Precise structure and polarization determination of Hf_0.5Zr_0.5O_2 with electron ptychography

Domain: neuroscience
Published: 2026-02-14
Editorial outcome: major_revision

Abstract
Hf0.5Zr0.5O2 emerges as a promising candidate for next-generation ferroelectric memories and transistors. However, the intrinsic nature of its ferroelectricity remains a subject of debate, primarily stemming from challenges in the precise characterization of nanoscale polycrystallinity and multiphase coexistence. Here, we investigate substrate-free Hf0.5Zr0.5O2 films using multislice electron ptychography, achieving a resolution of 25 picometers with capabilities for oxygen imaging, depth resolution, and vacancy quantification. Precise measurements reveal that the polarization displacement in ferroelectric phase is ∼56 ± 6 picometers (corresponding to a polarization ∼34 ± 4 μC/cm2). We further identify significant polarization suppression near grain boundaries, while there is negligible change in the 180° neutral domain walls. Furthermore, we demonstrate the existence of the 180° head-to-head charged domain wall in Hf0.5Zr0.5O2, which is confined within a single unit cell layer. At such a charged domain wall, the atomic displacement is reduced to ∼4 picometers, with oxygen vacancies accumulating up to 20%. Notably, the polar layers neighboring the 180º head-to-head charged domain wall remain unchanged. The precise determination of these structural features with ultra-high spatial resolution offers critical information for optimizing and designing new hafnium-based ferroelectric devices.

Introduction
Hf0.5Zr0.5O2 (HZO) has gained widespread attention due to its robust ferroelectricity at room temperature and excellent compatibility with complementary metal-oxide-semiconductor (CMOS) technology1–3. As a continuous solid solution of HfO2 and ZrO2, HZO benefits from Zr-induced stabilization of the ferroelectricity and exhibits the highest remanent polarization in the Hf1-xZrxO2 series4–8. This material is also regarded as a promising candidate for the next generation of ferroelectric random-access memories (FeRAMs) and ferroelectric field-effect transistors (FeFETs)7,9,10. For example, its switchable ferroelectricity in 1 nm-thick films (surpassing traditional perovskites) for high-density FeRAMs and negative capacitance for low-power FeFETs have been demonstrated1,5,7,11. To further optimize core applications like FeRAMs (enhancing storage density and switching speed) and FeFETs (improving power efficiency and operation stability), it is essential to seek and investigate novel polarization structures at the nanoscale in HZO, such as 180° charged domain walls (CDWs)12–14. These 180° CDWs enable the opposite polarization (head-to-head or tail-to-tail) at the unit cell scale, where charge accumulation at the walls stabilizes sharp domain boundaries14,15. Such charge-mediated stabilization significantly lowers the switching barrier, thereby offering a solid physical basis for realizing high-density and low-power ferroelectric devices14–17. However, although theoretical predictions suggest that these 180° CDWs can exist in hafnium-based oxide, experimental observations are still lacking14,16,17.

Besides, the origin of HZO’s ferroelectricity itself remains a topic of ongoing discussion18–22. The mainstream view is that the ferroelectricity in hafnium oxide films arises from the ferroelectric orthorhombic phase (OIII phase, space group Pca21) supported by experimental evidence3,21,23–25, but other mechanisms (e.g., polar rhombohedral phase) are also proposed2,22,26–29. Therefore, accurately analyzing the intrinsic atomic structures of HZO, e.g., oxygen configurations and domain walls (DWs), is crucial for understanding the nature of ferroelectricity. However, such analysis is typically challenging due to its substrate effects and polycrystalline nature16,30–32. On the one hand, the substrate effects can lead to lattice clamping29,33 and interfacial charge screening2,34 in the hafnium-based oxide films, which hinder the detection of intrinsic ferroelectric nature. They can also introduce structural artifacts affectting the accurate atomic-scale structural analysis. Recent advances in freestanding membranes can mitigate these issues and enable precise atomic characterization in HZO13,21,30. On the other hand, the polycrystalline nature lead to different atomic-scale features present even within a single grain at the nanoscale, including surfaces, grain boundaries (GBs) and DWs, necessitating high spatial resolution characterization. Conventional high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM, with typical resolution ~60 pm) fails to detect low atomic number oxygen, whereas oxygen sensitive transmission electron microscopy (TEM) techniques are highly sensitive to imaging conditions (e.g., specimen mistilt, thickness variation and residual aberrations), which can easily lead to artifacts35–38. Furthermore, traditional diffraction-based techniques like position-averaged convergent beam electron diffraction (PACBED) and 4D-STEM methods have been widely used for polarization analysis in ferroelectrics23,39–42. However, these methods are limited by finite spatial resolution, challenges in polarization quantification, and lack of depth information. Fortunately, state-of-the-art multislice electron ptychography (MEP) offers superior resolution (~20 pm) and uniquely enables simultaneous imaging of cation and oxygen positions, depth information retrieval and specimen mistilt correction, which is ideal for atomic structure quantification43–52.

Herein, we used MEP to achieve ultra-high-resolution imaging (~25 pm) of polycrystalline HZO freestanding films. We determined the atomic structures of multiple phases and measured the intrinsic polarization displacement of HZO to be ~56 ± 6 pm, corresponding to a polarization of ~34 ± 4 μC/cm2. At GBs, significant polarization suppression up to the fourth polar layer was observed. Moreover, we observed a 180° head-to-head (H-H) CDW in HZO. Such a CDW is a one-dimensional line, i.e., its width is only about one unit cell, and confined within a single polar layer. The atomic polar displacement at the CDW is reduced to ~4 pm, accompanied with ~20% oxygen vacancies (VO) based on the depth-resolved reconstruction. In contrast, no detectable polarization changes are observed in the neighboring polar layers of the 180° H-H CDW. These findings provided basic insights into the HZO ferroelectricity and related applications.

Results
Various phases in HZO
The 5-nm-thick HZO freestanding film shown in Fig. 1a was studied to eliminate the influence of phenomena such as interface effects, grain overlap, and sample preparation damage33,34, thereby ensuring precise structural analysis. The morphology distribution of grains shown in Fig. 1b, with an average size of ~10 nm, is consistent with previous studies30. The P-E hysteresis measurement (Fig. 1c) shows that polarization of the film is ~16 µC/cm2. Experimental setup for MEP technique is schematically shown in Fig. 1d. The sample was scanned with an overfocused probe and collected diffraction patterns (Figure. S1) via a pixelated detector, and the datasets were then reconstructed using the MEP algorithm with post-alignment method correcting slight mistilt (Figure. S1) to resolve the 5 nm HZO film in three-dimensions (Fig. S2)44–46,53. The reconstructed real-space resolution is ~25 pm (Fig. 1e), which is much better than that of HAADF image [~61 pm, Fig. S3 in Supplementary Material (SM)]. The reconstructed probe structures (Figure. S4 in SM) are robust and consistent with those reported in previous studies48,54–56. Projected MEP images in Fig. 1f show multiple phases of HZO including the ferroelectric (FE) phase, the antiferroelectric (AFE) phase, the monoclinic-like (M’) phase and the cubic (C) or tetragonal (T) phase, in excellent agreement with the simulated reconstructions and atomic model in Fig. S5. These abundant results as well as the monoclinic (M) phase (Figs. S6 and S7 in SM) unveiled several key discoveries. 1) By combining MEP images with corresponding simulations, we confirmed that the intrinsic FE phase in HZO adopts O phase with space group Pca21. 2) We identified the AFE nature of the M phase along the [100] direction (Figure. S7 in SM), with notable variations in displacements between neighboring layers. 3) We also captured a novel {010}-Hf/Zr antiphase boundary (APB) defect in the M phase, which has not been previously reported. The crystal structure demonstrate its significant influence on the nearby polarization (see Figure. S7 in SM for details).

Based on the reconstructed atomic images shown in Figs. S8 and S9 of the SM, the lattice structures of various phases were analyzed in detail (Fig. 1f). The FE phase features centrosymmetric non-polar oxygen atoms (O1) and non-centrosymmetric polar oxygen atoms (O2) with measured interatomic distances of 41 ± 2 pm and 60 ± 5 pm, respectively. The corresponding O1 and O2 distances for the AFE and M’ phases are summarized in Fig. 1f representing the statistical distributions obtained from our measurements. The extracted O phase lattice parameters fall within the range reported in previous experimental and computational studies (Table S1 in SM)57–61. It should be mentioned that the MEP images cannot differentiate whether the metallic sites are occupied by Zr or Hf due to the limitation of depth resolution. In addition, the angle of adjacent metallic atoms is ~75° in M’ phase and 70° in M phase, providing more details of the coexistence of M’ and M phases including strain effects and atomic relaxations (discussed in Fig. S6 of the SM). For the C/T phase, the structural parameters (indistinguishable from c-axis) are consistent with previous studies62. Analysis of nine MEP images totaling 70 × 70 nm2 (Figure. S9 in SM) revealed that the FE-O phase (~50%) dominates over the AFE-O (~21%) and M (~23%) phases. Minor phases M’ and T/C are rarely observed, typically appearing as single atomic layers within O phase grains.

Polarization in bulk and grain boundaries
In Fig. 2a, we show a FE grain image along the [010] axis and mapped the distribution of displacements between cation and oxygen. Statistical analysis of O phase grains (Fig. 2b) suggests that the polarization displacement is ~56 ± 6 pm with corresponding spontaneous polarization (Ps) of 34 ± 4 μC/cm2, consistent with the reported theoretical values19,20. The distribution near the zero point in the histogram originates from the non-polarized layers, and in-plane displacement (0.8 ± 3 pm, see Fig. S10 in SM) along the a-axis indicates that the polarization direction is along the c-axis. Our extensive measurements show that even in the pristine films, grains with uniform polarization direction (Fig. 2a) are very rare. Most O phase grains exhibit a mixture of FE and AFE phases, as shown in Fig. 2c. This is reasonable due to the similar energies of the FE and AFE phases, along with the independently switchable characteristics of polar layers20. The polarization magnitude mapping in Fig. 2d shows no detectable polarization variation across the opposite polarization directions (Fig. 2e), i.e., 180° DWs. But there is significant polarization suppression near GBs as shown in Fig. 2f. Partial oxygen ions in polarized layers near the GBs are relaxed towards the center position but still non-overlapping to each other, whereas the lattice along the c-axis with no obvious decrease (Fig. S10 in SM), resulting in polarization suppression throughout the entire relaxed polar layer. This typical polarization suppression extended beyond the outermost three polar layers (Fig. 2f), the underlying mechanism of suppression is usually very complicated at GBs, but our observation provides critical clues that reconstructed region near GBs clearly reveal the presence of VO. Electron energy loss spectroscopy (EELS) measurements (Fig. S11 in SM) further confirm significant and widespread VO accumulation at these boundaries. Specifically, the blurring of O-K edge doublets in EELS spectra indicates a higher concentration of VO at GBs63–65, suggesting their potential role in modulating local polarization behavior.

180° head-to-head charged domain wall
As common intrinsic defects in FE materials, VO play a crucial role in influencing the FE properties of materials and device performance66–68. Notably, computational studies have investigated the formation and structures of the 180° CDW in hafnium-based oxides and proposed the VO as a key contributing factor14,16,17, but experimental evidence has remained lacking until now. Inspired by the above observations, we further report an experimental observation of a localized 180° H-H CDW near the GBs in HZO (Fig. 3a). The corresponding HAADF image (Figure. S12 in SM) with a larger field of view confirm that the CDW exists near the GB. The atomic structure of the 180° H-H CDW indicated that there are two oxygen columns (i.e., col. 5 and 5’) within the CDW’s unit cell. The depth profile of these oxygen columns (Fig. 3b) revealed the presence of VO and the distortion of the columns, especially for the columns 5 and 5’. We further analyzed the polarization, VO, and the lattice constants of the 180° H-H CDW structure based on the MEP result. Specifically, we observed single-unit-cell layers with head-to-head polarization (highlighted by the red box in Fig. 3a). As shown in Figs. 3c and S13 in SM, there are a non-polar unit cell at the center of the CDW with almost equal but opposite polarization on either side (Layer_2) along depth. The polarization suppression observed in the right-hand region primarily arises from the proximity to GBs, as discussed above. The polar layers (i.e., Layer_1 and Layer_3, black and yellow boxes in Fig. 3a) adjacent to the 180° H-H CDW retain bulk-like polarization. They are not affected by the CDW itself. The coexistence of FE and AFE phases within a single grain furthers support the scale-free ferroelectric nature of hafnium oxide20. The phase intensity of the O columns in Fig. 3d clearly reveals pronounced reduction at both the 180° H-H CDW and GBs. Quantitative analysis (Fig. 3d) shows that the concentration of VO within the cell at the CDW reaches up to 20%, whereas the concentration near the GBs is approximately 7-12%. Notably, we found that VO are not only confined to the DW (the non-polar unit cell) but also exist in at least one polar unit cell on both sides of the CDW. Furthermore, the extracted lattice constants around the CDW with no significant changes (Figs. 3e and S12 in SM) indicate no notable structural alterations. These experimental results reveal a clear spatial correlation between oxygen vacancy accumulation and local ferroelectric polarization behavior in HZO, particularly at grain boundaries and the 180° H-H CDW, directly demonstrating their coexistence at the atomic scale. Detailed understanding of how the vacancies exactly influence polarization stabilization and domain-wall formation requires further in-depth investigation.

Methods
Sample preparation
The HZO films with 5 nm thickness were synthesized as HZO/La0.8Sr0.2MnO3 (LSMO) heterostructures on single crystal SrTiO3 (STO) through pulsed laser deposition (PLD) method using a XeCl laser (λ = 308 nm) and the deposition temperatures was 780 °C. The laser energy fluence was 1.75 J/cm2, and the repetition rates used for both films were the same (2 Hz). The deposition rate of films was calibrated by X-ray Reflection. After growth, the HZO films were released from the STO substrate by selective etching of the sacrificial LSMO layer. The unclamped thin films were removed from the substrate by slowly dipping it into deionized water. A homemade copper wire loop was used to catch the freestanding HZO membranes from the water surface, held in place by a thin water layer inside the loop. The films were then transferred to target substrates on a 95 °C hot plate. The freestanding HZO films remained on the copper TEM grids (with holey carbon supporting layer) after water evaporated.

Experimental 4D-STEM datasets acquisition
The 4D-STEM experiments and HAADF imaging were operated at 300 kV on a double-aberration-corrected JEOL JEM-ARM300F2 microscope. Considering the thickness of film, convergence semi-angle (α) of 32.8 mrad was selected for all datasets78. We adopted an overfocus probe ~10 nm above the sample surface to collect the datasets. The electron probe current used was approximately 20 pA. The 4D-STEM datasets were recorded with 0.819 mrad/pixel by using a Medipix3 Merlin1R direct electron pixelated detector with 256 × 256 pixels. The datasets were acquired using a dynamic range of 12-bit in electron-counting mode with 0.617 ms dwell time per diffraction pattern with scan step size about 0.304 Å. The first two rows of raw datasets were deleted to avoid scan noise.

Ptychographic reconstructions and data analysis
Ptychographic reconstructions were performed based on the mixed-state multislice algorithm available in the fold-slice package44,45,79, using 5 slices with slice thickness of 1 nm. For the reconstruction in Fig. 3, we used 0.5 nm/slice for depth analysis. For each dataset, multiple reconstructions were iterated to improve the resolution with each undergoing more than 600 iterations. We corrected the mistilt in experiment by performing post-alignment of all slices46. As illustrated in Supplementary Fig. 13, based on the position averaged convergent beam electron diffraction (PACBED), we chose grains with tiny mistilt for further reconstruction. For our ultra thin samples, Kikuchi patterns were difficult to distinguish, where mistilt was quantified via analysis of center shift between the zero-order Laue zone (ZOLZ) and the first-order Laue zone (FOLZ)39,80. The mistilt of FOLZ is estimated ~6 mrad (Fig. S1 in SM) and corresponding offset for sample ~6 pm/nm. The corrected shift (Fig. S1 in SM) proves that the mistilt was considered and corrected effectively. The probe positions were updated with relaxed constraint applied about every 50 iterations79. The moderate regularization parameters ranging from 1 to 0.5 were applied for high-quality reconstructions44,46. The step of least square in least square maximum likelihood (LSQ-ML) algorithm was set 0.1 for initial convergence and decrease to 0.05 for final refine44. We considered the point spread function (PSF) effects of the detector we used.

Based on the complex structures of HZO, AtomAI81 and Atomap82 were used to fit and analyze the atomic positions, intensities and structures. The atomic positions were predicted using the custom-trained model in AtomAI and then Atomap was used for 2D-Gaussian fitting to refine the positions ensuring precision. First, we trained custom models with a ResHedNet-like network for semantic segmentation of atomic images in AtomAI with simulated and experimental HZO images. To enhance the robustness especially for blurred atoms, we applied various image “distortions” (e.g., noise, blurring, and zoom) to the cropped images, as illustrated in Fig. S16. The network was trained to process these input images and produce outputs of clean, circular-shaped “blobs” on a uniform background, from which the (x, y) centers of atoms could be identified. The training process involved 1000 epochs to achieve convergence, as shown in Fig. S14. We further refined the cation atomic positions using Atomap in two steps: 1. Center of Mass Calculation: Preliminary refinement of atom positions; 2. 2D-Gaussian Fitting: Every atomic column was further refined with an elliptical 2D-Gaussian function: f(x,y) = A exp [-(x-μx)2 / 2σx2 - (y-μy)2 / 2σy2], where the A is the magnitude, (μx, μy) is the position, σx and σy are the standard deviation in x and y direction respectively. For light elements, we accounted for the lower intensity by subtracting the Gaussian of cations from the images. The positions of light elements were then refined in same way as the cation positions. All functions used for refinement are built-in features of Atomap with additional details available in reference82. The O1 distances were accurately determined by fitting columns with Gaussian functions. For polarization analysis, the obtained relative displacement δ of cations and anions was used to calculate polarization by Ps = V e Σ δi Zi, where e is the electronic charge, V is the volume of unit cell and Zi is Born charge values, δ is displacement/shift of atom (i) from their centrosymmetric position83. The Born charge value for the A site is 5.15, which is derived as the mean value of 5.0 for Hf and 5.3 for Zr84,85. The polarization of the CDW was determined by calculating the center position of the two pairs of O columns as the mean anion position in the cell of the CDW. We choose the smallest polarization in the outermost polar layer to obtain the suppression maximum of 13 pm indicated by blue arrow in Fig. 2d. The normalization in the study is normalized based on the corresponding mean value.

Simulation of 4D-STEM datasets
All simulated 4D-STEM datasets were implemented with abTEM86 using Kirkland’s parametrization of atomic potentials. Thirty frozen phonon configurations were averaged to account for the thermal diffuse scattering. Parameters such as beam energy, sample thickness, scan step, defocus and convergence semi-angle from the experiments were used in the simulations. The aberrations were set to zero for simplicity. All simulated datasets were generated under the assumption of an infinite electron dose, meaning that Poisson noise was not introduced, aiming to preserve clear structural details in the ptychographic reconstructions. Additionally, the datasets (i.e., the collected diffraction patterns) were Gaussian-blurred to account for source size.

STEM-EELS
The energy loss spectra were acquire data Nion U-HERMES200 electron microscope equipped with both the monochromator and the aberration corrector operated at 60 kV. The probe convergence semi-angle was 35 mrad, while the collection semi-angle was 25 mrad. The core-level EEL spectrum was recorded as spectrum image with 1.6 nm × 8 nm and 0.08 nm per pixel. EEL spectra were processed using the Gatan Microscopy Suite and custom-written MATLAB code. The spectra were summed along the direction parallel to the interface to obtain the line-scan data with a good signal-to-noise ratio.

P-E hysteresis measurement
The ferroelectric P-E hysteresis loops were measured using a capacitor-like structure comprising a Pt/HZO/LSMO heterostructure. A precision multiferroic analyzer (RADIANT Tec. Inc.) was employed to measure the polarization intensity of the HZO films on a macroscopic scale. A tungsten probe was used for P-E measurements, with a frequency of 10 kHz for the triangular pulses applied to switch the polarization of the ferroelectric layer. The analyzer applied a periodic electric field sweep while measuring the current/charge response, integrating the displacement current to calculate the polarization (P), which was related to the applied electric field (E = V/t), where t is the thickness of the ferroelectric layer. Consequently, the P-E loop was generated, elucidating the ferroelectric properties of the HZO films.

Data availability
The 4D-STEM data presented in this study are available in Zenodo https://doi.org/10.5281/zenodo.18373896.

Code availability
The code for MEP is available Zenodo https://doi.org/10.5281/zenodo.18373896.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript shows interesting results and clearly elucidates the structure of HZO, including polarization displacements, head-to-head CDWs and their influence on ferroelectric polarization. With some revisions, this manuscript is enough to be published.\n1. Not only atomic-scale imaging but also diffraction-based method, such as PACBED has been used for measuring degree of polarization of ferroelectric materials. In order to emphasize MEP as an effective method to clarify the atomic structure, adding previous diffraction-based studies (especially their limitations) in the introduction section is recommended.\n2. Is so-called ‘substrate effect (page 3, line 60)’ is related to synthesizing ‘Substrate-free’ or ‘freestanding film’? Explaining clearly why freestanding films were used as the subject of analysis in this paper, both from the perspective of ferroelectric devices and atomic resolution imaging is highly recommended.\n3. Does the PACBED analysis in Fig. S13 provide sufficient evidence to conclude that the film is a 5-nm-thick freestanding HZO layer? On page 4, line 80, the thickness of the HZO film is mentioned, but it would be helpful to clarify the measurement method and present the corresponding results.\n4. The descriptions for Figs S13 and 14 are missing from the main text of the manuscript. Even if they are supporting information, they should be included in the main text.\n5. In this manuscript, polarization field is only analyzed in a ‘single’ HZO grain. In order to understand the total polarization, 4D STEM orientation mapping is recommended.\n6. There are minor considerations for the revisions. The authors should correct some typos.\n1) Page 11, line 248: Kumar P., Gupta D., Lee J. H. Negative Gradient Energy Facilitates Charged Domain 248 Walls in ${\\mathrm{HfO}}_{2}$. Phys Rev Lett 134, 166101 (2025).\n2) Page 12, line 315: Sha H., et al. Sub-nanometer-scale mapping of crystal orientation and depth-dependent 315 structure of dislocation cores in SrTiO(3). Nat Commun 14, 162 (2023).", "reviewer_2": "The manuscript submitted by the authors focuses on atomically-resolved microscopy of ultra-thin polycrystalline Hf0.5Zr0.5O2 (HZO) films using electron ptychography. The use of this technique on this material is very valuable as it allows to resolve lighter elements (i.e., oxygen) which play an essential role in the polarisation in HZO. The spatial resolution of this method (of the order of several pm) is also remarkable and allows to make finer structural observations than in conventional electron microscopy. Their results reveal the existence of a multitude of structural phases in HZO (previously unknown, or offering clear experimental evidence to support them and close a debate on the nature of ferroelectricity in HZO), and observe a range of line defects, including charged domain walls (CDW), head-to-head domains and anti phase boundaries within single-grain images. These findings shed light on the mechanisms behind the ferroelectricity in HZO, of high relevance for the design of future smaller-scale electronic devices in particular FE memories.\nI believe that the data, analysis and interpretation in this paper are very solid, and the evidence strong and of sufficiently high quality.\nAdditionally, there are many smaller points in the manuscript that could substantially be improved; most of them having to do with general properties of HZO as well as some important details in the structure which appear, in my opinion, overlooked. Most of the points below are relatively minor compared with the quality of general findings, which are again, of high quality. I believe however that these points should be clarified and/or discussed to make this paper fully suitable for publication and increase overall publication quality. If the points below are considered/discussed, I believe that the paper is suitable for publication in Nature Communications.\nStructural HZO phases: points to clarify\n1. Given the large variety of phases of HZO discussed in this paper, a summary figure displaying the unit cells with structural models of FE-O; AFE-O; M; M’; C/T phases is necessary in my opinion (this can be supplementary information figure). Some of these phases are referred to by their polarisation (AFE, FE) and some by their crystallography (M, C/T) and it is sometimes confusing, a structural summary figure would definitely improve this significantly. Additionally, qualitative polarisation vectors should also be drawn in this new figure to directly visualise the nature of the dipoles in all these new phases, if possible. \n2. While the image reconstructions (which lead to higher resolution images) are convincing, possible twinning from the structures have not been considered to explain the different apparent phases. The lattice parameters of HfO2 (I could not find a structural file for HZO) in the Pca21 structure are 5.005 Å, 5.033 Å and 5.219 Å in the a, b, and c directions respectively, sufficiently close together (especially a ≈ b, within ~0.5%) which suggests that 90º-rotated twin domains should be considered, at least in principle. Is twinning a possibility here, or can it be ruled out? In other words, can some of the new phases be explained by local domains that are simply rotated by 90º?\n3. The first sentence in the introduction refers to HZO, but references 1-3 supporting it concern HfO2 and not Hf0.5Zr0.5O2. A very brief paragraph describing the differences between HfO2 and HZO is required in my opinion: why is Zr required here, and what are the (physical and engineering) advantages to adding Zr to the HfO2 matrix, already natively ferroelectric? Generally there is a little bit of confusion throughout the article as to whether the literature and referred-to physics concerns HfO2 or to HZO; I am guessing that a lot of the physics are similar, but this should be made clear in the text in my opinion.\n4. In general, where is the Zr in the HZO matrix? Are we in presence of a Zr/Hf solid solution, where occupancy of the metallic sites randomly distributed, or is there inherent structure where Zr and Hf occupy preferential sites? Based on the data, the contrast in MEP images does not allow to distinguish Zr/Hf. Can the authors comment on that, and mention it in the text? Are there other studies that mention this Zr/Hf distribution, whether experimentally resolving Zr/Hf or theoretically investigating this aspect of the crystalline structure of HZO? Generally, (similar to questions 3) does Zr/Hf occupancy impact the ferroelectric nature of the material? Can these questions be answered at least partly with a energy dispersive measurements where presumably Hf and Zr lead to different contrasts? \n5. One of the main result is the observation of the head-to-head (H-H) configurations and domain wall. Have the authors also observed a tail-to-tail (T-T) domain wall, where polarisation is reversed in both domains with respect to the head-to-head configuration? Do the authors expect that H-H and T-T have identical energies? \n6. Is MEP acquired before or after the P-E measurements (or on a different set of grains/sample altogether) ? Are the different phases uncovered in this paper “temporary” and will not survive polarisation at large fields? e.g. does the AFE phase become FE above a certain field? Without possibility of reversal onto the AFE phase? Line 175, do FE and AFE coexist within the same grain even after an applied field (such as those utilised in Fig 1c)? Or is the AFE state robust and its polarisation remains antiparallel after applied field? \n7. Line 112, the relative presence of the different phases is calculated and suggests a most significant presence of FE-O phase. Does this contradict the claims where AFE and FE phases have the same energy? I think in light of the future applications of this materials, a claim on whether the AFE phase can be switched into the FE phase by applied field, and if the AFE phase is reversible after polarisation is possible would be of great value. Beyond the energy difference between the two FE and AFE phase, it would be interesting to know (approximately or if there are calculations that indicate this) the value of the energy barrier ∆ that separates FE to AFE, to know if switching is indeed feasible at reasonable biases/fields. I’m aware this is a difficult question, but if these have been investigated in the past by the authors or in a different group, this should be made clear in the text.  \n8. Line 154, how does the observations agree with a “scale-free FE feature” and what does this mean in this context? \nRegarding the oxygen vacancies\n9. The observation that oxygen vacancies are key to the presence of CDW is interesting, but is also concerning in terms of the supposed mobility of these CDW, potentially crucial for the development of HZO-based memory devices. Did the authors observe CDW mobility? Can the authors comment on the mobility of oxygen vacancies? Do the oxygen vacancies stem from a non-stoichiometric composition of HZO? Is it possible to have a control the effective oxygen vacancy concentration during the growth/synthesis of HZO?  \n10. Can the density of oxygen vacancies be estimated on the overall material, and in the grain boundary areas?\n11. Can the authors resolve with MEP whether the oxygen vacancies (near the GB) occur preferentially at the O1 or O2 sites (centro- and non-centro-symmetric sites)? Given the large suppression of the polarisation near GBs, it is expected that at least the O2 sites are primarily affected, but considering the quality of the MEP data, it may be possible that the authors have the experimental data to support this. Line 195, “The Vo acts as active structural mediators rather than passive pinning centers” can the author develop this sentence? It is not clear what is meant here.\n12. Related to Fig. 3: is the O-related phase decrease a consequence of vacancies that are localised there? Can the authors rule out a depth-dependent configuration, where each atomic layer parallel to the image plane has a different polarisation, and the data is an average of all these configurations? i.e the exact boundary between the two polarisation in Layer_2 is not exactly perpendicular to the image plane, but tilted?\nRegarding the instrumentation\n13. How does possible Joule heating affects the local temperature of the material? Could this affect the polarisation of the material? What is the Curie/ferroelectric ordering temperature in HZO? \n14. Naively, the sentence line 72 is confusing since it is mentioned that the lateral resolution of MEP is 25 pm, while the displacement is measured with a precision of ±6pm. Can the authors briefly explain how it is possible to resolve displacement with a precision 4x finer than the instrumental resolution? \n15. It is not clear to me whether the MEP resolves a single atomic plane parallel to the image plane, or if it resolves the whole crystal thickness and obtain a integrated intensity originating from every atomic plane in the crystal? In other words, what is the probed thickness of the MEP method? \n16. How was the P-E measurement done? Supplementary material paragraph page 4 does not mention if this was this done over a single grain, or over a macroscopic sample. The P-E measurement suggests that the polarisation can still be enhanced using a larger field (not saturated within the applied field range). Are there limitations such as breakdown effects upon too-large applied fields?\n17. The reconstructed probe structures are briefly discussed (line 89). What do these figures tell us about the probe? Is it sharp enough and of good quality? Just a very brief comment is expected here.\nModeling and theory of HZO, future applications\n18. The polarisation is calculated as if proportional to the displacement in HZO? Are there theoretical models that describe the polarisation with respect to the displacement in HZO? Could the new phases uncovered in this paper be described using the same theory? Intuitively, small displacements leading to a proportional polarisation feels like a valid approximation, but the displacement involved here are significant (~ 50-60 pm) and it would be good to cite the correct work if appropriate. A brief comment on this would be greatly appreciated.\n19. The authors mention that HZO is compatible with Si-based electronics as supported by a number of references which mostly mention HfO2. Do the authors have hypotheses in terms of the impact of a Si substrate in terms of impact over the ferroelectric properties in HZO? Could the substrate interactions lead to the quenching of the polarisation, or to its pinning, or other effects?\nTypos/grammar\nLine 43 “For example, …” misses a verb such as “have been demonstrated”.\nLine 72, it reads “intrinsic polarization magnitude of HZO to be ~ 56±6 pm” but the polarisation (usually in C/m2 or similar) is expressed in terms of displacement (pm); I believe it should be clarified.\nLine 80, “to eliminate the influence [of phenomena] such as interface effects, …”\nLine 102, “analyzed [in detail] in Fig. 1f”\nLine 105, “the oxygen atomic distances in the AFE and M’ phases [are] slightly larger than in the FE phase”\nLine 109, the phase “transformation” is not really mentioned, rather the coexistence of the two phases is discussed.\nLine 143, “with larger field of view confirms that the CDW is exist near the GB.” This is grammatically strange.\nLine 154, “This observation supports that the scale-free FE feature of hafnium oxide.” this is grammatically strange, too.", "reviewer_3": "Gao et al. present the application of multislice electron ptychography to the HFO material system, which is a promising candidate for the realisation of novel ferroelectric devices.\nThe authors achieve an impressive resolution of 25 pm allowing them to measure atomic displacements and polarisations directly. Several different sample regions exhibiting different crystal phases and defects like grain boundaries were analyzed and their detailed atomic structure is revealed.\nThe results presented are highly relevant and worth publication and are potentially suitable for an high-impact journal like Nature Communications. However, the manuscript is not well organized so that the story line is hard to follow. The reader has to switch back and forth between manuscript and SI to follow the story. Clearer structuring the manuscript, e.g. by adding sub-chapter headings would clearly improve the readability. Moreover, several important experimental details are missing, hindering the reproducibility of the findings. This might be caused by shortening an existing manuscript in order to fit the guidelines of Nature Communication. In addition, there is a significant amount of wording issues. Therefore, I recommend proof reading by a native speaker.\nAccordingly, I suggest major revision prior to publication.\nPlease find my detailed comments below.\nDetailed scientific comments\n90-92: To allow an easier comparison of simulation and experiment, both should be depicted next to each other. This means, the simulated pictures should be shown in Fig 1 or the experimental images should be shown in Fig S5.\n104-106: The authors claim O1 and O2 distances in the FE phase (41±2, 60±5) are slightly smaller than those in the AFE (44±3, 68±6) and M’ (46±4, 113±6). This feels unwarranted for O1, since the differences lie well within the margin of error and confusing for O2, since the distance in M’ is nearly double that of FE.\n106-107: The provided literature overview (table S1) shows experimental results ranging from 5.01-5.10 for a and 5.00-5.09 for c. Firstly, the authors only provide half lattice parameters for their own results, hindering a direct comparison. Secondly the authors’ results (a: 5.00, 4.97, 5.17; c: 5.14, 5.22, 5.22) all lie outside the literature range, undercutting their assessment of being “highly consistent”.\n116-118: Here ref 53 is cited for the theoretical value of the polarization. Later on (line 171) refs 17,18,53 are cited in this context. This is inconsistent. Moreover, in refs 18 and 53, I could not find a value for the polarization. Please verify if the correct sources are referenced.\n127: The authors claim to see no polarization suppression along the c-axis, referring to Figure S8. Figure S8e however seems to show a clear drop in polarization towards the edges of the grain. At first glance it is unclear where the information on c-axis polarization stems from. Adding information on the recorded zone-axis, labeling a- and c- axis in S8a and clarification of which plane “in-plane” polarization is in S8b could help here.\n134: The authors claim that the blurring of O-K edge doublets in EELS spectra indicates a higher concentration of VO at GBs. I do not understand this conclusion. If this is common knowledge, the authors should underpin this claim with a reference to literature.\n155: Please explain the value of 7-12%. Does projection play a role?\n164: Please elaborate more on the close relationship between the Vo and the ferroelectric properties of HZO\n175: The authors state “FE and AFE [...] always coexist within a grain”. This is in tension with Figure 2a which shows “a FE grain”.\n187-204: After reporting on successfully imaging oxygen atoms in [111] zone axis, the authors again remark on the observation of 180° H-H CDWs. This section feels misplaced, as this is already discussed in some detail in 141-164\n189: The authors emphasize the importance of being able to reconstruct the sample phase in 3D. This ability is however never put to use. The depth information in the depth slice shown in Fig 3b is never used, as the phase is summed along the depth direction afterwards.\nFigure 1: The authors should show at least one CBED image from their 4D datasets, since this is the input for all the ptychography work later on.\nFigure 1e and right hand side of f: In the main text, it is not mentioned at all what is shown there.\nFigure 1f and all other reconstructions: The metal columns in Hf0.5Zr0.5O2 should be occupied partially by Hf and Zr atoms differing significantly in atomic number. For a sample thickness as thin as the 5 nm stated, I would expect intensity/phase variations on the metal columns reflecting different ratios of Hf and Zr? Why do all metal columns have nearly the same intensity even in the simulations? IS the maximum value cut?\nFigure 2: The orange arrows in a and c are close to invisible. Probably show a magnified ROI as inset. In 2f it is unclear what the red arrow indicates and what is meant with “blue, the rest part”\nFigure 3: 3c lacks information on how the displacement was determined at the CDW (since there are two pairs of O-columns here). 3d lacks information on what the phase was normalized to and how exactly the “phase of the O-colums” was determined (projected phase at a certain position or sum over a region around O-positions or similar)\nSI\n39: What TEM grids were used? Are there some supporting layers, e.g. lacey carbon? Do these layers impact the ptychography?\n63: Reconstruction details such as regularization parameters and constraints should be specified, as these could have an influence on the reconstructed phase.\nFig S1 : b and e should be shown with the same contrast. THe line cuts presented in c and f are rather noisy. A radial average instead of line cut would be beneficial.\nFig S5 : It is unclear what the reconstructions based on simulated datasets add. By choosing an infinite dose and no aberrations for the simulated diffraction patterns the authors essentially reconstruct the potential they constructed for the simulation in the first place (up to frequencies corresponding to the maximum collected scattering angle). The only difference is the added gaussian blur (SI: line 100), although it is unclear whether this was applied to the diffraction patterns or to the reconstructed phase image. The authors should add some details here.\nFig S6: Some more information would be beneficial here. The colorbar is missing labels\nHere is an incomplete list of wording issues\n34: layers [...] remains unchanged\n59: the ferroelectricity nature\n59: However it is\n67-69: Reword whole sentence\n73: Layers → layer\n80: Suggestion: “The HAADF image of the 5-nm-thick …”\n92: “simulated reconstructions” -> “reconstructions on simulated data”\n93: [...] results [...] have unveiled [...] key discoveries\n94-100: tense in sentence 1) different from 2) and 3)\n102: detailly\n126: there are [...] suppression\n127: Partial polarized\n127: but [are] still overlapping\n127: “whereas [the] lattice along [the] c-axis maintained no obvious suppression, resulting in polarization suppression[...]”. Sentence seems contradictory\n131: “[...] observations [...] provide clues [...] that regions [...] clearly reveal” wording\n143: is exist → is existing\n144: indicted\n154: “This observation supports that the scale-free FE feature of hafnium oxide”. Sentence seems incomplete\n164 the closely relationship\n184: duo to [...] distance [...] is\n184:”Benefits from the ultra-resolution of MEP, we successfully image the oxygen atoms (Figs. S11 and S12 in SM) from the O-[111] orientation.” Sentence seems incomplete\n188: our [..] precisely measurements\n190: “In the traditional systems, where… “ Sentence seems incomplete\n195: the VO acts as mediators\n196: [...] lattice constants [...] indicates\n197: reinforcing the nature\n209: reconstruction further demonstrate\n404: polarization [...] that noted with the corresponding [...] lines\nSI\n55: we → We\n66: the detector we used during the algorithms\n86: column → columns\n88: born → Born", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to Referees’ Comments\nFor ‘Precise structure and polarization determination of Hf Zr O\n0.5 0.5 2\nwith electron ptychography’\nWe appreciate the highly constructive reviews concerning our manuscript from the\nreviewers, which help us to substantially improve our manuscript. In response to their\ncomments and suggestions, we have conducted further analysis, with which we have\nrevised our manuscript carefully to address all the concerns made by the reviewers.\nThese revisions are detailed in our point-to-point responses below, and key revisions\nare highlighted in the revised manuscript.\nOur point-by-point responses to the reviewers’ comments are listed below, with\nour reply written in blue and excerpts from the text in blue. Edits and additions to the\nMain Text and Supplementary Material have been highlighted in yellow. Additionally,\nthe revised manuscript with tracked changes is included for your reference. “Line”\nnumbers are in reference to the original submission before revision, while “New line”\nnumbers mean the lines in revised manuscript. Modification to Fig. 1(f), Fig. 2(c), Fig.\nS3 and Fig. S8 for clarity and new Supplementary Figures (Fig. S1, Fig. S2, Fig. S5,\nFig. S13 and Fig. S17) have been added. Sub-chapter headings were added to improve\nthe readability. The references are also adjusted according to the reviewer’s comments.\nThe manuscript is revised accordingly.\n*******************************************************************************\nReviewer #1\nComment: This manuscript shows interesting results and clearly elucidates the\nstructure of HZO, including polarization displacements, head-to-head CDWs and their\ninfluence on ferroelectric polarization. With some revisions, this manuscript is enough\nto be published.\nResponse: We sincerely appreciate the reviewer’s recognition of our manuscript.\nComment 1: Not only atomic-scale imaging but also diffraction-based method, such\nas PACBED has been used for measuring degree of polarization of ferroelectric\nmaterials. In order to emphasize MEP as an effective method to clarify the atomic\nstructure, adding previous diffraction-based studies (especially their limitations) in the\nintroduction section is recommended.\nResponse 1: Thanks to the reviewers for his/her helpful suggestions. The MEP is also\na diffraction-based reconstruction imaging method, which reconstructed the object and\nprobe using the diffraction patterns. To emphasize its advantages in atomic-structure\nclarification, we have supplemented relevant content on traditional diffraction-based\ntechniques in the Introduction, highlighting their limitations. This revision strengthens\nthe rationale for selecting MEP, underscoring its effectiveness in resolving fine atomic\nstructures:\nNew line 73-81: Furthermore, traditional diffraction-based techniques like position-\naveraged convergence beam electron diffraction (PACBED) and 4D-STEM methods\nhave been widely used for polarization analysis in ferroelectrics 21, 36-39. However, these\nmethods are limited by finite spatial resolution, challenges in polarization\nquantification, and lack of depth information. Fortunately, the state-of-the-art\nmultislice electron ptychography (MEP) offers superior resolution (~20 pm) and\nuniquely enables simultaneous imaging of cation and oxygen positions, depth\ninformation retrieval and specimen mistilt correction, which is ideal for atomic\nstructure quantification 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.\n‘Substrate-free’ or ‘freestanding film’? Explaining clearly why freestanding films were\nused as the subject of analysis in this paper, both from the perspective of ferroelectric\ndevices and atomic resolution imaging is highly recommended.\nResponse 2: We appreciate the reviewer’s valuable comment. The ‘substrate effect’\nspecifically refers to the influence of supporting substrates (e.g., TiN/HZO/TiN\nheterostructures or Si wafers) on HZO’s structural and ferroelectric properties. First,\nfrom the ferroelectric device perspective, practical HZO-based devices often rely on\nsubstrate-supported heterostructures, but substrate-induced effects (e.g., interfacial\nstrain and charge transfer) can alter HZO’s intrinsic phase composition and polarization\nbehavior 11, 12, 13, 14, 15. Decoupling these extrinsic influences is critical for understanding\nthe fundamental ferroelectric mechanism of HZO, which serves as the basis for\noptimizing device performance. Our freestanding film platform eliminates substrate\nconstraints, enabling the study of HZO’s intrinsic ferroelectric nature, which is essential\nfor the rational design of next-generation high-performance ferroelectric devices.\nSecond, from the atomic-resolution imaging perspective, substrate-supported HZO\nfilms suffer from limited imaging quality, while substrate-induced strain may introduce\nstructural artifacts, making it challenging to resolve fine atomic-scale features (e.g.,\noxygen configurations and domain walls). In contrast, freestanding HZO films\nminimize these perturbations, allowing MEP to achieve its ultra-high-resolution\nimaging (~ 25 pm) for quantitative structural analysis. Consequently, freestanding\nHZO films not only avoids substrate-induced artifacts but also enables the discovery of\nintrinsic structural phenomena. As highlighted in our work, this approach allowed us to\nidentify the 180° head-to-head (H-H) charged domain wall (CDW) in HZO for the first\ntime. Relevant content has been integrated into the main text to strengthen the rationale\nfor our experimental design:\nNew line 61-69: However, such analysis is typically challenging due to its substrate\neffects and polycrystalline nature 16, 17, 18, 19. On the one hand, the substrate effects can\n3\nlead to lattice clamping 14, 20 and interfacial charge screening 15, 21 in hafnium-based\noxide films, which hinders the detection of intrinsic ferroelectric nature. They can also\nintroduce structural artifacts that affect the accurate atomic-scale structural analysis.\nRecent advances in freestanding membranes can mitigate these issues and enable\nprecise atomic characterization in HZO 16, 22, 23. On the other hand, the polycrystalline\nnature leads to different atomic-scale features present even within a single grain at the\nnanoscale, including surfaces, grain boundaries (GBs) and DWs, necessitating high\nspatial resolution characterization.\nNew line 91-93: The 5-nm-thick HZO freestanding film shown in Fig. 1a was studied\nto eliminate the influence of phenomena such as interface effects, grain overlap, and\nsample preparation damage 20, 21, thereby ensuring precise structural analysis.\nComment 3: Does the PACBED analysis in Fig. S13 provide sufficient evidence to\nconclude that the film is a 5-nm-thick freestanding HZO layer? On page 4, line 80, the\nthickness of the HZO film is mentioned, but it would be helpful to clarify the\nmeasurement method and present the corresponding results.\nResponse 3: We appreciate the reviewer’s valuable comment. First, we clarify that Fig.\nS13’s PACBED analysis is not used for thickness measurement, but rather for\nestimating the mistilt of datasets. Regarding the 5-nm thickness of the freestanding\nHZO film (Page 4, Line 80), we determined it primarily based on multislice electron\nptychography (MEP) results, following the reliable protocol from previous work4.\nSpecifically, the sample thickness is initially assumed as 8 nm during the reconstruction,\nbut the retrieved sample thickness is 5 nm, as shown in the Fig. 1R.\nWe add the object slices and intensity profile as Fig. S2 in the revised SM.\nof phase intensity along the columns marked in a by the red dash-dotted line.\nComment 4: The descriptions for Figs S13 and 14 are missing from the main text of\nthe manuscript. Even if they are supporting information, they should be included in the\nmain text.\nResponse 4: We appreciate the reviewer’s valuable comment. We have merged the Fig.\nS13 into the new Fig. S1 and added descriptions of the Figures corresponding section\nof the main text, improving the manuscript’s completeness and readability:\nFig. S1. a, The CBED in Fig. 1d with colorbar.. b, The PACBED image shown in log\nscale intensity. c, The profile of corrected shift measured by post-alignment method.\nNew line 97-99: The sample was scanned with an overfocused probe and collected\ndiffraction patterns (Fig. S1) via a pixelated detector, and the datasets were then\nreconstructed using the MEP algorithm with post-alignment method correcting slight\nmistilt (Fig. S1) […]\nNew line 184-185: By accurately fitting the atomic position with custom-trained\n5\nstnuoc\nb c\n300\n200\n0\n).u.a(\nytisnetni\ngoL\nDepth Slice (nm)\n)mp(\ntfihS\na\nmodels (Fig. S14) and measuring the polarizations, we confirmed that […]\nComment 5: In this manuscript, polarization field is only analyzed in a ‘single’ HZO\ngrain. In order to understand the total polarization, 4D STEM orientation mapping is\nrecommended.\nResponse 5: We sincerely appreciate the reviewer’s insightful suggestion. We clarify\nthe following points:\n1. Our study does not rely on the analysis of a single HZO grain. Multiple grains were\nreconstructed and analyzed using MEP (see Fig. S9 in SM). Due to the MEP\nreconstruction’s requirement and the complexity of grain orientations in the film,\neach reconstruction does focus on a single grain to ensure ultra-high-precision\natomic structure quantification.\n2. For HZO, crystallographic orientation mapping alone is insufficient to determine\nthe polarization distribution. This is because, for example, the orthorhombic (O)\nphase family includes the ferroelectric (FE) and antiferroelectric (AFE) phases and\ncan share similar crystallographic orientations while exhibiting fundamentally\ndifferent polarization configurations. As a result, conventional 4D-STEM\norientation mapping cannot unambiguously distinguish FE and AFE polarization\nstates or resolve local polarization textures in HZO.\n3. Therefore, we employ MEP to directly resolve oxygen sublattice displacements\nand polarization at the atomic scale, which provides a more reliable and phase-\nsensitive characterization of polarization distributions in HZO. Representative\nresults from multiple grains are shown and summarized in Fig. S9. Moreover, the\nproportions of each phase have also been quantified, demonstrating the robustness\nand generality of our observations.\n4. Besides, orientation analysis of HZO grains based on HAADF imaging (Fig. R2)\nhas been studied and reported in our previous work 16, which is consistent with the\ngrain characteristics observed herein. Considering the diversity of HZO phase\nstructures and calibration requirements, comprehensive 4D STEM orientation\n6\nmapping would involve substantial additional work, which is a future research\ndirection.\nFig. S9. Analysis of FE-O, AFE-O, M, M’ and T/C phases. a, Images with classification\nof phases. The regions of phases are highlighted with color. The colored arrows indicate\nthe directions of polarization. b, Histograms of the phases.\n[Figure Redacted]\nFig. R2. Orientation and crystallographic phase analysis of the HZO freestanding film\n(adapt from Zhong et al., 2022).\nComment 6: There are minor considerations for the revisions. The authors should\ncorrect some typos. 1) Page 11, line 248: Kumar P., Gupta D., Lee J. H. Negative\nGradient Energy Facilitates Charged Domain 248 Walls in ${\\mathrm{HfO}}_{2}$.\nPhys Rev Lett 134, 166101 (2025). 2) Page 12, line 315: Sha H., et al. Sub-nanometer-\nscale mapping of crystal orientation and depth-dependent 315 structure of dislocation\ncores in SrTiO(3). Nat Commun 14, 162 (2023).\nResponse 6: We are grateful for the referee’s suggestions. We have rechecked all the\ncitations in the article and corrected them：\nPage 11, Line 248:\n12. Kumar P., Gupta D., Lee J. H. Negative Gradient Energy Facilitates Charged\nDomain Walls in HfO . Phys Rev Lett 134, 166101 (2025).\n2\n41. Sha H., et al. Sub-nanometer-scale mapping of crystal orientation and depth-\ndependent structure of dislocation cores in SrTiO . Nat Commun 14, 162 (2023).\n3\n*******************************************************************************\nReviewer #B\nComment: The manuscript submitted by the authors focuses on atomically-resolved\nmicroscopy of ultra-thin polycrystalline Hf0.5Zr0.5O2 (HZO) films using electron\nptychography. The use of this technique on this material is very valuable as it allows to\nresolve lighter elements (i.e., oxygen) which play an essential role in the polarisation\nin HZO. The spatial resolution of this method (of the order of several pm) is also\nremarkable and allows to make finer structural observations than in conventional\nelectron microscopy. Their results reveal the existence of a multitude of structural\nphases in HZO (previously unknown, or offering clear experimental evidence to\nsupport them and close a debate on the nature of ferroelectricity in HZO), and observe\na range of line defects, including charged domain walls (CDW), head-to-head domains\nand anti phase boundaries within single-grain images. These findings shed light on the\nmechanisms behind the ferroelectricity in HZO, of high relevance for the design of\nfuture smaller-scale electronic devices in particular FE memories.\nI believe that the data, analysis and interpretation in this paper are very solid, and the\nevidence strong and of sufficiently high quality.\nAdditionally, there are many smaller points in the manuscript that could substantially\nbe improved; most of them having to do with general properties of HZO as well as\nsome important details in the structure which appear, in my opinion, overlooked. Most\nof the points below are relatively minor compared with the quality of general findings,\nwhich are again, of high quality. I believe however that these points should be clarified\nand/or discussed to make this paper fully suitable for publication and increase overall\npublication quality. If the points below are considered/discussed, I believe that the paper\nis suitable for publication in Nature Communications.\nResponse: We sincerely appreciate the reviewer’s recognition of our manuscript. We\n8\nalso thank the reviewer for the rigorous comments and valuable suggestions which\nhelped us to further improve our work. For each point, we have made a detailed answer,\nas shown below.\nStructural HZO phases: points to clarify\nComment 1: Given the large variety of phases of HZO discussed in this paper, a\nsummary figure displaying the unit cells with structural models of FE-O; AFE-O; M;\nM’; C/T phases is necessary in my opinion (this can be supplementary information\nfigure). Some of these phases are referred to by their polarization (AFE, FE) and some\nby their crystallography (M, C/T) and it is sometimes confusing, a structural summary\nfigure would definitely improve this significantly. Additionally, qualitative polarization\nvectors should also be drawn in this new figure to directly visualise the nature of the\ndipoles in all these new phases, if possible.\nResponse 1: We thank the reviewer for raising this important point. In the revised\nversion, we have added a structural summary figure (Fig. S5, with space group and\nqualitative polarization vectors). We also revised Fig. 1 to address the confusion\nbetween crystallographic and polarization-based phase denominations.\nThe explicit denotation of ferroelectric (FE) and antiferroelectric (AFE) subphases\nwithin the orthorhombic (O) phase of HZO is based on the key consideration that under\nthe b-axis out-of-plane orientation, all other phases (e.g., M, M’, C/T) are non-polar,\nwhereas the O phase hosts two distinct subphases: FE (with net polarization) and AFE\n(with antiparallel dipoles), thus we add explicit labeling to distinguish their intrinsic\npolarization characteristics. We have labeled the polarization vectors in the Fig.1 and\nvalues in the caption. We believe these revisions significantly improve the readability\nand completeness of the manuscript.\nmagnification plan-view HAADF-STEM of HZO freestanding film. White arrow\nindicates sample’s edge. b, HAADF-STEM image shows the grain distribution of film.\nc, Polarization–electric field (P–E) hysteresis loops at 10 kHz. d, Experimental setup\nof MEP. The inset is a convergent beam electron diffraction (CBED) image from dataset.\ne, Fourier transform of projected phase image in Fig. S3 of the SM, as dashed circle\ndenotes real space resolution of 25 pm. f, Projected phase images from multislice\nelectron ptychographic reconstructions of experiments (left side) overlapped with\natomistic structure models, the corresponding simulated reconstructions (middle side),\nand the experimental histograms of lattice parameters for each phase (right side). FE\nphase (O1 is 41±2 pm, O2 is 60±5 pm, a1 is 235±6 pm, c is 257±3 pm and a2 is 265±6\npm, polarization is 56±6 pm), AFE phase (O1 is 44±3 pm, O2 is 68±6 pm, a1 is 233±5\npm, c is 261±4 pm and a2 is 264±5 pm, polarization is 56±6 pm), […]\nof phases. The regions of phases are highlighted with color. The colored arrows\nindicate the directions of polarization. b, Histograms of the phases.\nFig. S5. Atomic models of various HZO phases with space group, annotated lattice\nparameters, and polarization vectors. The corresponding lattice constants and\npolarization values are labeled in the caption of Figure 1 in the main text.\nComment 2: While the image reconstructions (which lead to higher resolution images) are convincing, possible twinning from the structures have not been considered to explain the different apparent phases. The lattice parameters of HfO2 (I could not find a structural file for HZO) in the Pca21 structure are 5.005 Å, 5.033 Å and 5.219 Å in\nthe a, b, and c directions respectively, sufficiently close together (especially a ≈ b,\nwithin ~0.5%) which suggests that 90º-rotated twin domains should be considered,\nat least in principle. Is twinning a possibility here, or can it be ruled out? In other words,\ncan some of the new phases be explained by local domains that are simply rotated by\n90º?\nResponse 2: We sincerely appreciate the reviewer for highlighting this critical\n11\nconsideration. First, we emphasize that multislice electron ptychography (MEP) is, in\nprinciple, particularly well-suited to identify 90° domain walls (DWs) or similar twin\ndomains, owing to its simultaneous, quantitative imaging of cation and oxygen\nsublattices, precise determination of lattice parameters, and direct mapping of local\npolarization with ultra-high atomic resolution. The 90° DWs would necessarily produce\na clear reorientation of the polarization vectors, which is easy to distinguish in MEP\nreconstructions. Second, we confirm that the 90° DWs in TiN/HZO/TiN capacitor\nstructures have been reported in previous studies 24, 25. Previous reports observing the\n90° DWs have mostly focused on TiN/HZO/TiN capacitor structures, and were often\nobserved in the rapid thermal annealing (RTA) cooling stage 24 or wake-up films 25,\nwhich also indicates that observing the 90° DWs is not easy. In the present freestanding\nHZO films, we do not observe the 90° DWs. This difference may be related to the\nproperties of the self-supporting thin film itself. To enhance the comprehensiveness of\nthe discussion, we have further supplemented the relevant discussion in the main text:\nNew line 226-230: Furthermore, MEP enables us to successfully identify the 180° H-\nH CDW in HZO freestanding films and provides a solid basis for further domain-wall\nstudies. Future work could focus on other domain structures, specifically 90° DWs that\nhave been previously observed in TiN/HZO/TiN capacitors 24, 25, to advance HZO\ndomain engineering.\nComment 3: The first sentence in the introduction refers to HZO, but references 1-3\nsupporting it concern HfO2 and not Hf0.5Zr0.5O2. A very brief paragraph describing\nthe differences between HfO2 and HZO is required in my opinion: why is Zr required\nhere, and what are the (physical and engineering) advantages to adding Zr to the HfO2\nmatrix, already natively ferroelectric? Generally there is a little bit of confusion\nthroughout the article as to whether the literature and referred-to physics concerns HfO2\nor to HZO; I am guessing that a lot of the physics are similar, but this should be made\nclear in the text in my opinion.\nResponse 3: We sincerely thank the reviewer for this insightful comment. The\n12\nreferences [1-3] primarily discuss the initial discovery of ferroelectricity in doped HfO₂\nor HfO -ZrO superlattices, we have revised the HZO related references and brief\n2 2\nexplanatory sentence as below. In HfO\n2\n-based ferroelectrics, ferroelectricity originates\nfrom a metastable polar phase, whose formation is strongly influenced by doping and\noxygen vacancies. Various dopants, such as Si, Al, Gd, Y, Zr, and Ce, can induce or\nenhance ferroelectricity through trivalent or tetravalent ion substitution or solid-\nsolution formation 26, 27, 28, 29. Among these, Among these, Zr is particularly noteworthy\ndue to its chemical similarity to Hf, which allows the formation of a continuous solid\nsolution across the HfO -ZrO system 30. Introducing Zr not only helps stabilize the\n2 2\nferroelectric orthorhombic phase but also offers practical advantages in property tuning\nand cost. Within the Hf Zr O system, the composition Hf Zr O (HZO) exhibits\n1-x x 2 0.5 0.5 2\nthe highest remanent polarization 30, which is why we selected it as the focus of this\nstudy. We acknowledge the need for clearer distinction. In the revised manuscript, we\nhave modified the introductory sentence and added a brief explanatory sentence to\nexplicitly clarify the relationship between HfO and HZO:\n0.5 0.5 2\nferroelectricity at room temperature and excellent compatibility with complementary\nmetal-oxide-semiconductor (CMOS) technology 15, 31, 32. As a continuous solid solution\nof HfO₂ and ZrO₂, HZO benefits from Zr-induced stabilization of the ferroelectricity\nand exhibits the highest remanent polarization in the Hf ZrₓO series 26, 27, 28, 29, 30.\n1-x 2\nComment 4: In general, where is the Zr in the HZO matrix? Are we in presence of a\nZr/Hf solid solution, where occupancy of the metallic sites randomly distributed, or is\nthere inherent structure where Zr and Hf occupy preferential sites? Based on the\ndata, the contrast in MEP images does not allow to distinguish Zr/Hf. Can the authors\ncomment on that, and mention it in the text? Are there other studies that mention this\nZr/Hf distribution, whether experimentally resolving Zr/Hf or theoretically\ninvestigating this aspect of the crystalline structure of HZO? Generally, (similar to\nquestions 3) does Zr/Hf occupancy impact the ferroelectric nature of the material? Can\n13\nthese questions be answered at least partly with a energy dispersive measurements\nwhere presumably Hf and Zr lead to different contrasts?\nResponse 4: We sincerely thank the reviewer for this insightful observation. HZO\nforms a continuous solid solution where Zr and Hf randomly distributed in the the\nmetallic sites 26. As our depth resolution is much inferior than the lattice scale, so the\ncontrast in MEP images does not allow to distinguish Zr/Hf. Currently, experimentally\nand atomically resolving the random Zr/Hf distribution in such solid solution is still\nchallenging, and EDS element mapping (Fig. R3) also confirm uniform Zr/Hf mixing\nacross the film. The theoretical calculations also validate this random occupancy 33, 34.\nWe hope that the development of MEP especially the ptychographic tomography could\nresolve the questions that you cautious. Absolutely, Zr/Hf occupancy impact the\nferroelectric nature of the material as noted in the response 3. And we revised the related\ncontent in the main text and add the Fig. R3 as Fig. S17:\nNew Line 122-123: It should be mentioned that the MEP images cannot differentiate\nwhether the metallic sites are occupied by Zr or Hf due to the limitation of depth\nresolution.\nNew line 210-214: Due to the continuous solid-solution nature 26 of Hf₀.₅Zr₀.₅O₂, the\ncontrast of metallic sites in MEP images does not allow direct discrimination between\nHf and Zr atoms. Atomic-resolution EDS mapping (Fig. S17) confirms a uniform Hf/Zr\ndistribution with an approximately 1:1 ratio across the film, consistent with random\ncation occupancy feature.\nFig. R3. Atomic EDS element mapping with HAADF (a), Hf (b) and Zr (c), while the\nrelative atomic ratio of Hf and Zr is 50.03% and 49.97%.\nconfigurations and domain wall. Have the authors also observed a tail-to-tail (T-T)\ndomain wall, where polarisation is reversed in both domains with respect to the head-\nto-head configuration? Do the authors expect that H-H and T-T have identical energies?\nResponse 5: We sincerely thank the reviewer for this important question. Despite\ncareful examination of the MEP images across multiple sample regions, we did not\nobserve tail-to-tail (T-T) domain walls in our HZO thin films.\nPrevious theoretical studies have suggested that the formation and relative stability\nof H-H and T-T domain walls in hafnium-based oxides are strongly influenced by local\nboundary conditions, including oxygen vacancy distribution, interfaces, and electrode\neffects 35. Under such conditions, the energetic equivalence between H-H and T-T\ndomain walls is not generally expected. Moreover, the experimentally observed H-H\ndomain wall structure in our work differs from existing theoretical models 35, 36,\nindicating that its stabilization mechanism may be more complex than currently\ncaptured by idealized calculations.\nAs a result, we refrain from directly comparing the energies of H-H and T-T domain\nwalls based on the present H-H CDW experimental data alone. Addressing the relative\nstability and energetics of H-H and T-T domain walls will require further systematic\nexperimental and theoretical efforts, which we consider an important direction for\nfuture work.\nComment 6: Is MEP acquired before or after the P-E measurements (or on a different\nset of grains/sample altogether) ? Are the different phases uncovered in this paper\n“temporary” and will not survive polarisation at large fields? e.g. does the AFE phase\nbecome FE above a certain field? Without possibility of reversal onto the AFE phase?\nLine 175, do FE and AFE coexist within the same grain even after an applied field (such\nas those utilised in Fig 1c)? Or is the AFE state robust and its polarisation remains\nantiparallel after applied field?\nResponse 6: The sample were removed from the substrate and further prepared for\nfilms. The films are in a pristine state, meaning that no external electric field or\nelectrical cycling was applied, where the observed phases therefore correspond to the\nas-grown, thermodynamically stabilized configurations. And the FE and AFE phases\n(as well as O and M phases, Martensitic phase transformation) can reverse under\nexternal field like previously reported 12, 23, 24, 37. The AFE state is robust and its\npolarization remains antiparallel after different process as shown in Fig. R4.\n[Figure Redacted]\nFig. R4. The observation of FE and AFE state in different state (a, pristine b, after wake-\nup effect and c, after fatigue process) of HZO. [adapted from Nature Communications\n(2022)13:645 ]\nComment 7: Line 112, the relative presence of the different phases is calculated and\nsuggests a most significant presence of FE-O phase. Does this contradict the claims\nwhere AFE and FE phases have the same energy? I think in light of the future\napplications of this materials, a claim on whether the AFE phase can be switched into\nthe FE phase by applied field, and if the AFE phase is reversible after polarisation is\npossible would be of great value. Beyond the energy difference between the two FE\nand AFE phase, it would be interesting to know (approximately or if there are\ncalculations that indicate this) the value of the energy barrier ∆ that separates FE to\nAFE, to know if switching is indeed feasible at reasonable biases/fields. I’m aware this\nis a difficult question, but if these have been investigated in the past by the authors or\nin a different group, this should be made clear in the text.\nResponse 7: We thank the reviewer for this insightful comment. First, the statistically\nhigher fraction of the FE-O phase observed in our experiments does not contradict\nprevious reports that the FE and AFE phases are nearly degenerate in energy. First-\nprinciples calculations have shown that the energy difference (12 meV / f.u. ) between\nthe FE-O and AFE phases is very small, [details in Lee et al., Science 369, 1343-1347\n(2020)] 38, while the experimentally observed phase distribution is additionally\n16\ninfluenced by strain, dopants, grain boundaries, and defect chemistry (particularly\noxygen vacancies), which can preferentially stabilize the FE-O phase during film\ngrowth and post-processing 26, 28, 39. Second, we further emphasize that HZO is not\nmerely a prospective material but is already implemented in practical device\napplications, like CMOS-compatible platforms, ferroelectric field-effect transistors\n(FeFETs) and ferroelectric capacitors for non-volatile memory technologies 29, 40, 41.\nThird, as mentioned in Response 6, previous experimental studies have demonstrated\nthat the AFE phase in HZO can be transformed into the FE phase under external fields,\nwhere the reversibility depending on microstructure, defect concentration, and cycling\nconditions 12, 23. This remains an important research direction in the field of hafnium\noxide, we have clarified this point in the revised manuscript:\nNew line 196-199: Due to the negligible energy difference between the FE-O and AFE-\nO phases 38, they always coexist within a single grain, but a higher presence of the FE-\nO phase in the pristine film is reasonable, as the phase distribution is strongly\ninfluenced by factors, like dopants, strain, and defect chemistry, preferentially stabilize\nthe FE-O phase in HZO thin films 26, 27, 28.\nComment 8: Line 154, how does the observations agree with a “scale-free FE feature”\nand what does this mean in this context?\nResponse 8: In this context, “scale-free” refers to the characteristic behavior of\nferroelectric hafnium-based oxide in which polarization is governed by local atomic\nconfigurations and can remain robust at the scale of individual unit cells, largely\nindependent of the lateral size of domains or the presence of nearby domain walls 38. In\nour experiments, we observed the polar layers immediately adjacent to the 180° H-H\nCDW retain bulk-like polarization as well as the FE and AFE phases coexisting in a\nsingle grain. These observations are consistent with previously computation reported\nscale-free ferroelectric behavior in hafnium oxide. And we revised this point in the\nrevised manuscript:\nLine 154: The polar layers (i.e., Layer_1 and Layer_3, black and yellow boxes in Fig.\n17\n3a) adjacent to the 180° H-H CDW retain bulk-like polarization. They are not affected\nby the DW itself. The coexistence of FE and AFE phases within a single grain further\nsupports the scale-free ferroelectric nature of hafnium oxide 38.\nRegarding the oxygen vacancies\nComment 9：The observation that oxygen vacancies are key to the presence of CDW\nis interesting, but is also concerning in terms of the supposed mobility of these CDW,\npotentially crucial for the development of HZO-based memory devices. Did the authors\nobserve CDW mobility? Can the authors comment on the mobility of oxygen vacancies?\nDo the oxygen vacancies stem from a non-stoichiometric composition of HZO? Is it\npossible to have a control the effective oxygen vacancy concentration during the\ngrowth/synthesis of HZO?\nResponse 9: We thank the reviewer for raising these important questions regarding the\nrole of oxygen vacancies. In our work, we did not perform in-situ experiments.\nTherefore, we do not make claims regarding CDW mobility in this work.\nRegarding oxygen vacancy mobility, prior studies have shown that oxygen vacancies\nin HZO can be mobile under sufficiently electric fields or ion bombardment 13, 15, 42. In\nthis sense, oxygen vacancies may allow field-driven redistribution during device\noperation. We think the oxygen vacancies observed in this work are most likely intrinsic\npoint defects commonly present in HZO thin films rather than originating from a non-\nstoichiometric composition.\nImportantly, the effective oxygen vacancy concentration in HZO is known to be\ntunable through growth and processing parameters, including oxygen partial pressure\nduring deposition, dopant chemistry, and thermal treatment 26, 29, 43, 44. This tunability\nhas been widely exploited to optimize ferroelectric phase stabilization, wake-up\nbehavior, and endurance in HZO-based memory devices. Our observations therefore do\nnot preclude CDW mobility, which remains experimentally challenging but represents\nan important direction for future investigations.\nComment 10：Can the density of oxygen vacancies be estimated on the overall material,\nand in the grain boundary areas?\nResponse 10: In this work, we performed EELS analysis around the grain\n18\nboundary areas (Fig. S9, as new Fig. S11), which provides qualitative evidence that\noxygen vacancies are enriched in the grain boundary regions. The EELS results\nconsist with our MEP reconstructions, indicating that oxygen vacancies preferentially\naccumulate at grain boundaries. Based on the quantitative phase analysis from MEP\n(Fig. 3d), we estimate that the oxygen vacancy concentration in the surrounding GB\nregions is approximately 7-12%, we as mentioned in main text. For the overall film,\na reliable quantitative estimation of the oxygen vacancy density remains challenging.\nFor example, X-ray photoelectron spectroscopy (XPS) measurements are hindered by\nsevere charging effects in the insulating HZO films, preventing accurate determination\nof the global vacancy concentration.\nNew line 174-176: This quantitative analysis (Fig. 3d) shows that the concentration of\nV within the cell at the CDW reaches up to 20%, whereas the concentration near the\nO\nGBs is approximately 7-12%.\nFig. S11. V near grain boundary. a, Enlarged image near the grain boundary from\nO\nFig. 2c. Bulk (b) and boundary (c) intensity profile show the exist of V . d, The HAADF\nO\nimage with corresponding region of eels. e, O-K EELS spectrum. Peak shape changes\nindicated by the red arrow also suggest higher concentration of V at grain boundary.\nO\nComment 11：Can the authors resolve with MEP whether the oxygen vacancies (near\nthe GB) occur preferentially at the O1 or O2 sites (centro- and non-centro-symmetric\nsites)? Given the large suppression of the polarisation near GBs, it is expected that at\nleast the O2 sites are primarily affected, but considering the quality of the MEP data,\nit may be possible that the authors have the experimental data to support this. Line 195,\n19\n“The Vo acts as active structural mediators rather than passive pinning centers” can the\nauthor develop this sentence? It is not clear what is meant here.\nResponse 11: We thank the reviewer for this insightful comment. As shown in Fig. S11\nand Fig. R5, we find that the oxygen vacancies near grain boundaries seems\npreferentially occur at the O2 sites (non-centro-symmetric sites), while the O1\n(centrosymmetric) sites remain comparatively less affected. We think the underlaying\nmechanisms may need more computational study.\nRegarding the statement that “oxygen vacancies act as active structural mediators\nrather than passive pinning centers,” we clarify that this refers to the role of oxygen\nvacancies in actively modifying the polarization configuration. Specifically, oxygen\nvacancies at O2 sites locally alter bond geometry, symmetry, and oxygen displacement\npatterns, facilitating polarization suppression near grain boundaries as our work\nobserved. Meanwhile, we observed that oxygen vacancies participate actively in the\nconfiguration and stabilization of H-H CDW, rather than merely immobilizing\npassively them. We have revised the manuscript to clarify this physical meaning.\nLine 195: The Vo act as active structural mediators by suppressing polarization near\ngrain boundaries (Fig. 2c and Fig. S11 in SM) and modifying the polarization\nconfiguration (e.g., the 180° H-H CDW), rather than passive pinning centers.\nFig. R5. The image with red arrows indicate the oxygen vacancies preferentially exist\nat the O2 sites.\nComment 12: Related to Fig. 3: is the O-related phase decrease a consequence of\nvacancies that are localised there? Can the authors rule out a depth-dependent\nconfiguration, where each atomic layer parallel to the image plane has a different\npolarisation, and the data is an average of all these configurations? i.e the exact\nboundary between the two polarisation in Layer_2 is not exactly perpendicular to the\n20\nimage plane, but tilted?\nResponse 12: We thank the reviewer for this insightful question. We have polarized\nmapping of different slices along the depth directions (Fig. R6), which shows that the\npolarization at the H-H CDW is basically unchanged and the Fig. 3c is the average of\nthe results with s.t.d.. As shown in Fig. 3b, the depth-resolved profile reveals the oxygen\ndistribution in Layer_2 along the beam direction, which shows that oxygen vacancies\nin the depth direction are also localized near the CDW. This observation is consistent\nwith analysis shown in Fig. 3d, supporting the interpretation that the reduced O-related\nphase contrast arises from localized oxygen vacancies. We have included the Fig. R6\nas Fig. S13 was added to the SI and revised the related content in main text.\nNew line 167-168: As shown in Fig. 3c and Fig. S13 in SM, there exists a non-polar\nunit cell at the center of the DW with almost equal but opposite polarization on either\nside (Layer_2) along depth.\nFig. R6. a-f, The depth-dependent polarization mappings of the H-H CDW, with\natomic fitted markers where the A atom means Hf/Zr atom.\nRegarding the instrumentation\nComment 13. How does possible Joule heating affects the local temperature of the\nmaterial? Could this affect the polarisation of the material? What is the\nCurie/ferroelectric ordering temperature in HZO?\nResponse 13: We thank the reviewer for raising this important point. Beam-induced\nJoule heating can affect the local temperature and polarization behavior of hafnium-\nbased ferroelectric materials that previous studies have investigated electron-beam-\ninduced effects in the films under high current density (e.g., Martinez transition) 22, 44.\nCurie/ferroelectric ordering temperatures typically in the range of ~ 400-500 °C\ndepending on composition and processing condition 45, 46, 47, 48. For instance, Nob et al.\ndemonstrated the presence of saturated P-E hysteresis loops of HZO films even at\n400 °C 47. In this work, our MEP measurements were conducted with defocused probe\n(~ 10 nm) and low probe current (~ 20 pA) in short time (< 1 min), where the beam-\ninduced heating is expected to be minimal. Based on these considerations, we conclude\nthat beam-induced thermal effects do not play a significant role in the polarization\nbehavior observed in this study, and do not affect the conclusions drawn from our\natomic-scale measurements.\nComment 14. Naively, the sentence line 72 is confusing since it is mentioned that the\nlateral resolution of MEP is 25 pm, while the displacement is measured with a precision\nof ±6pm. Can the authors briefly explain how it is possible to resolve displacement with\na precision 4x finer than the instrumental resolution?\nResponse 14: The quoted 25 pm lateral resolution refers to the smallest spatial feature\nthat can be directly resolved in the reconstructed image, whereas the reported ±6 pm\ndisplacement precision reflects the statistical precision with which atomic positions can\nbe determined by fitting to high signal-to-noise atomic intensity maxima. These two\nquantities describe fundamentally different limits. Similar phenomena are very normal\nin MEP studies4, 49. In MEP, the atomic column positions are obtained by sub-pixel\nfitting of the reconstructed phase contrast, enabling localization precision better than\nthe nominal spatial resolution, similar to what is routinely achieved in HAADF images.\nComment 15. It is not clear to me whether the MEP resolves a single atomic plane\nparallel to the image plane, or if it resolves the whole crystal thickness and obtain a\nintegrated intensity originating from every atomic plane in the crystal? In other words,\nwhat is the probed thickness of the MEP method?\nResponse 15: For now, we cannot resolve the single atomic plane parallel to the image\nplane, we used the multi slices to get the projection information of different depth.\nFor example, we used 0.5 nm/slice for the reconstruction in Fig. 3, which means we get\nthe average information of every 0.5 nm along the depth direction.\nComment 16. How was the P-E measurement done? Supplementary material\nparagraph page 4 does not mention if this was this done over a single grain, or over a\n22\nmacroscopic sample. The P-E measurement suggests that the polarisation can still be\nenhanced using a larger field (not saturated within the applied field range). Are there\nlimitations such as breakdown effects upon too-large applied fields?\nResponse 16: Thank you for your valuable comment, we would like to provide\nadditional details on the ferroelectric P-E measurements. A ferroelectric P-E\n(polarization-electric field) hysteresis loop is typically measured using a capacitor-like\nstructure: a ferroelectric layer sandwiched between top and bottom electrodes. In this\nwork, we used Pt/HZO/LSMO heterostructure to measure the polarization intensity of\nHZO films, therefore this was done over a macroscopic sample. A ferroelectric tester\napplies a periodic electric-field sweep to the sample while measuring the current/charge\nresponse. The instrument integrates the displacement current to obtain the polarization\n(P), and relates it to the applied field (E = V/t) (where t is the ferroelectric thickness) to\ngenerate the P-E loop.\nIn ferroelectric polarization measurements, increasing the applied voltage can indeed\nlead to a higher remanent polarization. However, because our ferroelectric samples are\nvery thin (5 nm), applying higher voltages often results in dielectric breakdown and/or\nsevere leakage currents. Therefore, during the measurements, we limited the applied\nvoltage to a safe operating range.\nLine 113-119 in SM: The ferroelectric P-E hysteresis loops were measured using a\ncapacitor-like structure comprising a Pt/HZO/LSMO heterostructure. A precision\nmultiferroic analyzer (RADIANT Tec. Inc.) was employed to measure the polarization\nintensity of the HZO films on a macroscopic scale. A tungsten probe was used for P-E\nmeasurements, with a frequency of 10 kHz for the triangular pulses applied to switch\nthe polarization of the ferroelectric layer. The analyzer applied a periodic electric field\nsweep while measuring the current/charge response, integrating the displacement\ncurrent to calculate the polarization (P), which was related to the applied electric field\n(E = V/t), where t is the thickness of the ferroelectric layer. Consequently, the P-E loop\nwas generated, elucidating the ferroelectric properties of the HZO films.\nComment 17. The reconstructed probe structures are briefly discussed (line 89). What\ndo these figures tell us about the probe? Is it sharp enough and of good quality?\nJust a very brief comment is expected here.\nResponse 17: We thank the reviewer for this question. The reconstructed mixed-state\nprobe indicates that the electron probe is robust and well-reconstrued. A reliable probe\nreconstruction is a necessary prerequisite for obtaining physically meaningful\n23\nptychographic images, we therefore include the probe reconstruction to demonstrate\nthat probe quality is not a limiting factor in the present study. And we polished the\nsentence in the main text to help understanding:\nNew line 101-102: The reconstructed probe structures (Fig. S4 in SM) are robust and\nconsistent with those reported in previous studies 6, 50, 51, 52.\nModeling and theory of HZO, future applications\nComment 18. The polarisation is calculated as if proportional to the displacement in\nHZO? Are there theoretical models that describe the polarisation with respect to the\ndisplacement in HZO? Could the new phases uncovered in this paper be described using\nthe same theory? Intuitively, small displacements leading to a proportional polarisation\nfeels like a valid approximation, but the displacement involved here are significant (~\n50-60 pm) and it would be good to cite the correct work if appropriate. A brief comment\non this would be greatly appreciated.\nResponse 18: Yes! First, the polarization is calculated as proportional to the\ndisplacement in HZO as we stated in SM:\nLine 86-90 in SM: For polarization analysis, the obtained relative displacement of\ncations and anions was used to calculate polarization by , where e is𝛿 t he\n𝑒\nelectronic charge, V is the volume of unit cell and Z\ni\nis𝑃 𝑠B=or𝑉n𝴴 c𝴴h𝴴𝑖a𝑍r𝴴𝑖ge values, δ is\ndisplacement/shift of atom (i) from their centrosymmetric position 53. The Born charge\nvalue for the A site is 5.15, which is derived as the mean value of 5.0 for Hf and 5.3 for\nZr 34, 54.\nAnd the new phases uncovered in this paper also can be described using the same\ntheory as the unit cell will change with different phases. As we cited the theorical works\nin the main text [e.g., Lee et al., Science 369, 1343-1347 (2020) and corresponding SI],\nwhich discuss in detail its polarization model and related numerical values align well\nwith our experimental results (we already discuss in main text). This material is indeed\ndifferent from conventional perovskite structures, with a polarization layer and a space\nlayer as we stated the atomic model. The polarization displacement of the polarization\nlayer is indeed as high as 50-60 pm.\nComment 19. The authors mention that HZO is compatible with Si-based electronics\nas supported by a number of references which mostly mention HfO2. Do the authors\nhave hypotheses in terms of the impact of a Si substrate in terms of impact over the\nferroelectric properties in HZO? Could the substrate interactions lead to the quenching\n24\nof the polarisation, or to its pinning, or other effects?\nResponse 19: We appreciate the reviewer’s insightful question. HZO and HfO₂ belong\nto the same hafnium-based oxide family, sharing similar Si-compatibility mechanisms, ,\nwhich is why Si compatibility is often discussed using HfO₂-based literature. In\npractical device structures, interactions with Si substrates, through interfacial strain,\nelectrostatic boundary conditions, and defect chemistry, are indeed known to influence\nthe ferroelectric properties of HZO, potentially affecting polarization magnitude,\npinning behavior, and phase stability13, 29, 55, 56.\nHowever, majority of the studies deliberately exploit substrate and electrode effects\nto enhance ferroelectric performance through strain engineering, dopant stabilization,\nand interface control. In contrast, the primary aim of the present work is to reveal the\nintrinsic atomic-scale polarization configurations and defects in HZO. For this reason,\nwe employed substrate-free freestanding HZO films, which eliminate substrate-induced\nclamping, interfacial charge effects, and strain gradients. This approach allows us to\nisolate the fundamental behavior of polarization, charged domain walls, and oxygen\nvacancies without complications arising from substrate interactions.\nTypos/grammar:\nLine 43 “For example, …” misses a verb such as “have been demonstrated”.\nLine 72, it reads “intrinsic polarization magnitude of HZO to be ~ 56±6 pm” but the polarisation\n(usually in C/m2 or similar) is expressed in terms of displacement (pm); I believe it should be\nclarified.\nLine 80, “to eliminate the influence [of phenomena] such as interface effects, …”\nLine 102, “analyzed [in detail] in Fig. 1f”\nLine 105, “the oxygen atomic distances in the AFE and M’ phases [are] slightly larger than in the\nFE phase”\nLine 109, the phase “transformation” is not really mentioned, rather the coexistence of the two\nphases is discussed.\nLine 143, “with larger field of view confirms that the CDW is exist near the GB.” This is\ngrammatically strange.\nLine 154, “This observation supports that the scale-free FE feature of hafnium oxide.” this is\ngrammatically strange, too.\nResponse: We appreciate the reviewer’s careful attention to these typos. Given the\nnumber of corrections made, we have addressed all identified typos in the revised\nmanuscript, and all changes are provided in our highlighted version for easy reference:\ntraditional perovskites) for high-density FeRAMs and negative capacitance for low-\npower FeFETs, which have been demonstrated 26, 29, 31, 57.\nLine 72: We determined the atomic structures of multiple phases and measured the\nintrinsic polarization displacement of HZO to be ~ 56±6 pm, corresponding to a\npolarization of ~ 34±4 μC/cm2.\nLine 80: to eliminate the influence of phenomena such as interface effects\nLine 102: were analyzed in detail [Fig. (1f)].\nLine 105: AFE and M’ phases are slightly larger than in the FE phase\nLine 109: providing more details of the coexistence of M’ and M phases including\nstrain effects and atomic relaxations\nLine 143: with a larger field of view confirms that the CDW exists near the GB.\nLine 154: retained a bulk-like state and remained unaffected by the DW itself,\nsupporting the scale-free FE feature of hafnium oxide\n*******************************************************************************\nReviewer #3\nComment: Gao et al. present the application of multislice electron ptychography to the\nHFO material system, which is a promising candidate for the realisation of novel\nferroelectric devices. The authors achieve an impressive resolution of 25 pm allowing\nthem to measure atomic displacements and polarisations directly. Several different\nsample regions exhibiting different crystal phases and defects like grain boundaries\nwere analyzed and their detailed atomic structure is revealed.\nThe results presented are highly relevant and worth publication and are potentially\nsuitable for an high-impact journal like Nature Communications. However, the\nmanuscript is not well organized so that the story line is hard to follow. The reader has\nto switch back and forth between manuscript and SI to follow the story. Clearer\nstructuring the manuscript, e.g. by adding sub-chapter headings would clearly improve\nthe readability. Moreover, several important experimental details are missing, hindering\nthe reproducibility of the findings. This might be caused by shortening an existing\nmanuscript in order to fit the guidelines of Nature Communication. In addition, there is\na significant amount of wording issues. Therefore, I recommend proof reading by a\n26\nnative speaker.\nAccordingly, I suggest major revision prior to publication.\nPlease find my detailed comments below.\nResponse: We sincerely appreciate the reviewer’s recognition of our manuscript and\nthe helpful comments for improving our work. Sub-chapter headings were added to\nimprove the readability. In addition, the manuscript has been thoroughly revised for\nclarity and language, with careful proofreading to improve wording and overall\npresentation. Detailed responses to each specific comment are provided below.\nDetailed scientific comments\nComment 1: 90-92: To allow an easier comparison of simulation and experiment, both\nshould be depicted next to each other. This means, the simulated pictures should be\nshown in Fig 1 or the experimental images should be shown in Fig S5.\nResponse 1: Thank the reviewer for the valuable comment. We have merged the Fig.\nS5 into the Fig.1 as shown below.\nFig. 1. Imaging atomic structures of HZO freestanding thin film. a, Low-\nmagnification plan-view HAADF-STEM of HZO freestanding film. White arrow\nindicates sample’s edge. b, HAADF-STEM image shows the grain distribution of film.\nc, Polarization–electric field (P–E) hysteresis loops at 10 kHz. d, Experimental setup\nof MEP. The inset is a convergent beam electron diffraction (CBED) image from dataset.\n27\ne, Fourier transform of projected phase image in Fig. S3 of the SM, as dashed circle\ndenotes real space resolution of 25 pm. f, Projected phase images from multislice\nelectron ptychographic reconstructions of experiments (left side) overlapped with\natomistic structure models, the corresponding simulated reconstructions (middle side),\nand the experimental histograms of lattice parameters for each phase (right side).[…]\nComment 2: 104-106: The authors claim O1 and O2 distances in the FE phase (41±2,\n60±5) are slightly smaller than those in the AFE (44±3, 68±6) and M’ (46±4, 113±6).\nThis feels unwarranted for O1, since the differences lie well within the margin of error\nand confusing for O2, since the distance in M’ is nearly double that of FE.\nResponse 2: We thank the reviewer for the careful reading and for pointing out the\nambiguity in the original wording. We agree that for the O1 sites, the differences in the\nmeasured interatomic distances among the FE, AFE, and M’ phases fall within the\nexperimental uncertainty and should not be overinterpreted. Our intention in Lines 104-\n106 was solely to report the statistical distributions of the measured O1 and O2\nseparations, rather than to imply a definitive structural difference. We have therefore\nrevised the text to remove the comparative statement and now present the values in a\npurely descriptive manner, avoiding qualitative interpretation beyond the reported\nuncertainties:\nLine 104-106: The FE phase features centrosymmetric non-polar oxygen atoms (O1)\nand non-centrosymmetric polar oxygen atoms (O2), with measured interatomic\ndistances of 41 ± 2 pm and 60 ± 5 pm, respectively. The corresponding O1 and O2\ndistances for the AFE and M’ phases are summarized in Fig. 1 representing the\nstatistical distributions obtained from our measurements.\nComment 3: 106-107: The provided literature overview (table S1) shows experimental\nresults ranging from 5.01-5.10 for a and 5.00-5.09 for c. Firstly, the authors only\nprovide half lattice parameters for their own results, hindering a direct comparison.\nSecondly the authors’ results (a: 5.00, 4.97, 5.17; c: 5.14, 5.22, 5.22) all lie outside the\nliterature range, undercutting their assessment of being “highly consistent”.\nResponse 3: We thank the reviewer for raising this point. As summarized in Table S1,\n28\nboth experimental and computational studies report a broad distribution of lattice\nparameters for ferroelectric HZO, with a and c values ranging approximately from 4.9\nto 5.25 Å, depending on dopant chemistry, strain state, substrate constraint, and\ncomputational methodology. Within this broader context, our measured values fall well\nwithin the reported spread. By merely comparing with previous experimental\nmeasurements, our results also show deviations of no more than 3% from earlier reports,\nwhich is considered reasonable. To enhance the precision and clarity of our expressions,\nwe have revised the wording in the main text:\nLine 106-107: The extracted O phase lattice parameters fall within the range reported\nin previous experimental and computational studies of ferroelectric HZO (Table S1 in\nSM).\nComment 4: 116-118: Here ref 53 is cited for the theoretical value of the polarization.\nLater on (line 171) refs 17,18,53 are cited in this context. This is inconsistent. Moreover,\nin refs 18 and 53, I could not find a value for the polarization. Please verify if the correct\nsources are referenced.\nResponse 4: We thank the reviewer for pointing out this inconsistency. We have\ncarefully re-checked the cited references and agree that the original citation was unclear.\nSpecifically, the ref. 18 [Lee et al., Science 369, 1343-1347 (2020)] stated the\npolarization and structural information that “Our estimated spontaneous polarization is\n41 µC/cm2, within the range of measured values (20-50 µC/cm2) (1, 38, 41-43)” (details\nwith its Fig. S2 in SI. The ref. 53 [ Materlik et al., Journal of Applied Physics 117,\n134109 (2015)] primarily focus on structural phase stability but do not explicitly report\na polarization value, thus we agree that citing Ref. 53 in this context was inappropriate.\nConsequently, we have revised the manuscript to correct the citations:\nLine 116-118：Statistical analysis of O phase grains (Fig. 2b) suggests that the\npolarization displacement is ~56±6 pm with corresponding spontaneous polarization\n(P ) of 34±4 μC/cm2, consistent with the reported theoretical values 38, 58.\ns\nLine 171: The polarization of the FE phase, obtained from polarization displacement\nmeasurement (56±6 pm), is ~34±4 µC/cm2, which aligns well with previous theoretical\n29\nvalues 38, 58.\nComment 5: 127: The authors claim to see no polarization suppression along the c-\naxis, referring to Figure S8. Figure S8e however seems to show a clear drop in\npolarization towards the edges of the grain. At first glance it is unclear where the\ninformation on c-axis polarization stems from. Adding information on the recorded\nzone-axis, labeling a- and c- axis in S8a and clarification of which plane “in-plane”\npolarization is in S8b could help here.\nResponse 5: We thank the reviewer for pointing out this potential source of confusion.\nWe would like to clarify that in Line 127, “… lattice along c-axis maintained no obvious\nsuppression ( as new Fig. S10 in SM),” we referred the lattice spacing along the c-\naxis, rather than the polarization itself. The statement was intended to indicate that\nno obvious decrease of the c-axis lattice parameter is observed, as shown in Fig. S10\n(original Fig. S8). In addition, we have revised the expression in main text and Fig.\nS10b. These revisions make the origin of the c-axis information and the polarization\nmapping unambiguous.\nLine 138: […] in-plane displacement (0.8±3 pm, see Fig. S10 in SM) along the a-axis\nindicates that the polarization direction is along the c-axis.\nNew line 145-146: whereas the lattice along the c-axis maintained no obvious decrease\n(Fig. S10 in SM),[…]\n30\na b\nc\nFig. S10. Analysis of Reconstructed images. a, Represented fitting result of atomic positions. b,\nThe histogram of polarization displacements component along a-axis. c, The half lattice c map\nof Fig. 2c. d, The intensity histograms of oxygen atoms in Fig. 2c sorted by O1 and O2. e, The\npolarization of layers marked by corresponding colored arrows in Fig. 2c.\nComment 6: 134: The authors claim that the blurring of O-K edge doublets in EELS\nspectra indicates a higher concentration of VO at GBs. I do not understand this\nconclusion. If this is common knowledge, the authors should underpin this claim with\na reference to literature.\nResponse 6: We thank the reviewer for raising this important point and for requesting\nclarification. The blurring of the O-K edge doublet in EELS spectra is a commonly used\nqualitative indicator of oxygen vacancies in transition-metal oxides (e.g., hafnium-\nbased oxides)59, 60, 61, 62. Physically, oxygen vacancies modify the local unoccupied O\n2p -metal hybridization, leading to a broadening and reduced energy separation of the\nO-K edge fine structure, where the characteristic doublet becomes less well resolved\nwith increasing oxygen vacancy concentration 61, 62, 63. We have now added appropriate\nliterature references to support this interpretation:\nLine 153-155: Specifically, the blurring of O-K edge doublets in EELS spectra\nindicates a higher concentration of V at GB 61, 62, 63, suggesting their potential role in\nO\nmodulating local polarization behavior.\n31\nstnuoC\n350 0.8 ±3 pm\n300\n250\n200\n150\n100\n50\n0\n0 20 40 60\nDisplacementalong a-axis(pm)\n80 d\n60\n40\n20\n0\n0 0.5 1.0\nPhase (normalized)\nstnuoC\n100 75\nO1 50\nO2 2 0 5 75\n50\n25\n0\n75 50\n25\n0\n75\n50\n25\n0\n75\n50\n25\n0 1.5 0 5 10 15 20\nLayer index\n)mp(\nthemecalpsiD\ne\nComment 7: 155: Please explain the value of 7-12%. Does projection play a role?\nResponse 7: We thank the reviewer for the question, the value “7-12 %” is the mean\nvalue of the oxygen vacancies concentration near the GBs (Fig. 3d) and the error bars\npresent the standard deviations along the depth slices.\nComment 8: 164: Please elaborate more on the close relationship between the Vo and\nthe ferroelectric properties of HZO.\nResponse 8: We thank the reviewer for this suggestion. We would like to emphasize\nthat the present study is primarily experimental. Our atomic-scale measurements\ndirectly reveal a clear spatial correlation between oxygen vacancy accumulation\nand local ferroelectric polarization behavior in HZO, particularly at grain\nboundaries and the 180° H-H CDW. However, the microscopic mechanisms by how\nthe V exactly influence polarization stabilization, suppression, or domain-wall\nO\nformation are highly complex and typically require detailed theoretical modeling and\nfirst-principles calculations. Such analyses are beyond the scope of this experimental\nwork and are therefore left for future studies. We have clarified this point in the revised\nmanuscript to avoid overinterpretation:\nLine 161-164: These experimental results reveal a clear spatial correlation between\noxygen vacancy accumulation and local ferroelectric polarization behavior in HZO,\nparticularly at grain boundaries and the 180° H-H CDW, directly demonstrating their\ncoexistence at the atomic scale. And the detailed understanding of how the vacancies\nexactly influence polarization stabilization and domain-wall formation requires further\nin-depth investigation.\nComment 9: 175: The authors state “FE and AFE [...] always coexist within a grain”.\nThis is in tension with Figure 2a which shows “a FE grain”.\nResponse 9: We sincerely thank the reviewer for pointing out this potential ambiguity\nin our wording. Our intention was to describe the predominant and most frequently\n32\nobserved microstructure, where the two phases commonly coexist within grains but\nthere are still pure FE grains exist, which means higher presence of the FE-O phase in\nthe pristine film. We have revised the original sentence to eliminate ambiguity:\nLine 191-194: Due to the negligible energy difference between the FE-O and AFE-O\nphases 38, they always coexist within a single grain, but a higher presence of the FE-O\nphase in the pristine film is reasonable, as the phase distribution is strongly influenced\nby factors, like dopants, strain, and defect chemistry, preferentially stabilize the FE-O\nphase in HZO thin films 26, 27, 28.\nComment 10: 187-204: After reporting on successfully imaging oxygen atoms in [111]\nzone axis, the authors again remark on the observation of 180° H-H CDWs. This section\nfeels misplaced, as this is already discussed in some detail in 141-164.\nResponse 10: The following section is a further discussion of the H-H CDWs, while\nthe preceding section presents the results of the 180° H-H CDWs experimental\nobservations. We believe that the two sections have different focuses.\nComment 11: 189: The authors emphasize the importance of being able to reconstruct\nthe sample phase in 3D. This ability is however never put to use. The depth information\nin the depth slice shown in Fig 3b is never used, as the phase is summed along the depth\ndirection afterwards.\nResponse 11: The 3D phase reconstruction depth information is indeed utilized\nand provided important insights. First, the phase along the depth direction in Fig. 3b\nis not summed as the y axis is the depth axis, which also reveals the slightly distorted\nof the column 5 and 5’. Second, we show directly the depth information in Fig. 3b and\nthe Fig. 3c-e w show depth-averaged results (not summed) to highlight lateral\ndistributions with standard deviations. And we added the polarization mapping along\nthe depth slices as Fig. S13 (Fig. 3c is the average of the results), which shows that the\npolarization at the H-H CDW is basically unchanged along depth even with the slightly\ndistorted of the column 5 and 5’.\natomic fitted markers where the A atom means Hf/Zr atom.\nLine 189: As shown in Fig. 3c and Fig. S13 in SM, there exists a non-polar unit cell at\nthe center of the DW with almost equal but opposite polarization on either side\n(Layer_2) along depth.\nComments to Figures\nFigure 1: The authors should show at least one CBED image from their 4D datasets,\nsince this is the input for all the ptychography work later on. Figure 1e and right hand\nside of f: In the main text, it is not mentioned at all what is shown there. Figure 1f and\nall other reconstructions: The metal columns in Hf0.5Zr0.5O2 should be occupied\npartially by Hf and Zr atoms differing significantly in atomic number. For a sample\nthickness as thin as the 5 nm stated, I would expect intensity/phase variations on the\nmetal columns reflecting different ratios of Hf and Zr? Why do all metal columns have\nnearly the same intensity even in the simulations? IS the maximum value cut?\nResponse: We thank the reviewer for these suggestions. First, there is a CBED image\nas a part of experimental setup in Fig. 1d and we revised the display as your suggestion;\nThe CBED image with colorbar was also added in SI. Second, as response in the\ncomment 1, we have merged the simulated results in Fig. 1 for easier reading. Third,\nin the original Line 86-114 we are analysis the results based on the Fig. 1e-f and related\n0.5 0.5 2\nHf randomly distributed in the the metallic sites 26. The theoretical calculations also\nvalidate this random occupancy 33, 34. Our atomic EDS mapping as shown in Fig. R3\nalso proved it. As our depth resolution is much higher than the lattice, so the contrast in\nMEP images does not allow to distinguish Zr/Hf that the intensity are no obvious\nchange in metallic sites. We hope that the development of MEP especially the\nptychographic tomography could resolve the questions that you cautious. And we have\nadded the Fig. R3 as Fig. S17 in SM and revised the main text as below:\nFig. 1. Imaging atomic structures of HZO freestanding thin film. a, Low-\nmagnification plan-view HAADF-STEM of HZO freestanding film. White arrow\nindicates sample’s edge. b, HAADF-STEM image shows the grain distribution of film.\nc, Polarization–electric field (P–E) hysteresis loops at 10 kHz. d, Experimental setup\nof MEP. e, Fourier transform of projected phase image in Fig. S3 of the SM, as dashed\ncircle denotes real space resolution of 25 pm. The inset is a convergent beam electron\ndiffraction (CBED) image from dataset. […]\nscale intensity. c, The profile of corrected shift measured by post-alignment method.\nFig. R3 . Atomic EDS element mapping with HAADF (a), Hf (b) and Zr (c), while the\nrelative atomic ratio of Hf and Zr is 50.03% and 49.97%.\nNew line 210-214: Due to the continuous solid-solution nature of Hf₀.₅Zr₀.₅O₂, the\ncontrast of metallic sites in MEP images does not allow direct discrimination between\nHf and Zr atoms. Atomic-resolution EDS mapping (Fig. S17) confirms a uniform Hf/Zr\ndistribution with an approximately 1:1 ratio across the film, consistent with random\ncation occupancy feature.\nFigure 2: The orange arrows in a and c are close to invisible. Probably show a magnified\nROI as inset. In 2f it is unclear what the red arrow indicates and what is meant with\n“blue, the rest part”\nResponse: We thank the reviewer for pointing out the clarity issues in Fig. 2. To\nimprove visibility, we have added inset in Fig. 2c and adjusted the figure to ensure that\nthe orange arrows are clearly distinguishable upon zooming. In Fig. 2f, the red arrows\ndenote polarization suppression near the grain boundaries. The blue bar chart indicate\n36\nthe polarization within the grain interior, excluding the three outermost polarization\nlayers. The figure and caption have been revised accordingly to improve clarity:\nFig. 2. Ferroelectric polarization mapping. a, Projected MEP phase image of a FE\ngrain along [010] direction with displacement arrows overlapped. b, Statistical\nhistogram of polarization displacements in O phase HZO grains. The fit curves\nrepresent Gaussian fitting. c, Projected MEP phase image from a FE-AFE mixed grain\nwith displacement arrows overlapped. Inset represents enlarged region of polarization\nmapping. The blue and red arrows in a and c indicate the direction of polarization in\neach polar layer. d, The displacement magnitude map corresponding to c. e, The mean\npolarization of every polar layer extracted from yellow dashed-line region in c. f,\nDisplacement distributions from the edge (red, three outermost layers of the grain) and\ninterior (blue, the rest center part of the grain excluding the edge) of grain shown in c.\nThe red arrow indicates the polarization suppression near the grain boundaries.\nFigure 3: 3c lacks information on how the displacement was determined at the CDW\n(since there are two pairs of O-columns here). 3d lacks information on what the phase\nwas normalized to and how exactly the “phase of the O-colums” was determined\n(projected phase at a certain position or sum over a region around O-positions or similar)\nResponse: We thank the reviewer for pointing out this point. The polarization of the\nCDW was determined by calculating the center position of the two pairs of O-columns\nas the mean anion position in the cell of the CDW (Fig. R7), following the rule as we\n37\nstated in the SI. In Fig. 3d, the normalized intensity was normalized based on the\ncorresponding mean value. In Fig. 3d, the O-column phase intensity was obtained from\ndepth-dependent multislice ptychographic reconstructions. The phase for each oxygen\ncolumn was calculated as the mean intensity over the atomic region, fitted using the\nAtomap Python package 64, with standard deviations reflecting the uncertainty along\ndepth. We have revised the caption in the Fig. 3 and description in SI.\nFig. R7. The polarization calculation schematic of the H-H CDW.\nFig.3. […] The depth-averaged phases of the O columns in the three layers. The error\nbars present the standard deviations along the depth.\nLine 90 in SI : The polarization of the CDW was determined by calculating the center\nposition of the two pairs of O-columns as the mean anion position in the cell of the\nCDW.\nLine 93 in SI: The normalization in the study is normalized based on the corresponding\nmean value.\nComments to SI\n39: What TEM grids were used? Are there some supporting layers, e.g. lacey carbon?\nDo these layers impact the ptychography?\nResponse: We use the common copper TEM grids with holey carbon supporting layer.\nWe specifically probed HZO films through the holes of the holey carbon (Fig. 1a) to\neliminate potential interference from supporting layers. We added the information to SI.\nLine 39: The freestanding HZO films remained on the copper TEM grids (with holey\n38\ncarbon supporting layer) after water evaporated.\n63: Reconstruction details such as regularization parameters and constraints should be\nspecified, as these could have an influence on the reconstructed phase.\nResponse: We have already provide reconstruction procedures in SI as the\nreconstructions are multiple and complex process, we will make the parameter file\navailable on GitHub after published.\nFig S1 : b and e should be shown with the same contrast. The line cuts presented in c\nand f are rather noisy. A radial average instead of line cut would be beneficial.\nResponse: We thank the reviewer for the comment. Panels b and e have now been\nrevised to use the same contrast for direct comparison. Regarding the line cuts in c and\nf, the noise reflects the true background fluctuations. Following the reviewer’s\nsuggestion, we also explored a radial average, but the results were not satisfactory\nbecause the FFT of our images is not fully radially symmetric ( the M’ phase in the\nimages). We have added the corresponding circle from Fig. 1e to the supplementary\nfigure and caption to aid interpretation. Therefore, we retained the line cuts to faithfully\nrepresent the actual signal.\nHAADF image with corresponding Fourier transform b. The linecut c is taken from the\nspectrum shown in b. d, Projected MEP image with corresponding Fourier transform\ne, where the region in Fig. 1e is an enlarged area of e. The linecut f is taken from the\nspectrum from zero point to circle shown in e. Circle in e is the corresponding circle of\nFig. 1e\nFig S5 : It is unclear what the reconstructions based on simulated datasets add. By\nchoosing an infinite dose and no aberrations for the simulated diffraction patterns the\nauthors essentially reconstruct the potential they constructed for the simulation in the\nfirst place (up to frequencies corresponding to the maximum collected scattering angle).\nThe only difference is the added gaussian blur (SI: line 100), although it is unclear\nwhether this was applied to the diffraction patterns or to the reconstructed phase image.\nThe authors should add some details here.\nResponse: All simulated datasets were generated under the assumption of an infinite\nelectron dose, meaning that Poisson noise was not introduced, as we aimed to preserve\nclear structural details in the simulated ptychographic reconstructions to comparison\nwith the experiments. In our experiments, the electron probe current used was\napproximately 20 pA. For simulations shown in Fig. 1(f), we utilized the abTEM\npackage 65 to conduct and followed the method described in article [Hui Zhang et al.,\nScience 380, 6333-638 (2023)], where the datasets (i.e., the collected diffraction\npatterns) were Gaussian-blurred to account for source size as we stated in Line 102, not\nthe reconstructed phase image. We have added the details in the SM:\nLine 100: Additionally, the datasets (i.e., the collected diffraction patterns) were\nGaussian-blurred to account for source size.\nFig S6: Some more information would be beneficial here. The colorbar is missing labels.\nResponse: We thank the reviewer for the suggestion. We have updated the Fig. S6 (new\nFig. S8) to include labeled colorbar for clarity, and we have added brief explanatory\ninformation in the figure.\nphases. b, grain with pure FE phase. c-d, grain with FE-O and AFE-O phases.\nHere is an incomplete list of wording issues\n34: layers [...] remains unchanged\n59: the ferroelectricity nature\n59: However it is\n67-69: Reword whole sentence\n73: Layers → layer\n80: Suggestion: “The HAADF image of the 5-nm-thick …”\n92: “simulated reconstructions” -> “reconstructions on simulated data”\n93: [...] results [...] have unveiled [...] key discoveries\n94-100: tense in sentence 1) different from 2) and 3)\n102: detailly\n126: there are [...] suppression\n127: Partial polarized\n127: but [are] still overlapping\n127: “whereas [the] lattice along [the] c-axis maintained no obvious suppression, resulting in\npolarization suppression[...]”. Sentence seems contradictory\n131: “[...] observations [...] provide clues [...] that regions [...] clearly reveal” wording\n143: is exist → is existing\n144: indicted\n154: “This observation supports that the scale-free FE feature of hafnium oxide”. Sentence seems\nincomplete\n164 the closely relationship\n184: duo to [...] distance [...] is\n184:”Benefits from the ultra-resolution of MEP, we successfully image the oxygen atoms (Figs. S11\nand S12 in SM) from the O-[111] orientation.” Sentence seems incomplete\n41\n188: our [..] precisely measurements\n190: “In the traditional systems, where… “ Sentence seems incomplete\n195: the VO acts as mediators\n196: [...] lattice constants [...] indicates\n197: reinforcing the nature\n209: reconstruction further demonstrate\n404: polarization [...] that noted with the corresponding [...] lines\nSI typos: 55: we → We; 66: the detector we used during the algorithms; 86: column → columns;\n88: born → Born\nResponse 6: We appreciate the reviewer’s careful attention to these typos. We have\naddressed all identified typos in the revised manuscript, and details of these changes\nare provided in our highlighted version for easy reference. Here, we list some important\nchanges:\nRegarding Line 80, we retain the original sentence as the subject is the “5-nm-thick\nHZO freestanding film” (not the HAADF image), accurately indicating the research\nobject.\nFor Line 127, the sentence is not contradictory: it describes two distinct phenomena\n(local oxygen ion relaxation vs. c-axis lattice integrity). Revised for clarity: “Partial\noxygen ions in polarized layers near the GBs were relaxed towards the center position\nbut are still non-overlapping to each other, whereas the lattice along the c-axis\nmaintained no obvious suppression (Fig. S8 in SM)”\nFor Line 154, we revised as: “The polarization of the polar layers (i.e., Layer_1 and\nLayer_3, black and yellow boxes in Fig. 2a) adjacent to the 180° H-H CDW retained a\nbulk-like state and remained unaffected by the DW itself, supporting the scale-free FE\nfeature of hafnium oxide.”\nFor Line 190, the sentence has been completed for clarity: “In the traditional systems\n(e.g., PbTiO ), where DWs are typically stabilized by long-range lattice strain or dipolar\n3\ninteractions differs from that of the CDW in the HZO system.”\n*******************************************************************************\nReviewer #4\nComment: I co-reviewed this manuscript with one of the reviewers who provided the\nlisted reports. 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The abTEM code: transmission electron microscopy from first principles.\nOpen Research Europe 2021, 1: 24.\n46"}, {"round": 2, "reviewer_comments": {"reviewer_1": "Thank you for providing the revised response and manuscript.\nI have carefully read the revision, and all points have been addressed satisfactorily.\nTherefore, I am happy to recommend acceptance of the manuscript entitled “Precise structure and polarization determination of Hf0.5Zr0.5O2 with electron ptychography.”", "reviewer_2": "The authors provided a very comprehensive and detailed point-by-point response for all of the remarks that required clarification in the first version of their submitted manuscript.\nI am satisfied by their response, and in light of this, I warmly recommend the updated manuscript for publication.", "reviewer_3": "The authors addressed all my remaining issues; accordingly, I recommend publishing the paper in Nature Communications in its current form. For completeness, the authors should add a scale bar to the CBEDS in Fig S1 a) and b) and correct the acronym PACBED in the main manuscript (line 74: convergence –> convergent). Probably during the proofing process.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": ""}]

Decision letter