Anomalous polarization enhancement in a van der Waals ferroelectric material under pressure

CuInP2S6 with robust room-temperature ferroelectricity has recently attracted much attention due to the spatial instability of its Cu cations and the van der Waals (vdW) layered structure. Herein, we report a significant enhancement of its remanent polarization by more than 50% from 4.06 to 6.36 µC cm−2 under a small pressure between 0.26 to 1.40 GPa. Comprehensive analysis suggests that even though the hydrostatic pressure suppresses the crystal distortion, it initially forces Cu cations to largely occupy the interlayer sites, causing the spontaneous polarization to increase. Under intermediate pressure, the condensation of Cu cations to the ground state and the polarization increase due cell volume reduction compensate each other, resulting in a constant polarization. Under high pressure, the migration of Cu cations to the center of the S octahedron dominates the polarization decrease. These findings improve our understanding of this fascinating vdW ferroelectric material, and suggest new ways to improve its properties.

The stress-induced phase transitions and strain engineering become especially important in nanoparticles and ultrathin films of Cu-based layered chalcogenides, CuInP2(S,Se)6; these materials are uniaxial ferroics, whose value for advanced applications is due to a possibility of the ferrielectricity and antiferrielectricity downscaling to the limit of a single layer. Despite the significant fundamental and practical interest in bulk and nano-sized CuInP2(S,Se)6, the influence of stress and strains on its spontaneous polarization is very poorly studied from experimental perspective, while some theoretical background is available. Hence, the experimental part of the peer-reviewed manuscript, reporting about anomalous polarization enhancement in a vdW ferroelectric material under pressure is original, well-written and perfectly illustrated. I regard that it deserves publication in Nature Communications. However, I have a principal remark regarding possible theoretical interpretation of the revealed polarization enhancement. Authors should semi-quantitively compare the experimentally observed polarization enhancement with earlier theoretical predictions (see . From a theoretical viewpoint, the polarization enhancement occurs due to the strong, negative, and temperature-dependent nonlinear electrostriction coupling coefficients (namely Z_i33<0 and W_ij3<0), and the "inverted" signs of the linear electrostriction coupling coefficients (namely Q_33<0, Q_23>0, and Q_13>0) for CIPS. The hydrostatic pressure effect on the polarization enhancement is complex and unusual in comparison with many ferroelectrics where Q_33>0, Q_23<0, and Q_13<0.

Reviewer #3 (Remarks to the Author):
Yao et al. present novel results in the effect of hydrostatic pressure on the ferroelectricity of CuInP2S6 (CIPS) and its crystallographic structure arrangement under such conditions. The experimental results are of good quality and the conclusions of the study might help engineer electronic and ionic properties of CIPS and other vdW ferroelectrics for device applications. I would recommend the article for publication after minor changes/comments are added or explained: 1. How does the hydrostatic pressure affect the domain distribution in the material? PFM in liquid is not trivial to perform (if even possible) but maybe micro-Raman spectroscopy could give a hint. Even in-situ AFM topography images of the surface of the sample should help gathering information about that. This information would be interesting to answer the following 2 question: 1.1 Does the hydrostatic pressure switch the material into one of the polarization states (either up or down)? If so, maybe in the intermediate range of pressures (0.24-1.5GPa) where the enhancement of the polarization is found, polarization is being switched or Cu ion position is being moved from LP to HP polarization states. The nanoscale distribution of the domains in normal conditions and under pressure should give a hint. 1.2 Is the surface affected/damaged by the hydrostatic pressure? (like it happens in1 and others). Some surface characterization should be added or at least commented in the text for clarification.
2. Continuing with the importance of the nanoscale domain distribution for the overall measured response of the material, the pressure ranges studied in this work are accessible with AFM. Therefore, the polarization enhancement could be addressed by performing PFM measurements at different force setpoints, similarly to how the authors performed in 2. In that case, the authors attributed the switching to flexoelectric interaction due to the nonuniform pressure exerted by the AFM tip, generating a strain gradient instead of a homogeneous strain. How can we separate both distributions? Performing PFM with varying tip radius and setpoints should directly affect the generated strain gradient fields, therefore accessing the deconvoluted information between strain and strain gradient being the responsible of the enhanced/suppressed ferroelectric response. Such characterization should be added or at least commented in the text for clarification.

(Research Article, NCOMMS-23-08192A)
We thank the reviewers for their valuable comments. The following are our point-bypoint responses.
Responses to Reviewer #1's comments 1. Please explain why silicone oil is used in the experiment. Is this the standard apparatus for this kind of experiment?
Authors' reply: Thanks for this comment. In high-pressure experiments, pressuretransmitting mediums (PTM) are used to achieve hydrostatic pressure condition. The common PTMs include silicone oil, glycerol, 4:1 methanol-ethanol, and Daphne 7377. In this work, silicone oil does not react with our sample, and was chosen as the PTM.
2. What does the merging of peaks at 549 cm -1 and 556 cm -1 mean to the structure change?
Authors' reply: We appreciated the reviewer's comment. Looking closely at the spectra, one would notice that the two peaks do not simply merge together, but rather the 549 cm -1 peak shifts gradually to the right of the 556 cm -1 peak. The trend is similar to some of the other peaks, but because of its relatively low intensity and close proximity to the 556 cm -1 peak, we didn't choose this peak for further analysis. Note that both the 549 and 556 cm -1 peaks are attributed to P-S oscillations [1] .
3. Fig. 2b and 2c need to be revised. Both figures share the same color between the two peaks, making it hard to distinguish the trend of the two separated peaks.
Authors' reply: Thank you for your suggestion. We have updated it in the revised manuscript.
4. Please explain why peaks at 264 cm -1 and 104/116 cm -1 (I cannot tell due to the same color coding in Fig. 2b) have a different turning point in trend than the other peaks.
Authors' reply: Thanks for this comment. We have changed the colors in the revised manuscript to make them distinguishable. The 116 cm -1 peak is attributed to the inplane displacement of Cu + In + S and the out-of-plane S vibration and the 264 cm -1 peak is attributed to the in-plane S vibration. [2] These peaks are independent of the displacement of P atoms, while majority of the other peaks involve P in some way. In CIPS, the S frame is mainly supported by P-P dimers along the c-axis, which changes much more significantly under hydrostatic pressure than that of the a-b plane. We thus speculate that the peaks involve P would be more sensitive to pressure increase than those that do not, such as the 116 and 264 cm -1 peaks. However, further theoretical analysis would be needed to confirm this hypothesis.
To better understand the change in Raman spectra and structural evolution under pressure, we have established a one-to-one correlation between the Raman peaks and vibration modes in CIPS as shown in Table R1 following reference [2], taking into consideration the conclusions of reference [1].

Raman shift
Displacement patterns 72 cm -1 out-of-plane Cu (polar for ′ and antipolar for ′′ displacements in the adjacent layers) + out-of-plane S vibration 104 cm -1 rigid out-of-plane displacement of P-P dimers (in-phase phase in adjacent layers) + In displacements opposite to that of P-P dimers  Table R1 Raman peaks and vibration modes in CIPS [2] Page 6 of the main text is revised and Figure 2 redrawn accordingly, but the main conclusions remain the same. Table R1 is also added to the Supplementary Information for reference. 5. The authors should comment on the significantly increased volume deviation upon increasing pressure (especially when pressure approaches 1GPa) in fig.3a.

Authors' reply:
Thanks for this comment. The number of diffraction spots that can be collected decreases with pressure, as shown in Figure S7 in the supplementary material. With less diffraction spots for the refinement, there is the significantly increased error bar upon increasing pressure.
Authors' reply: Thank you for your suggestion. We have updated it in the revised manuscript.
7. Please comment on why the intensity of peaks at 264 cm -1 and 116 cm -1 decrease upon increasing pressure up to ~0.75 GPa in fig. 2b.

Authors' reply:
Thanks for this comment. The decrease of 264 cm -1 peak intensity has been reported before. For example, Vysochanskii et al have observed that the relative intensity of 264 cm -1 peak gradually decreases when temperature drops, as shown in Ref [1] figure 3. [1] Both peaks involve in-plane movement of S, which is strongly affected by the Cu ions. We suggest that, with decreasing temperature or increasing pressure, the dispersion of Cu cations gradually decreases, leading to a more stable S frame which is more resistant to in-plane distortion, thus the intensities both peaks drop.
8. The author indicates that the pressure-induced suppression of ferroelectricity is opposite to the usual behavior of other materials. However, the materials are different, and this method only seems effective to CIPS. Does this imply that the finding is exclusively for CIPS?
Authors' reply: Thanks for this comment. Indeed, the unusual enhancement of ferroelectricity in CIPS is directly related to its unique vdW structure. The strong effect of pressure on the c-axis lattice alters the interaction of cations (Cu) within one layer with the anions (S) in the next layer, changing the location of cations and the macroscopic polarization. However, with more and more vdW ferroelectric materials being discovered, we do expect that similar behavior may be observed in other vdW materials, e.g. sliding ferroelectrics. [3] Furthermore, it has been reported that the ferroelectricity of multiferroics CuCrO2 and TbMnO3 [4,5] enhances within a certain pressure range, in which case the mechanism was attributed to the pressure-induced magnetoelectric phase transition.
To describe the background more accurately, we added the following sentences on page 3 in the revised manuscript. "For example, the spontaneous polarizations of PbTiO3 and BaTiO3 at room temperature were totally suppressed under pressures of 10 GPa and 2 GPa, respectively. 17,18 Though it has been reported that the ferroelectricity of multiferroic CuCrO2 and TbMnO3 19,20 enhances within a certain pressure range, but they were attributed to pressure-induced magnetoelectric phase transitions. The enhancement of remanent polarization in vdW ferroelectric CIPS is another example worthy of further investigation." 9. But in 1e, the material has a smaller ferroelectricity in growing pressure. And eventually goes to almost zero ferroelectricity. This is saying there are ranges of pressure that could enhance and decrease the ferroelectricity. The pressure range of enhancing the ferroelectricity is quite small. This small enhancement does not indicate a significant improvement in performance.

Authors' reply:
We appreciated the reviewer's comment. It is the unusual behavior that is interesting here. In conventional ferroelectric materials with continuous threedimensional lattice, i.e., except type-II multiferroics where the polarization arises from certain magnetic order, hydrostatic pressure will suppress lattice distortion and the ferroelectricity. This remains to be true for CIPS under high pressure. However, the existence of vdW gaps changes the low pressure behavior completely. We believe that clarifying the mechanism behind offers valuable information for bettering understanding of the growing family of vdW ferroelectrics.
10. The Cu ion's migration is confusing to the reviewer. Why is the 0.26 GPa so special? At this point, the Cu ion is moving up below this point, while beyond this point, the Cu ion is moving downwards.
Authors' reply: Thanks for this comment. The 0.26 GPa is not so special. The pressure changes the lattice and the relative energy of Cu at different sites, resulting in the redistribution of Cu. For CIPS, due to its particular mechanical properties such as elastic modulus, it happens to reach the maximum polarization (metastable state) at 0.26 GPa. Perhaps with a different material such as CuInP2Se6, the maximum polarization may not be at 0.26 GPa.
At high pressure, the pressure dependence of polarization is similar to BaTiO3 and PbTiO3. [6,7] The widely used theory suggests that short-range repulsions increase more rapidly than long-range attractions as pressure increases, leading to the reduction of ferroelectricity. [8] The distance of Cu from the center of the S octahedron has been decreasing under pressure, so the Cu ion is moving downwards. Accordingly, we added the following discussion on page 9 in the revised manuscript. "To summarize, within the relatively low pressure range, the pressure mainly affects the interlayer distance of the material, reducing the relative energy of Cu interlayer sites and resulting in the enhancement of polarization. On the other hand, under higher pressures, the off-center displacement of Cu gradually decreases, similar to the behavior of Ti 4+ in PbTiO3 and BaTiO3 under pressure. 17,18 The short-range repulsions which prefer the undistorted paraelectric increase more rapidly than longrange attractions which favor ferroelectric distortions as pressure increases, leading to the suppression of ferroelectricity. 34 "

Responses to Reviewer #2
The stress-induced phase transitions and strain engineering become especially important in nanoparticles and ultrathin films of Cu-based layered chalcogenides, CuInP2(S,Se)6; these materials are uniaxial ferroics, whose value for advanced applications is due to a possibility of the ferrielectricity and antiferrielectricity downscaling to the limit of a single layer. Despite the significant fundamental and practical interest in bulk and nano-sized CuInP2(S,Se)6, the influence of stress and strains on its spontaneous polarization is very poorly studied from experimental perspective, while some theoretical background is available. Hence, the experimental part of the peer-reviewed manuscript, reporting about anomalous polarization enhancement in a vdW ferroelectric material under pressure is original, well-written and perfectly illustrated. I regard that it deserves publication in Nature Communications. . From a theoretical viewpoint, the polarization enhancement occurs due to the strong, negative, and temperature-dependent nonlinear electrostriction coupling coefficients (namely Z_i33<0 and W_ij3<0), and the "inverted" signs of the linear electrostriction coupling coefficients (namely Q_33<0, Q_23>0, and Q_13>0) for CIPS. The hydrostatic pressure effect on the polarization enhancement is complex and unusual in comparison with many ferroelectrics where Q_33>0, Q_23<0, and Q_13<0.