Atomic-scale strain-confined ferroelectricity in fluorite hafnium dioxide

Atomic-scale strain-confined ferroelectricity in fluorite hafnium dioxide | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Atomic-scale strain-confined ferroelectricity in fluorite hafnium dioxide Haohai Yu, Yihao Shen, Xiaochun Ma, Yuxiao Liu, Hongzheng Wang, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7867840/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract HfO 2 -based ferroelectrics hold exceptional promise for next-generation microelectronics, offering robust ferroelectricity down to the nanoscale while maintaining compatibility with CMOS technology. However, stabilization of the ferroelectric orthorhombic phase ( o -FE) is consistently challenged by the simultaneous formation of its antiferroelectric counterpart ( o -AFE). This unresolved o -FE/ o -AFE competition, particularly under strain, is a critical factor driving undesirable device phenomena like ‘wake-up’ and ‘fatigue’. To decipher the strain-confinement effects governing o -FE stability at coherent o -phase interfaces, we have developed a bulk-crystal strategy. This approach overcomes thin-film strain complexities by leveraging larger grain sizes and simplified strain landscapes. Integrating advanced microscopy with theoretical calculations, we demonstrate that specific biaxial strain—tensile along the a -axis coupled with compressive along the b -axis—proves sufficient to stabilize the o -FE phase, while strain relaxation favors o -AFE dominance. Direct atomistic tracking reveals the mechanisms underlying the formation of the o -FE phase and the evolution pathway between o -FE and o -AFE phases. Our work establishes a unified strain-mediated mechanism for the ubiquitous phase switching between the o -FE and o -AFE phases observed in HfO 2 -based materials, delivering a fundamental framework to design high-performance fluorite ferroelectrics. This has broad implications for advancing microelectronics and neuromorphic computing. Physical sciences/Materials science/Condensed-matter physics/Phase transitions and critical phenomena Physical sciences/Materials science/Condensed-matter physics/Ferroelectrics and multiferroics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction HfO 2 -based ferroelectric materials are garnering considerable research interest for next-generation microelectronic devices such as ferroelectric random-access memory (FeRAM) and ferroelectric field-effect transistors (FeFETs) 1–5 . This interest stems from their unique ability to maintain robust ferroelectricity at ultrathin thicknesses and exceptional compatibility with established complementary metal-oxide-semiconductor (CMOS) technology 6–8 . Since the initial discovery of ferroelectricity in doped HfO 2 , the underlying crystal structure responsible for this property has remained highly debated. Conventional temperature-dependent polymorphs ( Fm -3 m ( c ), P 4 2 / nmc ( t ), monoclinic P 2 1 / c ( m )) and pressure-dependent phases ( Pbca and Pnma ) cannot readily explain this phenomenon due to their non-polar characteristics 9,10 . More recent theoretical and experimental investigations have identified different ferroelectric phases, involving the rhombohedral R 3 m and orthorhombic Pbc 2 1 and Pmn 2 1 11–13 . Research on both HfO 2 -based films and bulk crystals cumulatively attributes intrinsic robust ferroelectricity to the orthorhombic polar Pbc 2 1 phase ( o -FE), while performance optimization often accompanies by the emergence of the orthorhombic antipolar Pbca phase ( o -AFE) 14,15 . The coexistence of these two phases and their mutual transformations are intrinsically linked to wake-up and fatigue phenomena 16,17 . This phase competition fundamentally impedes optimization of ferroelectric stability and complicates the mechanistic understanding behind domain switching and domain-wall motions 1,18 . To further optimize ferroelectricity in HfO 2 -based materials, diverse modulation strategies have been proposed, such as strain design, ion doping, defect engineering, and surface electrochemical state control 1,19–22 . Among these, strain modulation represents a versatile approach for tailoring ferroelectric properties, achievable through substrate selection, capping layers, and coherent phase interfaces within or between grains 23,24 . Strain can stabilize the o -FE phase by modulating the free energy difference between competing polymorphs through the combination of processing strategies, such as high-pressure annealing, fast quenching, and surface energy modulation 25,26 . Furthermore, anisotropic strain effects serve as a critical pathway for optimizing ferroelectric performance across diverse material scales, from ultrathin films to micron-scale layers and bulk crystals 27–29 . While strain critically governs the formation of o -FE versus o -AFE phases, the majority of existing knowledge stems from theoretical calculations 26,30 . Experimental investigations, however, predominantly focus on HfO 2 -based films. Within these systems, the stabilization of the desired o -FE phase and a fundamental understanding of the structure-property relationship are impeded by complex, superimposed strain effects arising from both extrinsic sources (e.g., substrate matching and capping layers) and intrinsic sources (primarily coherent phase interfaces within or between grains). Moreover, small grain sizes and unavoidable m -phase interference pose significant characterization challenges 17,31 . These factors directly contribute to the substantial performance variability observed among HfO 2 -based ferroelectrics 31,32 . The inherent multiphase interference in strain-mediated HfO 2 films makes it hard to optimize the material’s performance and understand the domain switching—both of which are crucial for developing functional devices 1,18 . The development of HfO 2 -based bulk crystals offers a distinct research opportunity for probing the strain-mediated formation of o -FE and o -AFE phases 11,26,30 . In bulk crystals, strain primarily arises from coherent phase interfaces within or between grains, contrasting with the convoluted, overlapping strain fields typically found in thin-film counteparts. Moreover, the persistent issue of m -phase interference can be effectively addressed by strategically combining ion doping with fast quenching processes 14,33,34 . Critically, the substantially larger grain sizes achieved in bulk crystals—compared to their thin-film counterparts—enable more detailed analysis of strain effects across diverse interfacial configurations 14,19 . Building on a bulk-crystal perspective, this study reveals the stabilization mechanism of the o -FE phase at coherent o -phase interfaces and elucidates its evolution process into the o -AFE phase. We fabricated HfO 2 -based bulk crystals (Lu:Hf 0.6 Zr 0.4 O 2 , Lu:HZO, 9.25 at.% Lu) via high-temperature floating zone growth to investigate strain effects across o -FE and o -AFE phases. Microstructural characterization combined with strain analysis demonstrates that biaxial strain with a -axis tensile strain and b -axis compressive strain favors the stabilization of the o -FE phase over the o -AFE phase. Subsequent tracking of oxygen atom displacements within polarization layers explicitly visualizes the phase evolution process at coherent o -FE/ o -AFE interfaces. These findings establish the critical role of strain at coherent phase interfaces in stabilizing the HfO 2 -based o -FE phase, which will benefit the understanding of associated domain switching mechanisms. This paves the way for designing strain-engineered fluorite-structured functional devices, broadening future applications in non-volatile memory and neuromorphic computing 1,35,36 . Results For HfO 2 -based systems, both o -FE and o -AFE phases are generally believed to originate from a phase transformation from the metastable t- phase 14 , 37 , 38 . Their coexistence often complicates the understanding of the ferroelectric nature and impedes performance enhancement 15 – 17 . Strain plays a key role in controlling polymorphic transformations and influences o -phase formation in the material. Although the free formation energy of the o -FE phase exceeds that of the o -AFE phase under ambient pressure, sufficiently large strain can alter the energy landscape, stabilizing the desired o -FE phase down to room temperature 23 , 26 , 30 . Therefore, understanding the strain-mediated mechanism that regulates o -phase formation is highly important. In the fabrication of HfO 2 -based material, strain generally originates from both extrinsic sources—including substrate lattice matching, buffer layers, and capping effects—and intrinsic factors, notably phase interfaces 1 , 23 . As Fig. 1 illustrates, both contributions combine to influence the formation of HfO 2 -based films. In ultrathin films approaching atomic-scale thickness, strong extrinsic strain constraints typically induce a textured arrangement along specific crystallographic orientations 27 , 39 . As the film thickness increases, extrinsic strain progressively diminishes, allowing polycrystalline and multiphase characteristics to become apparent with increased orientation diversity of HfO 2 -based polymorphs 27 , 40 . As material systems approach the bulk crystal state, the dominant strain mechanism stems exclusively from intrinsic phase interfaces induced by crystallographic misorientations. This clarifies why overlapping strain sources in HfO 2 -based films frequently obscure strain-modulation mechanisms. In contrast, bulk crystals provide a superior platform for isolating and analyzing the impact of this intrinsic strain contribution on o -FE phase stabilization. Moreover, compared to thin films, the larger grain sizes achievable in bulk crystals—reaching hundreds of nanometers—facilitate a detailed investigation of distinct strain-driven phase evolution pathways across different interface configurations 14 . Herein, we propose a bulk-crystal perspective to investigate strain effects on o -FE phase formation and the subsequent evolution between o -FE and o -AFE phases. As Supplementary Fig. 1 shows, the as-grown Lu:HZO crystal exhibits good crystalline quality and is free of cracks, with a 3-mm diameter, attributable to the successful suppression of the m -phase formation. Associated X-ray diffraction (XRD) data reveal characteristic peaks of the t - and o -phases (Supplementary Fig. 2). Subsequent Raman spectrum confirms the presence of t -phase vibrational modes (A 1 g and B 1 g modes at ~ 270 cm − 1 ) and o -AFE phase modes (A g mode at ~ 363 cm − 1 ) (Supplementary Fig. 3) 41 . Furthermore, a strong second harmonic generation (SHG) response indicates the presence of the o -FE phase within the as-grown crystal (Supplementary Fig. 4). Rietveld refinement was employed to determine structural parameters and phase composition of the sample quantitatively (Supplementary Fig. 5, Supplementary Table 1, o -FE: a = 5.0756 Å, b = 5.2215 Å, and c = 5.0550 Å; o -AFE: a = 10.1580 Å, b = 5.1915 Å, and c = 5.0874 Å). The a -axis lattice constant of the o -FE phase is approximately half that of the o -AFE phase. To enable direct comparison of structural parameters, we utilized half the a -axis value of the o -AFE phase for parameter comparison. This structural similarity between the o -FE and o -AFE phases suggests that interfacial strain between o -phases predominantly arises from lattice mismatch at coherent interfaces. Therefore, a detailed examination of these interfaces becomes essential for understanding the fundamental mechanisms governing o -FE phase formation. Using the average lattice parameters of the o -FE and o -AFE phases, we modeled possible o -phase interfacial configurations (Supplementary Table 2). To simplify strain analysis, we calculated strain states in right-hand o -phases along their crystallographic axes arising from coherent interfaces with left-hand o -phases (connecting via ba l , cb l , or ca l planes). Figure 2 b and Supplementary Table 2 summarize eighteen distinct coherent interface types with corresponding axis-resolved strain calculations. The lattice anisotropy of the o -phase produces pronounced strain at phase interfaces, particularly between the b -axis and a / c -axes. Calculated strain ranges in right-hand o -phases are: −0.12% to + 2.54% ( a -axis), − 2.59% to 0 ( b -axis), and 0.12% to + 2.67% ( c -axis)—demonstrating the favorite tensile strain along a / c -axes and compressive strain along the b -axis. Based on the strain states of the interface along the principal axes, all interfaces can be categorized into four groups: Group 1 has six weak strain types, encompassing three zero-strain interface types ( o b − al / o b − ar , o c − bl / o c − br , and o c − al / o c − ar ) and three minimal-strain interface types ( o b − al / o b − cr , o c − bl / o a − br , and o c − al / o a − cr ), indicating these interfaces almost do not influence the connected phase. Group 2 comprises four interface types exhibiting strong uniaxial tension along the a r -axis or c r -axis ( o c − bl / o c − ar , o b − al /o c − ar , o b − al / o a − cr , and o c − bl / o a − cr ), meaning these interfaces stretch the phase significantly along a single direction. In comparison, Group 3 corresponds to four interface types with strong uniaxial compression along the b r -axis ( o c − al / o c − br , o c − al / o b − ar , o c − al / o a − br , and o c − al / o b − cr ), suggesting these interfaces squeeze the phase significantly along a single direction. Of particular importance is that Group 4 includes four biaxial-strain interfaces characterized by strong tension along either the a r -axis or c r -axis coupled with strong compression along the b r -axis ( o b − al / o a − br , o b − al / o c − br , o c − bl / o b − ar , and o c − bl / o b − cr ), meaning these interfaces simultaneously stretch the phase in one direction and squeeze it in another. We examined the o c − bl / o b − ar -type interface from Group 4 as a representative example (Fig. 2 ). This coherent structure arises at the interface where the cb l plane of the left o -phase meets the ba r plane of the right o -phase under significant biaxial strain. The right o -phase experiences a theoretical maximum of + 2.54% tension along its a -axis and − 2.59% compression along its b -axis. Then, we combined theoretical HfO 2 phase structures with advanced scanning transmission electron microscopy (STEM) to resolve strain states at coherent o -phase interfaces in Lu:HZO crystals. As shown in Fig. 3 a,b, oxygen displacement differences along the b -axis observation direction provide an unambiguous distinction between o -FE and o -AFE phases by revealing distinct polarization arrangements. Conversely, similar atomic distributions along the c -axis (Fig. 3 c,d) and dense oxygen configurations along the a -axis preclude reliable differentiation (Supplementary Fig. 6) 9 , 10 . Consequently, we exclusively analyze coherent o -phase interfaces where at least one observation direction aligns with the b -axis, identifying five distinct interface types. The coherent interfaces suitable for o -phase identification include o b − al / o b − ar and o b − al / o b − cr of Group 1, o c − al / o b − ar and o c − al / o b − cr of Group 3, and o c − bl / o b − ar and o c − bl / o b − cr of Group 4. Theoretical vertical views of these coherent o -phase interfaces are provided in Supplementary Fig. 7. As displayed in Fig. 3 e, high-angle annular dark-field STEM (HAADF-STEM) imaging, combined with theoretical atomic arrangements, indicates viewing along b -axis and c -axis observation directions based on characteristic cation distributions. The clear contrast between Hf atomic columns identifies the o -phase interface. Subsequent EDS mapping shows no elemental segregation near this o -phase interface, confirming compositional uniformity from the t -to- o phase transformation. This implies that interface strain originates primarily from direction variations in coherent atomic arrangements, rather than compositional heterogeneity. Further phase identification at interfaces employed integrated differential phase contrast STEM (iDPC-STEM), resolving both heavy-cation and light-oxygen atomic columns 42 , 43 . This analysis reveals coexisting t , o -FE, and o -AFE phases in the bulk crystal (Figs. 3 j-l, Supplementary Fig. 8), supporting prior structural analyses. Critically, o -phase mixed regions exhibit coherent interfaces between b -axis and c -axis oriented o -phases. Within b -axis regions, both o -FE and o -AFE phases coexist, directly highlighting the pivotal role of interface strain in o -phase formation 11 , 44 . Next, we employed atomic-scale analysis to quantify the strain states at coherent o -phase interfaces within the bulk Lu:HZO crystal. For clarity, our strain description primarily focuses on the connected right-hand o -phase. As shown in Supplementary Fig. 9, the o b − al / o b − cr -type interface connects two b -axis oriented o -phases. Evaluation of Hf-Hf bond lengths revealed zero strain along the b -axis orientation, combined with minimal horizontal c -axis oriented tensile strain at the o b − al / o b − cr -type interface (0.13%). This negligible strain arises from the near-identical a -axis and c -axis lattice parameters, which result in the exclusive stabilization of the o -AFE phase in both connected o -phases. Four additional interface types— o c − al / o b − ar , o c − al / o b − cr , o c − bl / o b − cr , and o c − bl / o b − ar —connect c -axis and b -axis oriented o -phases (Supplementary Figs. 10–14). While phase assignment of c -axis oriented o -phases cannot be determined solely from microstructural data, neighboring b -axis oriented o -phases were unambiguously identified through polarization vector directionality. Direct observation of o c − al / o b − ar -type and o c − al / o b − cr -type interfaces (Supplementary Figs. 10 and 11) confirms near-zero horizontal strain due to negligible lattice parameter differences between the a -axis and c -axis. Along the b -axis oriented direction, however, both interfaces experience compressive strain, reaching a theoretical maximum of − 2.59%. Crucially, the o -phases along the b -axis at these interfaces develop o -AFE characteristics, exhibiting adjacent antiparallel polarization vectors. This result indicates that single b -axis compressive strain originating from phase interfaces is insufficient to stabilize the o -FE phase, consistent with previous reports on o -phase control 45 . Furthermore, the o c − bl / o b − cr -type interface exhibits coexisting b -axis compressive strain (maximum − 2.59% in theory) and c -axis tensile strain (with an average value of 0.5%) (Supplementary Fig. 12). Despite this significant biaxial strain, the b -axis oriented o -phase also belongs to the o -AFE phase, which further underscores the critical importance of specific strain mediation in stabilizing the o -FE phase. Next, we observed the o c − bl / o b − ar -type coherent interface between adjacent c -axis and b -axis oriented o -phases (Fig. 4 and Supplementary Figs. 13 and 14). Interestingly, the segment of the b -axis o -phase closest to the c -axis o -phase exhibits o -FE characteristics with parallel polarization vectors, whereas the segment further away shows o -AFE characteristics with antiparallel polarization vectors. This suggests that strain modulation across o -phases can directly control o -phase formation and thereby modulate subsequent phase transformations 39 , 46 . To analyze structural changes near the o c − bl / o b − ar -type interface, we examined the distributions of Hf-Hf bond lengths between c -axis and b -axis oriented o -phases (Fig. 4 a). Taking Rows 19 − 20 and 29 − 30 as representative examples (Fig. 4 c), the c -axis oriented o -phase on the left exhibits Hf-Hf bonds with characteristic alternating long/short distances along its a -axis. As the structure transitions through the interface into the polarization layers, this alternating pattern shifts to the structure of the b -axis oriented o -phase, where the bond lengths become nearly uniform along the c -axis direction (Fig. 4 e). Corresponding oxygen atom analysis shows pronounced displacement differences between adjacent oxygen columns in the left region. This inter-column contrast gradually diminishes, while a distinct step-wise difference emerges between neighboring atomic rows. Ultimately, this rearrangement results in a well-defined distribution discrepancy separating oxygen atoms within the polarization and spacer layers of the right a -axis oriented o -FE phase. Based on these observations, the phase distribution from left to right columns was identified as o c (left), o c -transitional ( o c − trans ), and o b -FE (right) (Fig. 4 b). To understand the strain effect driving the formation of the o -FE phase near the o c − bl / o b − ar -type coherent interface, we quantified the interfacial strain using the distant o -AFE region (Supplementary Fig. 13) as a reference. This analysis reveals that the b -axis oriented o -phase on the right side experiences biaxial strain imposed by the adjacent c -axis oriented o -phase: tensile strain along its a -axis and compressive strain along its b -axis. We analyzed the variation in a -axis oriented strain across the interface (Fig. 4 d). In Rows 17 − 20, the differential strain between the b -axis of the o c phase and the a -axis of the neighboring o b -FE phase is ~ 2.8%, consistent with theoretical prediction (Supplementary Fig. 15). To determine the strain limit stabilizing the o b -FE phase, we averaged the b -axis strain across the entire o c region ( Rows 13 − 26). This reveals a consistent ~ 1.5% strain difference between the b -axis of the o c phase and the a -axis of the neighboring o b -FE phase (Fig. 4 d). In regions where the left columns do not extend to the o c region, we instead compared the o c − trans and o b phases. The strain difference is significantly lower within the o -AFE formation region ( Rows 9 − 12 and 27 − 30), averaging only ~ 0.8% between the o c − trans and o b -AFE phases. In addition to the a -axis tensile strain, the o b -FE phase is also subjected to strong b -axis compressive strain from the adjacent o c − trans region. Therefore, the formation of the o b -FE phase adjacent to the o c − bl / o b − ar -type coherent interface strongly correlates with this specific biaxial strain state—a characteristic distinguishing it from the strain configurations present at four other coherent interfaces ( o b − al / o b − cr , o c − al / o b − ar , o c − al / o b − cr , and o c − bl / o b − cr ) between connected o -phases. To elucidate the strain-driven stabilization mechanism of the o -FE phase in the Lu:HZO bulk crystal, we performed theoretical calculations incorporating experimentally determined interfacial strain distributions. Our initial step involved computing the formation energy differences between the o -FE (Δ E o −FE ) and o -AFE (Δ E o −AFE ) phases under uniaxial a -axis, b -axis, or c -axis strain. As shown in Fig. 4 f and Supplementary Fig. 16, Δ E o −AFE remains lower than Δ E o −FE under − 5% to 5% strains along a -axis (4.72–5.25 Å) or c -axis (4.76–5.27 Å), confirming the intrinsic stability of the o -AFE phase. Conversely, compressive strain along the b -axis stabilizes o -AFE (Δ E o −AFE < Δ E o −FE ), whereas tensile strain reduces the Δ E o −AFE – Δ E o −FE gap, destabilizing o -AFE relative to o -FE. Increasing b -axis tensile strain causes Δ E o −FE and Δ E o −AFE to converge, until a phase-inversion point is reached at tensile strain exceeding 3.4% (~ 5.40 Å), beyond which the o -FE becomes more stable. This aligns with existing theoretical predictions that tensile strain stabilizes o -FE 45 . However, interfacial constraints in Lu:HZO bulk crystals can only induce tensile strain along the a -axis or c -axis during orientation mismatches, not along the b -axis. Consequently, the uniaxial strains achievable at phase interfaces (e.g., o b − al / o b − cr -type and o c − al / o b − ar -type interfaces) remain insufficient to lower Δ E o −FE below Δ E o −AFE . This accounts for the observed lack of o -FE stabilization and the prevailing dominance of the o -AFE under uniaxial strain. We next modeled biaxial strain conditions, which are characteristic of coherent interfaces such as o c − al / o b − cr , o c − bl / o b − cr , and o c − bl / o b − ar (Fig. 4 g and Supplementary Fig. 17). Consistent with Fig. 2 , analysis of the right o -phase reveals the presence of compressive strain along the b -axis coupled with tensile strain along either the a -axis or c -axis. In our theoretical approach, we applied equal-magnitude opposing strains along orthogonal axes (e.g., for the cb -plane: tensile strain along the c -axis paired with compressive strain along the b -axis, or vice versa). Biaxial strain calculations in the cb -plane (Supplementary Fig. 17) reveal that Δ E o −AFE remains lower than Δ E o −FE across strains from − 5% to 5% (with o -FE c -axis lengths spanning from 4.76 Å to 5.27 Å), confirming that the o -AFE phase remains favored over o -FE under such a strain configuration. This explains the persistent dominance of o -AFE near o c − al / o b − cr or o c − bl / o b − cr interfaces. Conversely, biaxial strain within the ab -plane dramatically alters stabilization thresholds: compressive strain along the b -axis substantially reduces the requisite tensile strain along the a -axis to trigger a phase inversion. Specifically, the o -FE becomes more stable than o -AFE once the a -axis length exceeds ~ 5.13 Å (the inversion point). For bulk Lu:HZO crystals near o c − bl / o b − ar -type interfaces, the observed a -axis tensile strain of the o b -FE phase originates from the adjacent o c − trans region. Here, the average a -axis length exhibits a critical threshold of ~ 5.13 Å. This close agreement between theoretical prediction (stabilization occurring at a > 5.13 Å) and experimental measurement (at 5.13 Å) confirms that the o -FE phase stabilization near the o c − bl / o b − ar -type coherent interface arises from o -phase interactions, directly supports previously reported strain-mediated o -FE stabilization mechanisms 47 , 48 . As Fig. 4 b,d demonstrates, under biaxial strain within the ba r plane, tensile strain along the a -axis of the o b -FE phase primarily derives from the o c phase through the o c − trans region. When the average tensile strain difference along the a -axis exceeds approximately 1.5% between the o c and o b -FE regions, the o -phase is preferentially stabilized as o -AFE rather than o -FE. To probe this transformation process in greater detail, we analyzed the interface between o -FE and o -AFE phases. Unlike the commonly reported o b − cl / o b − cr -type coherent interface 25 , we identified an o b − al / o b − ar -type coherent interface ( Group 1). This particular configuration offers superior insight into the phase transformation process by revealing explicit pathways for oxygen atom reorganization within both the polarization and spacer layers during structural evolution. Figure 5 a shows that a partial inversion of polarization vectors across the region from left to right columns clearly indicates the transformation from o -FE to o -AFE. To elucidate the atomic-scale evolution at this o b − al / o b − ar interface, we systematically tracked both the vertically projected Hf-Hf distances and the horizontal Hf-O distances ( d Hf−O , defined as the lateral separation between oxygen atoms and their adjacent right Hf columns). As Supplementary Fig. 19 shows, Hf-Hf bond lengths remain relatively stable across the interface, in contrast to d Hf−O , which exhibits significant spatial heterogeneity. Statistical analysis of d Hf−O distinguishes three regions: o b -FE (left), o b -transitional ( o b − trans ), and o b -AFE (right) (Fig. 5 b). The o -FE region spans approximately 10 atomic layers, corresponding to a thickness of ~ 2 nm—consistent with previous reports in textured films 27 . Taking Rows 14–16 as a representative example (Fig. 5 c), d Hf−O in Row 14 (polarization layer) exhibits evolutionary behavior similar to that in Row 15 (spacer layer), with only minimal displacement variation. In contrast, d Hf−O in Row 16 (also a polarization layer) gradually increases from left to right columns, indicating substantial positional reorganization of the associated oxygen atoms. Initially clustering around ~ 86.8 pm within the o -FE polarization layers, this distance progressively increases, eventually reaching ~ 179.2 pm in the o -AFE region. Furthermore, as seen in Figs. 5 b,d, the vertically projected O-O distances within the transformed polarization layers undergo an initial shortening followed by lengthening across the phase transformation from o -FE to o -AFE. This behavior parallels the theoretical N -pathway polarization switching in HZO ferroelectrics, wherein oxygen atoms within polarization layers do not pass through the cation planes 49 , 50 . The crystal symmetry of the intermediate o b − trans region lacks mirror symmetry within the c -axis oriented crystallographic plane, precluding Pbcm symmetry where oxygen atoms pass through cationic planes. Furthermore, primary structural changes are localized to oxygen atoms within specific polarization layers, thereby also excluding Pbcn symmetry that requires oxygen atom displacements across both adjacent polarization and spacer layers. Analysis of the atomic distribution, particularly regarding oxygen atoms, within the o b − trans region indicates that the most probable symmetry along the c -axis is a 2 1 screw axis, lacking an accompanying mirror or glide plane (Fig. 5 d). This structure confirms its non-centrosymmetric character. Within this specific o b − trans region, the atomic arrangement consists of three spacer layers separating adjacent polarization layers, unlike the extensively studied ferroelectric phase possessing a single spacer layer. Building upon the established relationship between domain wall distribution and coercive field 51 , this increased number of spacer layers is expected to reduce constraints on the coercive field. This predicted reduction offers a promising pathway for achieving lower operating voltages, thereby enhancing compatibility with the requirements of silicon-based CMOS technology. Consequently, the identified o b − al / o b − ar -type coherent interface between the o -FE and o -AFE phases, along with its observed phase evolution, provides crucial fundamental insights that support performance optimization in HfO 2 -based ferroelectrics and enable a more comprehensive understanding of domain switching mechanisms. The observed o b − trans polar phase presents significant advantages for developing advanced HfO 2 -based ferroelectric devices, exhibiting lower operational coercive fields compared to the established ferroelectric phase. Discussion The o -AFE phase, a commonly existing byproduct of o -FE phase formation, not only complicates the understanding of HfO 2 -based ferroelectricity but also contributes to wake-up/fatigue phenomena that severely compromise device operational stability 1 , 17 , 52 . Resolving o -phase formation dynamics and enhancing resultant device performance are thus critical priorities for the HfO 2 -based ferroelectric community. Strain engineering offers a promising pathway to modulate this challenging coexistence of o -FE/ o -AFE phases 15 , 16 . Nevertheless, most studies on strain effects in HfO 2 systems focus on thin films, where complex interactions between extrinsic/intrinsic strains, m -phase interference, and nanometer-scale grain sizes obscure clear structure-property relationships 23 . Consequently, the strain-mediated polymorphic transformation between o -FE and o -AFE remains poorly understood, and proposed evolution pathways remain largely theoretical due to the absence of experimentally observed coherent interfaces. To address this gap, we employ the bulk Lu:HZO crystal to investigate strain-mediated control of o -phase polymorphism. The primary strain source in bulk crystals originates from phase lattice mismatch, effectively avoiding the extrinsic strain contributions common in film counterparts. Rapid high-temperature-to-room-temperature phase transformation yields abundant coherent o -phase interfaces 14 . Crucially, bulk crystal growth suppresses m -phase interference while producing grains significantly larger than those in films, facilitating precise phase interface observation and strain analysis within grains 14 , 19 . Detailed structural and optical characterizations confirm the coexistence of o -FE/ o -AFE phases within Lu:HZO bulk crystals. Through microstructural analysis, we identified potential coherent o -phase interfaces and their associated strain states. Observations indicate that among the six observed interface types ( o b − al / o b − cr , o c − al / o b − ar , o c − al / o b − cr , o c − bl / o b − cr , o c − bl / o b − ar , and o b − al / o b − ar ), only o c − bl / o b − ar interfaces (formed between adjacent c -axis and b -axis oriented o -phases) support the formation of the o -FE phase under biaxial strain. Subsequent theoretical calculations confirm that isolated uniaxial strain along the a -axis alone cannot stabilize the o -FE phase in Lu:HZO bulk crystals, even across a broad length range (4.72 Å–5.25 Å). However, concurrent b -axis compressive strain stabilizes the o -FE phase over the o -AFE when the a -axis length exceeds ~ 5.13 Å under tensile strain—consistent with experimental measurements. In strain-relaxed regions lacking o -FE-stabilizing strain, our atomic-scale observations of coherent interfaces reveal the transformation pathway from o -FE to o -AFE. The identified phase evolution mechanism—driven by specific cation and oxygen displacements—clarifies the structural framework governing this polymorphic transition. Our study establishes a universal principle that explains how to achieve and maintain strong ferroelectric properties in HfO 2 , regardless of whether the material is an ultra-thin film or a much larger bulk crystal. We reveal that the stability of the desired o -FE phase depends almost entirely on the specific strain states at the interfaces between different o -phases. This insight identifies selective phase interface engineering—actively designing these interfaces to promote the right kind of strain. Specifically, enhancing o c − bl / o b − ar -type connections through coordinated extrinsic/intrinsic strain tuning is the key strategy for optimizing o -FE phase fraction and polarization direction. In extensively studied HfO 2 -based films, where increased thickness typically degrades ferroelectricity via strain relaxation. Our study shows that advanced layered architectures (e.g., superlattices, nanolaminates) can maintain precise strain control, preserving ferroelectricity beyond the nanometer scale 17 , 52 , 53 . Our discovery provides a blueprint for optimizing these layers to enhance ferroelectric performance over a broader range of thicknesses 54 , 55 . For bulk HfO 2 , our o -phase modulation mechanism provides a viable strategy to stabilize the o -FE phase. Combining advanced strain modulation—including grain control, lattice parameter adjustment, and oriented growth design, we can create the specific internal strain needed to stabilize the ferroelectric phase, achieving performance that rivals thin films, reminiscent of perovskite ferroelectrics 14 , 19 , 54 . We also directly observed how the ferroelectric phase transforms into a non-functional one. This gives us a complete model of phase behavior, which is crucial for fundamental understanding of the competing phase dynamics, enabling rational domain-switching strategies and tailoring interfacial device design 51 , 56 . Collectively, our work deciphers the strain-based mechanism that controls the competition between key phases in HfO 2 —a breakthrough critical for enhancing performance and reliability in CMOS-compatible fluorite-structure ferroelectrics. These insights will accelerate the adoption of HfO 2 in non-volatile memories (FeRAM, FeFET, neuromorphic computing) and propel emerging multifunctional applications for information and energy systems (e.g., piezoelectrics, pyroelectrics), significantly broadening their technological impact. Conclusion In summary, this work uncovers the atomistic mechanism underlying strain-mediated o -phase formation at coherent o -phase interfaces in HfO 2 , highlighting how interfacial strain selectively stabilizes the metastable o -FE phase by modifying specific connecting interfaces. Leveraging bulk crystals free from epitaxial constraints enables unparalleled insights into strain sources, grain size control, and phase interface distribution—surpassing thin-film limitations. Our integrated microstructural and theoretical analyses reveal that biaxial strain ( a -axis tension coupled with b -axis compression) locally stabilizes the o -FE phase near o -phase interfaces, while the o -AFE phase dominates further away from the formed interface. By directly mapping transformation pathways at the atomic level through tracking dynamic oxygen displacements, we decipher the evolution between o -FE and o -AFE phases. These findings establish a fundamental optimization principle for designing HfO 2 -based ferroelectrics. We show how to optimize strain in layered films to maintain performance at greater thicknesses, and how to enhance ferroelectricity in bulk crystals. This establishes controlled strain as a key design tool, enabling the creation of high-performance, CMOS-compatible materials for next-generation memory and neuromorphic computing. Declarations Data availability The experimental data generated in this study are provided in the Supplementary Information/Source data file. The uploaded source data includes the obtained data that can reproduce all the findings of this study. Source data are provided with this paper. Acknowledgments We thank J.Wu (University of Jinan) for the structural refinement and X.Zhao (Shandong University) for the assistance with theoretical calculations. This work is supported by the National Natural Science Foundation of China (grant nos. 52025021 (H.Y.), 52472008 (S.W.), U24A2027 (S.W.), and 52422201 (F.L.)), the National Key Research and Development Program of China (2021YFB3601504 (H.Z.)), the Natural Science Foundation of Shandong Province (ZR2022LLZ005 (S.W.)), and the Future Plans of Young Scholars at Shandong University (S.W.). Author contributions S.W., H.Y., S.Z. and H.Z. conceived the research idea of this study. 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Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryInformation.docx Supplementary Information Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7867840","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":541274979,"identity":"e1545d4b-679c-4b98-85da-3d41613ee6b8","order_by":0,"name":"Haohai 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University","correspondingAuthor":false,"prefix":"","firstName":"Huaijin","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2025-10-15 11:56:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7867840/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7867840/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96145055,"identity":"352a4934-2370-4d9d-934b-6f69a312d98b","added_by":"auto","created_at":"2025-11-18 06:25:49","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":161330,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStrain-mediated stabilization mechanisms of \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-FE phase in HfO\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e-based systems across different thickness scales.\u003c/strong\u003e Thickness-dependent strain evolution: Extrinsic factors (substrate, buffer/capping layers) and intrinsic contributions (phase interfaces within or between grains, expressed by different colors) accumulate to the total strain. Extrinsic contributions diminish with increasing thickness, while intrinsic strain originating from coherent phase interfaces becomes dominant. Inset: Transformation pathway from metastable \u003cem\u003et\u003c/em\u003e phase to \u003cem\u003eo\u003c/em\u003e-phases under strain-free and strain-modulated conditions. Without interfacial strain, the \u003cem\u003eo\u003c/em\u003e-AFE phase is energetically favored. Application of appropriate strain can stabilize the metastable \u003cem\u003eo\u003c/em\u003e-FE phase within the samples.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7867840/v1/3bfa4d91650412140549b028.jpg"},{"id":96145057,"identity":"167cb2a2-0762-4da5-82b1-dc7f5758f1e3","added_by":"auto","created_at":"2025-11-18 06:25:50","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":215514,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagrams and corresponding strain calculations for different types of coherent interfaces between orthorhombic phases, i.e., \u003cem\u003eo\u003c/em\u003e-FE or \u003cem\u003eo\u003c/em\u003e-AFE. a, Schematic diagram of a matched phase interface illustrating the coherent \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type interface between adjacent \u003cem\u003eo\u003c/em\u003e-phases. The subscript \u003cem\u003el\u003c/em\u003e or \u003cem\u003er\u003c/em\u003e refers to the left or right \u003cem\u003eo\u003c/em\u003e-phase. When describing the \u003cem\u003ecb\u003c/em\u003e or \u003cem\u003eba\u003c/em\u003e plane, the order is always vertical, then horizontal. For example, the interface type remains the same for \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ecl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ebr\u003c/em\u003e\u003c/sub\u003e-type configurations, because they represent the same coherent interface viewed from a different direction. \u003cstrong\u003eb\u003c/strong\u003e, Calculated strain distributions at the interface. When two different phases connect, the mismatch creates internal strain. We calculated this strain for many types of interfaces and sorted the results into four distinct groups based on the strain’s strength and direction: \u003cem\u003eGroup\u003c/em\u003e 1: blue region with weak strain, six types, \u003cem\u003eGroup\u003c/em\u003e 2: green region with strong uniaxial tension, four types, \u003cem\u003eGroup\u003c/em\u003e 3: orange region with strong uniaxial compression, four types, and \u003cem\u003eGroup\u003c/em\u003e 4: gray region with strong biaxial strain, four types. Detailed interface types are listed in Supplementary Table 2. Within the plots, blank, hatched, and cross-hatched areas represent strain states where the right \u003cem\u003eo\u003c/em\u003e-phase aligns its \u003cem\u003ea\u003c/em\u003e-axis, \u003cem\u003eb\u003c/em\u003e-axis, and \u003cem\u003ec\u003c/em\u003e-axis, respectively.\u003cem\u003e \u003c/em\u003eThe star symbol highlights the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type interface, which belongs to \u003cem\u003eGroup\u003c/em\u003e 4 interface. \u003cstrong\u003ec\u003c/strong\u003e,\u003cstrong\u003ed\u003c/strong\u003e,\u003cstrong\u003e \u003c/strong\u003eAtomic arrangements of the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type interface (take the \u003cem\u003eo\u003c/em\u003e-AFE phase as an example) viewed along the vertical (\u003cstrong\u003ec\u003c/strong\u003e) and horizontal (\u003cstrong\u003ed\u003c/strong\u003e) directions, respectively, revealing that the right \u003cem\u003eo\u003c/em\u003e-phase experiences tensile strain along its \u003cem\u003ea\u003c/em\u003e-axis and compressive strain along its \u003cem\u003eb\u003c/em\u003e-axis orientation. All strain calculations were performed using the average lattice parameters of the \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7867840/v1/46520dab6ed655e39975e9af.jpg"},{"id":96145059,"identity":"1607c1c7-0f5e-4833-86f9-d747cdb041e0","added_by":"auto","created_at":"2025-11-18 06:25:50","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":813355,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematic diagrams of \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-FE and \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-AFE phases and atomic-resolution STEM images of the Lu:HZO bulk crystal. a-d\u003c/strong\u003e, Atomic arrangements of the \u003cem\u003eo\u003c/em\u003e-phase viewed along different crystallographic orientations: (\u003cstrong\u003ea\u003c/strong\u003e) \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-AFE, (\u003cstrong\u003eb\u003c/strong\u003e) \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-FE, (\u003cstrong\u003ec\u003c/strong\u003e) \u003cem\u003ec\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-AFE, and (\u003cstrong\u003ed\u003c/strong\u003e) \u003cem\u003ec\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-FE. The polarization layers (Ⅰ) and space layers (Ⅱ) in (\u003cstrong\u003ea\u003c/strong\u003e,\u003cstrong\u003eb\u003c/strong\u003e) are labeled. Standard structures derived from ICSD No. 79913 (\u003cem\u003eo\u003c/em\u003e-AFE) and Ref.\u003csup\u003e11\u003c/sup\u003e (\u003cem\u003eo\u003c/em\u003e-FE), respectively. \u003cstrong\u003ee\u003c/strong\u003e, Experimental HAADF-STEM image showing a coherent interface between a \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phase and a \u003cem\u003ec\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phase. The red dashed line marks the \u003cem\u003eo\u003c/em\u003e-phase interface. \u003cstrong\u003ef-h\u003c/strong\u003e, Composite images overlaying HAADF-STEM and EDS elemental maps for: (\u003cstrong\u003ef\u003c/strong\u003e) Lu, (\u003cstrong\u003eg\u003c/strong\u003e) Hf, and (\u003cstrong\u003eh\u003c/strong\u003e) Zr. \u003cstrong\u003ei\u003c/strong\u003e, iDPC-STEM image featuring both \u003cem\u003eb\u003c/em\u003e-axis and \u003cem\u003ec\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases. \u003cstrong\u003ej-l\u003c/strong\u003e, Magnified views of regions marked by dashed boxes in \u003cstrong\u003ei\u003c/strong\u003e: (\u003cstrong\u003ej\u003c/strong\u003e) \u003cem\u003ec\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phase (blue box), (\u003cstrong\u003ek\u003c/strong\u003e) \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-FE phase (orange box), and (\u003cstrong\u003el\u003c/strong\u003e) \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-AFE phase (purple box). Insets show corresponding theoretical atomic models, demonstrating strong agreement with experimental observations. Cyan and orange arrows in (\u003cstrong\u003ea\u003c/strong\u003e,\u003cstrong\u003eb\u003c/strong\u003e,\u003cstrong\u003ek\u003c/strong\u003e,\u003cstrong\u003el\u003c/strong\u003e) indicate the polarization vectors in these polarization layers. Scale bar: 1\u0026nbsp;nm (\u003cstrong\u003ee-l\u003c/strong\u003e).\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7867840/v1/f15322d38f7e12b5eae4e16d.jpg"},{"id":96145060,"identity":"b30016e4-b3b8-4d9c-9f47-4027016e378f","added_by":"auto","created_at":"2025-11-18 06:25:50","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":845961,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDirect observation and local strain analysis of the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e\u003cstrong\u003e-\u003c/strong\u003e\u003c/sub\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003ebl\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e\u003cstrong\u003e/\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003eb\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e\u003cstrong\u003e-\u003c/strong\u003e\u003c/sub\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003ear\u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003e\u003cstrong\u003e-type coherent interface in the Lu:HZO crystal connecting \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-axis and \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eb\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-axis oriented \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-phases. a\u003c/strong\u003e, Atomic-resolution iDPC-STEM image revealing the coherent interface and associated variation in vertical Hf-Hf atomic distances across the interface between \u003cem\u003ec\u003c/em\u003e-axis and \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases. \u003cstrong\u003eb\u003c/strong\u003e, Phase distribution adjacent to the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type\u003cem\u003e \u003c/em\u003ecoherent interface. For clarity, the illustration depicts not only the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase regions surrounding this interface but also includes the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e, and\u003cem\u003e o\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE phase regions for comparison. Note that\u003cem\u003e o\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e represents the \u003cem\u003ec\u003c/em\u003e-axis oriented\u003cem\u003e o\u003c/em\u003e-phase, while \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE denote the \u003cem\u003eb\u003c/em\u003e-axis oriented\u003cem\u003e o\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases, respectively.\u003cem\u003e o\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e designates the transition region between the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e phases, while\u003cem\u003e o\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e corresponds to the transition region between the \u003cem\u003eb\u003c/em\u003e-axis oriented\u003cem\u003e o\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE phases. Arrows represent the polarization vectors. \u003cstrong\u003ec\u003c/strong\u003e, Vertical Hf-Hf distance variations of\u003cem\u003e Rows\u003c/em\u003e 19-20 and \u003cem\u003eRows\u003c/em\u003e 29–30 across the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type coherent interface. \u003cstrong\u003ed\u003c/strong\u003e,\u003cstrong\u003e \u003c/strong\u003eVertical strain evolution across the interface between the \u003cem\u003eb\u003c/em\u003e-axis and \u003cem\u003ec\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases. To quantify strain change accurately, we performed strain calculations for the \u003cem\u003eo\u003c/em\u003e-FE phase by averaging values across the polarization and spacers within \u003cem\u003eRows\u003c/em\u003e 13−26. The remaining \u003cem\u003eRows\u003c/em\u003e were employed to analyze the strain change of the \u003cem\u003eo\u003c/em\u003e-AFE formation case. The \u003cem\u003eo\u003c/em\u003e-AFE phase region shown in Supplementary Fig. 13 served as the reference state. Colored regions correspond to distinct phases: blue (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e), green (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e), orange (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE), yellow (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e), and gray (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE). \u003cstrong\u003ee\u003c/strong\u003e, Schematic diagram illustrating the structural evolution from the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e to \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phases. The cyan and black arrows display the movements of the O and Hf ions, respectively. In addition, the cyan arrows within the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase represent the polarization vectors. \u003cstrong\u003ef\u003c/strong\u003e,\u003cstrong\u003eg\u003c/strong\u003e, Calculated relative formation energy of the \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases under varying strain conditions, corresponding to the uniaxial strain along the \u003cem\u003ea\u003c/em\u003e-axis \u003cstrong\u003e(f)\u003c/strong\u003e and the biaxial strain along \u003cem\u003ea\u003c/em\u003e and \u003cem\u003eb\u003c/em\u003e axes \u003cstrong\u003e(g)\u003c/strong\u003e (characterized by tensile strain along the \u003cem\u003ea\u003c/em\u003e-axis and compressive strain along the \u003cem\u003eb\u003c/em\u003e-axis, or vice versa). The formation energy difference Δ\u003cem\u003eE\u003c/em\u003e = \u003cem\u003eE\u003c/em\u003e −\u003cem\u003e E\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e,\u003cem\u003e \u003c/em\u003ewhere \u003cem\u003eE \u003c/em\u003eand\u003cem\u003e E\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e \u003c/em\u003erepresent the formation energies of the \u003cem\u003eo\u003c/em\u003e phases and the \u003cem\u003em\u003c/em\u003e phase (without strain). Scale bars: 1\u0026nbsp;nm (\u003cstrong\u003ea\u003c/strong\u003e,\u003cstrong\u003eb\u003c/strong\u003e).\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7867840/v1/b9fb5c7fb4840df4a50ea415.jpg"},{"id":96145061,"identity":"e249517e-a08b-4bc3-af26-fd9be2028d1a","added_by":"auto","created_at":"2025-11-18 06:25:50","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":208916,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePhase transformation mechanism from the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo-\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003eFE to \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-AFE phases in the Lu:HZO crystal. a\u003c/strong\u003e, Difference in horizontal polarization vectors across an \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type coherent interface between \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases. Arrow direction denotes polarization direction, and length represents the in-plane polarization magnitude (Supplementary Fig. 18). \u003cstrong\u003eb\u003c/strong\u003e, Phase distribution adjacent to the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type coherent interface. Color-coded regions represent distinct phases: orange (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE), yellow (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e), and grey (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE). \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE denote the \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases within the \u003cem\u003eb\u003c/em\u003e-axis oriented\u003cem\u003e o\u003c/em\u003e-phase, respectively, while\u003cem\u003e o\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e corresponds to the transition region between the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE phases. Arrows represent the polarization vectors. \u003cstrong\u003ec\u003c/strong\u003e, Distribution of horizontal Hf-O distances (\u003cem\u003ed\u003c/em\u003e\u003csub\u003eHf-O\u003c/sub\u003e) across the interface from left (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE) to right (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE) columns. \u003cem\u003ed\u003c/em\u003e\u003csub\u003eHf-O\u003c/sub\u003e is defined as the distance between a vertical Hf atomic column and the nearest oxygen column to its right along the horizontal direction. \u003cem\u003eRow\u003c/em\u003es 14 (polarization layer, Ⅰ), 15 (space layer, Ⅱ), and 16 (polarization layer, Ⅰ) are demonstrated. \u003cstrong\u003ed\u003c/strong\u003e, Proposed structural evolution mechanism for the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE to \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE phase transformation. The horizontal and vertical arrows indicate the displacement of O atoms in the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e phase relative to the\u003cem\u003e o\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase. The\u003cem\u003e o\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-\u003c/sub\u003e\u003csub\u003e\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e phase structurally diverges from the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase through the transformation of one polarization layer into a spacer layer. Scale bars: 1\u0026nbsp;nm (\u003cstrong\u003ea\u003c/strong\u003e,\u003cstrong\u003eb\u003c/strong\u003e).\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7867840/v1/38f5b0df15a186f9932145db.jpg"},{"id":96250295,"identity":"c70b8e74-77a5-43ee-a5c6-0bb88e065c51","added_by":"auto","created_at":"2025-11-19 07:38:02","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3712391,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7867840/v1/b7247a4a-5b1d-4d83-9f1c-477843bf4454.pdf"},{"id":96145065,"identity":"4d256e29-384d-4909-89f1-78f1818a8448","added_by":"auto","created_at":"2025-11-18 06:25:51","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":23861985,"visible":true,"origin":"","legend":"Supplementary Information","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-7867840/v1/05d092537c917992cd45efc8.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Atomic-scale strain-confined ferroelectricity in fluorite hafnium dioxide","fulltext":[{"header":"Introduction","content":"\u003cp\u003eHfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectric materials are garnering considerable research interest for next-generation microelectronic devices such as ferroelectric random-access memory (FeRAM) and ferroelectric field-effect transistors (FeFETs)\u003csup\u003e1\u0026ndash;5\u003c/sup\u003e. This interest stems from their unique ability to maintain robust ferroelectricity at ultrathin thicknesses and exceptional compatibility with established complementary metal-oxide-semiconductor (CMOS) technology\u003csup\u003e6\u0026ndash;8\u003c/sup\u003e. Since the initial discovery of ferroelectricity in doped HfO\u003csub\u003e2\u003c/sub\u003e, the underlying crystal structure responsible for this property has remained highly debated. Conventional temperature-dependent polymorphs (\u003cem\u003eFm\u003c/em\u003e-3\u003cem\u003em\u003c/em\u003e (\u003cem\u003ec\u003c/em\u003e), \u003cem\u003eP\u003c/em\u003e4\u003csub\u003e2\u003c/sub\u003e/\u003cem\u003enmc\u003c/em\u003e (\u003cem\u003et\u003c/em\u003e), monoclinic \u003cem\u003eP\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e/\u003cem\u003ec\u003c/em\u003e (\u003cem\u003em\u003c/em\u003e)) and pressure-dependent phases (\u003cem\u003ePbca\u003c/em\u003e and \u003cem\u003ePnma\u003c/em\u003e) cannot readily explain this phenomenon due to their non-polar characteristics\u003csup\u003e9,10\u003c/sup\u003e. More recent theoretical and experimental investigations have identified different ferroelectric phases, involving the rhombohedral \u003cem\u003eR\u003c/em\u003e3\u003cem\u003em\u003c/em\u003e and orthorhombic \u003cem\u003ePbc\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003ePmn\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e\u003csup\u003e11\u0026ndash;13\u003c/sup\u003e. Research on both HfO\u003csub\u003e2\u003c/sub\u003e-based films and bulk crystals cumulatively attributes intrinsic robust ferroelectricity to the orthorhombic polar \u003cem\u003ePbc\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e phase (\u003cem\u003eo\u003c/em\u003e-FE), while performance optimization often accompanies by the emergence of the orthorhombic antipolar \u003cem\u003ePbca\u003c/em\u003e phase (\u003cem\u003eo\u003c/em\u003e-AFE)\u003csup\u003e14,15\u003c/sup\u003e. The coexistence of these two phases and their mutual transformations are intrinsically linked to wake-up and fatigue phenomena\u003csup\u003e16,17\u003c/sup\u003e. This phase competition fundamentally impedes optimization of ferroelectric stability and complicates the mechanistic understanding behind domain switching and domain-wall motions\u003csup\u003e1,18\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo further optimize ferroelectricity in HfO\u003csub\u003e2\u003c/sub\u003e-based materials, diverse modulation strategies have been proposed, such as strain design, ion doping, defect engineering, and surface electrochemical state control\u003csup\u003e1,19\u0026ndash;22\u003c/sup\u003e. Among these, strain modulation represents a versatile approach for tailoring ferroelectric properties, achievable through substrate selection, capping layers, and coherent phase interfaces within or between grains\u003csup\u003e23,24\u003c/sup\u003e. Strain can stabilize the \u003cem\u003eo\u003c/em\u003e-FE phase by modulating the free energy difference between competing polymorphs through the combination of processing strategies, such as high-pressure annealing, fast quenching, and surface energy modulation\u003csup\u003e25,26\u003c/sup\u003e. Furthermore, anisotropic strain effects serve as a critical pathway for optimizing ferroelectric performance across diverse material scales, from ultrathin films to micron-scale layers and bulk crystals\u003csup\u003e27\u0026ndash;29\u003c/sup\u003e. While strain critically governs the formation of \u003cem\u003eo\u003c/em\u003e-FE versus \u003cem\u003eo\u003c/em\u003e-AFE phases, the majority of existing knowledge stems from theoretical calculations\u003csup\u003e26,30\u003c/sup\u003e. Experimental investigations, however, predominantly focus on HfO\u003csub\u003e2\u003c/sub\u003e-based films. Within these systems, the stabilization of the desired \u003cem\u003eo\u003c/em\u003e-FE phase and a fundamental understanding of the structure-property relationship are impeded by complex, superimposed strain effects arising from both extrinsic sources (e.g., substrate matching and capping layers) and intrinsic sources (primarily coherent phase interfaces within or between grains). Moreover, small grain sizes and unavoidable \u003cem\u003em\u003c/em\u003e-phase interference pose significant characterization challenges\u003csup\u003e17,31\u003c/sup\u003e. These factors directly contribute to the substantial performance variability observed among HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectrics\u003csup\u003e31,32\u003c/sup\u003e. The inherent multiphase interference in strain-mediated HfO\u003csub\u003e2\u003c/sub\u003e films makes it hard to optimize the material\u0026rsquo;s performance and understand the domain switching\u0026mdash;both of which are crucial for developing functional devices\u003csup\u003e1,18\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe development of HfO\u003csub\u003e2\u003c/sub\u003e-based bulk crystals offers a distinct research opportunity for probing the strain-mediated formation of \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases\u003csup\u003e11,26,30\u003c/sup\u003e. In bulk crystals, strain primarily arises from coherent phase interfaces within or between grains, contrasting with the convoluted, overlapping strain fields typically found in thin-film counteparts. Moreover, the persistent issue of \u003cem\u003em\u003c/em\u003e-phase interference can be effectively addressed by strategically combining ion doping with fast quenching processes\u003csup\u003e14,33,34\u003c/sup\u003e. Critically, the substantially larger grain sizes achieved in bulk crystals\u0026mdash;compared to their thin-film counterparts\u0026mdash;enable more detailed analysis of strain effects across diverse interfacial configurations\u003csup\u003e14,19\u003c/sup\u003e. Building on a bulk-crystal perspective, this study reveals the stabilization mechanism of the \u003cem\u003eo\u003c/em\u003e-FE phase at coherent \u003cem\u003eo\u003c/em\u003e-phase interfaces and elucidates its evolution process into the \u003cem\u003eo\u003c/em\u003e-AFE phase. We fabricated HfO\u003csub\u003e2\u003c/sub\u003e-based bulk crystals (Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e, Lu:HZO, 9.25 at.% Lu) via high-temperature floating zone growth to investigate strain effects across \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases. Microstructural characterization combined with strain analysis demonstrates that biaxial strain with \u003cem\u003ea\u003c/em\u003e-axis tensile strain and \u003cem\u003eb\u003c/em\u003e-axis compressive strain favors the stabilization of the \u003cem\u003eo\u003c/em\u003e-FE phase over the \u003cem\u003eo\u003c/em\u003e-AFE phase. Subsequent tracking of oxygen atom displacements within polarization layers explicitly visualizes the phase evolution process at coherent \u003cem\u003eo\u003c/em\u003e-FE/\u003cem\u003eo\u003c/em\u003e-AFE interfaces. These findings establish the critical role of strain at coherent phase interfaces in stabilizing the HfO\u003csub\u003e2\u003c/sub\u003e-based \u003cem\u003eo\u003c/em\u003e-FE phase, which will benefit the understanding of associated domain switching mechanisms. This paves the way for designing strain-engineered fluorite-structured functional devices, broadening future applications in non-volatile memory and neuromorphic computing\u003csup\u003e1,35,36\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eFor HfO\u003csub\u003e2\u003c/sub\u003e-based systems, both \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases are generally believed to originate from a phase transformation from the metastable \u003cem\u003et-\u003c/em\u003ephase\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e,\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. Their coexistence often complicates the understanding of the ferroelectric nature and impedes performance enhancement\u003csup\u003e\u003cspan additionalcitationids=\"CR16\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Strain plays a key role in controlling polymorphic transformations and influences \u003cem\u003eo\u003c/em\u003e-phase formation in the material. Although the free formation energy of the \u003cem\u003eo\u003c/em\u003e-FE phase exceeds that of the \u003cem\u003eo\u003c/em\u003e-AFE phase under ambient pressure, sufficiently large strain can alter the energy landscape, stabilizing the desired \u003cem\u003eo\u003c/em\u003e-FE phase down to room temperature\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. Therefore, understanding the strain-mediated mechanism that regulates \u003cem\u003eo\u003c/em\u003e-phase formation is highly important. In the fabrication of HfO\u003csub\u003e2\u003c/sub\u003e-based material, strain generally originates from both extrinsic sources\u0026mdash;including substrate lattice matching, buffer layers, and capping effects\u0026mdash;and intrinsic factors, notably phase interfaces\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. As Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates, both contributions combine to influence the formation of HfO\u003csub\u003e2\u003c/sub\u003e-based films. In ultrathin films approaching atomic-scale thickness, strong extrinsic strain constraints typically induce a textured arrangement along specific crystallographic orientations\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. As the film thickness increases, extrinsic strain progressively diminishes, allowing polycrystalline and multiphase characteristics to become apparent with increased orientation diversity of HfO\u003csub\u003e2\u003c/sub\u003e-based polymorphs\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. As material systems approach the bulk crystal state, the dominant strain mechanism stems exclusively from intrinsic phase interfaces induced by crystallographic misorientations. This clarifies why overlapping strain sources in HfO\u003csub\u003e2\u003c/sub\u003e-based films frequently obscure strain-modulation mechanisms. In contrast, bulk crystals provide a superior platform for isolating and analyzing the impact of this intrinsic strain contribution on \u003cem\u003eo\u003c/em\u003e-FE phase stabilization. Moreover, compared to thin films, the larger grain sizes achievable in bulk crystals\u0026mdash;reaching hundreds of nanometers\u0026mdash;facilitate a detailed investigation of distinct strain-driven phase evolution pathways across different interface configurations\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. Herein, we propose a bulk-crystal perspective to investigate strain effects on \u003cem\u003eo\u003c/em\u003e-FE phase formation and the subsequent evolution between \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs Supplementary Fig.\u0026nbsp;1 shows, the as-grown Lu:HZO crystal exhibits good crystalline quality and is free of cracks, with a 3-mm diameter, attributable to the successful suppression of the \u003cem\u003em\u003c/em\u003e-phase formation. Associated X-ray diffraction (XRD) data reveal characteristic peaks of the \u003cem\u003et\u003c/em\u003e- and \u003cem\u003eo\u003c/em\u003e-phases (Supplementary Fig.\u0026nbsp;2). Subsequent Raman spectrum confirms the presence of \u003cem\u003et\u003c/em\u003e-phase vibrational modes (A\u003csub\u003e1\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e and B\u003csub\u003e1\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e modes at ~\u0026thinsp;270 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and \u003cem\u003eo\u003c/em\u003e-AFE phase modes (A\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e mode at ~\u0026thinsp;363 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) (Supplementary Fig.\u0026nbsp;3)\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. Furthermore, a strong second harmonic generation (SHG) response indicates the presence of the \u003cem\u003eo\u003c/em\u003e-FE phase within the as-grown crystal (Supplementary Fig.\u0026nbsp;4). Rietveld refinement was employed to determine structural parameters and phase composition of the sample quantitatively (Supplementary Fig.\u0026nbsp;5, Supplementary Table\u0026nbsp;1, \u003cem\u003eo\u003c/em\u003e-FE: \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.0756 \u0026Aring;, \u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.2215 \u0026Aring;, and \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.0550 \u0026Aring;; \u003cem\u003eo\u003c/em\u003e-AFE: \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;10.1580 \u0026Aring;, \u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.1915 \u0026Aring;, and \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.0874 \u0026Aring;). The \u003cem\u003ea\u003c/em\u003e-axis lattice constant of the \u003cem\u003eo\u003c/em\u003e-FE phase is approximately half that of the \u003cem\u003eo\u003c/em\u003e-AFE phase. To enable direct comparison of structural parameters, we utilized half the \u003cem\u003ea\u003c/em\u003e-axis value of the \u003cem\u003eo\u003c/em\u003e-AFE phase for parameter comparison. This structural similarity between the \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases suggests that interfacial strain between \u003cem\u003eo\u003c/em\u003e-phases predominantly arises from lattice mismatch at coherent interfaces.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTherefore, a detailed examination of these interfaces becomes essential for understanding the fundamental mechanisms governing \u003cem\u003eo\u003c/em\u003e-FE phase formation. Using the average lattice parameters of the \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases, we modeled possible \u003cem\u003eo\u003c/em\u003e-phase interfacial configurations (Supplementary Table\u0026nbsp;2). To simplify strain analysis, we calculated strain states in right-hand \u003cem\u003eo\u003c/em\u003e-phases along their crystallographic axes arising from coherent interfaces with left-hand \u003cem\u003eo\u003c/em\u003e-phases (connecting via \u003cem\u003eba\u003c/em\u003e\u003csub\u003e\u003cem\u003el\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003ecb\u003c/em\u003e\u003csub\u003e\u003cem\u003el\u003c/em\u003e\u003c/sub\u003e, or \u003cem\u003eca\u003c/em\u003e\u003csub\u003e\u003cem\u003el\u003c/em\u003e\u003c/sub\u003e planes). Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb and Supplementary Table\u0026nbsp;2 summarize eighteen distinct coherent interface types with corresponding axis-resolved strain calculations. The lattice anisotropy of the \u003cem\u003eo\u003c/em\u003e-phase produces pronounced strain at phase interfaces, particularly between the \u003cem\u003eb\u003c/em\u003e-axis and \u003cem\u003ea\u003c/em\u003e/\u003cem\u003ec\u003c/em\u003e-axes. Calculated strain ranges in right-hand \u003cem\u003eo\u003c/em\u003e-phases are: \u0026minus;0.12% to +\u0026thinsp;2.54% (\u003cem\u003ea\u003c/em\u003e-axis), \u0026minus;\u0026thinsp;2.59% to 0 (\u003cem\u003eb\u003c/em\u003e-axis), and 0.12% to +\u0026thinsp;2.67% (\u003cem\u003ec\u003c/em\u003e-axis)\u0026mdash;demonstrating the favorite tensile strain along \u003cem\u003ea\u003c/em\u003e/\u003cem\u003ec\u003c/em\u003e-axes and compressive strain along the \u003cem\u003eb\u003c/em\u003e-axis. Based on the strain states of the interface along the principal axes, all interfaces can be categorized into four groups: \u003cem\u003eGroup\u003c/em\u003e 1 has six weak strain types, encompassing three zero-strain interface types (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebr\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e) and three minimal-strain interface types (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u0026minus;\u003cem\u003ebr\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e), indicating these interfaces almost do not influence the connected phase. \u003cem\u003eGroup\u003c/em\u003e 2 comprises four interface types exhibiting strong uniaxial tension along the \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e-axis or \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e-axis (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/o\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e), meaning these interfaces stretch the phase significantly along a single direction. In comparison, \u003cem\u003eGroup\u003c/em\u003e 3 corresponds to four interface types with strong uniaxial compression along the \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e-axis (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebr\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u0026minus;\u003cem\u003ebr\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e), suggesting these interfaces squeeze the phase significantly along a single direction. Of particular importance is that \u003cem\u003eGroup\u003c/em\u003e 4 includes four biaxial-strain interfaces characterized by strong tension along either the \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e-axis or \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e-axis coupled with strong compression along the \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e-axis (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u0026minus;\u003cem\u003ebr\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebr\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e), meaning these interfaces simultaneously stretch the phase in one direction and squeeze it in another. We examined the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type interface from \u003cem\u003eGroup\u003c/em\u003e 4 as a representative example (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). This coherent structure arises at the interface where the \u003cem\u003ecb\u003c/em\u003e\u003csub\u003e\u003cem\u003el\u003c/em\u003e\u003c/sub\u003e plane of the left \u003cem\u003eo\u003c/em\u003e-phase meets the \u003cem\u003eba\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e plane of the right \u003cem\u003eo\u003c/em\u003e-phase under significant biaxial strain. The right \u003cem\u003eo\u003c/em\u003e-phase experiences a theoretical maximum of +\u0026thinsp;2.54% tension along its \u003cem\u003ea\u003c/em\u003e-axis and \u0026minus;\u0026thinsp;2.59% compression along its \u003cem\u003eb\u003c/em\u003e-axis.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThen, we combined theoretical HfO\u003csub\u003e2\u003c/sub\u003e phase structures with advanced scanning transmission electron microscopy (STEM) to resolve strain states at coherent \u003cem\u003eo\u003c/em\u003e-phase interfaces in Lu:HZO crystals. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea,b, oxygen displacement differences along the \u003cem\u003eb\u003c/em\u003e-axis observation direction provide an unambiguous distinction between \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases by revealing distinct polarization arrangements. Conversely, similar atomic distributions along the \u003cem\u003ec\u003c/em\u003e-axis (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec,d) and dense oxygen configurations along the \u003cem\u003ea\u003c/em\u003e-axis preclude reliable differentiation (Supplementary Fig.\u0026nbsp;6)\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Consequently, we exclusively analyze coherent \u003cem\u003eo\u003c/em\u003e-phase interfaces where at least one observation direction aligns with the \u003cem\u003eb\u003c/em\u003e-axis, identifying five distinct interface types. The coherent interfaces suitable for \u003cem\u003eo\u003c/em\u003e-phase identification include \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e of \u003cem\u003eGroup\u003c/em\u003e 1, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e of \u003cem\u003eGroup\u003c/em\u003e 3, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e of \u003cem\u003eGroup\u003c/em\u003e 4. Theoretical vertical views of these coherent \u003cem\u003eo\u003c/em\u003e-phase interfaces are provided in Supplementary Fig.\u0026nbsp;7. As displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee, high-angle annular dark-field STEM (HAADF-STEM) imaging, combined with theoretical atomic arrangements, indicates viewing along \u003cem\u003eb\u003c/em\u003e-axis and \u003cem\u003ec\u003c/em\u003e-axis observation directions based on characteristic cation distributions. The clear contrast between Hf atomic columns identifies the \u003cem\u003eo\u003c/em\u003e-phase interface. Subsequent EDS mapping shows no elemental segregation near this \u003cem\u003eo\u003c/em\u003e-phase interface, confirming compositional uniformity from the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transformation. This implies that interface strain originates primarily from direction variations in coherent atomic arrangements, rather than compositional heterogeneity. Further phase identification at interfaces employed integrated differential phase contrast STEM (iDPC-STEM), resolving both heavy-cation and light-oxygen atomic columns\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e,\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. This analysis reveals coexisting \u003cem\u003et\u003c/em\u003e, \u003cem\u003eo\u003c/em\u003e-FE, and \u003cem\u003eo\u003c/em\u003e-AFE phases in the bulk crystal (Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ej-l, Supplementary Fig.\u0026nbsp;8), supporting prior structural analyses. Critically, \u003cem\u003eo\u003c/em\u003e-phase mixed regions exhibit coherent interfaces between \u003cem\u003eb\u003c/em\u003e-axis and \u003cem\u003ec\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases. Within \u003cem\u003eb\u003c/em\u003e-axis regions, both \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases coexist, directly highlighting the pivotal role of interface strain in \u003cem\u003eo\u003c/em\u003e-phase formation\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eNext, we employed atomic-scale analysis to quantify the strain states at coherent \u003cem\u003eo\u003c/em\u003e-phase interfaces within the bulk Lu:HZO crystal. For clarity, our strain description primarily focuses on the connected right-hand \u003cem\u003eo\u003c/em\u003e-phase. As shown in Supplementary Fig.\u0026nbsp;9, the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e-type interface connects two \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases. Evaluation of Hf-Hf bond lengths revealed zero strain along the \u003cem\u003eb\u003c/em\u003e-axis orientation, combined with minimal horizontal \u003cem\u003ec\u003c/em\u003e-axis oriented tensile strain at the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e-type interface (0.13%). This negligible strain arises from the near-identical \u003cem\u003ea\u003c/em\u003e-axis and \u003cem\u003ec\u003c/em\u003e-axis lattice parameters, which result in the exclusive stabilization of the \u003cem\u003eo\u003c/em\u003e-AFE phase in both connected \u003cem\u003eo\u003c/em\u003e-phases. Four additional interface types\u0026mdash;\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e\u0026mdash;connect \u003cem\u003ec\u003c/em\u003e-axis and \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases (Supplementary Figs.\u0026nbsp;10\u0026ndash;14). While phase assignment of \u003cem\u003ec\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases cannot be determined solely from microstructural data, neighboring \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases were unambiguously identified through polarization vector directionality. Direct observation of \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e-type interfaces (Supplementary Figs.\u0026nbsp;10 and 11) confirms near-zero horizontal strain due to negligible lattice parameter differences between the \u003cem\u003ea\u003c/em\u003e-axis and \u003cem\u003ec\u003c/em\u003e-axis. Along the \u003cem\u003eb\u003c/em\u003e-axis oriented direction, however, both interfaces experience compressive strain, reaching a theoretical maximum of \u0026minus;\u0026thinsp;2.59%. Crucially, the \u003cem\u003eo\u003c/em\u003e-phases along the \u003cem\u003eb\u003c/em\u003e-axis at these interfaces develop \u003cem\u003eo\u003c/em\u003e-AFE characteristics, exhibiting adjacent antiparallel polarization vectors. This result indicates that single \u003cem\u003eb\u003c/em\u003e-axis compressive strain originating from phase interfaces is insufficient to stabilize the \u003cem\u003eo\u003c/em\u003e-FE phase, consistent with previous reports on \u003cem\u003eo\u003c/em\u003e-phase control\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e. Furthermore, the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e-type interface exhibits coexisting \u003cem\u003eb\u003c/em\u003e-axis compressive strain (maximum \u0026minus;\u0026thinsp;2.59% in theory) and \u003cem\u003ec\u003c/em\u003e-axis tensile strain (with an average value of 0.5%) (Supplementary Fig.\u0026nbsp;12). Despite this significant biaxial strain, the \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phase also belongs to the \u003cem\u003eo\u003c/em\u003e-AFE phase, which further underscores the critical importance of specific strain mediation in stabilizing the \u003cem\u003eo\u003c/em\u003e-FE phase.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eNext, we observed the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type coherent interface between adjacent \u003cem\u003ec\u003c/em\u003e-axis and \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Supplementary Figs.\u0026nbsp;13 and 14). Interestingly, the segment of the \u003cem\u003eb\u003c/em\u003e-axis \u003cem\u003eo\u003c/em\u003e-phase closest to the \u003cem\u003ec\u003c/em\u003e-axis \u003cem\u003eo\u003c/em\u003e-phase exhibits \u003cem\u003eo\u003c/em\u003e-FE characteristics with parallel polarization vectors, whereas the segment further away shows \u003cem\u003eo\u003c/em\u003e-AFE characteristics with antiparallel polarization vectors. This suggests that strain modulation across \u003cem\u003eo\u003c/em\u003e-phases can directly control \u003cem\u003eo\u003c/em\u003e-phase formation and thereby modulate subsequent phase transformations\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. To analyze structural changes near the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type interface, we examined the distributions of Hf-Hf bond lengths between \u003cem\u003ec\u003c/em\u003e-axis and \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). Taking \u003cem\u003eRows\u003c/em\u003e 19\u0026thinsp;\u0026minus;\u0026thinsp;20 and 29\u0026thinsp;\u0026minus;\u0026thinsp;30 as representative examples (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec), the \u003cem\u003ec\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phase on the left exhibits Hf-Hf bonds with characteristic alternating long/short distances along its \u003cem\u003ea\u003c/em\u003e-axis. As the structure transitions through the interface into the polarization layers, this alternating pattern shifts to the structure of the \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phase, where the bond lengths become nearly uniform along the \u003cem\u003ec\u003c/em\u003e-axis direction (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee). Corresponding oxygen atom analysis shows pronounced displacement differences between adjacent oxygen columns in the left region. This inter-column contrast gradually diminishes, while a distinct step-wise difference emerges between neighboring atomic rows. Ultimately, this rearrangement results in a well-defined distribution discrepancy separating oxygen atoms within the polarization and spacer layers of the right \u003cem\u003ea\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-FE phase. Based on these observations, the phase distribution from left to right columns was identified as \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e (left), \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e-transitional (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e), and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE (right) (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). To understand the strain effect driving the formation of the \u003cem\u003eo\u003c/em\u003e-FE phase near the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type coherent interface, we quantified the interfacial strain using the distant \u003cem\u003eo\u003c/em\u003e-AFE region (Supplementary Fig.\u0026nbsp;13) as a reference. This analysis reveals that the \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phase on the right side experiences biaxial strain imposed by the adjacent \u003cem\u003ec\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phase: tensile strain along its \u003cem\u003ea\u003c/em\u003e-axis and compressive strain along its \u003cem\u003eb\u003c/em\u003e-axis. We analyzed the variation in \u003cem\u003ea\u003c/em\u003e-axis oriented strain across the interface (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed). In \u003cem\u003eRows\u003c/em\u003e 17\u0026thinsp;\u0026minus;\u0026thinsp;20, the differential strain between the \u003cem\u003eb\u003c/em\u003e-axis of the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e phase and the \u003cem\u003ea\u003c/em\u003e-axis of the neighboring \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase is ~\u0026thinsp;2.8%, consistent with theoretical prediction (Supplementary Fig.\u0026nbsp;15). To determine the strain limit stabilizing the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase, we averaged the \u003cem\u003eb\u003c/em\u003e-axis strain across the entire \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e region (\u003cem\u003eRows\u003c/em\u003e 13\u0026thinsp;\u0026minus;\u0026thinsp;26). This reveals a consistent\u0026thinsp;~\u0026thinsp;1.5% strain difference between the \u003cem\u003eb\u003c/em\u003e-axis of the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e phase and the \u003cem\u003ea\u003c/em\u003e-axis of the neighboring \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed). In regions where the left columns do not extend to the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e region, we instead compared the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e phases. The strain difference is significantly lower within the \u003cem\u003eo\u003c/em\u003e-AFE formation region (\u003cem\u003eRows\u003c/em\u003e 9\u0026thinsp;\u0026minus;\u0026thinsp;12 and 27\u0026thinsp;\u0026minus;\u0026thinsp;30), averaging only\u0026thinsp;~\u0026thinsp;0.8% between the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE phases. In addition to the \u003cem\u003ea\u003c/em\u003e-axis tensile strain, the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase is also subjected to strong \u003cem\u003eb\u003c/em\u003e-axis compressive strain from the adjacent \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e region. Therefore, the formation of the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase adjacent to the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type coherent interface strongly correlates with this specific biaxial strain state\u0026mdash;a characteristic distinguishing it from the strain configurations present at four other coherent interfaces (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e) between connected \u003cem\u003eo\u003c/em\u003e-phases.\u003c/p\u003e\u003cp\u003eTo elucidate the strain-driven stabilization mechanism of the \u003cem\u003eo\u003c/em\u003e-FE phase in the Lu:HZO bulk crystal, we performed theoretical calculations incorporating experimentally determined interfacial strain distributions. Our initial step involved computing the formation energy differences between the \u003cem\u003eo\u003c/em\u003e-FE (Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;FE\u003c/sub\u003e) and \u003cem\u003eo\u003c/em\u003e-AFE (Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;AFE\u003c/sub\u003e) phases under uniaxial \u003cem\u003ea\u003c/em\u003e-axis, \u003cem\u003eb\u003c/em\u003e-axis, or \u003cem\u003ec\u003c/em\u003e-axis strain. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ef and Supplementary Fig.\u0026nbsp;16, Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;AFE\u003c/sub\u003e remains lower than Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;FE\u003c/sub\u003e under \u0026minus;\u0026thinsp;5% to 5% strains along \u003cem\u003ea\u003c/em\u003e-axis (4.72\u0026ndash;5.25 \u0026Aring;) or \u003cem\u003ec\u003c/em\u003e-axis (4.76\u0026ndash;5.27 \u0026Aring;), confirming the intrinsic stability of the \u003cem\u003eo\u003c/em\u003e-AFE phase. Conversely, compressive strain along the \u003cem\u003eb\u003c/em\u003e-axis stabilizes \u003cem\u003eo\u003c/em\u003e-AFE (Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;AFE\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;FE\u003c/sub\u003e), whereas tensile strain reduces the Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;AFE\u003c/sub\u003e \u0026ndash; Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;FE\u003c/sub\u003e gap, destabilizing \u003cem\u003eo\u003c/em\u003e-AFE relative to \u003cem\u003eo\u003c/em\u003e-FE. Increasing \u003cem\u003eb\u003c/em\u003e-axis tensile strain causes Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;FE\u003c/sub\u003e and Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;AFE\u003c/sub\u003e to converge, until a phase-inversion point is reached at tensile strain exceeding 3.4% (~\u0026thinsp;5.40 \u0026Aring;), beyond which the \u003cem\u003eo\u003c/em\u003e-FE becomes more stable. This aligns with existing theoretical predictions that tensile strain stabilizes \u003cem\u003eo\u003c/em\u003e-FE\u003csup\u003e45\u003c/sup\u003e. However, interfacial constraints in Lu:HZO bulk crystals can only induce tensile strain along the \u003cem\u003ea\u003c/em\u003e-axis or \u003cem\u003ec\u003c/em\u003e-axis during orientation mismatches, not along the \u003cem\u003eb\u003c/em\u003e-axis. Consequently, the uniaxial strains achievable at phase interfaces (e.g., \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e-type and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type interfaces) remain insufficient to lower Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;FE\u003c/sub\u003e below Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;AFE\u003c/sub\u003e. This accounts for the observed lack of \u003cem\u003eo\u003c/em\u003e-FE stabilization and the prevailing dominance of the \u003cem\u003eo\u003c/em\u003e-AFE under uniaxial strain.\u003c/p\u003e\u003cp\u003eWe next modeled biaxial strain conditions, which are characteristic of coherent interfaces such as \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eg and Supplementary Fig.\u0026nbsp;17). Consistent with Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, analysis of the right \u003cem\u003eo\u003c/em\u003e-phase reveals the presence of compressive strain along the \u003cem\u003eb\u003c/em\u003e-axis coupled with tensile strain along either the \u003cem\u003ea\u003c/em\u003e-axis or \u003cem\u003ec\u003c/em\u003e-axis. In our theoretical approach, we applied equal-magnitude opposing strains along orthogonal axes (e.g., for the \u003cem\u003ecb\u003c/em\u003e-plane: tensile strain along the \u003cem\u003ec\u003c/em\u003e-axis paired with compressive strain along the \u003cem\u003eb\u003c/em\u003e-axis, or vice versa). Biaxial strain calculations in the \u003cem\u003ecb\u003c/em\u003e-plane (Supplementary Fig.\u0026nbsp;17) reveal that Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;AFE\u003c/sub\u003e remains lower than Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;FE\u003c/sub\u003e across strains from \u0026minus;\u0026thinsp;5% to 5% (with \u003cem\u003eo\u003c/em\u003e-FE \u003cem\u003ec\u003c/em\u003e-axis lengths spanning from 4.76 \u0026Aring; to 5.27 \u0026Aring;), confirming that the \u003cem\u003eo\u003c/em\u003e-AFE phase remains favored over \u003cem\u003eo\u003c/em\u003e-FE under such a strain configuration. This explains the persistent dominance of \u003cem\u003eo\u003c/em\u003e-AFE near \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e or \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e interfaces. Conversely, biaxial strain within the \u003cem\u003eab\u003c/em\u003e-plane dramatically alters stabilization thresholds: compressive strain along the \u003cem\u003eb\u003c/em\u003e-axis substantially reduces the requisite tensile strain along the \u003cem\u003ea\u003c/em\u003e-axis to trigger a phase inversion. Specifically, the \u003cem\u003eo\u003c/em\u003e-FE becomes more stable than \u003cem\u003eo\u003c/em\u003e-AFE once the \u003cem\u003ea\u003c/em\u003e-axis length exceeds\u0026thinsp;~\u0026thinsp;5.13 \u0026Aring; (the inversion point). For bulk Lu:HZO crystals near \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type interfaces, the observed \u003cem\u003ea\u003c/em\u003e-axis tensile strain of the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase originates from the adjacent \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e region. Here, the average \u003cem\u003ea\u003c/em\u003e-axis length exhibits a critical threshold of ~\u0026thinsp;5.13 \u0026Aring;. This close agreement between theoretical prediction (stabilization occurring at \u003cem\u003ea\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;5.13 \u0026Aring;) and experimental measurement (at 5.13 \u0026Aring;) confirms that the \u003cem\u003eo\u003c/em\u003e-FE phase stabilization near the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type coherent interface arises from \u003cem\u003eo\u003c/em\u003e-phase interactions, directly supports previously reported strain-mediated \u003cem\u003eo\u003c/em\u003e-FE stabilization mechanisms\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e,\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb,d demonstrates, under biaxial strain within the \u003cem\u003eba\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e plane, tensile strain along the \u003cem\u003ea\u003c/em\u003e-axis of the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE phase primarily derives from the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e phase through the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e region. When the average tensile strain difference along the \u003cem\u003ea\u003c/em\u003e-axis exceeds approximately 1.5% between the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE regions, the \u003cem\u003eo\u003c/em\u003e-phase is preferentially stabilized as \u003cem\u003eo\u003c/em\u003e-AFE rather than \u003cem\u003eo\u003c/em\u003e-FE. To probe this transformation process in greater detail, we analyzed the interface between \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases. Unlike the commonly reported \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e-type coherent interface\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e, we identified an \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type coherent interface (\u003cem\u003eGroup\u003c/em\u003e 1). This particular configuration offers superior insight into the phase transformation process by revealing explicit pathways for oxygen atom reorganization within both the polarization and spacer layers during structural evolution. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea shows that a partial inversion of polarization vectors across the region from left to right columns clearly indicates the transformation from \u003cem\u003eo\u003c/em\u003e-FE to \u003cem\u003eo\u003c/em\u003e-AFE. To elucidate the atomic-scale evolution at this \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e interface, we systematically tracked both the vertically projected Hf-Hf distances and the horizontal Hf-O distances (\u003cem\u003ed\u003c/em\u003e\u003csub\u003eHf\u0026minus;O\u003c/sub\u003e, defined as the lateral separation between oxygen atoms and their adjacent right Hf columns). As Supplementary Fig.\u0026nbsp;19 shows, Hf-Hf bond lengths remain relatively stable across the interface, in contrast to \u003cem\u003ed\u003c/em\u003e\u003csub\u003eHf\u0026minus;O\u003c/sub\u003e, which exhibits significant spatial heterogeneity. Statistical analysis of \u003cem\u003ed\u003c/em\u003e\u003csub\u003eHf\u0026minus;O\u003c/sub\u003e distinguishes three regions: \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-FE (left), \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-transitional (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e), and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-AFE (right) (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb). The \u003cem\u003eo\u003c/em\u003e-FE region spans approximately 10 atomic layers, corresponding to a thickness of ~\u0026thinsp;2 nm\u0026mdash;consistent with previous reports in textured films\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. Taking \u003cem\u003eRows\u003c/em\u003e 14\u0026ndash;16 as a representative example (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec), \u003cem\u003ed\u003c/em\u003e\u003csub\u003eHf\u0026minus;O\u003c/sub\u003e in \u003cem\u003eRow\u003c/em\u003e 14 (polarization layer) exhibits evolutionary behavior similar to that in \u003cem\u003eRow\u003c/em\u003e 15 (spacer layer), with only minimal displacement variation. In contrast, \u003cem\u003ed\u003c/em\u003e\u003csub\u003eHf\u0026minus;O\u003c/sub\u003e in \u003cem\u003eRow\u003c/em\u003e 16 (also a polarization layer) gradually increases from left to right columns, indicating substantial positional reorganization of the associated oxygen atoms. Initially clustering around ~\u0026thinsp;86.8 pm within the \u003cem\u003eo\u003c/em\u003e-FE polarization layers, this distance progressively increases, eventually reaching\u0026thinsp;~\u0026thinsp;179.2 pm in the \u003cem\u003eo\u003c/em\u003e-AFE region. Furthermore, as seen in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb,d, the vertically projected O-O distances within the transformed polarization layers undergo an initial shortening followed by lengthening across the phase transformation from \u003cem\u003eo\u003c/em\u003e-FE to \u003cem\u003eo\u003c/em\u003e-AFE. This behavior parallels the theoretical \u003cem\u003eN\u003c/em\u003e-pathway polarization switching in HZO ferroelectrics, wherein oxygen atoms within polarization layers do not pass through the cation planes\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e,\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. The crystal symmetry of the intermediate \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e region lacks mirror symmetry within the \u003cem\u003ec\u003c/em\u003e-axis oriented crystallographic plane, precluding \u003cem\u003ePbcm\u003c/em\u003e symmetry where oxygen atoms pass through cationic planes. Furthermore, primary structural changes are localized to oxygen atoms within specific polarization layers, thereby also excluding \u003cem\u003ePbcn\u003c/em\u003e symmetry that requires oxygen atom displacements across both adjacent polarization and spacer layers. Analysis of the atomic distribution, particularly regarding oxygen atoms, within the \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e region indicates that the most probable symmetry along the \u003cem\u003ec\u003c/em\u003e-axis is a 2\u003csub\u003e1\u003c/sub\u003e screw axis, lacking an accompanying mirror or glide plane (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed). This structure confirms its non-centrosymmetric character. Within this specific \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e region, the atomic arrangement consists of three spacer layers separating adjacent polarization layers, unlike the extensively studied ferroelectric phase possessing a single spacer layer. Building upon the established relationship between domain wall distribution and coercive field\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e, this increased number of spacer layers is expected to reduce constraints on the coercive field. This predicted reduction offers a promising pathway for achieving lower operating voltages, thereby enhancing compatibility with the requirements of silicon-based CMOS technology. Consequently, the identified \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type coherent interface between the \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases, along with its observed phase evolution, provides crucial fundamental insights that support performance optimization in HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectrics and enable a more comprehensive understanding of domain switching mechanisms. The observed \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003etrans\u003c/em\u003e\u003c/sub\u003e polar phase presents significant advantages for developing advanced HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectric devices, exhibiting lower operational coercive fields compared to the established ferroelectric phase.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe \u003cem\u003eo\u003c/em\u003e-AFE phase, a commonly existing byproduct of \u003cem\u003eo\u003c/em\u003e-FE phase formation, not only complicates the understanding of HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectricity but also contributes to wake-up/fatigue phenomena that severely compromise device operational stability \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. Resolving \u003cem\u003eo\u003c/em\u003e-phase formation dynamics and enhancing resultant device performance are thus critical priorities for the HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectric community. Strain engineering offers a promising pathway to modulate this challenging coexistence of \u003cem\u003eo\u003c/em\u003e-FE/\u003cem\u003eo\u003c/em\u003e-AFE phases\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Nevertheless, most studies on strain effects in HfO\u003csub\u003e2\u003c/sub\u003e systems focus on thin films, where complex interactions between extrinsic/intrinsic strains, \u003cem\u003em\u003c/em\u003e-phase interference, and nanometer-scale grain sizes obscure clear structure-property relationships\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Consequently, the strain-mediated polymorphic transformation between \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE remains poorly understood, and proposed evolution pathways remain largely theoretical due to the absence of experimentally observed coherent interfaces. To address this gap, we employ the bulk Lu:HZO crystal to investigate strain-mediated control of \u003cem\u003eo\u003c/em\u003e-phase polymorphism. The primary strain source in bulk crystals originates from phase lattice mismatch, effectively avoiding the extrinsic strain contributions common in film counterparts. Rapid high-temperature-to-room-temperature phase transformation yields abundant coherent \u003cem\u003eo\u003c/em\u003e-phase interfaces\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. Crucially, bulk crystal growth suppresses \u003cem\u003em\u003c/em\u003e-phase interference while producing grains significantly larger than those in films, facilitating precise phase interface observation and strain analysis within grains\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. Detailed structural and optical characterizations confirm the coexistence of \u003cem\u003eo\u003c/em\u003e-FE/\u003cem\u003eo\u003c/em\u003e-AFE phases within Lu:HZO bulk crystals. Through microstructural analysis, we identified potential coherent \u003cem\u003eo\u003c/em\u003e-phase interfaces and their associated strain states. Observations indicate that among the six observed interface types (\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ecr\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003eal\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e), only \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e interfaces (formed between adjacent \u003cem\u003ec\u003c/em\u003e-axis and \u003cem\u003eb\u003c/em\u003e-axis oriented \u003cem\u003eo\u003c/em\u003e-phases) support the formation of the \u003cem\u003eo\u003c/em\u003e-FE phase under biaxial strain. Subsequent theoretical calculations confirm that isolated uniaxial strain along the \u003cem\u003ea\u003c/em\u003e-axis alone cannot stabilize the \u003cem\u003eo\u003c/em\u003e-FE phase in Lu:HZO bulk crystals, even across a broad length range (4.72 \u0026Aring;\u0026ndash;5.25 \u0026Aring;). However, concurrent \u003cem\u003eb\u003c/em\u003e-axis compressive strain stabilizes the \u003cem\u003eo\u003c/em\u003e-FE phase over the \u003cem\u003eo\u003c/em\u003e-AFE when the \u003cem\u003ea\u003c/em\u003e-axis length exceeds\u0026thinsp;~\u0026thinsp;5.13 \u0026Aring; under tensile strain\u0026mdash;consistent with experimental measurements. In strain-relaxed regions lacking \u003cem\u003eo\u003c/em\u003e-FE-stabilizing strain, our atomic-scale observations of coherent interfaces reveal the transformation pathway from \u003cem\u003eo\u003c/em\u003e-FE to \u003cem\u003eo\u003c/em\u003e-AFE. The identified phase evolution mechanism\u0026mdash;driven by specific cation and oxygen displacements\u0026mdash;clarifies the structural framework governing this polymorphic transition.\u003c/p\u003e\u003cp\u003eOur study establishes a universal principle that explains how to achieve and maintain strong ferroelectric properties in HfO\u003csub\u003e2\u003c/sub\u003e, regardless of whether the material is an ultra-thin film or a much larger bulk crystal. We reveal that the stability of the desired \u003cem\u003eo\u003c/em\u003e-FE phase depends almost entirely on the specific strain states at the interfaces between different \u003cem\u003eo\u003c/em\u003e-phases. This insight identifies selective phase interface engineering\u0026mdash;actively designing these interfaces to promote the right kind of strain. Specifically, enhancing \u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u0026minus;\u003cem\u003ebl\u003c/em\u003e\u003c/sub\u003e/\u003cem\u003eo\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u0026minus;\u003cem\u003ear\u003c/em\u003e\u003c/sub\u003e-type connections through coordinated extrinsic/intrinsic strain tuning is the key strategy for optimizing \u003cem\u003eo\u003c/em\u003e-FE phase fraction and polarization direction. In extensively studied HfO\u003csub\u003e2\u003c/sub\u003e-based films, where increased thickness typically degrades ferroelectricity via strain relaxation. Our study shows that advanced layered architectures (e.g., superlattices, nanolaminates) can maintain precise strain control, preserving ferroelectricity beyond the nanometer scale\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e,\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. Our discovery provides a blueprint for optimizing these layers to enhance ferroelectric performance over a broader range of thicknesses\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e,\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e. For bulk HfO\u003csub\u003e2\u003c/sub\u003e, our \u003cem\u003eo\u003c/em\u003e-phase modulation mechanism provides a viable strategy to stabilize the \u003cem\u003eo\u003c/em\u003e-FE phase. Combining advanced strain modulation\u0026mdash;including grain control, lattice parameter adjustment, and oriented growth design, we can create the specific internal strain needed to stabilize the ferroelectric phase, achieving performance that rivals thin films, reminiscent of perovskite ferroelectrics\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e. We also directly observed how the ferroelectric phase transforms into a non-functional one. This gives us a complete model of phase behavior, which is crucial for fundamental understanding of the competing phase dynamics, enabling rational domain-switching strategies and tailoring interfacial device design\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e,\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e. Collectively, our work deciphers the strain-based mechanism that controls the competition between key phases in HfO\u003csub\u003e2\u003c/sub\u003e\u0026mdash;a breakthrough critical for enhancing performance and reliability in CMOS-compatible fluorite-structure ferroelectrics. These insights will accelerate the adoption of HfO\u003csub\u003e2\u003c/sub\u003e in non-volatile memories (FeRAM, FeFET, neuromorphic computing) and propel emerging multifunctional applications for information and energy systems (e.g., piezoelectrics, pyroelectrics), significantly broadening their technological impact.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn summary, this work uncovers the atomistic mechanism underlying strain-mediated \u003cem\u003eo\u003c/em\u003e-phase formation at coherent \u003cem\u003eo\u003c/em\u003e-phase interfaces in HfO\u003csub\u003e2\u003c/sub\u003e, highlighting how interfacial strain selectively stabilizes the metastable \u003cem\u003eo\u003c/em\u003e-FE phase by modifying specific connecting interfaces. Leveraging bulk crystals free from epitaxial constraints enables unparalleled insights into strain sources, grain size control, and phase interface distribution\u0026mdash;surpassing thin-film limitations. Our integrated microstructural and theoretical analyses reveal that biaxial strain (\u003cem\u003ea\u003c/em\u003e-axis tension coupled with \u003cem\u003eb\u003c/em\u003e-axis compression) locally stabilizes the \u003cem\u003eo\u003c/em\u003e-FE phase near \u003cem\u003eo\u003c/em\u003e-phase interfaces, while the \u003cem\u003eo\u003c/em\u003e-AFE phase dominates further away from the formed interface. By directly mapping transformation pathways at the atomic level through tracking dynamic oxygen displacements, we decipher the evolution between \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases. These findings establish a fundamental optimization principle for designing HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectrics. We show how to optimize strain in layered films to maintain performance at greater thicknesses, and how to enhance ferroelectricity in bulk crystals. This establishes controlled strain as a key design tool, enabling the creation of high-performance, CMOS-compatible materials for next-generation memory and neuromorphic computing.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe experimental data generated in this study are provided in the Supplementary Information/Source data file. The uploaded source data includes the obtained data that can reproduce all the findings of this study. Source data are provided with this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe thank J.Wu (University of Jinan) for the structural refinement and X.Zhao (Shandong University) for the assistance with theoretical calculations. This work is supported by the National Natural Science Foundation of China (grant nos. 52025021 (H.Y.), 52472008 (S.W.),\u0026nbsp;U24A2027 (S.W.), and 52422201 (F.L.)), the National Key Research and Development Program of China (2021YFB3601504 (H.Z.)), the Natural Science Foundation of Shandong Province (ZR2022LLZ005 (S.W.)), and the Future Plans of Young Scholars at Shandong University (S.W.).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eS.W., H.Y., S.Z. and H.Z. conceived the research idea of this study. Y.S. and S.W. conducted the crystal growth and related characterizations, including XRD, Raman and SHG. Under the guidance of B.G. and H.Y., Y.S., S.W., H.W., X.M. and P.N. performed the STEM characterization and relevant strain analyses. Y.L. and F.L. conducted the theoretical calculations. Y.S. and S.W. wrote the original manuscript. H.Y., S.Z. and H.Z. revised the manuscript. All authors contributed to the manuscript discussion.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eSchroeder, U., Park, M. H., Mikolajick, T. \u0026amp; Hwang, C. S. The fundamentals and applications of ferroelectric HfO\u003csub\u003e2\u003c/sub\u003e. \u003cem\u003eNat. Rev. Mater.\u003c/em\u003e \u003cstrong\u003e7\u003c/strong\u003e, 653\u0026ndash;669 (2022).\u003c/li\u003e\n\u003cli\u003eKhan, A. I., Keshavarzi, A. \u0026amp; Datta, S. The future of ferroelectric field-effect transistor technology. \u003cem\u003eNat. Electron.\u003c/em\u003e \u003cstrong\u003e3\u003c/strong\u003e, 588\u0026ndash;597 (2020).\u003c/li\u003e\n\u003cli\u003eSalahuddin, S., Ni, K. \u0026amp; Datta, S. The era of hyper-scaling in electronics. \u003cem\u003eNat. 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Mater.\u003c/em\u003e \u003cstrong\u003e37\u003c/strong\u003e, 1820\u0026ndash;1825, (2025).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7867840/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7867840/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectrics hold exceptional promise for next-generation microelectronics, offering robust ferroelectricity down to the nanoscale while maintaining compatibility with CMOS technology. However, stabilization of the ferroelectric orthorhombic phase (\u003cem\u003eo\u003c/em\u003e-FE) is consistently challenged by the simultaneous formation of its antiferroelectric counterpart (\u003cem\u003eo\u003c/em\u003e-AFE). This unresolved \u003cem\u003eo\u003c/em\u003e-FE/\u003cem\u003eo\u003c/em\u003e-AFE competition, particularly under strain, is a critical factor driving undesirable device phenomena like ‘wake-up’ and ‘fatigue’. To decipher the strain-confinement effects governing \u003cem\u003eo\u003c/em\u003e-FE stability at coherent \u003cem\u003eo\u003c/em\u003e-phase interfaces, we have developed a bulk-crystal strategy. This approach overcomes thin-film strain complexities by leveraging larger grain sizes and simplified strain landscapes. Integrating advanced microscopy with theoretical calculations, we demonstrate that specific biaxial strain—tensile along the \u003cem\u003ea\u003c/em\u003e-axis coupled with compressive along the \u003cem\u003eb\u003c/em\u003e-axis—proves sufficient to stabilize the \u003cem\u003eo\u003c/em\u003e-FE phase, while strain relaxation favors \u003cem\u003eo\u003c/em\u003e-AFE dominance. Direct atomistic tracking reveals the mechanisms underlying the formation of the \u003cem\u003eo\u003c/em\u003e-FE phase and the evolution pathway between \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases. Our work establishes a unified strain-mediated mechanism for the ubiquitous phase switching between the \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases observed in HfO\u003csub\u003e2\u003c/sub\u003e-based materials, delivering a fundamental framework to design high-performance fluorite ferroelectrics. This has broad implications for advancing microelectronics and neuromorphic computing.\u003c/p\u003e","manuscriptTitle":"Atomic-scale strain-confined ferroelectricity in fluorite hafnium dioxide","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-18 06:25:45","doi":"10.21203/rs.3.rs-7867840/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"1e8e1ee2-06e1-4d11-a424-28b38d1338f7","owner":[],"postedDate":"November 18th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":57584127,"name":"Physical sciences/Materials science/Condensed-matter physics/Phase transitions and critical phenomena"},{"id":57584128,"name":"Physical sciences/Materials science/Condensed-matter physics/Ferroelectrics and multiferroics"}],"tags":[],"updatedAt":"2025-11-18T06:25:45+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-18 06:25:45","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7867840","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7867840","identity":"rs-7867840","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}