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 reverse size effect, which is characterized by enhanced and robust ferroelectricity at reduced thickness1,2,3,4,5,6,7,8. 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 fraction11,12,13,14,15,16. Various dopants such as Zr, La, Al, and Y, have been widely employed to further enhance Pr17,18,19,20,21,22,23,24,25,26. 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 properties29,30,31,32. 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\(\times\)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 sharper 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.

Fig. 1: Schematic illustration and XRD characterization of HZO and HZO/HLO multilayer films.
Fig. 1: Schematic illustration and XRD characterization of HZO and HZO/HLO multilayer films.
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a Schematic of the HZO/HLO multilayer structure. b ω − 2θ XRD scan of the HZO film (~ 7 nm). c ω − 2θ XRD scan of the HZO/HLO film (~ 7 nm). d Rocking curves of HZO(111) and HZO/HLO(111) diffraction peaks. e Pole figure around the (111) peak of 7 nm HZO/HLO film at 2θ = 29.95°. f Schematic illustration of a standard orthorhombic lattice (left) and an orthorhombic lattice with rhombohedral distortion (right).

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.

Table 1 Structural parameters of HZO and HZO/HLO on LSMO/STO(001)
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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 strains (Fig. 2f) 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.

Fig. 2: HAADF-STEM characterization and strain analysis of the HZO/HLO film.
Fig. 2: HAADF-STEM characterization and strain analysis of the HZO/HLO film.
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a Cross-sectional HAADF-STEM image of the HZO/HLO film. b Zoomed-in cross-sectional image with corresponding FFT simulation. Larger light-blue dots represent Hf/Zr/La atoms, whereas smaller light-blue dots represent oxygen atoms. c Interplanar spacing measurements for the (111) and (11-1) planes. Error bars indicate the uncertainty in interplanar spacing calculated from a statistical analysis of multiple measurements performed on different regions of the sample. d Wide range cross-sectional STEM image of the HZO/HLO film. GPA analysis of the (e) in-plane strain (εxx) and (f) out-of-plane strain (εyy) within the HZO/HLO film. Positive values represent tensile strain, while negative values indicate compressive strain.

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\(\times\)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 relative 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 corresponds 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.

Fig. 3: Ferroelectric characterizations.
Fig. 3: Ferroelectric characterizations.
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a Positive-up-negative-down (PUND) polarization-electric field (P-E) loops of HZO/HLO and HZO films. b Typical ferroelectric current-electric field switching curves for HZO/HLO and HZO films. c Endurance test of the HZO/HLO film. d Benchmarking of HZO/HLO film reported in this work against some reported doped-HfO2 ferroelectric thin films regard to film thickness20,24,25,26,27,38,39,40,41,42,43,44,45,46. e Temperature-dependent P-E loops of the HZO/HLO film from 10 K to 300 K. f Pr as a function of temperature for the HZO/HLO film. Error bars indicate the uncertainty in Pr derived from a statistical analysis of multiple measurements performed on three different devices for each sample.

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)]x4 (same sample in Fig. 1a), [HZO(1.2 nm)/HLO(1.2 nm)]x3 and [HZO(1.8 nm)/HLO(1.8 nm)]x2, 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)]x4 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)]x2 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)]x4 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)]x2 film versus approximately 1.095 for the [HZO(0.9 nm)/HLO(0.9 nm)]x4 film. The reduced ferroelectricity observed in the [HZO(1.8 nm)/HLO(1.8 nm)]x2 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 r3m-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 r3m-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 r3m-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 r3m-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.

Fig. 4: Formation energies and polarization switching energy barriers in HZO with/without La doping.
Fig. 4: Formation energies and polarization switching energy barriers in HZO with/without La doping.
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Calculated formation energies of the o-, m- and r3m-phases of HZO as functions of in-plane with lattice parameters under (a) stoichiometric conditions (no oxygen vacancies) and (b) 4.17% concentration of oxygen vacancies. c Schematic illustration of two 180° polarization switching pathways: the conventional non-crossing path (N-path), where threefold coordinated oxygen atoms do not cross the Hf atomic plane, and the unconventional crossing traversal path (T-path), where they do. Calculated electric polarization values for both paths are also presented. d Calculated energy barriers for the N- and T-path switching under strain-free, – 1% compressive, and + 1% tensile strain conditions. e Energy profiles of N- and T-path switching in HZO films with 6.0% and 25% La doping concentrations.

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  oC 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 sputtering 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 FRWRtools 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 (r3m-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 [1 1 1] direction or r3m-phase film in the [0 0 1] direction. Here, we applied the transformation matrix to expose the (1 1 1) surface of o-Hf0.5Zr0.5O2 and m-Hf0.5Zr0.5O2, and the (0 0 1) surface of r3m-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 (\({E}_{f}\)) of oxygen vacancy is calculated with \({E}_{f}={{E}_{V}+{\mu }_{O}-E}_{{ideal}}\), where \({E}_{V}\) (\({E}_{{ideal}}\)) is the total energy of 2 × 2 × 2 supercells of Hf0.5Zr0.5O2 with (without) one oxygen vacancy, and \({\mu }_{O}\) is the chemical potential of oxygen, and is obtained with \(\frac{1}{2}{E}_{{O}_{2}}\), where \({E}_{{O}_{2}}\) is the total energy of the oxygen molecule. The energy barriers are 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 HfZrO2 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 HfZrO2, one Hf atom in the unit cell of HfZrO2 is substituted.