Approaching theoretical polarization limit in HfZrO2/HfLaO2 multilayers

Domain: chemistry
Published: 2026-02-24
Editorial outcome: major_revision

Abstract
Hafnia-based ferroelectric materials have garnered considerable attention due to robust ferroelectricity in ultrathin films and excellent compatibility with silicon-based technology. Theoretical predictions of the polarization along [001] direction of ferroelectric HfO2 are 50 μC/cm2 and 70 μC/cm2, respectively, depending on the switching mechanism. However, most experimental observations of the intrinsic polarization are much lower than these predictions. Here, we report that an intrinsic remnant polarization up to 40 μC/cm2 is achieved in epitaxially grown (111)-oriented Hf0.5Zr0.5O2/Hf0.9La0.1O2 multilayer film, corresponding to 69.3 μC/cm2 along [001], approaching the theoretical limit. Structural analyses reveal a rhombohedral-distorted orthorhombic phase in the Hf0.5Zr0.5O2/Hf0.9La0.1O2 multilayers, stabilized by an in-plane compressive strain. Density functional theory calculations demonstrate that La doping in Hf0.5Zr0.5O2/Hf0.9La0.1O2 promotes an unconventional switching pathway and contributes to the high intrinsic polarization. These findings provide a compelling strategy for achieving high intrinsic polarization and establish a design paradigm for high-performance hafnia-based ferroelectric devices.

Introduction
The discovery of ferroelectricity in HfO2-based thin films has paved the way for advanced ferroelectric-based electronic devices such as nonvolatile memory and ferroelectric field-effect transistors, owing to their good compatibility with complementary metal-oxide semiconductor (CMOS) technology and the size effect, which is characterized by enhanced and robust ferroelectricity at reduced thickness1–8. For ferroelectric materials, remnant polarization (Pr) is the most critical property that is essential for enhanced ferroelectric device performance. However, achieving high Pr in HfO2-based films remains challenging due to the metastability of the ferroelectric orthorhombic phase (o-phase)9,10.

Recent research efforts have concentrated on stabilizing the ferroelectric phase to enhance Pr in HfO2-based films. In polycrystalline films fabricated by atomic layer deposition followed by thermal annealing, Pr has been improved through extrinsic modulation—such as controlling oxygen vacancy concentrations and engineering interfacial layers to increase the o-phase fraction11–16. Various dopants such as Zr, La, Al, and Y, have been widely employed to further enhance Pr17–26. In addition, charge transfer at the electrode–film interface has been shown to significantly influence the stability of the ferroelectric o-phase27,28. In epitaxial films, the strain induced by the substrate or electrode layer can be an effective tool to tailor polarization properties29–32. Notably, epitaxial HfO2-based films on perovskite substrates and electrode layers (such as La0.67Sr0.33MnO3/SrTiO3) typically crystallize along the [111] orientation. Because of the angle between the (111) and (001) planes, the theoretically measurable Pr of the o-phase is limited to ~28 μC/cm2 along [111], corresponding to ~50 μC/cm2 along [001]. Conventionally, polarization switching in HfO2-based ferroelectrics follows the non-crossing pathway (N-path), where oxygen displacement is confined within the unit cell boundaries. Recently, Wu et al. proposed an unconventional switching mechanism in HfO2-based ferroelectrics, referred to as the T-path33. In this mechanism, three-fold coordinated oxygen atoms traverse across unit-cell boundaries defined by the Hf/Zr atomic planes. The T-path predicts a spontaneous polarization of about 70 μC/cm2, which is approximately 50% larger than the commonly accepted value associated with the N-path. However, up to now, most experimentally observed Pr values fall below this theoretical prediction, particularly when considering extrinsic effects such as oxygen vacancy contributions24. A deeper understanding of the factors that may trigger the T-path, and developing strategies to achieve high Pr while maintaining phase stability, remains a key challenge for enabling practical applications of HfO2-based ferroelectrics.

Here, we report a multilayer strategy that introduces strain in HfO2-based ferroelectric films, enabling ultrahigh Pr. In the Hf0.5Zr0.5O2/Hf0.9La0.1O2 (HZO/HLO) multilayers, an in-plane compressive strain is observed. The ferroelectric hysteresis loop measured at 10 K shows an intrinsic Pr of ~40 μC/cm2, corresponding to ~69.3 μC/cm2 along the [001] direction, approaching the theoretical limit. Moreover, the HZO/HLO multilayer film exhibits good endurance of up to 3×109 cycles at room temperature. Based on scanning transmission electron microscopy (STEM) measurements and density functional theory (DFT) calculations, we attribute the stabilization of the ferroelectric o-phase to in-plane compression strain. In addition, La doping lowers the energy barrier associated with the T-path and stabilizes this unconventional switching process in the HZO/HLO multilayers to achieve the theoretical-limit-high ferroelectric polarization.

Results
We begin by synthesizing and characterizing the HZO and HZO/HLO films with a La0.67Sr0.33MnO3 (LSMO) bottom electrode layer on a SrTiO3 (STO)(001) substrate using pulsed laser deposition (PLD). For the HZO/HLO multilayer structure, each HZO and HLO layer has a thickness of ~0.9 nm, repeated 4 times (Fig. 1a). High-resolution XRD patterns of the HZO and HZO/HLO films with the same film thickness of ~7 nm are shown in Fig. 1b, c. All three films exhibit a characteristic peak at around 30°, corresponding to the commonly reported o-phase. We observed a sharp o-phase peak with a higher peak intensity of HZO/HLO film compared with the two other films, indicating a higher o-phase crystallinity in HZO/HLO film. This is further verified with the rocking curves in Fig. 1d, where the full width at half maximum (FWHM) of the HZO and HZO/HLO films are 0.098° and 0.065°, respectively. Notably, distinct satellite peaks, which are typically characteristic of superlattice/multilayer structures, are not resolved in the XRD pattern. This absence is attributed to the combined effects of ultrathin sub-layers (~0.9 nm) and inevitable interfacial interdiffusion during high-temperature growth, and the modest scattering contrast between two HfO2-based layers, which together result in a diffraction profile reflecting the average coherent lattice structure. For thicker films (12 nm and 20 nm, Supplementary Fig. 1), secondary phases appear. Characteristic peaks at around 28.5° and 35° in the measured XRD data correspond to the m-phase (m-HZO (−111)) and monoclinic/tetragonal phase (m/t-HZO (002)), respectively. Epitaxial HZO films generally exhibit coexistence of the o-phase and m/t-phases, with the fraction of m/t-phase increasing as thickness increases. This trend is observed in HZO single layers (Supplementary Fig. 1). However, the HZO/HLO multilayer films show a strong o-phase peak with minimal secondary phases (Supplementary Fig. 1b, d), demonstrating that the ferroelectric phases are well stabilized.

Pole figure measurements were performed around the {113} peaks of the 7-nm-thick HZO/HLO film. As shown in Fig. 1e, 12 reflections instead of 3 are found at χ = 30.5°, indicating that the crystallographic domains follow the four-fold symmetry of the underlying STO substrate. This finding reveals the orthorhombic or rhombohedral symmetry of the HZO/HLO film. To further investigate its crystallographic characteristics, reciprocal space vectors (RSVs) analysis was performed using a sophisticated method to determine accurate lattice parameters of epitaxial thin films by high-resolution XRD34. Table 1 presents the corrected Bravais angles for the HZO and HZO/HLO films, with detailed RSVs results provided in Supplementary Table 1. The HZO film has the Bravais angles very closely to 90°, consistent with the orthorhombic structure. In contrast, the HZO/HLO film grown on LSMO/STO(001) exhibits orthorhombic symmetry with r-distortion, as evidenced by the tilted Bravais angles in Table 1. An r-distortion of ~0.476° was identified in the HZO/HLO film, which can be visualized as stretching the o-phase unit cell along the [111] direction, as schematically illustrated in Fig. 1f.

We present a high-resolution HAADF-STEM image of the cross-section of the HZO/HLO film viewed along the [1–10] zone axis (Fig. 2a). The high-quality epitaxial relationship of the bottom LSMO (001) with respect to the STO substrate is evident. The HZO/HLO layers demonstrate a highly textured growth on the LSMO layer. Atomic-resolution energy-dispersive x-ray (EDX) elemental maps of the HZO/HLO film (Supplementary Fig. 2) reveal a mixture of La, Hf and Zr elements within the structure. This observed intermixing is attributed to the combined effects of interfacial diffusion during high-temperature growth and the projection nature of EDX mapping, where the interaction volume is comparable to the ultrathin layer thickness. Further evidence for the compositional modulation is provided by HAADF-STEM of a [HZO(1.8 nm)/HLO(1.8 nm)]×2 film grown under identical conditions, which reveals a layered contrast (Supplementary Fig. 7). This confirms that the deposition sequence yields a HZO/HLO layered architecture, even though distinct superlattice/multilayer satellites are not resolved for the [HZO(0.9 nm)/HLO(0.9 nm)]×4 film. Based on the magnified image and fast Fourier transform (FFT) analysis (Fig. 2b), distinct (111) and (11-1) reflections are observed in the HZO/HLO film, confirming the orthorhombic nature of this phase. In addition, comparison with the standard (111) atomic model of o-HZO (Fig. 2b, upper) reveals an r-distortion within the HZO/HLO structure, which aligns with our XRD results. The average interplanar spacings along the (111) and (11-1) planes, measured over 20 regions in the HZO/HLO film, are plotted in Fig. 1c. From these measurements, we deduce that d111 = 3.05-3.18 Å and d11-1 = 2.76-2.93 Å, further confirming the r-distortion of this phase. To analyze the strain distribution, we performed geometric phase analysis (GPA) over a broader region of the HZO/HLO film (Fig. 2d). Taking the bottom electrode layer, LSMO, as a reference, we measured both the in-plane (Fig. 2e) and out-of-plane (Fig. 2f) strains within the HZO/HLO heterostructure. Along the in-plane xx-direction (Fig. 2e), the internal strain of the HZO/HLO layer (~6%) is compressive relative to the significantly higher strain (~16%) observed at the interface with LSMO. This predominant in-plane compressive strain originates from the lattice mismatch competition between the alternating HZO and HLO layers. Specifically, the La-doped HLO layers possess a larger equilibrium lattice volume due to the larger ionic radius of La3+ compared to Hf4+/Zr4+. However, due to the ultrathin layer thickness and the epitaxial constraint from the alternating HZO layers, the HLO lattice is prevented from relaxing. This mutual clamping effect induces a substantial compressive stress state that acts to stabilize the ferroelectric o-phase. Conversely, along the out-of-plane yy-direction (Fig. 2f), the internal strain of the HZO/HLO layer (−12%) exhibits tensile characteristics compared to the larger interface strain with LSMO (−24%). These GPA findings are consistent with the presence of an r-distorted o-phase, as indicated by our XRD and interplanar spacing analyses.

Figure 3a shows a typical hysteresis loop for the 7 nm-thick HZO/HLO film (blue curve), after subtracting the non-ferroelectric switching contribution through positive up negative down (PUND) measurements. As a comparison, the polarization-electric field (P-E) loop of the HZO film with the same thickness is also shown (red curve). The typical ferroelectric current-electric field (I-E) curves for HZO/HLO and HZO films, measured under an electric field up to 7.5 MV/cm, are shown in Fig. 3b. Currently, the highest reported Pr values among doped-HfO2 films is ~50 μC/cm2 in Y-doped HfO224, while HZO films achieve up to 34 μC/cm2 (ref. 26). Remarkably, our 7-nm-thick HZO/HLO film reaches a record Pr of ~56 μC/cm2 — the highest reported value among all epitaxial HfO2-based films. Furthermore, the HZO/HLO film displays minimal wake-up effect and shows a high endurance up to 3×109 cycles before breakdown (Fig. 3c). Ferroelectric P-E loops for HZO/HLO and HZO films with increased thicknesses are shown in Supplementary Fig. 3. HZO/HLO films display Pr of ~34 μC/cm2 and ~26 μC/cm2 at 12 nm and 20 nm, respectively. In contrast, the 12-nm-thick HZO film shows Pr of 9.5 μC/cm2 and the 20 nm-thick HZO film shows Pr of only 6.5 μC/cm2. This finding can be rationalized by our XRD observations in Supplementary Fig. 1 showing that the non-ferroelectric secondary phases gradually appear with increasing thickness. For further comparison, a 7 nm-thick epitaxial HLO single layer was fabricated. XRD characterization and ferroelectric P-E loop measurements (Supplementary Fig. 4) reveal a single o-phase HLO with a relatively low Pr of ~10 μC/cm2. This highlights the effectiveness of the HZO/HLO multilayer structure in enhancing ferroelectric polarization. To further distinguish the effect of the HZO/HLO multilayer architecture from that of simple La doping, we prepared a single-layer La-doped HZO solid-solution film, Hf0.7Zr0.25La0.05O2, with the same total thickness and average composition as the HZO/HLO multilayers, grown on the same LSMO/STO(001) substrate. Supplementary Fig. 5 shows its XRD and P–E characteristics. The film clearly exhibits coexisting o- and m-phase peaks, indicating incomplete stabilization of the o-phase. The corresponding P–E loop (Supplementary Fig. 5b) confirms ferroelectric switching but with a much smaller Pr of ~10.2 µC/cm2. This comparison demonstrates that La doping alone is insufficient to achieve near-theoretical polarization and highlights the crucial role of the HZO/HLO multilayer architecture. When compared with the Pr value and film thickness reported in the literature (Fig. 3d), our HZO/HLO thin film as thin as 7 nm exhibits a significant improvement in Pr compared to doped-HfO2 films at their optimal polarization thickness (5–15 nm). Figure 3e shows the P-E loops of the HZO/HLO multilayer film measured across a temperature range from 10 K to 300 K. Pr decreases from 56 μC/cm2 at 300 K to about 40 μC/cm2 at 10 K. This trend contrasts with conventional ferroelectric materials, where lower temperatures typically enhance ferroelectric order. It was reported that for HfO2-based ferroelectrics, extrinsic factors such as oxygen vacancy migration often lead to higher measured Pr values at elevated temperatures compared to those arising solely from intrinsic ferroelectric behavior5,35,36. In this study, as depicted in Fig. 3f, the Pr values remain relatively constant below 50 K, suggesting minimal contribution from extrinsic mechanisms under cryogenic conditions. Notably, the observed Pr of ~40 μC/cm2 at both 10 K and 50 K correspond to an effective polarization of approximately 69.3 μC/cm2 along the [001] direction, approaching the theoretical limit for HfO2-based ferroelectrics33. This observation indicates that the high polarization in the HZO/HLO multilayers is predominantly intrinsic.

We fabricated HZO/HLO films with varying HZO and HLO layer thicknesses while maintaining a total thickness of ~7 nm. The heterostructures, with different numbers of interfaces, are schematically shown in Supplementary Fig. 6a. They are noted as [HZO(0.9 nm)/HLO(0.9 nm)]×4 (same sample in Fig. 1a), [HZO(1.2 nm)/HLO(1.2 nm)]×3 and [HZO(1.8 nm)/HLO(1.8 nm)]×2, based on the thickness of each layer and the repetition times. The XRD measurements and ferroelectric P-E loops test results of these heterostructures are presented in Supplementary Fig. 6b–d. It is found that the [HZO(0.9 nm)/HLO(0.9 nm)]×4 film exhibits the strongest ferroelectric o-phase peak and the highest Pr value among the three films. With increasing HZO and HLO layer thickness and therefore fewer interfaces, the o-phase peak intensity decreases, accompanied by a reduction in Pr. To explore the role of interfaces in stabilizing ferroelectricity, we performed the STEM characterizations for the [HZO(1.8 nm)/HLO(1.8 nm)]×2 film (Supplementary Fig. 7). The average interplanar spacings along the [111] and [11-1] directions were measured and plotted in Supplementary Fig. 7b. d111 = 3.03-3.11 Å and d11-1 = 2.86-2.95 Å are deduced from these measurements. The in-plane compressive strain in this film is less pronounced, leading to a lower degree of lattice distortion of the o-phase compared to the [HZO(0.9 nm)/HLO(0.9 nm)]×4 film. This observation is supported by the measured d111/d11-1 ratios, approximately 1.057 for the [HZO(1.8 nm)/HLO(1.8 nm)]×2 film versus approximately 1.095 for the [HZO(0.9 nm)/HLO(0.9 nm)]×4 film. The reduced ferroelectricity observed in the [HZO(1.8 nm)/HLO(1.8 nm)]×2 film may be attributed to this reduced in-plane compressive strain.

As discussed above, our experimental measurements indicate that the HZO/HLO film deposited on a LSMO buffer layer exhibits pseudo-hexagonally symmetric structures. These structures could correspond to the o- or m-phase of HZO/HLO in the (111) orientation, or to the r 3m-phase of HZO/HLO in the (001) orientation. Notably, an intrinsic Pr of 40 μC/cm2 at 10 K was achieved, which approaches the theoretical limit. To understand these experimental observations, we conducted comprehensive DFT calculations. Figure 4a, b present the formation energies of the o-, m-, and r 3m-phases of HZO as functions of in-plane lattice parameters under rhombohedral confinement. The results indicate that the o- and m-phases are energetically competitive on an LSMO buffer layer, while the r 3m-phase consistently represents a higher energy state, regardless of the presence of oxygen vacancies. For HZO films devoid of oxygen vacancies, the o-phase serves as the ground state when the in-plane lattice parameter is less than 7.43 Å. Conversely, when the lattice parameter exceeds 7.43 Å, the m-phase becomes the ground state, with the r 3m-phase remaining the highest in energy. Even with oxygen vacancy concentrations as high as 4.17% (Fig. 4b), the trends persist, indicating that the o- and m-phases remain energetically comparable on the LSMO buffer layer. The o-phase of HZO is consistently the stable structure under compressive strain.

To elucidate the origin of the exceptionally high remnant polarization observed in this work, we investigated the ferroelectric switching mechanisms, focusing on the conventional N-path and the unconventional T-path. The schematic diagram of these two polarization switching pathways are shown in Fig. 4c. The N-path typically yields a polarization of ~50 µC/cm2 along the [001] direction, whereas the T-path can achieve up to ~70 µC/cm2 along [001]. Given the exceptionally high Pr observed in this work, we propose that the T-path switching mechanism is operative in our HZO/HLO films. To substantiate this, we performed systematic nudged elastic band (NEB) method calculations to determine the switching barriers for both N- and T-paths under various strain conditions. As shown in Fig. 4d, for undoped HZO, the N-path consistently exhibits the lower energy barriers compared to the T-path, regardless of strain. Specifically, the N-path barriers are approximately 0.23 eV (strain-free), 0.27 eV (−1% compressive strain), and 0.25 eV (+1% tensile strain), while the T-path barriers are higher, at about 0.31, 0.43, and 0.33 eV, respectively. These results indicate that, in the absence of doping, the N-path is energetically favored, leading to lower polarization values.

However, introducing La doping alters this energy landscape. Our NEB calculations for HZO films with 6% La doping reveal a significant reduction of the T-path energy barrier to 0.140 eV/f.u, making it lower than the N-path energy barrier, 0.16 eV/f.u. Further increasing the La doping concentration to 25% reduces the T-path energy barrier even more, to 0.09 eV/f.u, while the N-path energy barrier remains higher at 0.15 eV/f.u (Fig. 4e). These findings suggest that La doping preferentially stabilizes the T-path switching mechanism, facilitating higher polarization values. All these La doping selected T-path in HZO could be understood from the structure variations during the switching process. In undoped HZO, the T-path involves simultaneous crossing of two oxygen atoms over the Hf-Hf plane, resulting in significant structural deformation and higher energy barriers. Conversely, La doping modifies this process, allowing oxygen atoms to cross the Hf-Hf plane sequentially, reducing structural strain and lowering the energy barrier (Supplementary Fig. 8). This sequential movement is energetically more favorable and accounts for the enhanced polarization observed in HZO/HLO film.

In this study, we report a lattice-distorted ferroelectric o-phase HZO/HLO thin film with a multilayer structure exhibiting enhanced ferroelectricity. The proposed multilayers demonstrate superior intrinsic Pr of ~40 μC/cm2, corresponding to ~69.3 μC/cm2 along the [001] direction, closely approaching the theoretical limit. High-resolution XRD and HAADF-STEM analyses reveal an in-plane compressive strain exists in the HZO/HLO multilayers, which can stabilize the ferroelectric o-phase. The improved ferroelectric performance is attributed to the selectively favored T-path polarization switching. In addition, La doping is identified as critical for promoting this unconventional T-path ferroelectric switching mechanism. This work demonstrates a useful HZO/HLO multilayer design to stabilize the ferroelectric phase, providing a new pathway for achieving robust ferroelectricity and advancing the design of high-performance ferroelectric devices.

Methods
Thin film deposition
The HZO and HZO/HLO multilayer films on La0.67Sr0.33MnO3 (LSMO) bottom electrode layer were epitaxially grown on single-crystalline SrTiO3 (001) substrates at the nominal substrate temperature of 800 °C by PLD using a KrF (λ = 248 nm) excimer laser. Prior to PLD growth, the STO (001) substrates were thermally treated at 875 °C for 3 h to obtain a clean, atomically flat step–terrace surface. The LSMO layers (~10 nm) were grown at a nominal substrate temperature of 950 °C with an oxygen pressure of 200 mTorr, while HZO and HLO films were deposited at a nominal substrate temperature of 800 °C with an oxygen pressure of 75 mTorr. The laser fluence was 1.2 J cm−2 with a repetition rate of 3 Hz for LSMO and 1.1 J cm−2 with a repetition rate of 3 Hz for HZO and HLO. After the deposition, the films were cooled down to room temperature at an oxygen pressure of 1 Torr with a cooling rate of 10 °C/min. The top Pt layer (~30 nm) was deposited by magnetron sputtering without breaking the vacuum by transferring the sample from the PLD system into the sputter system for in situ growth. Then, an array of 15×15 µm2 top Pt electrodes was patterned via an Ultraviolet Maskless Lithography machine (TuoTuo Technology, UV Litho-ACA) and ion etching for electrical measurements.

Material characterization
The crystal structure and epitaxial quality were characterized by synchrotron XRD using a four-circle diffractometer with an X-ray wavelength of 1.5406 Å at the Singapore Synchrotron Light Source (SSLS) and BL02U2 at Shanghai Synchrotron Radiation Facility (SSRF). Microstructure of the samples, interfacial structure, EDX elemental mapping, and atomic layer-by-layer EELS were obtained by aberration corrected STEM at room temperature. Cross-sectional TEM samples were prepared with a focused ion beam setup (DA300, FEI). Geometric phase analysis was performed using a free FRWR tools plugin for Gatan Digital Micrograph based on the original work by Hytch et al.37. The strain in the LSMO layer was used as a reference.

Ferroelectricity measurements
The ferroelectric measurements (P-E hysteresis loops) and endurance characteristics were performed using a Radiant Precision Multiferroic II tester. A 30 nm of Pt with a device feature of 15×15 µm2 was sputtered as the top electrode material prior to the ferroelectric test. In all the measurements, the bias was applied to the top electrode. The LSMO bottom electrode was grounded. The ferroelectric measurements at cryogenic temperatures (10–300 K) were conducted in a vacuum cryogenic probe station (Lakeshore), using a Radiant Precision Multiferroic II tester and the top electrodes were connected using Ag wires and Ag paint.

Theoretical modeling and DFT calculations
DFT calculations were performed using the Vienna Ab-initio Simulation Package (VASP). The projector augmented wave potential (PAW) and generalized gradient approximation (GGA) with Perdew-Burke Ernzerhof (PBE) parameterization were used to describe the electron-ion and electron-electron exchange-correlation interactions, respectively. The energy cutoff for plane waves was set to 500 eV. The energy convergence threshold for the self-consistent loop was set to 10−5 eV. For structural optimization, the force convergence was set to 0.001 eV/Å. For HZO without defects, the lattice parameters of the ferroelectric orthorhombic phase (o-phase) are optimized to be a=5.07 Å, b=5.09 Å, c=5.28 Å, and α=β=γ=90°. The lattice parameters of the paraelectric monoclinic phase (m-phase) are a=5.16 Å, b=5.21 Å, c=5.26 Å, and α=γ=90°, β=99.71°. The lattice parameters of rhombohedral phase (r 3m-phase) are optimized to a=5.16 Å, b=5.21 Å, c=5.26 Å, and α=β=90°, γ=120°. All experimental results show that Hf0.5Zr0.5O2 films on LSMO substrate exhibit pseudo-orthogonal confinement characters. These Hf0.5Zr0.5O2 films could be o-Hf0.5Zr0.5O2 and m-Hf0.5Zr0.5O2 films along the [111] direction or r 3m-phase film in the [001] direction. Here, we applied the transformation matrix to expose the (111) surface of o-Hf0.5Zr0.5O2 and m-Hf0.5Zr0.5O2, and the (0 0 1) surface of r 3m-phase. The strain is uniformly added along the in-plane direction, and the out-of-plane direction is fully optimized. The out-of-plane electric polarization is calculated with the Berry phase method, and 29 intermediate structures are applied between the electric up- and down-polarization states. The formation energy (Ef) of oxygen vacancy is calculated with Ef = EV + μO − Eideal, where EV (Eideal) is the total energy of 2×2×2 supercells of Hf0.5Zr0.5O2 with (without) one oxygen vacancy, and μO is the chemical potential of the oxygen, and is calculated with the nudged elastic band method, and 8 intermediate images are inserted between the initial and final images. For the 6% concentration of La-doped HfZrO systems, the 2×2×1 supercell is used with one Hf is replaced by a La atom, and for the 25% concentration of La doped HfZrO, one Hf atom in the unit cell of HfZrO2 is substituted.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript presents the observation of a high remnant polarization (Pr ≈ 56 μC/cm²) in epitaxially grown (111)-oriented Hf₀.₅Zr₀.₅O₂/Hf₀.₉La₀.₁O₂ (HZO/HLO) superlattice films. The authors attribute this enhanced ferroelectric response to the stabilization of a rhombohedrally distorted orthorhombic phase induced by in-plane compressive strain. Such a large polarization, would indeed be significant for the development of hafnia-based ferroelectrics and could provide new insights into strain-mediated phase stabilization mechanisms.\nWhile the reported polarization is potentially significant for the field of ferroelectric oxides, the mechanism underlying this enhancement remains ambiguous. It is crucial to clarify how the multilayer HZO/HLO architecture influences the polarization, especially given that HZO single layers typically exhibit higher remnant polarization than HLO. The authors should discuss whether similar polarization levels could be obtained in a La-doped HZO single films under comparable strain conditions.\nFurthermore, if the films are composed of alternating HZO and HLO layers, the origin and nature of the in-plane strain should be clearly defined. It seems likely that the strain arises from the competition between the lattice mismatch of the two alternating layers and the substrate, yet this is not addressed in the manuscript.\nAnother important concern lies in the XRD analysis. The absence of satellite peaks, which are typical signatures of superlattice periodicity, must be discussed.\nIn summary, while the reported polarization value high, the structural origin and physical mechanism behind this enhancement remain insufficiently supported. The manuscript requires substantial clarification and additional analysis before it can be considered for publication in Nature Communications.\nRecommendation: Major revision.", "reviewer_2": "The manuscript presents a interesting study on achieving near-theoretical polarization in HZO/HLO superlattices, supported by a combination of structural characterization, ferroelectric measurements, and DFT calculations. However, the clarity of the presentation and the robustness of certain experimental claims need significant improvement before the manuscript can be considered for publication.\n1. The switching pathways are confusingly introduced. The authors first mention a “conventional T-pathway” and then refer to a “conventional N-pathway,” which is inconsistent with the literature. The definitions of T-path and N-path should be clearly and consistently explained early in the text, with references to prior work (e.g., Wu et al., PRL 2023).\n2. The phrase “demonstrating well stabilized the ferroelectric phases” is grammatically incorrect and should be rephrased for clarity.\n3. The use of the term “superlattice” is not fully supported by the experimental evidence. The EDX mapping shows a mixture of La, Hf, and Zr, and the authors acknowledge non-uniform La distribution due to resolution limits. This undermines the claim of a well-defined superlattice structure. Additional evidence (e.g., EELS line scans, XRD satellite peaks) is needed to substantiate the superlattice claim.\n4. The statement “This work presents the first reported superlattice structure of its kind in HfO₂-based ferroelectric systems” is premature without clearer structural validation.\n5. The description of “perfect epitaxial relationship” is an overstatement. Dislocations and imperfections are visible in the TEM images. The language should be tempered to reflect the actual microstructural quality.\n6. The yellow lines in Figure 2d obscure structural details at the interface. Replacing them with arrows or dashed lines would improve clarity.\n7. The xx and yy directions for strain analysis (Fig. 2e,f) should be clearly labeled in the figure or caption to aid interpretation, especially for non-specialist readers.\n8. The GPA results are unusual. The LSMO reference region shows significant strain, which contradicts the assumption of a zero-strain reference. This raises concerns about the validity of the strain analysis. The authors should clarify the reference selection and compare their methodology with established practices in the literature.\n9. The Methods section lacks sufficient detail to reproduce the work. Key parameters such as laser fluence, substrate preparation, and characterization details should be described more thoroughly.\n10. Figures 3c and 3f present single data points without error bars or statistical validation. Multiple measurements or error estimates are necessary to support the reliability of the endurance and temperature-dependent polarization data.\n11. The authors note that reducing layer thickness (increasing interface density) enhances ferroelectricity. It would be valuable to test even thinner layers (e.g., <0.9 nm) to explore the limit of this effect and strengthen the interface-stabilization argument."}, "author_response": "Response to the reviewers’ comments\nDiscussion of reviewers’ comments (the reviewer’s comments are quoted in blue and\nour responses in black. Revision related parts are highlighted)\nReviewer #1 (Remarks to the Author):\nThe manuscript presents the observation of a high remnant polarization (Pr ≈ 56\nμC/cm²) in epitaxially grown (111)-oriented Hf₀.₅Zr₀.₅O₂/Hf₀.₉La₀.₁O₂ (HZO/HLO)\nsuperlattice films. The authors attribute this enhanced ferroelectric response to the\nstabilization of a rhombohedrally distorted orthorhombic phase induced by in-plane\ncompressive strain. Such a large polarization, would indeed be significant for the\ndevelopment of hafnia-based ferroelectrics and could provide new insights into strain-\nmediated phase stabilization mechanisms.\nResponse: We thank the reviewer for their positive evaluation of our work,\nhighlighting the significance of the high remnant polarization observed. We have\ncarefully addressed the concerns regarding the mechanism, strain origin, and\nstructural characterization below.\nComment 1: While the reported polarization is potentially significant for the field of\nferroelectric oxides, the mechanism underlying this enhancement remains ambiguous.\nIt is crucial to clarify how the multilayer HZO/HLO architecture influences the\npolarization, especially given that HZO single layers typically exhibit higher remnant\npolarization than HLO. The authors should discuss whether similar polarization levels\ncould be obtained in a La-doped HZO single films under comparable strain conditions.\nResponse: We thank the reviewer for this insightful comment. We agree that clarifying\nthe enhancement mechanism is critical. As noted in the manuscript, the HLO single\nlayer shows a relatively low P, whereas the HZO/HLO film reaches ~56 μC/cm2. Thus,\nr\nalthough HZO exhibits higher P than HLO, the enhanced polarization in the multilayer\nr\ncannot be explained by simply “adding HLO” or by a weighted average of the two\ncomponents. Instead, it already points to an interface-mediated enhancement\nmechanism. In the response to Comment 2, we have clarified that the alternating\nHZO/HLO layers, when clamped to the LSMO/STO substrate, generate an in-plane\ncompressive strain and rhombohedral distortion, which are crucial for the enhanced\nferroelectricity.\nThis is also an excellent suggestion to distinguish the effect of the superlattice\nstructure from simple chemical doping. To address this, we fabricated a control sample:\na single-layer La-doped HZO (Hf Zr La O ) solid-solution film with the same\n0.7 0.25 0.05 2\nthickness (~7 nm) and average composition as the superlattice, grown on the same\nLSMO/STO substrate. Fig. R1a shows the XRD result of the Hf Zr La O film. A\n0.7 0.25 0.05 2\npeak at ~30.2° is observed, corresponding to the ferroelectric o-phase. However, a\nsecond peak appears at ~28.6°, which can be assigned to the non-ferroelectric m-\nphase. In contrast to the HZO/HLO multilayer, where the repeated HfO -based\n2\ninterfaces and epitaxial clamping strongly stabilize the distorted o-phase, the solid-\nsolution film does not suppress the m-phase completely. This incomplete phase\nstabilization is detrimental to the overall ferroelectric response, as reflected in the P–\nE loop in Fig. R1b.\nFig. R1 | XRD and ferroelectric characterization of the Hf Zr La O film. a,\n0.7 0.25 0.05 2\nω−2θ XRD scan of the Hf Zr La O film (~7 nm). b, P-E loop of the same film.\n0.7 0.25 0.05 2\nQuantitatively, the Hf Zr La O solid-solution film exhibits a remanent\n0.7 0.25 0.05 2\npolarization of only ~10.2 μC/cm2, which is much lower than that of the HZO/HLO\nmultilayer. This comparison shows that La doping alone, even at the same average\ncomposition and on the same substrate, is insufficient to achieve the high polarization.\nInstead, the enhanced ferroelectricity in our system arises from the synergistic\ncombination of (i) in-plane compressive strain and rhombohedral distortion enforced\nby the HZO/HLO multilayer architecture, which stabilizes the ferroelectric o-phase, and\n(ii) La doping, as shown by our DFT/NEB calculations, favours the unconventional T-\npath switching with a large intrinsic polarization. Together, these factors explain why\nthe multilayer architecture yields a much higher P than both the HLO single layer and\nr\nthe La-doped HZO solid-solution film.\nWe note that the reviewer specifically asked whether similar polarization levels could\nbe obtained in a La-doped HZO single film under comparable strain conditions. Our\nHf Zr La O control sample was deposited under the same PLD conditions, but\n0.7 0.25 0.05 2\nwe cannot independently tune its strain state to match the in-plane strain realized in\nthe HZO/HLO multilayer. In practice, a single La–HZO layer with this composition and\nthickness tends to partially relax the strain by accommodating the m-phase, as\nevidenced by the coexistence of o- and m-phase peaks and the much lower P.\nr\nFrom\na theoretical perspective, our DFT calculations indeed show that La-doped HZO under\nsufficiently large in-plane compression can follow the unconventional T-path and reach\nhigh polarization. In this sense, a La–HZO single layer subjected to the same strong\ncompressive strain could, in principle, approach a similar polarization. However, our\nexperimental comparison indicates that achieving such a strain state in a single solid-\nsolution film without triggering relaxation and the m-phase is highly non-trivial. The\nshort-period HZO/HLO multilayer provides a more practical route to simultaneously\nimpose strong in-plane compressive strain and stabilize the o-phase, while benefiting\nfrom La doping at the same time.\nWe realise that exploring strain-engineered La–HZO single layers is an interesting\ndirection for future work. For example, one could systematically vary the in-plane\nlattice constraint using different substrates and buffer/capping layers, and map out the\nferroelectric phase diagram of La-HZO as a function of La content, Hf:Zr ratio, and\nepitaxial strain. Such studies would further test the limits of La–HZO single films under\ncontrolled strain conditions and provide a complementary pathway to the interface-\nengineered multilayer approach demonstrated in the present work.\nChanges in the revised manuscript:\nWe have incorporated these control experiment results into both the revised main text\nand the Supplementary Information to strengthen our argument.\n(i) We have added the XRD and ferroelectric characterization of the single-layer La-\ndoped HZO solid-solution film to the Supplementary Information as Supplementary\nFig. 5.\n(ii) We have inserted a corresponding discussion in the Main Text (Page 12) to\nexplicitly distinguish the superlattice effect from simple chemical doping. The added\ntext is highlighted in the revised manuscript and reads as follows:\n“…This highlights the effectiveness of HZO/HLO superlattice structure in enhancing\nferroelectric polarization. To further distinguish the effect of the HZO/HLO superlattice\narchitecture from that of simple La doping, we prepared a single-layer La-doped HZO\nsolid-solution film, Hf Zr La O , with the same total thickness and average\n0.7 0.25 0.05 2\ncomposition as the HZO/HLO multilayer, grown on the same LSMO/STO(001)\nsubstrate. Supplementary Fig. 5 shows its XRD and P–E characteristics. The film\nclearly exhibits coexisting o- and m-phase peaks, indicating incomplete stabilization\nof the o-phase. The corresponding P–E loop (Supplementary Fig. 5b) confirms\nferroelectric switching but with a much smaller P of ~ 10.2 µC/cm2. This comparison\nr\ndemonstrates that La doping alone is insufficient to achieve near-theoretical\npolarization, and highlights the crucial role of the HZO/HLO superlattice architecture.\nWhen compared with the P value…”\nr\nComment 2: Furthermore, if the films are composed of alternating HZO and HLO\nlayers, the origin and nature of the in-plane strain should be clearly defined. It seems\nlikely that the strain arises from the competition between the lattice mismatch of the\ntwo alternating layers and the substrate, yet this is not addressed in the manuscript.\nResponse: We appreciate this insightful comment. We fully agree that clarifying the\norigin of the in-plane strain is crucial for understanding the enhanced ferroelectricity in\nour superlattices. In the revised manuscript we have added a dedicated discussion to\nclarify this, and we summarise the key aspects here.\nAs the reviewer correctly points out, HZO and HLO do not have identical lattice\nparameters. The HLO layers contain La3+ dopants, which have a larger ionic radius\n(1.16Å) compared to Hf4+ (0.83Å) and Zr4+ (0.84Å). Consequently, the equilibrium bulk\nlattice volume of HLO is larger than that of HZO. The HLO layers therefore introduce\nan intrinsic tendency for lattice expansion. Despite the tendency of HLO to expand,\nthe ultrathin nature of the sub-layers (0.9 nm) forces them to grow coherently with the\nadjacent HZO layers and the LSMO/STO substrate. The HZO layers and the substrate\neffectively \"clamp\" the HLO layers in the in-plane direction. This competition results in\na significant in-plane compressive strain throughout the superlattice film. The HLO\nlayers are prevented from relaxing to their bulk equilibrium parameter, thereby\ngenerating an internal compressive stress state. This stress stabilizes the\nrhombohedral-distorted o-phase against the non-ferroelectric m-phase, as confirmed\nby our GPA analysis (Fig. 2) and DFT calculations (Fig. 4).\nThe influence of this strain state is further supported by the HZO/HLO multilayer with\ndifferent individual layer thickness but the same total thickness (Supplementary Fig.\n7). When the thickness of each HZO and HLO layer is increased ([HZO(1.8\nnm)/HLO(1.8 nm)] ), the number of interfaces is reduced and the lattice has more\n×2\nfreedom to locally relax. In this case, both the rhombohedral distortion (as quantified\nby the d /d ratio) and the remanent polarization are smaller than in the [HZO(0.9\n111 11-1\nnm)/HLO(0.9 nm)] sample.\n×4\nRevision in Manuscript: below is the additional discussion on the origin of the in-plane\nstrain in the revised manuscript (highlighted).\n\"...Along the in-plane xx-direction (Fig. 2e), the internal strain of the HZO/HLO layer\n(~6%) is compressive relative to the significantly higher strain (~16%) observed at the\ninterface with LSMO. This predominant in-plane compressive strain originates from\nthe lattice mismatch competition between the alternating HZO and HLO layers.\nSpecifically, the La-doped HLO layers possess a larger equilibrium lattice volume due\nto the larger ionic radius of La3+ compared to Hf4+/Zr4+. However, due to the ultrathin\nlayer thickness and the epitaxial constraint from the alternating HZO layers, the HLO\nlattice is prevented from relaxing. This mutual clamping effect induces a substantial\ncompressive stress state that acts to stabilize the ferroelectric o-phase. Conversely,\nalong the out-of-plane yy-direction...\"\nComment 3: Another important concern lies in the XRD analysis. The absence of\nsatellite peaks, which are typical signatures of superlattice periodicity, must be\ndiscussed.\nResponse: We thank the reviewer for this insightful comment regarding the XRD\nanalysis. We agree that satellite peaks are typically hallmarks of superlattice structures.\nHowever, we believe their absence in this specific [HZO(0.9 nm)/HLO(0.9 nm)]\nx4\nsample is due to the combined effects of interface interdiffusion relative to the ultrathin\nlayer thickness and significant peak broadening, as explained below:\n(i) The sub-layer thickness in our design is extremely thin (0.9 nm). In our PLD growth\nat elevated temperatures, atomic interdiffusion at the heterointerfaces is inevitable.\nThis \"interface smearing\" is expected to suppress the intensity of satellite peaks.\n(ii) The visibility of satellite peaks is fundamentally governed by the Laue interference\nfunction. Theoretically, the diffracted intensity (𝐼) scales with the number of repeating\nperiods (𝑁) according to the relationship:\nsin(𝑁∙𝑄 ∙Λ/2)\n𝐼(𝜃) ∝ ( )2\nsin(𝑄∙Λ/2)\nwhere 𝑄 is the scattering vector and Λ is the superlattice period vector1,2.\nAccording to this relationship, the peak intensity scales as 𝐼 ∝ 𝑁2. For our [HZO(0.9\nnm)/HLO(0.9 nm)] film, N = 4 and the total thickness is only ~7.2 nm, therefore the\n×4\ninterference fringes are intrinsically weak and the satellites are broad. Combined with\nfinite-size (Scherrer) broadening of the main Bragg peak, any residual satellite\nintensity is easily buried in the tails of the main peak and in the background.\n(iii) Satellite peaks arise from the periodic modulation of the structure factor (𝐹) along\nthe growth direction. The intensity of the 𝑚 -th order satellite (𝐼 ) is approximately\nm\nproportional to the square of the difference in structure factors between the sub-layers2:\n𝐼 ∝ |𝐹 −𝐹 |2\nm 𝐻𝑍𝑂 𝐻𝐿𝑂\nwhere 𝐹 ∝ ∑𝑓 is the structure factor determined by the atomic scattering factors (𝑓),\nj 𝑗\nwhich roughly scale with the atomic number Z. Although there is a difference in atomic\nnumber between Zr (Z=40) and La (Z=57), both layers are HfO -based. The scattering\n2\ncontrast |𝐹 −𝐹 | between the layers is likely insufficient to produce satellite\n𝐻𝑍𝑂 𝐻𝐿𝑂\npeaks distinguishable from the background noise and the broadened main peak.\nIn addition, we have provided a STEM image of a [HZO(1.8 nm)/HLO(1.8 nm)] film.\nx2\nAs shown in Supplementary Fig. 7, the STEM image reveals the layered contrast,\nconfirming that our PLD process successfully achieves the designed modulation. It is\ntherefore reasonable to infer that the 0.9 nm superlattice sample retains this structural\nperiodicity, even though its XRD satellite signatures are strongly diminished by the\nabove geometrical and interfacial factors.\nBelow is the additional discussion in the revised manuscript (the additional information\nis highlighted):\nPage 6 \"... This is further verified with the rocking curves in Fig. 1d, where the full width\nat half maximum (FWHM) of the HZO and HZO/HLO films are 0.098° and 0.065°,\nrespectively. Notably, distinct satellite peaks, which are typically characteristic of\nsuperlattice structures, are not resolved in the XRD pattern. This absence is attributed\nto the combined effects of ultrathin sub-layers (~0.9 nm) and inevitable interfacial\ninterdiffusion during high-temperature growth, and the modest scattering contrast\nbetween two HfO -based layers, which together result in a diffraction profile reflecting\n2\nthe average coherent lattice structure. For thicker films (12 nm and 20 nm,\nSupplementary Fig. 1), secondary phases appear. Characteristic peaks at...\"\nPage 9 “Atomic-resolution energy-dispersive x-ray (EDX) elemental maps of the\nHZO/HLO film (Supplementary Fig. 2) reveal a mixture of La, Hf and Zr elements within\nthe structure. This observed intermixing is attributed to the combined effects of\ninterfacial diffusion during high-temperature growth and the projection nature of EDX\nmapping, where the interaction volume is comparable to the ultrathin layer thickness.\nFurther evidence for the compositional modulation is provided by HAADF-STEM of a\n[HZO(1.8 nm)/HLO(1.8 nm)] film grown under identical conditions, which reveals a\n×2\nlayered contrast (Supplementary Fig. 7). This confirms that the deposition sequence\nyields a HZO/HLO layered architecture, even though distinct superlattice satellites are\nnot resolved for the [HZO(0.9 nm)/HLO(0.9 nm)] film. Based on the magnified\n×4\nimage…”\nReviewer #2 (Remarks to the Author):\nThe manuscript presents a interesting study on achieving near-theoretical\npolarization in HZO/HLO superlattices, supported by a combination of structural\ncharacterization, ferroelectric measurements, and DFT calculations. However, the\nclarity of the presentation and the robustness of certain experimental claims need\nsignificant improvement before the manuscript can be considered for publication.\nComment 1: The switching pathways are confusingly introduced. The authors first\nmention a “conventional T-pathway” and then refer to a “conventional N-pathway,”\nwhich is inconsistent with the literature. The definitions of T-path and N-path should be\nclearly and consistently explained early in the text, with references to prior work (e.g.,\nWu et al., PRL 2023).\nResponse: We thank the reviewer for pointing this out. We have carefully re-examined\nour manuscript. While our original text in the Introduction described the T-pathway as\n\"unconventional\" and the N-pathway as \"conventional,\" we acknowledge that the\nsentence structure may have been complex, potentially leading to ambiguity. To\nimprove clarity and follow a more logical flow, we have rewritten the introduction of\nthese pathways. We now introduce the conventional non-crossing pathway (N-path)\nfirst, followed by the unconventional traversal pathway (T-path) proposed by Wu et al.\nThis revision ensures strict consistency with the literature and provides a clearer\ncontext for the readers.\nRelevant changes in the Introduction (highlighted):\n“Conventionally, polarization switching in HfO -based ferroelectrics follows the non-\n2\ncrossing pathway (N-path), where oxygen displacement is confined within the unit cell\nboundaries. Recently, Wu et al. proposed an unconventional switching mechanism in\nHfO2-based ferroelectrics, referred to as the T-path33. In this mechanism, three-fold\ncoordinated oxygen atoms traverse across unit-cell boundaries defined by the Hf/Zr\natomic planes.”\nComment 2: The phrase “demonstrating well stabilized the ferroelectric phases” is\ngrammatically incorrect and should be rephrased for clarity.\nResponse: We thank the reviewer for this pointing this out. We have corrected this\nsentence to: \"demonstrating that the ferroelectric phases are well stabilized.\" And we\nhave also carefully proofread the entire manuscript to eliminate similar grammatical\nissues.\nComment 3: The use of the term “superlattice” is not fully supported by the\nexperimental evidence. The EDX mapping shows a mixture of La, Hf, and Zr, and the\nauthors acknowledge non-uniform La distribution due to resolution limits. This\nundermines the claim of a well-defined superlattice structure. Additional evidence\n(e.g., EELS line scans, XRD satellite peaks) is needed to substantiate the\nsuperlattice claim.\nResponse: We appreciate this rigorous critique. We agree that the combination of\nmixed EDX signals and the absence of XRD satellite peaks raises questions about the\nsharpness of the layers and the use of the term “superlattice”.\nFirst, regarding the XRD satellites, we have provided a detailed discussion of their\nexpected weakness in our response to Reviewer 1, Comment 3, including the Laue\ninterference function and the dependence of satellite intensity on period number, total\nthickness, and structure-factor contrast. In brief, the [HZO(0.9 nm)/HLO(0.9 nm)] film\n×4\nhas extremely thin sub-layers, only 4 periods, a small total thickness (~7.2 nm),\ninevitable interfacial interdiffusion at the nominal substrate temperature of 800 °C, and\nonly modest scattering contrast between two HfO -based sub-layers. These factors\n2\ntogether lead to intrinsically weak and broadened satellites that are easily buried in the\nScherrer-broadened main peak and background.\nSecond, for the EDX mapping, the individual layer thickness (~0.9 nm) is comparable\nto or smaller than the effective spatial resolution and interaction volume of STEM–\nEDX. As a result, the “mixed” appearance of La, Hf, and Zr in the elemental maps\nprimarily reflects projection and averaging over multiple ultrathin layers rather than a\ncomplete loss of modulation. More direct real-space evidence of layering can be found\nin a STEM image of a [HZO(1.8 nm)/HLO(1.8 nm)] film grown under identical PLD\n×2\nconditions but with slightly thicker periods (Supplementary Fig. 7). This image shows\nlayered contrast, confirming that our deposition process reliably produces an\nHZO/HLO layered architecture. We therefore infer that the [HZO(0.9 nm)/HLO(0.9\nnm)] film also retains this structural periodicity.\n×4\nThird, the use of the term “superlattice” in our work reflects not only the structural\nmodulation but also the underlying strain-engineering design. The goal of this design\nwas to utilize the lattice mismatch between HZO and HLO to induce specific lattice\ndistortions and stabilize the ferroelectric o-phase. To separate this effect from simple\nchemical doping, we fabricated a control sample: a single-layer La-doped HZO\n(Hf Zr La O ) solid-solution film with the same thickness (~7 nm) and average\n0.7 0.25 0.05 2\ncomposition as the HZO/HLO superlattice. As shown in Fig. R1, this solid-solution film\ncontains secondary m-phase peaks and exhibits a much lower P of ~10.2 μC/cm2\nr\nthan the HZO/HLO superlattice film. In contrast, the HZO/HLO superlattice shows a\nunique rhombohedral distortion and record-high polarization, distinct from the\nproperties typically observed in HZO-HLO solid solutions or simple doped films. This\nindicates that a periodic strain field associated with the HZO/HLO layering is operative,\neven if the chemical interfaces are broadened.\nIn response to the reviewer's concern, we have revised the manuscript to describe this\nmore precisely. While we retain the term \"superlattice\" for the structural design, we\nhave added a discussion in the revised manuscript (highlighted):\n“Atomic-resolution energy-dispersive x-ray (EDX) elemental maps of the HZO/HLO\nfilm (Supplementary Fig. 2) reveal a mixture of La, Hf and Zr elements within the\nstructure. This observed intermixing is attributed to the combined effects of interfacial\ndiffusion during high-temperature growth and the projection nature of EDX mapping,\nwhere the interaction volume is comparable to the ultrathin layer thickness. Further\nevidence for the compositional modulation is provided by HAADF-STEM of a\n[HZO(1.8 nm)/HLO(1.8 nm)] film grown under identical conditions, which reveals a\n×2\nlayered contrast (Supplementary Fig. 7). This confirms that the deposition sequence\nyields a HZO/HLO layered architecture, even though distinct superlattice satellites are\nnot resolved for the [HZO(0.9 nm)/HLO(0.9 nm)] film. Based on the magnified\n×4\nimage…”\nComment 4: The statement “This work presents the first reported superlattice\nstructure of its kind in HfO₂-based ferroelectric systems” is premature without clearer\nstructural validation.\nResponse: We thank the reviewer for this important remark. We agree that, given the\nfinite interfacial interdiffusion, the original statement was too strong.\nAs detailed in our response to Comment 3, we have now provided additional analysis\nand explanation to substantiate the superlattice structure including (i) direct\nvisualization of the periodic layering of the [HZO(1.8 nm)/HLO(1.8 nm)] sample\nx2\n(Supplementary Fig. 7) and (ii) functional validation: the observed record-high\npolarization and unique strain state (discussed in Response to Reviewer 1) are distinct\nproperties that arise specifically from this periodic modulation, differentiating our film\nfrom random solid solutions.\nTo address the reviewer’s concern about the \"premature\" nature of the statement and\nto reflect the structural reality more precisely, we have refined the sentence in the\nConclusions part. We have revised the statement “This work presents the first reported\nsuperlattice structure of its kind in HfO₂-based ferroelectric systems” to “This work\ndemonstrates a novel HZO/HLO superlattice design to stabilize the ferroelectric\nphase”.\nComment 5: The description of “perfect epitaxial relationship” is an overstatement.\nDislocations and imperfections are visible in the TEM images. The language should\nbe tempered to reflect the actual microstructural quality.\nResponse: We thank the reviewer for this comment. We have carefully revised the\nrelevant passages. The phrase \"perfect\" has been replaced by \"high-quality\".\nComment 6: The yellow lines in Figure 2d obscure structural details at the interface.\nReplacing them with arrows or dashed lines would improve clarity.\nResponse: We appreciate this practical suggestion. We have removed the solid yellow\nlines in Figure 2d and replaced them with discrete dashed markers that indicate the\ninterfaces without covering the underlying atomic columns. The improved figure (Fig.\nR2 below) allows the interface structure to be viewed more clearly.\nComment 7: The xx and yy directions for strain analysis (Fig. 2e,f) should be clearly\nlabeled in the figure or caption to aid interpretation, especially for non-specialist\nreaders.\nResponse: We thank the reviewer for pointing this out. The xx direction corresponds\nto the in-plane direction, while the yy direction corresponds to the out-of-plane\ndirection. In the revised strain analysis maps (Fig. 2e,f), we now include this\ninformation (ε (in-plane strain), ε (out-of-plane strain)) to improve the readability.\nxx yy\nThis should make the strain analysis more accessible to non-specialist readers.\nComment 8: The GPA results are unusual. The LSMO reference region shows\nsignificant strain, which contradicts the assumption of a zero-strain reference. This\nraises concerns about the validity of the strain analysis. The authors should clarify\nthe reference selection and compare their methodology with established practices in\nthe literature.\nResponse: We thank the reviewer for catching this potential point of confusion. The\nLSMO region correctly serves as a zero-strain reference along the xx-direction [Nature\nCommunications 14, 8174 (2023)3; Physical Review B 92, 024419 (2015)4]. However,\nnon-negligible strain is observed along the yy-direction, exactly as the reviewer noted.\nThis difference arises because LSMO viewed from the [110] direction has densely\npacked atomic columns along the yy-direction. This high atomic density makes\ngeometric phase analysis more sensitive to signal interference in this orientation, so\nthe HZO region is used as the zero-strain reference in out-of-plane direction. Crucially,\nthe relative strain distribution across the heterostructure remains consistent, thereby\npreserving the validity of our conclusions regarding strain evolution. We gratefully\nacknowledge the reviewer's insight and have accordingly recalibrated the GPA results.\nIn the revised analysis, we explicitly select a region inside the LSMO layer as the zero-\nstrain reference for both ε (in-plane) and ε (out-of-plane). The updated maps\nxx yy\ntherefore show the LSMO reference region with strain values very close to zero in both\ndirections. Importantly, after recalibration the relative strain distribution across the\nheterostructure is unchanged.\nThe updated results are shown in Fig. R2 below and have been incorporated as Fig.\n2 in the revised version.\nFig. R2 | HAADF-STEM characterization and strain analysis of the HZO/HLO film.\na, Cross-sectional HAADF-STEM image of the HZO/HLO film. b, Zoomed-in cross-\nsectional image with corresponding FFT simulation. c, Interplanar spacing\nmeasurements for the (111) and (11-1) planes. d, Wide range cross-sectional STEM\nimage of the HZO/HLO film. GPA analysis of the e, in-plane strain (ε ) and f, out-of-\nxx\nplane strain (ε ) within the HZO/HLO film. Positive values represent tensile strain,\nyy\nwhile negative values indicate compressive strain.\nComment 9: The Methods section lacks sufficient detail to reproduce the work. Key\nparameters such as laser fluence, substrate preparation, and characterization details\nshould be described more thoroughly.\nResponse: We thank the suggestion from the reviewer, we have significantly\nexpanded the Methods section. We have added: Laser fluence for LSMO layer;\nSubstrate preparation; Details on electrical measurements; Details on the GPA\nsoftware and parameters used for strain calculation.\nHere is the revised Method section in the revised manuscript (the additional\ninformation is highlighted):\n“Thin film deposition. The HZO and HZO/HLO superlattice films on La Sr MnO\n0.67 0.33 3\n(LSMO) bottom electrode layer were epitaxially grown on single-crystalline SrTiO\n3\n(001) substrates at a nominal substrate temperature of 800 ℃ by PLD using a KrF (λ\n= 248 nm) excimer laser. Prior to PLD growth, the STO (001) substrates were\nthermally treated at 875 °C for 3 h to obtain a clean, atomically flat step–terrace surface.\nThe LSMO layers (~10 nm) were grown at a nominal substrate temperature of 950 ℃\nwith an oxygen pressure of 200 mTorr, while HZO and HLO films were deposited at a\nnominal substrate temperature of 800 ℃ with an oxygen pressure of 75 mTorr. The\nlaser fluence was 1.2 J cm−2 with a repetition rate of 3 Hz for LSMO and 1.1 J cm−2\nwith a repetition rate of 3 Hz for HZO and HLO. After the deposition, the films were\ncooled down to room temperature at an oxygen pressure of 1 Torr with a cooling rate\nof 10 ℃/min. The top Pt layer (~30 nm) was deposited by magnetron sputtering without\nbreaking the vacuum by transferring the sample from the PLD system into the\nsputtering system for in situ growth. Then, an array of 15 × 15 µm2 top Pt electrodes\nwas patterned via an Ultraviolet Maskless Lithography machine (TuoTuo Technology,\nUV Litho-ACA) and ion etching for electrical measurements.\nMaterial characterization. The crystal structure and epitaxial quality were\ncharacterized by synchrotron XRD using a four-circle diffractometer with an X-ray\nwavelength of 1.5406 Å at the Singapore Synchrotron Light Source (SSLS) and\nBL02U2 at Shanghai Synchrotron Radiation Facility (SSRF). Microstructure of the\nsamples, interfacial structure, EDX elemental mapping, and atomic layer-by-layer\nEELS were obtained by aberration corrected STEM at room temperature. Cross-\nsectional TEM samples were prepared with a focused ion beam setup (DA300, FEI).\nGeometric phase analysis was performed using a free FRWRtools plugin for Gatan\nDigital Micrograph based on the original work by Hytch et al5. The strain in the LSMO\nlayer was used as a reference.\nFerroelectricity measurements. The ferroelectric measurements (P-E hysteresis\nloops) and endurance characteristics were performed using a Radiant Precision\nMultiferroic II tester. A 30 nm of Pt with a device feature of 15 × 15 µm2 was sputtered\nas the top electrode material prior to the ferroelectric test. In all the measurements,\nthe bias was applied to the top electrode. The LSMO bottom electrode was grounded.\nThe ferroelectric measurements at cryogenic temperatures (10 K to 300 K) were\nconducted in a vacuum cryogenic probe station (Lakeshore), using a Radiant\nPrecision Multiferroic II tester and the top electrodes are connected using Ag wires\nand Ag paint.\nTheoretical modeling and DFT calculations. DFT calculations were performed\nusing the Vienna Ab-initio Simulation Package (VASP). The projector augmented\nwave potential (PAW) and generalized gradient approximation (GGA) with Perdew-\nBurke Ernzerhof (PBE) parameterization were used to describe the electron-ion and\nelectron-electron exchange-correlation interactions, respectively. The energy cutoff for\nplane waves was set to 500 eV. The energy convergence threshold for the self-\nconsistent loop was set to 10-5 eV. For structural optimization, the force convergence\nwas set to 0.001 eV/Å. For HZO without defects, the lattice parameters of the\nferroelectric orthorhombic phase (o-phase) are optimized to be a = 5.07 Å, b = 5.09 Å,\nc = 5.28 Å, and α = β = γ =90°. The lattice parameters of the paraelectric monoclinic\nphase (m-phase) are a = 5.16 Å, b = 5.21 Å, c = 5.26 Å, and α = γ = 90°, β = 99.71°.\nThe lattice parameters of rhombohedral phase (r -phase) are optimized to a = 5.16\n3m\nÅ, b = 5.21 Å, c = 5.26 Å, and α = β = 90°, γ= 120°. All experimental results show that\nHf Zr O films on LSMO substrate exhibit pseudo-orthogonal confinement\n0.5 0.5 2\ncharacters. These Hf Zr O films could be o- Hf Zr O and m- Hf Zr O films\n0.5 0.5 2 0.5 0.5 2 0.5 0.5 2\nalong the [1 1 1] direction or r -phase film in the [0 0 1] direction. Here, we applied\n3m\nthe transformation matrix to expose the (1 1 1) surface of o- Hf Zr O and m-\n0.5 0.5 2\nHf Zr O , and (0 0 1) surface of r -phase. The strain is uniformly added along the\n0.5 0.5 2 3m\nin-plane direction, and the out-of-plane direction is fully optimized. The out-of-plane\nelectric polarization is calculated with the berry phase method, and 29 intermediate\nstructures are applied between the electric up-and down-polarization states. The\nformation energy (𝐸 ) of oxygen vacancy is calculated with 𝐸 = 𝐸 + 𝜇 − 𝐸 , where\nf 𝑓 𝑉 𝑂 𝑖𝑑𝑒𝑎𝑙\n𝐸 (𝐸 ) is the total energy of 2×2×2 supercells of Hf Zr O with (without) one\n𝑉 𝑖𝑑𝑒𝑎𝑙 0.5 0.5 2\noxygen vacancy, and 𝜇𝑂 is the chemical potential of oxygen, and is obtained with 𝐸 ,\n𝑂2\nwhere 𝐸 is the total energy of oxygen molecular. The energy barriers are calculated\n𝑂2\nwith nudged elastic band method, and 8 intermediate images are inserted between\ninitial and final images. For the 6% concentration of La doped HfZrO systems, the\n2\n2×2×1 supercell is used with one Hf is replaced by La atom, and for the 25%\nconcentration of La doped HfZrO , one Hf atom in the unit cell of HfZO is substituted.”\n2 2\nComment 10: Figures 3c and 3f present single data points without error bars or\nstatistical validation. Multiple measurements or error estimates are necessary to\nsupport the reliability of the endurance and temperature-dependent polarization data.\nResponse: We appreciate this important point about data robustness. In the revised\nmanuscript, we have performed additional measurements on multiple capacitor\ndevices for both endurance and temperature-dependent polarization tests. Figure 3f\nhas been updated to include error bars that represent the standard deviation of P at\nr\neach temperature point. We have also verified the endurance characteristics on\nadditional devices on the same sample. As shown in Fig. R4 below, the endurance\nbehavior is reproducible across different devices.\nFig. R3 | Ferroelectric characterizations. a, Positive-up-negative-down (PUND)\npolarization-electric field (P-E) loops of HZO/HLO and HZO films. b, Typical\nferroelectric current-electric field switching curves for HZO/HLO and HZO films. c,\nEndurance test of the HZO/HLO film. d, Benchmarking of HZO/HLO film reported in\nthis work against some reported doped-HfO ferroelectric thin films regard to film\n2\nthickness20,24–27,37–45. e, Temperature-dependent P-E loops of the HZO/HLO film from\nr\nFig. R4 | Endurance test of the multiple HZO/HLO capacitor devices.\nComment 11: The authors note that reducing layer thickness (increasing interface\ndensity) enhances ferroelectricity. It would be valuable to test even thinner layers\n(e.g., <0.9 nm) to explore the limit of this effect and strengthen the interface-\nstabilization argument.\nResponse: We thank the reviewer for this valuable suggestion. Motivated by this\ncomment, we fabricated an additional HZO/HLO sample with an even smaller sub-\nlayer thickness of 0.45 nm by reducing the deposition time per layer, namely\n[HZO(0.45 nm)/HLO(0.45 nm)] , and grown under identical PLD conditions on\n×8\nLSMO/STO(001). We characterized its structural and ferroelectric properties, and the\nresults are presented in Fig. R5 below.\nAs shown in Fig. R5a, the XRD pattern of this sample still exhibits a characteristic peak\naround 30°, similar to the o-phase signature observed in the 0.9 nm, 1.2 nm and\n1.8 nm period multilayers, indicating that an o-phase–dominated structure is still\npresent. However, the FWHM of this o-phase peak is noticeably larger than that of the\noptimal [HZO(0.9 nm)/HLO(0.9 nm)] film (Fig. 1c), suggesting a reduced coherent\n×4\ncrystallite size and/or increased structural disorder in the ultrashort-period multilayer.\nConsistently, the ferroelectric P–E loop (Fig. R5b) reveals that this ultrashort-period\nsample exhibits pronounced leakage: the hysteresis ends are relatively rounded rather\nthan sharp, and the evaluated remanent polarization is ~16 µC/cm2, significantly lower\nthan the [HZO(0.9 nm)/HLO(0.9 nm)] film. These results indicate that, under our\n×4\ncurrent growth conditions, further reducing the individual layer thickness does not lead\nto a monotonic increase in polarization. Instead, when the sub-layers approach\n~0.45 nm (less than 1–2 fluorite unit cells), the structural and electrical quality begins\nto degrade. We attribute this degradation to two primary factors: interdiffusion and\nhigher concentration of interfacial defects. As discussed in our response to Comment\n3, atomic interdiffusion is inevitable at the nominal substrate temperature (800°C). At\nthe 0.45 nm scale, the diffusion length is likely comparable to the individual layer\nthickness. The layers are more susceptible to interfacial roughening and defect\nformation, which in turn increases leakage and limits the effective switching\npolarization.\nWe also note that exploring growth-condition optimization (e.g. lower deposition rate,\nadjusted temperature/pressure, alternative substrates or buffer/capping layers) to\nstabilize even thinner continuous HZO/HLO sub-layers, and mapping how the\nremanent polarization evolves in this ultrathin limit, will be an interesting direction for\nfuture work to further refine the interface-engineering strategy demonstrated here.\nFig. R5 | XRD and ferroelectric characterization of the\n[HZO(0.45 nm)/HLO(0.45 nm)] film. a, ω−2θ XRD scan of the\n×8\n[HZO(0.45 nm)/HLO(0.45 nm)] film (~7 nm). b, P-E loop of the same film.\n×8\nReference:\n1. Miller, A.M. et al. Extracting information from X-ray diffraction patterns containing\nLaue Oscillations, Zeitschrift für Naturforschung B 77, 313-322 (2022).\n2. Pietsch, U., Holy, V. & Baumbach, T. High-Resolution X-Ray Scattering: From Thin\nFilms to Lateral Nanostructures Ch. 4 (Springer, Berlin, 2004).\n3. Cai, X. et al. In-plane charged antiphase boundary and 180° domain wall in a\nferroelectric film. Nat. Commun. 14, 8174 (2023).\n4. Maurel, L. et al. Nature of antiferromagnetic order in epitaxially strained multiferroic\nSrMnO thin films. Phys. Rev. B 92, 024419 (2015).\n3\n5. Hytch, M. J., Snoeck, E., Kilaas, R. Quantitative measurement of displacement and\nstrain fields from HREM micrographs. Ultramicroscopy 74, 133-146 (1998)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Based on the authors’ responses and the changes made to the manuscript, I recommend publication of this paper", "reviewer_2": "Recommendation: Do not recommend publication in current form)\nThe manuscript is built around the central claim of an epitaxial HZO/HLO superlattice, which is explicitly highlighted in the title and presented as the core novelty. However, despite the revisions, the evidence provided for a true superlattice in the key structure [HZO(0.9 nm)/HLO(0.9 nm)]×4 remains largely explanatory rather than experimentally demonstrated.\nSpecifically, the manuscript does not present unambiguous signatures expected for a superlattice. XRD satellite reflections (or equivalent reciprocal-space evidence) are not shown. The explanation that satellites may be absent due to ultrathin periods, interdiffusion, and limited scattering contrast is plausible, but it does not constitute proof. Likewise, the reported STEM–EDX results do not directly establish a periodic compositional modulation in the nominal superlattice; instead, they are consistent with significant intermixing at this length scale. The added HAADF evidence from a different, thicker-period sample (e.g., [HZO(1.8)/HLO(1.8)]×2) is not sufficient to validate the superlattice nature of the ultrathin-period structure that underpins the title and primary novelty claim.\nBecause this point is fundamental to the manuscript’s main message, I cannot recommend publication unless the authors provide direct experimental evidence that the 0.9 nm ×4 stack exhibits genuine periodic layering/modulation. Without direct evidence establishing a superlattice in the studied ultrathin stack, the title and central novelty claim are not justified."}, "author_response": "Response to the reviewers’ comments\nDiscussion of reviewers’ comments (the reviewer’s comments are quoted in blue and\nour responses in black. Revision related parts are highlighted)\nReviewer #1 (Remarks to the Author):\nBased on the authors’ responses and the changes made to the manuscript, I\nrecommend publication of this paper.\nResponse: We sincerely thank the reviewer for the positive evaluation and\nrecommendation for publication.\nReviewer #2 (Remarks to the Author):\nThe manuscript is built around the central claim of an epitaxial HZO/HLO\nsuperlattice, which is explicitly highlighted in the title and presented as the core\nnovelty. However, despite the revisions, the evidence provided for a true superlattice\nin the key structure [HZO(0.9 nm)/HLO(0.9 nm)] remains largely explanatory rather\n×4\nthan experimentally demonstrated.\nSpecifically, the manuscript does not present unambiguous signatures expected for a\nsuperlattice. XRD satellite reflections (or equivalent reciprocal-space evidence) are\nnot shown. The explanation that satellites may be absent due to ultrathin periods,\ninterdiffusion, and limited scattering contrast is plausible, but it does not constitute\nproof. Likewise, the reported STEM–EDX results do not directly establish a periodic\ncompositional modulation in the nominal superlattice; instead, they are consistent\nwith significant intermixing at this length scale. The added HAADF evidence from a\ndifferent, thicker-period sample (e.g., [HZO(1.8)/HLO(1.8)] ) is not sufficient to\n×2\nvalidate the superlattice nature of the ultrathin-period structure that underpins the\ntitle and primary novelty claim.\nBecause this point is fundamental to the manuscript’s main message, I cannot\nrecommend publication unless the authors provide direct experimental evidence that\nthe 0.9 nm ×4 stack exhibits genuine periodic layering/modulation. Without direct\nevidence establishing a superlattice in the studied ultrathin stack, the title and central\nnovelty claim are not justified.\nResponse: We thank the reviewer for this critical comment and fully agree that direct\nexperimental evidence is required to support claims of periodic layering, particularly\nfor ultrathin period heterostructures. To address this point and provide direct\nexperimental evidence for periodic modulation in the [HZO(0.9 nm)/HLO(0.9 nm)]\n×4\nstack, we performed elemental concentration line-scan profile analysis based on\natomic resolution EDX mapping.\nSpecifically, an elemental concentration line-scan profile of Zr and La was extracted\nalong the film growth direction over a thickness range of ~3.6 nm, corresponding to\nfour nominal sub-layers with a designed thickness of ~0.9 nm each. As shown in Fig.\nR1, the line scan profile was divided into four consecutive regions (I–IV), each around\n0.9 nm thick, and the average elemental concentrations of Zr and La were calculated\nwithin each region. The horizontal dashed lines are provided as guides to the eye to\nvisualize the periodic variations of Zr and La. The analysis reveals that Zr-rich and La-\nrich regions alternate with a spatial periodicity of ~0.9 nm, consistent with the designed\nHZO/HLO stacking sequence.\nFig. R1 | Elemental concentration line-scan profile of the HZO/HLO multilayer. a,\nZoomed-in atomic resolution EDX mapping of the HZO/HLO film. b, Extracted top-\ndown elemental concentration line-scan analysis for La and Zr, demonstrating the\nperiodic compositional modulation matching the designed layer thickness.\nThese results provide direct experimental evidence that, although interfacial\ninterdiffusion is present at this ultrathin length scale, the film does not form a random\nalloy. Instead, a reproducible short-period compositional modulation persists\nthroughout the multilayer stack. This conclusion is further supported by our control\nexperiment on a single-layer La-doped HZO solid-solution film with the same average\ncomposition, which exhibits significantly lower remanent polarization and secondary\nphase formation.\nWe acknowledge that the ultrathin-period structure does not exhibit the atomically\nsharp interfaces or reciprocal-space satellite reflections expected of a superlattice. To\navoid overstatement, we have therefore revised the title and manuscript to replace the\nterm “superlattice” with “multilayers” throughout.\nRevisions in Manuscript:\n- Title change: From “Approaching Theoretical Polarization Limit in\nHfZrO /HfLaO Superlattices” to “Approaching Theoretical Polarization Limit in\n2 2\nHfZrO /HfLaO Multilayers”.\n2 2\n- Terminology: We have replaced the term “superlattice” with “multilayers” (or\n“multilayer film”) throughout the text.\nImportantly, this terminological refinement does not affect the central conclusions of\nthis work. Our main finding is that a short-period, epitaxially coherent HZO/HLO\nmultilayer—with dense interfaces and periodic compositional modulation—can impose\na strong in-plane compressive strain, stabilize a rhombohedrally distorted ferroelectric\no-phase, and enable near-theoretical polarization values. These physical conclusions\nremain supported by the combined structural, ferroelectric, and theoretical analyses\npresented in the revised manuscript."}, {"round": 3, "reviewer_comments": {"reviewer_1": "I have examined the authors’ revisions and their responses to the reviewers’ comments. The major concern raised by Reviewer #2 was the claim of a superlattice structure without any clear experimental evidence. The authors provide additional measurements via atomic-resolution EDX line-scan analysis to show compositional modulation, but this is not sufficient to call the studied samples a superlattice. I agree with the change of terminology from “superlattice” to “multilayers” throughout the manuscript in order to avoid any overstatement.\nIn my opinion, the revised manuscript is now suitable for publication.", "reviewer_2": "I do not have remarks for the authors."}, "author_response": ""}]

Decision letter