with arbitrary lattice symmetry and thus has been utilized to generate many extraordinary phenomena and functionalities, such as enhanced piezoelectricity [34][35][36][37] , the nanoscale polar vortices 38 , and anomalous photovoltaics [39][40][41] . To utilize flexoelectricity in polarization reorientation, the key is the generation of giant strain gradients 42,43 . In conventional oxides ferroelectrics, due to the bulk nature with rigid covalence/ionic bond, mechanical domain control can only be realized under the involvement of a SPM tip via nanoscale imprinting or through atomicscale misfit lattice strain [44][45][46] . For 2D vdW ferroelectrics with genuine mechanical flexibility, the flexoelectric modulating of polarization is relatively easy 47,48 , offering the feasibility of further voltage-free domain engineering at large scale.
In this work, for the first time, we demonstrate the mechanical formation of artificial strip domains in ultrathin CuInP2S6 (CIPS). The required strain gradients (~10 6 m -1 ) at nanoscale in CIPS was introduced from periodic pre-strained substrate. With in-situ piezoresponse force microscopy (PFM) measurement, we observed bidirectional modulation of the polarization in rippled CIPS and large ferroelectric domains with single domain lateral size at the order of several hundred microns. The flexoelectric control of polarization in CIPS is understood with a distorted Landau-Ginzburg-Devonshire (LGD) double well model, which is evidenced by the shifted ferroelectric hysteresis loops and the first-principle calculations. Through substrate mechanical strain engineering, the stripe domain density is controllable. Our results not only highlight the potential of developing vdW ferroelectrics based high-density memories but also offer the opportunity to study ferroelectric domain physics in 2D electronic systems.

Demonstration of the flexoelectric modulation in 2D CIPS.
To begin with, we start from the lattice structure of CIPS. As shown in Fig. 1a, Cu, In, and P-P pair atoms are bound in a framework which is formed by S atoms through covalent bonds. In each single layer, the atomic position deviation of Cu ions breaks the lattice inversion symmetry, resulting in explicitly OOP ferroelectricity. The two thermodynamically-equivalent polarized states in ferroelectrics can be described by the LGD double well model (see Fig. 1a). When reversing the polarization, the degeneracy of the ground states should be lifted off via external stimulus such as electric field or inhomogeneous strain (i.e. strain gradients) that lowers the switching energy barrier between the two energy minima. The latter, known as the flexoelectricity effect 32,33 , is with the benefit of voltage-free and large-scale uniformity for 2D vdW ferroelectrics with atomic thickness and ultrahigh flexibility. Therefore, we apply this method to ultrathin CIPS as an ideal platform in this study.
We first attest the ferroelectricity of CIPS nanoflakes by employing the PFM. CIPS thin flakes were mechanically exfoliated from bulk and were transferred onto the Au/SiO2 substrate (details can be found in Methods). The single crystal nature of the samples studied here was confirmed by Raman spectroscopy (see Fig. S1), where featured phonon modes were observed. The room-temperature ferroelectricity in CIPS can be evidenced from two aspects. As shown in Fig. 1b, typical single/butterfly-like ferroelectric hysteresis loop in the PFM phase/amplitude spectra were measured from a 20 nm thick CIPS sample. We estimate the coercive field for ultrathin CIPS to be around 3.5×10 5 V/cm. This value is consistent with the results in previous studies 6 S2c). The scattered domains are due to the relatively low ferroelectric transition temperature (Tc) of CIPS at 320 K, which is close to room temperature. Therefore, under ambient condition, strong thermal fluctuation will hinder the formation of large size domains in CIPS. We also used the DC electric poling via PFM to check the quality of artificial domains. As shown in Fig. S3, a box-in-box pattern has been poled with ±7 VDC tip bias. However, consistent with others report of electric poling CIPS, 6, 7, 10 electric field writing does not guarantee effective switch of all the polarizations as indicated by the poor quality of artificially poled domains.
The key to flexoelectric control of the electric polarization in ferroelectrics is to apply large enough strain gradients, which scale inversely with the dimensionality and the size of materials. Benefited from the flexural out-of-plane bending mode of ultrathin 2D materials, the giant strain gradients can be introduced in regions with high curvature. Therefore, corrugating the 2D CIPS at nanoscale is a good scenario. As summarized in  Fig. 3b and Fig. 3c, respectively. It must be emphasized here, relative to the continuously changing topography, the two plateaus of the phase profile and the rapid switching behavior implies that the phase is not disturbed by crosstalk of surface topography. Since the flexoelectric modulation relies on substrate strain transfer, it is necessary to check the adhesion between the CIPS and the PDMS substrate. Therefore, we extracted the line profiles of height along (marked by red line in Fig. 3a) and perpendicular to (marked by black line in Fig. 3a) the rippled structure. As shown in Fig. 3d, the rippled structure has a near-symmetric double-arc geometry of upward and downward bending. In the region with CIPS samples, there is an offset change in height. By comparing the offset with the CIPS sample thickness, we found that they are in high consistence. This result demonstrates that the CIPS samples have good adhesion to the PDMS substrate, which guarantees the transfer of the strain.  (1), the strain gradients is inversely proportional to , which can be calculated by the Pythagorean theorem as where ℎ and are the half of the wrinkle depth and the half of the periodicity. From the height profile in Fig. 3d, the ℎ and are found to be 50 nm and 600 nm, respectively. In this case, R is calculated to be 925 nm, and is as large as 1.
where 0 is the permittivity of free space and is relative dielectric permittivity, respectively, is the polarization induced by flexoelectricity, and is the flexoelectric coefficient. According to Tagantsev's phenomenological studies of the flexoelectric effect in crystalline materials, can be approximately expressed as 32,33 ~, where is the dielectric susceptibility ( = − 1 ≈ ) , and is the lattice constant.
For CIPS, the is 40 and is 6×10 -10 m. We have the flexoelectric coefficient to be 10.8 nC/m. Therefore, the flexoelectric field in the rippled structure is around 3× 10 5 V/cm. The strength of the flexoelectric field is comparable to the coercive field of CIPS nanoflakes extracted from the hysteresis loops measurement (~3.5×10 5 V/cm) and in previous report. 6 It further proves the validity of flexoelectric modulation on the electric polarizations of CIPS in this study. Furthermore, it should be pointed out that the flexoelectric coefficients of ferroelectric materials is much larger near the Curie temperature Tc. 52 The Tc of CIPS is 320 K which is relatively low and close to the room temperature. 8 Thus, the flexoelectric coefficients and the flexoelectric field in our bending geometry under ambient conditions may be much larger than we estimated.

Modeling of the flexoelectric effect in 2D CIPS.
The demonstrated geometry-induced flexoelectric effect in 2D CIPS can be understood through the distorted LGD double-well potential model. As a phenomenological theory, it is often employed to qualitatively explain the flexoelectric effect in ferroelectrics. Here, in this work, the potential energy profiles (PEP) are quantificationally obtained for CIPS system based on first-principle calculations as shown in Fig. 4a. The details of calculation methods and models are given in Supplementary note1. From the calculations, for both the flat and bended CIPSs, the migration barriers of Cu from one surface to the other surface are calculated (see Fig. 4e and Fig. S10). It is found that, the PEP of the flat CIPS has a symmetric double well for the migration of Cu (see Fig. S8); and the PEP of the bended CIPS also has a double-well structure, but is asymmetric (see Fig. 4a). Obviously, it is the strain gradients that break the symmetry of potential energy surface. These calculated results are consistent with the phenomenological theory. It is worth noting that, in bended CIPS the migration barrier of Cu from the contraction surface to stretched surface is much smaller than that between upper and lower surfaces in flat CIPS. The former has only a value of 10 meV, which means that the substrate geometry-induced flexoelectric effect can be observed even at very low temperature.
To verify the distorted LGD double-well potential model, we further investigate the ferroelectric switching behavior of rippled CIPS nanoflakes via single electric poling. The bulk CIPS crystals used in this study were synthesized by using chemical vapor transport method 55 .The large-scale thin CIPS flakes was prepared by gold-assisted peeling method 56 and was post transferred to the rippled PDMS substrate by using thermal release tape 57 .
Raman spectroscopy characterization. Raman spectrum was conducted on a Horiba micro-Raman system (LabRAM HR Evolution) with a 100x objective lens (NA = 0.9) to verify the lattice structure of CIPS. The excitation wavelength was 532 nm with on-sample power at 150 μW. As shown in Fig. S1, the characteristic Raman modes of single crystal CIPS were observed to be at 275, 325, and 384 cm -1 , respectively, which confirm the ferroelectric phase and are consistent with previous studies 6 .