Beyond morphotropic phase boundaries: Atomic-scale mechanism unlocks thermal-stable high-κ performance in HfO2 via coherent interfaces

Beyond morphotropic phase boundaries: Atomic-scale mechanism unlocks thermal-stable high-κ performance in HfO2 via coherent interfaces | 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 Beyond morphotropic phase boundaries: Atomic-scale mechanism unlocks thermal-stable high-κ performance in HfO 2 via coherent interfaces Haohai Yu, Yihao Shen, Hongzheng Wang, Xiaochun Ma, Yuxiao Liu, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7347248/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Jan, 2026 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract CMOS-compatible HfO 2 -based high- κ dielectrics are pivotal for next-generation electronics in the post-Moore’s Law era. However, establishing coherent interfaces via morphotropic phase boundaries (MPBs) across the tetragonal ( t ) and orthorhombic (ferroelectric, o -FE or antiferroelectric, o -AFE) phases—a key strategy for enhancing dielectric properties—remains challenging due to unclear atomic-scale mechanisms and inherent thermal instability, which compromises long-term stability and reliability. To address this, we leverage metallurgical quenching principles to stabilize t / o -AFE MPBs in HfO 2 -based (Lu:Hf 0.6 Zr 0.4 O 2 ) bulk crystals. Through precise composition tuning and growth optimization, we stabilize these metastable t / o -AFE MPBs at the t / t + o -AFE interface at room temperature, achieving a comparable κ -value (57) to actively studied t / o -FE MPBs. Microstructural characterization reveals how tensile strain within the t -phase drives dielectric enhancement through softening of the low-frequency E u phonon mode. Critically, the t / o -AFE MPB demonstrates a ~58% reduction in κ variation rate over 30–200°C relative to t / o -FE MPBs, signifying superior thermal stability. Our study establishes a generalizable design paradigm for developing high- κ dielectrics in fluorite-structured materials, advancing next-generation CMOS-integrated functional devices for data storage, energy harvesting, sensing, and integrated photonics. Physical sciences/Materials science/Condensed-matter physics/Structure of solids and liquids Physical sciences/Materials science/Condensed-matter physics/Phase transitions and critical phenomena Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction As the demand for reducing equivalent oxide thickness continues to grow in the ongoing miniaturization of microelectronic devices, such as dynamic random-access memory (DRAM) and field-effect transistors (FET), modern downscaling efforts increasingly rely on the transformative utilization of gate materials that combine a high dielectric constant ( κ ), wide bandgap, and excellent compatibility with silicon-based integrated circuit technology 1-6 . Over the past decades, HfO 2 -based fluorite-structure materials have demonstrated remarkable compatibility with mature complementary metal-oxide-semiconductor (CMOS) technology and superior dielectric performance in contrast to traditional SiO 2 -based dielectrics. Among HfO 2 polymorphs, including Fm -3 m ( c ), P 4 2 / nmc ( t ), ferroelectric Pbc 2 1 ( o -FE), antiferroelectric Pbca ( o -AFE), and monoclinic P 2 1 / c ( m ) phases 7,8 , the t -phase is widely regarded as the primary high- κ candidate due to its high theoretical κ (~70), which far exceeds those of other polymorphs with κ -values typically below 40 9 . However, the experimentally achievable κ in t -phase HfO 2 -based materials rarely exceeds ~40, even with optimized manufacturing processes and compositional engineering 10 , falling short of the stringent demands for next-generation high-density/high-speed electronic and memory devices in the post-Moore’s Law era 1,11 . Beyond high κ , robust dielectric thermal stability has become equally critical for ensuring the operational reliability of these CMOS-integrated systems 12 , necessitating innovative approaches to simultaneously enhance both κ and dielectric thermal stability in HfO₂-based materials. Constructing coherent phase interfaces represents an established strategy for tailoring material properties in metals and ceramics 13-16 . For HfO₂-based materials, engineering morphotropic phase boundaries (MPBs) between the t and o ( o -FE or o -AFE) phases has emerged as an effective strategy for enhancing dielectric properties 17 . However, despite their promising dielectric improvements, the lack of microstructural characterization obscures the origin of this enhancement, leading to an inconsistent κ variation range (38–68) 18-30 . Furthermore, the inherently low energy barrier (~46.0 meV per f.u.) between the t and o -FE phases readily facilitates a phase transition under thermal or electric field stimuli, severely compromising dielectric stability and degrading device endurance 17,31,32 . In contrast, the energy barrier for the t -to- o -AFE transition is significantly higher (~68.8 meV per f.u.), approximately 1.5 times that of the t / o -FE interface (Fig. 1a) 32 , suggesting t / o -AFE MPBs could deliver superior dielectric stability. Current t / o MPB research in HfO 2 -based dielectrics focuses primarily on thin films, where the intermediate free energy of the o -FE phase between the t and o -AFE phases often leads to mixed o -FE and o -AFE phases (Fig. 1b) 33,34 . Critically, this higher energy barrier for the t -to- o -AFE transition, as opposed to the t -to- o -FE transition, makes t / o -AFE MPB formation more challenging than t / o -FE MPBs, leaving the interplay between t / o -AFE MPB configurations and their dielectric properties poorly understood. This gap highlights the need for systematic exploration into t / o -AFE MPBs to unlock their full potential. Recent advances in HfO₂-based bulk crystals, prepared via the optical floating zone (OFZ) technique, have demonstrated successful stabilization of both t and o ( o -AFE or o -FE) phases 32,35 . Significantly, precise control over t -to- o phase transition pathways can be realized by strategic composition engineering combined with controlled temperature gradient distribution 35 , providing a feasible avenue for stabilizing HfO₂-based t / o -AFE MPBs. In this study, inspired by the metallurgical quenching principles, we successfully grow HfO 2 -based (Lu:Hf 0.6 Zr 0.4 O 2 , Lu:HZO) bulk crystals featuring a well-defined t-o phase boundary. Our structural analyses reveal that the t - o phase boundary primarily represents the interface between the non-polar t and antiferroelectric o -AFE phases. Subsequent dielectric characterization reveals that our t / o -AFE MPBs achieve a comparable κ -value (57) to actively studied t / o -FE MPBs. Through detailed microstructural observations and strain analyses, we identify the mechanism behind the dielectric enhancement near the t / o -AFE MPBs, which is primarily attributed to the frequency shift in the infrared-active low-frequency E u phonon mode of the t -phase driven by local structural modifications at the phase boundary. Moreover, t / o -AFE MPBs exhibit significantly enhanced thermal stability, demonstrating less than half the κ variation rate observed in the t / o -FE MPBs across the temperature range from 30 to 200°C. Our findings establish a clear structure-property relationship in HfO₂-based t / o -AFE MPBs, and provide a versatile design framework for fluorite-structured functional devices with applications in CMOS-integrated data storage, energy harvesting, sensing, and photonic technologies 36,37 . Results Design strategy and growth of Lu:HZO bulk crystals As illustrated in Fig. 1 c, our approach for achieving t / o -AFE MPBs in HfO₂-based bulk crystals involves three sequential steps, corresponding to the formation of the t -phase (Step 1), controlled t -to- o phase transition (Step 2), and preserving t / o -AFE MPBs to room temperature (Step 3). The t -phase is metastable at room temperature due to its higher formation energy relative to orthorhombic phases ( o -AFE or o -FE). Its critical nucleation dimension typically falls within a few nanometers, rendering its stabilization challenging even in thin films or nanoparticles 39 , 40 . To address this challenge, in Step 1, we employed the OFZ growth method for preserving high-temperature metastable phases down to room temperature via ultrahigh heating temperatures (up to 3000°C), steep thermal gradients, and controllable growth rates 41 . Codoping with rare-earth (RE) and Zr⁴⁺ ions offers a direct solution to stabilize t -phase HfO₂-based bulk crystals at room temperature by effectively suppressing m -phase interference and modulating the t -to- o phase transition temperature 32 , 35 . Here we used the Hf 0.6 Zr 0.4 O 2 (HZO) doped with Lu (Lu:HZO)—a composition optimized for t -phase stability—to systematically explore dopant concentrations 35 . Regarding Step 2, controlled temperature-driven t -to- o phase transition enables the formation of o phases ( o -AFE or o -FE) from the high-temperature metastable t -phase 6 . The steep temperature gradient and fast growth rate intrinsic to the OFZ growth strategy offer a feasible control over the t -phase conversion, benefiting the formation of well-defined t / o phase boundaries within Lu:HZO bulk crystals. As the as-grown crystal traverses its Curie temperature ( T C ) during cooling, the o -phase precipitation initiates 31 . The cooling pathway from the high-temperature supplies sufficient transformation energy to overcome the activation barriers for both t → o -AFE and t → o -FE conversions. The o -AFE phase possesses a lower formation energy than the o -FE phase, thus favoring its preferential nucleation during the t -to- o conversion 32 . Consequently, combining with the pure t -phase region, t / o -AFE MPBs will form at the t / t + o -AFE phase interface within Lu:HZO bulk crystals. Step 3 aims to stabilize the t / o -AFE MPBs in Lu:HZO bulk crystals to room temperature utilizing a non-equilibrium processing strategy. Post-growth rapid quenching (cooling within ~ 2s) quickly removes the as-grown crystal from the high-temperature regime, effectively suppressing further t -to- o phase transition. This non-equilibrium process preserves the formed t / o -AFE MPBs to room temperature by minimizing high-temperature exposure. Leveraging this OFZ strategy, we grew a series of Lu:HZO bulk crystals. To identify the optimal dopant concentration, three distinct Lu doping levels were chosen: 9.25 at.%, 9.75 at.%, and 10 at.%, all exhibit crack-free, high crystallinity (Supplementary Fig. 2), validating the efficacy and feasibility of the OFZ growth strategy for scalable production. The different bond vibrational properties among HfO 2 polymorphic phases serve as effective markers for phase identification within Lu:HZO bulk crystals. Specifically, the t -phase exhibits robust A 1 g and B 1 g Raman modes around 270 cm − 1 , while the o phases manifest strong bond vibrations in the vicinity of 370 cm − 1 , including the A g mode for o -AFE and A 1 mode for o -FE 38 . We employed Raman spectroscopy to analyze the phase distribution along the crystal growth direction. The Lu:HZO (9.25 at.%) crystal simultaneously presents the t - and o -phase phonon vibrational modes, suggesting that the Lu doping level is insufficient to achieve the pure t -phase. With a rise of Lu doping concentration to 9.75 at.%, apart from the mixture region of t and o phases, the pure t -phase is observed in the top region, yielding an unequivocal t / t + o phase interface within the as-grown bulk crystal. As the Lu doping level is further raised to 10 at.%, the pure t -phase existing range is expanded by reducing the t + o phase region, underscoring the critical role of composition optimization in manipulating the t / o MPB interface within Lu:HZO bulk crystals. Focusing on the optimized Lu:HZO (10 at.%) phase component, we further refined the OFZ growth parameters to verify the controllability of the t / t + o phase boundary formation. Three different movement distances ( d ) after the growth process, before quenching, were tested, corresponding to 0 mm ( Crystal 1), 5 mm ( Crystal 2), and 10 mm ( Crystal 3), with results shown in Fig. 1 d. With increasing the d value, the t / t + o phase boundary moves towards the top of the as-grown crystal, accompanied by a shrinking t -phase region and an expanding t + o mixed phase region. The observed o -phase Raman signature at 370 cm⁻¹ closely matches the characteristic vibrational mode of the o -AFE phase, providing compelling support for the structurally stabilized o -AFE phase formation. This aligns with expectations since the o -AFE phase has a lower formation energy than the o -FE phase 32 . Upon enlarging the d value to 10 mm, the t -phase region completely disappears, leaving only the t + o mixed phase region in the as-fabricated bulk crystal. These findings highlight the versatility of the OFZ growth method in precisely tuning phase distribution within the bulk crystal, even without altering the raw material component. As exhibited in Fig. 2 a, multiple polymorphs can coexist in fabricating HfO 2 -based materials. With regard to HfO 2 -based thin films, the frequent presence of the m phase complicates the phase component and hampers the relevant MPB analysis 17 . In contrast, for bulk-crystal growth, combining ion adjustment and growth control effectively disentangles the m -phase interference and allows straightforward adjustment of the t / t + o -AFE interface 35 , 42 , facilitating deeper insight into how the phase boundary influences dielectric property. The Lu:HZO bulk crystals experience a series of phase transitions during the crystal growth process. The crystallization from the melt will form the c phase first. Then, following the downward movement across the transition temperature (above 2500 o C) 6 , the c phase rapidly transforms into the t -phase by expanding its (220) interplanar spacing and contraction of its (004) interplanar spacing (Supplementary Fig. 3). Subsequently, the steep temperature gradient along the growth direction further brings a partial t -phase section into the o -AFE phase once the location temperature falls below the t - o transition threshold. The rapid quenching process following growth benefits the stabilization of different phase distributions within the bulk crystal, providing an opportunity to obtain a well-defined t / t + o -AFE interface and permitting exploration of its MPB influence. To further analyze the phase difference between the pure t and mixed t + o -AFE regions with as-grown Lu:HZO crystals, we took Crystal 2 as a representative case and collected XRPD data from the t -phase ( S t ) and t + o -AFE ( S t+o ) regions. As shown in Fig. 2 b, the XRPD pattern from S t region matches well with the standard t -phase reference, showing no evidence of o -phase diffraction peaks. By comparison, the o -phase diffraction peaks around 53 o and 56 o are observed in S t+o region. This result coincides with the above-mentioned Raman analysis that t and o -AFE phases coexist in the t + o -AFE region. On that basis, we surveyed the element distribution of Crystal 2 using electron probe microanalysis (EPMA) from the t -phase to t + o -AFE regions. As exhibited in Fig. 2 c, the selected zone with different phases demonstrates uniform element distribution, indicating that the phase variation mainly stems from the modulation role of the OFZ growth strategy rather than compositional gradients. The detailed structural difference between S t and S t+o was analyzed by performing Rietveld refinement characterization (Supplementary Figs. 3 and 4). As shown in Supplementary Table 1, the t -phase c /(2 0.5 a ) of S t is determined to be 1.010, a value smaller than that of the theoretically standard t -phase (1.028) but larger than that within S t+o (1.007) 43 . This phenomenon reveals that the as-obtained t -phase in Lu:HZO bulk crystals shows a weak structural anisotropy in contrast to the ideal t -phase, with position located at a lower-temperature region prior to quenching, displaying further reduced lattice distortion. Dielectric characterization and t / o -AFE MPBs in Lu:HZO bulk crystals In the subsequent context, we conducted the frequency-dependent dielectric characterization of as-grown Lu:HZO crystals and compared the dielectric properties across various phase components, involving m , o , t , c , and different MPB-engineered configurations (Supplementary Figs. 5 and 6). All bulk crystalline samples exhibit low dielectric loss (< 0.02), comparable to those reported in thin films 44 – 46 . Nevertheless, their κ -values show notable variation. As elucidated in Fig. 2 d, m-phase HfO 2 (~ 14) and HZO (~ 15) show low ε r values in contrast to other polymorphs, being in good agreement with the theoretical calculations 9 . The o -AFE sample exhibits an ε r value of 33, which is slightly higher than those of c -HfO 2 (~ 28) and c -ZrO 2 (~ 29) 8 , 47 . By contrast, the t -phase sample exhibits a clear dielectric advantage with a value on the order of 40, aligning well with the experimental results achieved in HfO 2 -based films 10 . Next, we compared the dielectric performances of three different MPB configurations, corresponding to t + o -AFE, t / o -FE, and t / o -AFE interfaces. The t + o -AFE and t / o -FE samples present a slight reduction in κ compared to the pure t -phase, indicating that the simple phase mixing within the MPB structure does not inherently enhance the dielectric property. It is worth noting that the sample around the t / t + o -AFE interface demonstrates an ε r value of 57, comparable to those of the t / o -FE MPB films (Supplementary Fig. 7, Supplementary Table 2), representing a 43% increase over the pure t -phase sample. Additionally, the temperature-dependent dielectric measurements (Fig. 2 e,f and Supplementary Fig. 8) reveal a significantly higher T C (~ 670 o C) in the t / o -AFE MPBs compared to their t / o -FE counterparts (~ 425 o C). This marked increase is attributed to the larger energy barrier for the t -to- o phase transition inherent in the t / o -AFE MPBs 32 . Consequently, when heated from room temperature to 200°C, the t / o -AFE MPBs exhibit minimal variation in κ — only 7%, compared to the 17% change observed in t / o -FE MPBs — directly reflecting their superior dielectric thermal stability. This finding highlights the universality of the MPB role in modulating the dielectric properties of HfO 2 -based materials, ranging from thin films to bulk crystals. The manipulation of MPB distribution of HfO 2 -based materials remains challenging owing to various influencing variables, such as ion doping, interface engineering, and post-processing 17 . Thus, an in-depth understanding of the interplay between the crystal structure of MPB and dielectric response becomes crucial. The robust κ observed at the t / t + o -AFE interface in the Lu:HZO crystal provides a valuable paradigm to clarify the MPB effects, benefiting from the absence of m -phase interference and the larger grain size in contrast to film counterparts 32 , 35 . The enhanced dielectric properties observed at the t / t + o -AFE phase boundary in Lu:HZO bulk crystals are intricately linked to the microstructural characteristics of the t / o -AFE phase boundaries. This underscores the critical role of analyzing the coherent interfaces at the t / o -AFE MPBs and their associated strain distribution to elucidate the underlying enhancement mechanisms. As summarized in Supplementary Table 1, the refined lattice parameters of the o -AFE phase ( a = 10.1365 Å, b = 5.2135 Å, and c = 5.0833 Å) exhibit apparent differences compared to those of the t -phase ( a = b = 3.6015 Å, and c = 5.1431 Å), indicating the presence of strain near the t / o MPB caused by the martensitic transformation characteristic in the t - o transition 6 , 48 . To assess the potential strain effect on the t -phase induced by the adjacent o -AFE phase near the t / o MPB, we theoretically modeled the strain variations across various coherent interfaces between the t and o -AFE phases. Combined with the reported t - o transformation routes, the possible coherent interfaces at the t / o MPB were identified and are presented in Fig. 3 a-i, focusing on the {001} and {110} planes of the t -phase. Among the investigated strain configurations on the t -phase, Case -(1) and Case -(2) induce tensile strain, whereas the other four cases result in compressive strain. Types Ⅰ, Ⅲ, Ⅶ, and Ⅷ coherent interfaces exhibit the maximum tensile strain, reaching 2.36% ( Case -(1)). In contrast, the largest compressive strain is observed in Types Ⅶ and Ⅷ coherent interfaces, with a value of -1.45% ( Case -(6)). Type Ⅶ demonstrates the most pronounced horizontal and vertical in-plane strain difference at the coherent interface ( Case -(1) and Case -(6)), while Type Ⅱ displays the minimal in-plane strain disparity ( Case -(3) and Case -(4)). Microstructural survey and local strain analysis in Lu:HZO bulk crystals Accurate identification of MPB configurations and their associated local strain fields in Lu:HZO bulk crystals necessitates atomic-scale structural characterization, particularly focusing on the interfacial strain mechanism by precise mapping of anion or cation distributions near the phase boundaries. To investigate these atomic-scale structural characteristics, we utilized integrated differential phase contrast scanning transmission electron microscopy (iDPC-STEM). This advanced technique was selected for its exceptional ability to simultaneously resolve both light (e.g., oxygen) and heavy (e.g., Hf/Zr/Lu) elements with high contrast (Fig. 4 ) 47 , 49 . As shown in Fig. 4 a and Supplementary Fig. 9, the b -axis serves as the optimal observation direction for identifying the o -phase, as it clearly reveals the characteristic oxygen displacement patterns within polarization layers 33 , 34 . Specifically, the o -AFE and o -FE phases can be distinguished by their antiparallel and parallel polarization vector alignments, respectively. In Crystal 2 (Fig. 4 e), the o phase exhibits o -AFE behavior, with antiparallel polarization along the c -axis, in full agreement with the prior structural and optical characterization results. As shown in Fig. 4 b and Supplementary Fig. 9, the atomic arrangements along the c -axis exhibit no major structural differences between o -FE and o -AFE phases. Key identifiers of the o -phase include periodic variations in vertical Hf-Hf projected distances and horizontal displacements of O atoms, facilitating the o -phase identification within the t / o MPB regions. Our observation reveals a trapezoidal arrangement of Hf atoms (Fig. 4 f), which shows excellent agreement with the predicted c -axis atomic distribution of the o phase. Given the predominance of the t -phase at the t / o MPBs, we aligned the imaging orientation with the t -phase crystal structure. As exhibited in Fig. 4 c,d, observations along the c -axis or directions of the t -phase are vital for defining subsequent t / o phase coherent interfaces. The atomic arrangements of the t -phase appear similar along both observation directions, making them difficult to distinguish in STEM characterization. To quantitatively characterize the t -phase observation direction, we introduced the R -value, defined as ( h 1 + h 2 )/( v 1 + v 2 ), which directly reflects tetragonality in the Hf atomic sublattice, as shown in Fig. 4 g. Theoretically, R = 1 represents the c -axis orientation, while R ≠ 1 signifies the orientation due to the anisotropic lattice parameter ( c ≠ √2 a ) in the t -phase structure 38 . R > 1 and R < 1 reflect the c -axis alignment of the associated t -phase crystalline grains along the horizontal and vertical directions, respectively. To verify the t -phase observation direction, we analyzed the observed t -phase R -value distribution corresponding to the original image (Supplementary Fig. 10a,c). In Fig. 4 h and Supplementary Fig. 10a,b, the R -value peaks at 1 with a range of 0.96–1.05, confirming observation along the c -axis direction of the t -phase. Conversely, statistical analysis in Fig. 4 i and Supplementary Fig. 10c,d reveals R values spanning from 0.95 to 1.045, with dominant peaks at 1.005 and 0.985, strongly indicating the observation direction of the t- phase. After confirming the coexistence of crystalline phases within Crystal 2, we systematically investigated the local structural evolution at the t / o MPBs. Our analysis focused on MPBs aligned with either the b - or c -axis of the o -AFE phase, corresponding to the c -axis or direction of the t -phase, respectively. The a -axis orientation of the o -AFE phase was excluded due to the dense arrangement of O atoms, which obscures a clear structural interpretation 47 . As demonstrated in Fig. 5 a,b, Fig. 6 a,c, and Supplementary Figs. 11 and 12, several different coherent interfaces between the t -phase and o -AFE phases were observed, suggesting the different t -to- o transformation pathways. As shown in Fig. 5 a, we systematically analyzed the local structural characteristics of a representative t / o coherent interface within the Lu:HZO bulk crystal. The upper-right region displays characteristic c -axis-oriented o -phase features, whereas the lower-left region exhibits distinct t -phase structural signatures 47 . To determine the crystallographic orientation of the t -phase, we performed a statistical analysis of the R values within the t -phase region based on the iDPC-STEM data presented in Fig. 5 a, as summarized in Supplementary Fig. 13. The dominant R values peak at 0.985 and 1.01, providing compelling evidence for the zone-axis alignment in the observed t -phase region 38 . We then established the projected Hf-Hf distance variation as a quantitative metric to track the structural phase evolution from the t -phase to the o -AFE phase (Supplementary Fig. 14). In the t -phase region, the Hf-Hf distances remain nearly constant, while in the o -AFE phase region, they exhibit periodic fluctuations between odd and even columns. This variation allowed us to identify three distinct phase regions during the structural evolution, corresponding to the t , transitional ( t t ), and o -AFE phases. As shown in Fig. 5 c, Row 8 predominantly exhibits t -phase characteristics, with only a localized right-side region developing the disparities of odd-even-column Hf-Hf distances indicative of the onset of the t t -phase. Row 22 captures a complete phase evolution sequence from the t -phase to the o -AFE phase, where the Hf-Hf distances progressively diverge in the t t -phase region before settling into characteristic values of ~ 319 pm (odd columns) and ~ 221 pm (even columns) in the o -AFE phase. In contrast, Row 38 presents a simple two-region distribution, where the o -AFE phase dominates with minimal t t -phase presence. Overall, Fig. 5 b summarizes the systematic variation in Hf-Hf distances across different Rows , clearly delineating the spatial distributions of the t , t t , and o -AFE phases. Building on these structural observations, we quantitatively analyzed strain evolution at the t / o -AFE MPBs. For this analysis, we first selected the coherent t / o interface configuration shown in Fig. 5 a,b to track strain variations through the complete t -to- o phase transition pathway. For strain calculations, we defined the reference state using the average Hf-Hf distance across the entire t -phase region. As shown in Fig. 5 b,d, we selected three different regions to systematically evaluate the local vertical strain variations throughout the t -to- o phase transition, corresponding to Rows 2–9, Rows 16–23, and Rows 34–41. To quantify strain evolution, we analyzed eight rows in each selected region, computing their average Hf-Hf distances relative to the reference t -phase state. During the phase transition process in Rows 2–9, the t -phase region exhibits minor vertical strain fluctuations (-0.7% to 0.3%) attributed to different grain orientations caused by the rapid quenching process. As the transformation progresses into the t t -phase region, a pronounced vertical tensile strain becomes evident. In Rows 16–23, the vertical strain remains near zero (-0.8% to 0.6%) in the t -phase region, then undergoes a substantial increase when transitioning to the t t -phase region. Upon complete transformation into the o -AFE phase, the vertical strain stabilizes at ~ 2%, as determined by averaging the strain values across the o -AFE phases in the selected eight Rows . A similar strain evolution is observed in Rows 34–41, where vertical strain increases from ~ 1.05% ( t t -phase) to ~ 2.3% ( o -AFE phase). Additionally, we selected the t -phase and o -AFE phase regions in Fig. 5 b to quantify the average vertical strain across the t -to- o phase transition, obtaining a value of 2.53%. The measured vertical strain shows excellent agreement with the theoretical prediction for Case -(1) in Fig. 3 j (2.36%). The complementary horizontal strain analysis of the iDPC-STEM data (Fig. 5 a,b) reveals distinct behavior. The observed average compressive strain of -0.83% occupies an intermediate position between the theoretical values for Case -(4) (-0.5%) and Case -(6) (-1.45%). This critical comparison of experimental and theoretical strain values provides compelling evidence for the non-uniform spatial distribution of t -phase grains along both and c -axis orientations, strongly supporting the proposed nanoscale disorder in t -phase grain arrangement 50 . Using the coherent interface featuring Case -(1) as a model system, we analyzed strain generation during the t -to- o phase transition. As illustrated in Fig. 5 e, the transition involves antiparallel displacement of Hf atoms within each row, contrasting with adjacent columns. Moreover, the Hf columns present periodic expansion and contraction of horizontal Hf-Hf distances along the c -axis of the t -phase. Simultaneously, the sublattice of O atoms reorganizes, exhibiting antiparallel displacements between neighboring rows. Specifically, O atoms in the spacer layers progressively overlap along the observation direction, while those in the polarization layers separate vertically, reflecting the structural differences between these two distinct atomic configurations. The atomic rearrangement during the t -to- o phase transition leads to distinct lattice configurations between the two phases. While the t -phase exhibits its maximum lattice parameter along the c -axis, the o -AFE phase maximizes along the b -axis instead. This structural reorganization generates substantial tensile strain along the direction of the original t -phase lattice. Additionally, as illustrated in Supplementary Fig. 11, we observed another t / o -AFE coherent interface viewed along the o -AFE c -axis direction. For the t -phase, this interfacial configuration generates tensile strain along its c -axis (1.56%) and compressive strain along its (-0.42%) direction, consistent with the strain states described for Case -(2) ( c t // b o −AFE ) and Case -(4) ( t // a o −AFE ) in Fig. 3 j. Regarding the c -axis observation direction of the o -AFE phase, another t / o coherent interface is also observed (Supplementary Fig. 12). The R -value comparative analysis highlights a distribution anisotropy of the t -phase, with a predominance of c -axis-aligned regions over those oriented along the direction. Building on the previously described phase identification methodology, the t / o phase boundary can be unambiguously resolved through atomic-scale analysis of Hf atom arrangements 34 . STEM imaging confirms the c -axis orientation of the t -phase in the right region, as evidenced by its R value centered near 1, while the left region aligns with the c -axis orientation of the o -AFE phase. The average strain calculation reveals a vertical tensile strain of 2.34% in the t -phase relative to the o -AFE region, closely matching the theoretical prediction for Case -(1) in Fig. 3 j. In contrast, the horizontal strain analysis yields an average compressive strain of -0.72%, located in the theoretical range between Case -(4) (-0.5%) and Case -(6) (-1.45%). Figure 6 a,b reveals a t / o -AFE coherent interface, with structural analysis confirming the b -axis alignment of the o -AFE phase through antiparallel polarization vector arrangements 34 . R -factor quantification (Supplementary Fig. 15) identifies the c -axis orientation in the t -phase region, while horizontal Hf-Hf bond length analysis deciphers the clear t -to- o transformation pathways. This interfacial configuration drives weak average compressive strain (-0.17%) in the t -phase along the vertical direction, aligning with the theoretical Case -(3) value (-0.2%) given in Fig. 3 j. Besides, as shown in Fig. 6 c,d, another t / o coherent interfacial configuration viewed along the o -AFE b -axis direction induces average compressive strains in the t -phase of approximately 0% (horizontal) and − 1.27% (vertical). The weak horizontal strain matches Case -(3) (-0.2%) in Fig. 3 j, while the stronger vertical strain lies between Case -(4) (-0.5%) and Case -(6) (-1.45%). This observation suggests a potential crystallographic match between the b -axis of the o -AFE phase and either the c -axis or direction of the t -phase. Enhancement mechanism of dielectric constant at t / o -AFE MPBs Systematic nanoscale strain mapping at the t / o MPBs in Lu-doped HZO bulk crystals reveals the strain-driven mechanisms governing t -to- o phase transitions. Through microscopic characterization, five distinct strain configurations ( Case -(1), Case -(2), Case -(3), Case -(4), and Case -(6)) have been identified. By correlating these configurations with strain distribution statistics, we propose detailed interfacial connectivity models (Supplementary Fig. 17 and Supplementary Table 3). Our analysis shows that variations in the coordinate matching relationships between the t and o -AFE phases lead to differential strain states in the t -phase. Notably, the maximum observed average tensile and compressive strains in the t -phase reach 2.53% and − 1.27%, respectively, demonstrating a pronounced dominance of tensile strain effects over compressive strain contributions. These structural insights provide a solid foundation for understanding how strain mediates dielectric response modulation within Lu-doped HZO bulk crystals. The static dielectric constant ( ε s ) mainly contains the electronic contribution ( ε ∞ ) and the ion contribution ( ε ion ). Although different HfO 2 -based polymorphs exhibit a similar ε ∞ value (~ 5), they show an evident discrepancy in ε ion originating from distinct infrared-active phonon vibrational modes 51 , 52 . The calculation of ε s can be expressed as, where e , M 0 , and V correspond to the electronic charge, a reference mass, and the lattice volume, respectively. ω TO represents the vibration frequency of infrared-active transverse optical (TO) phonons, and Z* denotes the relevant mode Born effective charge. Note that the ε ion contribution is positively proportional to the Z* / ω TO 2 , implying that the variation of ω TO can seriously affect the associated dielectric property. The vibrational modes of HfO 2 -based materials are inherently connected to the alteration of their crystal structures. Strain serves as an effective modulation strategy for controlling crystal phases in HfO 2 -based materials 53 , 54 , enabling precise modulation of lattice vibration frequencies across different phonon modes and potentially inducing phase transitions between polymorphs. In the t -phase HfO 2 , the three infrared-active TO vibrational modes consist of two distinct E u modes (~ 129 cm − 1 and ~ 460 cm − 1 ) and an A 2 u mode (~ 321 cm − 1 ) 38 . Notably, the low-frequency E u mode exhibits exceptional strain sensitivity compared to the other two vibrational modes, demonstrating a negative correlation with applied strain 42 . Experimental characterization at the t / o -AFE MPBs in Lu:HZO bulk crystals reveals substantially enhanced tensile lattice strain in the t -phase compared to compressive strain, establishing tensile strain dominance in the underlying mechanism. This experimental finding aligns with first-principles predictions for HfO 2 -based systems that tensile strain can give rise to the t - o phase transition 47 . The application of tensile strain induces pronounced softening of the low-frequency E u phonon mode (~ 129 cm − 1 ) in the t -phase, ultimately driving the martensitic phase transition from the t to o -AFE phases 55 , 56 . The comparable magnitudes of Z * among the three infrared-active TO vibrational modes suggest that the frequency blueshift of the t -phase E u phonon mode at ~ 129 cm − 1 will significantly enhance the ε ion 38 . This enhancement originates from the dominant contribution of the low-frequency E u mode to ε ion , which is typically two-fold greater than that of the A 2 u mode and five-fold larger than the high-frequency E u mode. These findings elucidate the dielectric enhancement mechanism at t / o MPBs in Lu:HZO bulk crystals, while underscoring the critical need for interface engineering in tailoring dielectric responses by selectively modulating specific phonon modes. Discussion The MPB engineering paradigm brings the transformative potential for HfO 2 -based dielectric systems, delivering exceptional performance enhancement beyond conventional single-phase configurations 5,26 . While current research on HfO 2 -based MPB systems predominantly targets t / o -FE coherent interfaces, insufficient study of the microstructural enhancement mechanism obscures fundamental structure-property correlations, leaving the intrinsic origin poorly understood. Furthermore, electric-field cycling or high-temperature operation often induces a phase transition between the t and o -FE phases, destabilizing the optimal phase composition and degrading dielectric properties 17,31 . In contrast, the t / o -AFE MPB configuration offers an alternative pathway for optimizing HfO 2 -based dielectric performance, owing to its higher energy barrier relative to the t -to- o -FE transition. This enhanced energy barrier promotes long-term functional stability by preserving phase content and phase interface during operation. A major challenge, however, lies in the thermodynamically driven coexistence of o -AFE and o -FE phases in HfO₂-based systems, resulting from their comparable free energies. This coexistence complicates both the establishment and characterization of exclusive t / o -AFE MPBs 33,34 . In this study, we address this challenge by employing an integrated composition-growth strategy in Lu:HZO bulk crystals. We achieved controlled fabrication of t / o -AFE MPBs via optimized dopant design and OFZ processing. Crucially, the synergistic application of a large temperature gradient and rapid quenching enables deterministic regulation of t-o phase evolution by kinetically trapping t / o phase interfaces. Comprehensive dielectric characterization confirms that the formed t / o -AFE MPBs within HfO₂-based bulk crystal exhibit a comparable κ -value to reported t / o -FE MPBs (Supplementary Table 2). The subsequent microstructural characterization deciphers that the t -phase near these t / o -AFE interfaces experiences pronounced tensile strain. The strain modifies the infrared-active phonon modes in the t -phase, influenced by the adjacent o -AFE phase, which directly governs the dielectric properties at t / o -AFE MPBs. Given the well-defined interplay relationship the tensile-strain-induced softening of the low-frequency E u phonon mode can drive a more substantial dielectric enhancement than that of A 2 u and high-frequency E u modes 42,46 . This study elucidates the fundamental dielectric enhancement mechanisms in t / o -AFE MPBs by establishing how strain states at coherent t / o interfaces directly govern the κ -value. Among the examined configurations, the Case -(1) strain configuration is more suitable for dielectric enhancement in contrast to other coherent interfaces due to its remarkable tensile strain (2.36%). Moreover, the larger energy barrier for the t -to- o transformation in t / o -AFE MPBs compared to t / o -FE MPBs underpins their superior dielectric thermal stability (Fig. 2e,f) 32 . This establishes the application potential of the t / o -AFE MPB design for the simultaneous optimization of both κ and dielectric thermal stability in HfO₂-based systems. These results validate the superior feasibility of t / o -AFE MPBs for optimizing HfO₂-based dielectrics and provide a blueprint for enhancing properties through precise control of interfacial strain states. Building on the insights gained from Lu-HZO bulk crystals, we can extend these principles to HfO₂-based films —a system widely studied for CMOS compatibility . While Zr⁴⁺ doping readily stabilizes the t -phase in such films 10 , the key challenge lies in promoting the formation of o -AFE domains at coherent t / o -AFE MPB interfaces. One promising strategy involves RE doping, which has already proven effective in modulating phase stability during the development of HfO₂-based ferroelectrics 32 . Furthermore, precise control over rapid thermal annealing kinetics can provide a viable pathway to mediate the t -to- o phase transition, enabling the tailored design of t / o -AFE MPB in thin-film systems. Collectively, this work lays the foundation for high-performance, miniaturized HfO₂-based devices essential for next-generation CMOS technologies. Furthermore, it introduces a bulk-crystal design framework for tailoring fluorite-structured materials, enabling the optimization of dielectric, piezoelectric, and ferroelectric functionalities, beyond just HfO₂-based systems, across diverse fields including data storage, energy harvesting, sensors, and photonic chips. Conclusion This study demonstrates a controlled preparation of t / o -AFE MPBs in Lu-doped HZO bulk crystals and elucidates the origin of their dielectric enhancement. The pronounced thermal gradients and rapid quenching rates inherent to the OFZ growth strategy enable precise control of t / o -AFE MPBs. Dielectric characterization reveals that samples rich in t / o -AFE MPBs exhibit superior performance compared to their single-phase or multiphase-mixed counterparts. Atomic-scale structural analysis identifies a predominant tensile strain over compressive strain within the t -phase localized near t/o phase boundaries. This tensile strain reduces the low-frequency infrared E u vibrational mode frequency, thereby enhancing the dielectric response. Moreover, t / o -AFE MPBs exhibit superior dielectric thermal stability than the extensively studied t / o -FE MPBs. The multimodal characterization approach developed herein elucidates the atomic-scale mechanisms responsible for the significant dielectric enhancement at t / o -AFE MPBs in HfO 2 -based systems. These findings establish a foundation for understanding structure-property relationships in fluorite-structured oxides, providing key insights for the rational design of high- κ components in next-generation CMOS-compatible electronics. 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 C.Wang and Q.Wang (Shandong University) for the dielectric survey and thank Z.Ye and J.Wu (University of Jinan) for the structural refinement. 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. Y.S., H.W., X.M., Y.L., F.L. and S.W. conducted the crystal growth and related characterizations, including XRD, Raman, EPMA, and dielectric measurement. 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.S., H.W. and S.W. wrote the original manuscript. 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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-7347248","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":504991335,"identity":"cfd09f6f-35d2-471a-aa96-27b7a3c84b20","order_by":0,"name":"Haohai 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\u003cem\u003et\u003c/em\u003e, \u003cem\u003eo\u003c/em\u003e-AFE and \u003cem\u003eo\u003c/em\u003e-FE phases. Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e/\u003c/sub\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e and Δ\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e/\u003c/sub\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e denote the energy barriers of the phase transitions from \u003cem\u003et\u003c/em\u003e to \u003cem\u003eo\u003c/em\u003e-AFE and \u003cem\u003eo\u003c/em\u003e-FE phases, respectively\u003csup\u003e6,35\u003c/sup\u003e. The cyan and orange vertical arrows represent the polarization directions.\u003cstrong\u003e b\u003c/strong\u003e, MPB schematic diagram between the \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e-AFE phases. The yellow region represents the connected interface. \u003cstrong\u003ec\u003c/strong\u003e, Designed growth strategy for stabilizing \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs to room temperature. The as-grown crystal (cyan shaded frame inside the figure) is moved along the growth direction. \u003cem\u003eT\u003c/em\u003e denotes temperature, and\u003cem\u003e T\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e corresponds to the Curie temperature. The blue curves represent the temperature distribution along the growth direction. The cyan region denotes the \u003cem\u003et\u003c/em\u003e-phase, while the gray spheres correspond to the formed \u003cem\u003eo\u003c/em\u003e-AFE phase. \u003cstrong\u003ed\u003c/strong\u003e, Photograph and room-temperature position-dependent Raman spectra of the as-grown Lu:HZO bulk crystals with different \u003cem\u003ed \u003c/em\u003evalues corresponding to the \u003cem\u003ed\u003c/em\u003e = 0 \u0026nbsp;mm, 5\u0026nbsp;mm, and \u003cem\u003ed\u003c/em\u003e = 10\u0026nbsp;mm, respectively. (\u003cem\u003ed\u003c/em\u003e represents the distance from the uppermost position of the as-grown crystal to the highest heating temperature point (Supplementary Fig. 1)). The theoretical Raman vibrational modes of the \u003cem\u003et\u003c/em\u003e,\u003cem\u003e o\u003c/em\u003e-AFE, and \u003cem\u003eo\u003c/em\u003e-FE\u003cem\u003e \u003c/em\u003ephases are from Ref.\u003csup\u003e38\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7347248/v1/a6fe531ee23c9b4b25071413.png"},{"id":92589604,"identity":"03746eff-6d50-4bd6-8190-68de108690d5","added_by":"auto","created_at":"2025-10-01 11:36:26","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":222040,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePhase evolution diagram within the HfO\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e-based bulk crystals and the corresponding structural, component, and dielectric properties.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, Phase evolution from the \u003cem\u003ec\u003c/em\u003e to \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e+\u003cem\u003eo\u003c/em\u003e(MPB) phases within Lu:HZO bulk crystals. \u003cstrong\u003eb\u003c/strong\u003e, Room-temperature XRPD data of the top (\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e) and bottom (\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eo+t\u003c/em\u003e\u003c/sub\u003e) part of \u003cem\u003eCrystal \u003c/em\u003e2. \u003cstrong\u003ec\u003c/strong\u003e, Room-temperature position-dependent (distance to the left side of the black dashed box) EPMA data of \u003cem\u003eCrystal \u003c/em\u003e2. \u003cstrong\u003ed\u003c/strong\u003e, Dielectric property comparison of HfO\u003csub\u003e2\u003c/sub\u003e-based bulk crystals with different polymorphs.\u003cem\u003e m\u003c/em\u003e-HfO\u003csub\u003e2\u003c/sub\u003e and \u003cem\u003em\u003c/em\u003e-HZO are polycrystalline samples, \u003cem\u003eo\u003c/em\u003e-AFE,\u003cem\u003e t\u003c/em\u003e+\u003cem\u003eo\u003c/em\u003e-AFE,\u003cem\u003e t\u003c/em\u003e-HZO, \u003cem\u003ec-\u003c/em\u003eHfO\u003csub\u003e2\u003c/sub\u003e, and \u003cem\u003ec-\u003c/em\u003eZrO\u003csub\u003e2\u003c/sub\u003e correspond to the Lu:HfO\u003csub\u003e2\u003c/sub\u003e (10\u0026nbsp;at.\u0026nbsp;%), \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e section of \u003cem\u003eCrystal\u003c/em\u003e 2, \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et+o\u003c/em\u003e\u003c/sub\u003e section of \u003cem\u003eCrystal\u003c/em\u003e 2, Lu:HfO\u003csub\u003e2\u003c/sub\u003e (16\u0026nbsp;at.\u0026nbsp;%), and Y:ZrO\u003csub\u003e2\u003c/sub\u003e (YSZ) bulk crystal samples, respectively. \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE represents the annealed \u003cem\u003et\u003c/em\u003e-phase part of \u003cem\u003eCrystal\u003c/em\u003e 2 (composed of \u003cem\u003et\u003c/em\u003e, \u003cem\u003eo\u003c/em\u003e-FE, and \u003cem\u003eo\u003c/em\u003e-AFE, where the \u003cem\u003eo\u003c/em\u003e-FE phase is the predominant \u003cem\u003eo\u003c/em\u003e phase). \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE denotes the phase boundary between the \u003cem\u003et\u003c/em\u003e and \u003cem\u003et\u003c/em\u003e+\u003cem\u003eo\u003c/em\u003e-AFE section within \u003cem\u003eCrystal\u003c/em\u003e 2. \u003cstrong\u003ee\u003c/strong\u003e,\u003cstrong\u003ef\u003c/strong\u003e,\u003cstrong\u003e \u003c/strong\u003eTemperature-dependent \u003cem\u003eκ\u003c/em\u003e-values of the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE samples measured at 100\u0026nbsp;kHz, respectively. The peak at the lower temperature range corresponds to \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE transition temperature, while the peak at the higher temperature range represents the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE phase transition. The inset is a partial enlarged detail.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7347248/v1/dccd6014e769f20f289f9122.png"},{"id":92589603,"identity":"7519b72f-670d-4ac1-8eaa-75d0ac1fd0c2","added_by":"auto","created_at":"2025-10-01 11:36:26","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":84547,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematic diagrams of \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e/\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-AFE MPB configurations and their associated strain distributions in the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-phase.\u003c/strong\u003e \u003cstrong\u003ea-c\u003c/strong\u003e, Coherent interfaces between the \u003cem\u003et\u003c/em\u003e-phase {001} plane and different \u003cem\u003eo\u003c/em\u003e-AFE phase planes (from \u003cem\u003eType\u003c/em\u003e Ⅰ to \u003cem\u003eType \u003c/em\u003eⅢ). \u003cstrong\u003ed-i\u003c/strong\u003e, Coherent interfaces between the \u003cem\u003et\u003c/em\u003e-phase {110} planes and different \u003cem\u003eo\u003c/em\u003e-AFE phase planes (from \u003cem\u003eType\u003c/em\u003e Ⅳ to \u003cem\u003eType \u003c/em\u003eⅨ). The red and gray arrows denote the tensile and compressive strains, respectively.\u003cstrong\u003e \u003c/strong\u003eFor instance, \u003cem\u003eType\u003c/em\u003e Ⅰ (\u0026lt;110\u0026gt;\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e // \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e) designates a coherent interface under horizontal observation, with the \u0026lt;110\u0026gt; direction of the \u003cem\u003et\u003c/em\u003e-phase parallel to the \u003cem\u003eb\u003c/em\u003e-axis of the \u003cem\u003eo\u003c/em\u003e-AFE phase. \u003cstrong\u003ej\u003c/strong\u003e, Horizontal (\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-H\u003c/sub\u003e) and vertical (\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-v\u003c/sub\u003e) strain variations of the \u003cem\u003et\u003c/em\u003e-phase across different MPB types. The cyan- and pink-shaded regions represent the strain states of the \u003cem\u003et\u003c/em\u003e-phase {001} and {110} planes, respectively. The red and gray symbols correspond to the tensile and compressive strains, respectively.\u003cstrong\u003e \u003c/strong\u003e\u003cem\u003eCase-\u003c/em\u003e(1) (\u0026lt;110\u0026gt;\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e // \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e), \u003cem\u003eCase-\u003c/em\u003e(2) (\u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e // \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e), \u003cem\u003eCase-\u003c/em\u003e(3) (\u0026lt;110\u0026gt;\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e // \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e), \u003cem\u003eCase-\u003c/em\u003e(4) (\u0026lt;110\u0026gt;\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e // \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e), \u003cem\u003eCase-\u003c/em\u003e(5) (\u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e // \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e), and \u003cem\u003eCase-\u003c/em\u003e(6) (\u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e // \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e) describe the different crystallographic correlations of the coherent interfaces between the \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e-AFE phases (Fig. 3a-i), and the strain magnitudes quantified in Fig. 3j. For instance, \u003cem\u003eCase\u003c/em\u003e-(1) can be found in \u003cem\u003eType\u003c/em\u003e Ⅰ,\u003cem\u003e Type\u003c/em\u003e Ⅲ, \u003cem\u003eType \u003c/em\u003eⅥ and \u003cem\u003eType \u003c/em\u003eⅦ.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7347248/v1/e6344e80b8b7a84df2eb1081.png"},{"id":92589606,"identity":"6c61bf4e-400b-49db-9a96-2b640c5f902a","added_by":"auto","created_at":"2025-10-01 11:36:26","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":331674,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStructural schematics and atomic-resolution iDPC-STEM images of the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e/\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e+\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-AFE phase boundary within \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eCrystal\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e 2.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e,\u003cstrong\u003eb\u003c/strong\u003e, Atomic arrangement along the \u003cem\u003eb\u003c/em\u003e- and \u003cem\u003ec\u003c/em\u003e-axis directions of the\u003cem\u003e o\u003c/em\u003e-AFE phase according to the standard card of ICSD No. 79913. The pink and light blue arrows in Fig. 4a represent the polarization direction. \u003cstrong\u003ec\u003c/strong\u003e,\u003cstrong\u003ed\u003c/strong\u003e, Atomic arrangement along the \u003cem\u003ec\u003c/em\u003e-axis and \u0026lt;110\u0026gt; directions of the\u003cem\u003e t\u003c/em\u003e-phase according to the standard card of ICSD No. 173966. \u003cstrong\u003ee\u003c/strong\u003e, Observed iDPC-STEM image along the \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e direction. The pink and light blue arrows represent two reversed \u003cem\u003ec\u003c/em\u003e-axis polarization states. \u003cstrong\u003ef\u003c/strong\u003e, Observed iDPC-STEM image along the \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e direction. The experimental data in (\u003cstrong\u003ee\u003c/strong\u003e) and (\u003cstrong\u003ef\u003c/strong\u003e) coincide with the \u003cem\u003eb\u003c/em\u003e-axis and \u003cem\u003ec\u003c/em\u003e-axis theoretical structural arrangements of the \u003cem\u003eo\u003c/em\u003e-AFE phase shown in (\u003cstrong\u003ea\u003c/strong\u003e) and (\u003cstrong\u003eb\u003c/strong\u003e), respectively. \u003cstrong\u003eg\u003c/strong\u003e, \u003cem\u003eR\u003c/em\u003e-value calculation rule of the \u003cem\u003et\u003c/em\u003e-phase. \u003cstrong\u003eh\u003c/strong\u003e, \u003cem\u003eR\u003c/em\u003e-value distribution corresponding to the observed iDPC-STEM image along the \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e direction (Supplementary Fig. 10a). \u003cstrong\u003ei\u003c/strong\u003e, \u003cem\u003eR\u003c/em\u003e-value distribution corresponding to the observed iDPC-STEM image along the \u0026lt;110\u0026gt;\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e direction (Supplementary Fig. 10c). All the scale bars correspond to 1 nm.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7347248/v1/bf13f43a2f92da81caf84e3c.png"},{"id":92590467,"identity":"3ddcdc66-e008-48f4-9ef5-247be493996d","added_by":"auto","created_at":"2025-10-01 11:44:26","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":499164,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eObserved coherent interfaces and strain analysis at the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e/\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e+\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-AFE phase boundary of\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003e Crystal\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e 2, with the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-AFE observed along the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-axis direction.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, iDPC-STEM image showing the \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e+\u003cem\u003eo\u003c/em\u003e-AFE interface with corresponding Hf-Hf distance distribution.\u003cstrong\u003e b\u003c/strong\u003e, Phase segmentation of the iDPC-STEM image in Fig. 5a based on Hf-Hf distance variations. The orange-, cyan-, and purple-shaded regions represent the \u003cem\u003et\u003c/em\u003e, \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e,\u003cem\u003e \u003c/em\u003eand \u003cem\u003eo\u003c/em\u003e-AFE phases, respectively.\u003cstrong\u003e c\u003c/strong\u003e, Hf-Hf distance evolution across \u003cem\u003eRows\u003c/em\u003e 4, 21, and 34 during phase transition. The circle and square symbols denote the odd and even columns, respectively.\u003cstrong\u003e d\u003c/strong\u003e, Strain analysis of the \u003cem\u003et\u003c/em\u003e-phase for \u003cem\u003eRows \u003c/em\u003e2-9, 16-23, and 34-41 during the phase evolution process. Data points represent averaged Hf-Hf distances of eight rows. \u003cstrong\u003ee\u003c/strong\u003e, Proposed phase evolution pathway from \u003cem\u003et\u003c/em\u003e to \u003cem\u003eo\u003c/em\u003e-AFE, illustrating the coherent interface, as described in \u003cem\u003eCase\u003c/em\u003e-(1) (\u0026lt;110\u0026gt;\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e // \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e-AFE\u003c/sub\u003e)\u003cem\u003e \u003c/em\u003ein Fig. 3j.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7347248/v1/428bf7620a4f73f49578769b.png"},{"id":92589605,"identity":"5037c400-714e-4444-9db3-6117ab0ebaba","added_by":"auto","created_at":"2025-10-01 11:36:26","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":285758,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTwo types of observed coherent interfaces and strain analysis at the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003et\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e/\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003et+o\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-AFE phase boundary of\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003e Crystal\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e2, with the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-AFEobserved along the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eb\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-axis direction.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, iDPC-STEM image of the \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e+\u003cem\u003eo\u003c/em\u003e-AFE interface revealing a distinct Hf-Hf distance distribution, with the \u003cem\u003et\u003c/em\u003e-phase observed along the \u003cem\u003ec\u003c/em\u003e-axis direction (Supplementary Fig. 15). \u003cstrong\u003eb\u003c/strong\u003e, Structural schematic diagram of the strain relationship on the \u003cem\u003et\u003c/em\u003e-phase induced by the \u003cem\u003eo\u003c/em\u003e-AFE phase, as described \u003cem\u003eCase\u003c/em\u003e-(3)\u003cem\u003e \u003c/em\u003ein Fig. 3j.\u003cstrong\u003ec\u003c/strong\u003e, iDPC-STEM image of the \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e+\u003cem\u003eo\u003c/em\u003e-AFE interface revealing a distinct Hf-Hf distance distribution, with the \u003cem\u003et\u003c/em\u003e-phase observed along the \u0026lt;110\u0026gt; direction (Supplementary Fig. 16). \u003cstrong\u003ed\u003c/strong\u003e, Structural schematic diagram of the strain relationship on the \u003cem\u003et\u003c/em\u003e-phase induced by the \u003cem\u003eo\u003c/em\u003e-AFE phase, as described \u003cem\u003eCase\u003c/em\u003e-(6)\u003cem\u003e \u003c/em\u003ein Fig. 3j.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7347248/v1/bf8470215821bc8904823b9e.png"},{"id":102977732,"identity":"7e70102f-ad0a-4f2b-bf96-b15b816ba92a","added_by":"auto","created_at":"2026-02-19 08:11:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3173132,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7347248/v1/900b872a-0aae-4d00-8404-523b1781e586.pdf"},{"id":92589608,"identity":"bd25b519-c8af-46a3-829a-2e5ad1908711","added_by":"auto","created_at":"2025-10-01 11:36:27","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":29790027,"visible":true,"origin":"","legend":"Supplementary","description":"","filename":"Supplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-7347248/v1/2dbaac35ba005a087dc033c2.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"\u003cp\u003eBeyond morphotropic phase boundaries: Atomic-scale mechanism unlocks thermal-stable high-κ performance in HfO\u003csub\u003e2\u003c/sub\u003e via coherent interfaces\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAs the demand for reducing equivalent oxide thickness continues to grow in the ongoing miniaturization of microelectronic devices, such as dynamic random-access memory (DRAM) and field-effect transistors (FET), modern downscaling efforts increasingly rely on the transformative utilization of gate materials that combine a high dielectric constant (\u003cem\u003eκ\u003c/em\u003e), wide bandgap, and excellent compatibility with silicon-based integrated circuit technology\u003csup\u003e1-6\u003c/sup\u003e. Over the past decades, HfO\u003csub\u003e2\u003c/sub\u003e-based fluorite-structure materials have demonstrated remarkable compatibility with mature complementary metal-oxide-semiconductor (CMOS) technology and superior dielectric performance in contrast to traditional SiO\u003csub\u003e2\u003c/sub\u003e-based dielectrics. Among HfO\u003csub\u003e2\u003c/sub\u003e polymorphs, including\u0026nbsp;\u003cem\u003eFm\u003c/em\u003e-3\u003cem\u003em\u003c/em\u003e (\u003cem\u003ec\u003c/em\u003e),\u0026nbsp;\u003cem\u003eP\u003c/em\u003e4\u003csub\u003e2\u003c/sub\u003e/\u003cem\u003enmc\u003c/em\u003e (\u003cem\u003et\u003c/em\u003e), ferroelectric\u0026nbsp;\u003cem\u003ePbc\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e (\u003cem\u003eo\u003c/em\u003e-FE),\u0026nbsp;antiferroelectric\u0026nbsp;\u003cem\u003ePbca\u003c/em\u003e (\u003cem\u003eo\u003c/em\u003e-AFE), and\u0026nbsp;monoclinic\u0026nbsp;\u003cem\u003eP\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e/\u003cem\u003ec\u003c/em\u003e (\u003cem\u003em\u003c/em\u003e) phases\u003csup\u003e7,8\u003c/sup\u003e, the \u003cem\u003et\u003c/em\u003e-phase is widely regarded as the primary high-\u003cem\u003eκ\u003c/em\u003e candidate due to its high theoretical \u003cem\u003eκ\u003c/em\u003e (~70), which far exceeds those of other polymorphs with \u003cem\u003eκ\u003c/em\u003e-values typically below 40\u003csup\u003e9\u003c/sup\u003e. However, the experimentally achievable \u003cem\u003eκ\u003c/em\u003e in \u003cem\u003et\u003c/em\u003e-phase HfO\u003csub\u003e2\u003c/sub\u003e-based materials rarely exceeds ~40, even\u0026nbsp;with optimized manufacturing processes and compositional engineering\u003csup\u003e10\u003c/sup\u003e, falling short of the stringent demands for next-generation high-density/high-speed electronic and memory devices in the post-Moore’s Law era\u003csup\u003e1,11\u003c/sup\u003e. Beyond high \u003cem\u003eκ\u003c/em\u003e, robust dielectric thermal stability has become equally critical for ensuring the operational reliability of these CMOS-integrated systems\u003csup\u003e12\u003c/sup\u003e, necessitating innovative approaches to\u0026nbsp;simultaneously enhance both \u003cem\u003eκ\u003c/em\u003e and dielectric thermal stability in HfO₂-based materials.\u003c/p\u003e\n\u003cp\u003eConstructing coherent phase interfaces represents an established strategy for tailoring material properties in metals and ceramics\u003csup\u003e13-16\u003c/sup\u003e. For HfO₂-based materials, engineering morphotropic phase boundaries (MPBs) between the \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e (\u003cem\u003eo\u003c/em\u003e-FE or \u003cem\u003eo\u003c/em\u003e-AFE) phases has emerged as an effective strategy for enhancing dielectric properties\u003csup\u003e17\u003c/sup\u003e. However, despite their promising dielectric improvements,\u0026nbsp;the lack of microstructural characterization obscures the origin of this enhancement, leading to an inconsistent \u003cem\u003eκ\u003c/em\u003e variation range (38–68)\u003csup\u003e18-30\u003c/sup\u003e.\u0026nbsp;Furthermore, the inherently low energy barrier (~46.0 meV per f.u.) between the \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e-FE phases readily facilitates a phase transition under thermal or electric field stimuli, severely compromising dielectric stability and degrading device endurance\u003csup\u003e17,31,32\u003c/sup\u003e. In contrast, the energy barrier for the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e-AFE transition is\u0026nbsp;significantly higher (~68.8 meV per f.u.), approximately 1.5 times that of the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE interface (Fig. 1a)\u003csup\u003e32\u003c/sup\u003e, suggesting \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs could deliver superior dielectric stability. Current \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e MPB research in HfO\u003csub\u003e2\u003c/sub\u003e-based dielectrics focuses primarily on\u0026nbsp;thin films,\u0026nbsp;where the intermediate free energy of the \u003cem\u003eo\u003c/em\u003e-FE phase between the \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e-AFE phases often leads to mixed \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases (Fig. 1b)\u003csup\u003e33,34\u003c/sup\u003e. Critically, this higher energy barrier for the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e-AFE transition, as opposed to the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e-FE transition, makes \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPB formation more challenging than \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE MPBs, leaving the interplay between \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPB configurations and their dielectric properties\u0026nbsp;poorly understood. This\u0026nbsp;gap highlights the need for\u0026nbsp;systematic exploration\u0026nbsp;into \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs to unlock their full potential.\u003c/p\u003e\n\u003cp\u003eRecent advances in HfO₂-based bulk crystals, prepared via the optical floating zone (OFZ) technique, have demonstrated successful stabilization of both \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e (\u003cem\u003eo\u003c/em\u003e-AFE or \u003cem\u003eo\u003c/em\u003e-FE) phases\u003csup\u003e32,35\u003c/sup\u003e.\u0026nbsp;Significantly, precise control over \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition pathways can be realized by strategic composition engineering combined with controlled temperature gradient distribution\u003csup\u003e35\u003c/sup\u003e,\u0026nbsp;providing a feasible avenue for stabilizing HfO₂-based \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs. In this study, inspired by the metallurgical quenching principles, we successfully grow HfO\u003csub\u003e2\u003c/sub\u003e-based (Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e, Lu:HZO) bulk crystals featuring a well-defined \u003cem\u003et-o\u003c/em\u003e phase boundary. Our structural analyses reveal that the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase boundary primarily represents the interface between the non-polar \u003cem\u003et\u003c/em\u003e and antiferroelectric \u003cem\u003eo\u003c/em\u003e-AFE phases. Subsequent dielectric characterization reveals that our\u0026nbsp;\u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs\u0026nbsp;achieve a comparable\u0026nbsp;\u003cem\u003eκ\u003c/em\u003e-value (57)\u0026nbsp;to\u0026nbsp;actively studied\u003cem\u003e\u0026nbsp;t\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE MPBs.\u0026nbsp;Through detailed microstructural observations and strain analyses, we identify the mechanism behind the dielectric enhancement near the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE\u0026nbsp;MPBs, which is primarily attributed to the frequency shift in the infrared-active low-frequency\u003cem\u003e\u0026nbsp;E\u003csub\u003eu\u003c/sub\u003e\u003c/em\u003e phonon mode\u0026nbsp;of the \u003cem\u003et\u003c/em\u003e-phase\u0026nbsp;driven by local structural modifications at the phase boundary.\u0026nbsp;Moreover,\u0026nbsp;\u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs\u0026nbsp;exhibit significantly enhanced thermal stability, demonstrating less than half the \u003cem\u003eκ\u003c/em\u003e variation rate observed in the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE MPBs across the temperature range from 30 to 200°C.\u0026nbsp;Our findings establish a clear structure-property relationship in HfO₂-based \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs, and provide a versatile design framework for fluorite-structured functional devices with applications in CMOS-integrated data storage, energy harvesting, sensing, and photonic technologies\u003csup\u003e36,37\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e\n \u003ch2\u003eDesign strategy and growth of Lu:HZO bulk crystals\u003c/h2\u003e\n \u003cp\u003eAs illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec, our approach for achieving \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs in HfO₂-based bulk crystals involves three sequential steps, corresponding to the formation of the \u003cem\u003et\u003c/em\u003e-phase (Step 1), controlled \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition (Step 2), and preserving \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs to room temperature (Step 3). The \u003cem\u003et\u003c/em\u003e-phase is metastable at room temperature due to its higher formation energy relative to orthorhombic phases (\u003cem\u003eo\u003c/em\u003e-AFE or \u003cem\u003eo\u003c/em\u003e-FE). Its critical nucleation dimension typically falls within a few nanometers, rendering its stabilization challenging even in thin films or nanoparticles\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. To address this challenge, in Step 1, we employed the OFZ growth method for preserving high-temperature metastable phases down to room temperature via ultrahigh heating temperatures (up to 3000\u0026deg;C), steep thermal gradients, and controllable growth rates\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. Codoping with rare-earth (RE) and Zr⁴⁺ ions offers a direct solution to stabilize \u003cem\u003et\u003c/em\u003e-phase HfO₂-based bulk crystals at room temperature by effectively suppressing \u003cem\u003em\u003c/em\u003e-phase interference and modulating the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition temperature\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. Here we used the Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e (HZO) doped with Lu (Lu:HZO)\u0026mdash;a composition optimized for \u003cem\u003et\u003c/em\u003e-phase stability\u0026mdash;to systematically explore dopant concentrations\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n \u003cp\u003eRegarding Step 2, controlled temperature-driven \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition enables the formation of \u003cem\u003eo\u003c/em\u003e phases (\u003cem\u003eo\u003c/em\u003e-AFE or \u003cem\u003eo\u003c/em\u003e-FE) from the high-temperature metastable \u003cem\u003et\u003c/em\u003e-phase\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. The steep temperature gradient and fast growth rate intrinsic to the OFZ growth strategy offer a feasible control over the \u003cem\u003et\u003c/em\u003e-phase conversion, benefiting the formation of well-defined \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e phase boundaries within Lu:HZO bulk crystals. As the as-grown crystal traverses its Curie temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e) during cooling, the \u003cem\u003eo\u003c/em\u003e-phase precipitation initiates\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. The cooling pathway from the high-temperature supplies sufficient transformation energy to overcome the activation barriers for both \u003cem\u003et\u003c/em\u003e\u0026rarr;\u003cem\u003eo\u003c/em\u003e-AFE and \u003cem\u003et\u003c/em\u003e\u0026rarr;\u003cem\u003eo\u003c/em\u003e-FE conversions. The \u003cem\u003eo\u003c/em\u003e-AFE phase possesses a lower formation energy than the \u003cem\u003eo\u003c/em\u003e-FE phase, thus favoring its preferential nucleation during the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e conversion\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Consequently, combining with the pure \u003cem\u003et\u003c/em\u003e-phase region, \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs will form at the \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE phase interface within Lu:HZO bulk crystals.\u003c/p\u003e\n \u003cp\u003eStep 3 aims to stabilize the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs in Lu:HZO bulk crystals to room temperature utilizing a non-equilibrium processing strategy. Post-growth rapid quenching (cooling within ~\u0026thinsp;2s) quickly removes the as-grown crystal from the high-temperature regime, effectively suppressing further \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition. This non-equilibrium process preserves the formed \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs to room temperature by minimizing high-temperature exposure. Leveraging this OFZ strategy, we grew a series of Lu:HZO bulk crystals. To identify the optimal dopant concentration, three distinct Lu doping levels were chosen: 9.25 at.%, 9.75 at.%, and 10 at.%, all exhibit crack-free, high crystallinity (Supplementary Fig.\u0026nbsp;2), validating the efficacy and feasibility of the OFZ growth strategy for scalable production.\u003c/p\u003e\n \u003cp\u003eThe different bond vibrational properties among HfO\u003csub\u003e2\u003c/sub\u003e polymorphic phases serve as effective markers for phase identification within Lu:HZO bulk crystals. Specifically, the \u003cem\u003et\u003c/em\u003e-phase exhibits robust A\u003csub\u003e1\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e and B\u003csub\u003e1\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e Raman modes around 270 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, while the \u003cem\u003eo\u003c/em\u003e phases manifest strong bond vibrations in the vicinity of 370 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, including the A\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e mode for \u003cem\u003eo\u003c/em\u003e-AFE and A\u003csub\u003e1\u003c/sub\u003e mode for \u003cem\u003eo\u003c/em\u003e-FE\u003csup\u003e38\u003c/sup\u003e. We employed Raman spectroscopy to analyze the phase distribution along the crystal growth direction. The Lu:HZO (9.25 at.%) crystal simultaneously presents the \u003cem\u003et\u003c/em\u003e- and \u003cem\u003eo\u003c/em\u003e-phase phonon vibrational modes, suggesting that the Lu doping level is insufficient to achieve the pure \u003cem\u003et\u003c/em\u003e-phase. With a rise of Lu doping concentration to 9.75 at.%, apart from the mixture region of \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e phases, the pure \u003cem\u003et\u003c/em\u003e-phase is observed in the top region, yielding an unequivocal \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e phase interface within the as-grown bulk crystal. As the Lu doping level is further raised to 10 at.%, the pure \u003cem\u003et\u003c/em\u003e-phase existing range is expanded by reducing the \u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e phase region, underscoring the critical role of composition optimization in manipulating the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e MPB interface within Lu:HZO bulk crystals.\u003c/p\u003e\n \u003cp\u003eFocusing on the optimized Lu:HZO (10 at.%) phase component, we further refined the OFZ growth parameters to verify the controllability of the \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e phase boundary formation. Three different movement distances (\u003cem\u003ed\u003c/em\u003e) after the growth process, before quenching, were tested, corresponding to 0 mm (\u003cem\u003eCrystal\u003c/em\u003e 1), 5 mm (\u003cem\u003eCrystal\u003c/em\u003e 2), and 10 mm (\u003cem\u003eCrystal\u003c/em\u003e 3), with results shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed. With increasing the \u003cem\u003ed\u003c/em\u003e value, the \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e phase boundary moves towards the top of the as-grown crystal, accompanied by a shrinking \u003cem\u003et\u003c/em\u003e-phase region and an expanding \u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e mixed phase region. The observed \u003cem\u003eo\u003c/em\u003e-phase Raman signature at 370 cm⁻\u0026sup1; closely matches the characteristic vibrational mode of the \u003cem\u003eo\u003c/em\u003e-AFE phase, providing compelling support for the structurally stabilized \u003cem\u003eo\u003c/em\u003e-AFE phase formation. This aligns with expectations since the \u003cem\u003eo\u003c/em\u003e-AFE phase has a lower formation energy than the \u003cem\u003eo\u003c/em\u003e-FE phase\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Upon enlarging the \u003cem\u003ed\u003c/em\u003e value to 10 mm, the \u003cem\u003et\u003c/em\u003e-phase region completely disappears, leaving only the \u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e mixed phase region in the as-fabricated bulk crystal. These findings highlight the versatility of the OFZ growth method in precisely tuning phase distribution within the bulk crystal, even without altering the raw material component.\u003c/p\u003e\n \u003cp\u003eAs exhibited in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea, multiple polymorphs can coexist in fabricating HfO\u003csub\u003e2\u003c/sub\u003e-based materials. With regard to HfO\u003csub\u003e2\u003c/sub\u003e-based thin films, the frequent presence of the \u003cem\u003em\u003c/em\u003e phase complicates the phase component and hampers the relevant MPB analysis\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. In contrast, for bulk-crystal growth, combining ion adjustment and growth control effectively disentangles the \u003cem\u003em\u003c/em\u003e-phase interference and allows straightforward adjustment of the \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE interface\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e, facilitating deeper insight into how the phase boundary influences dielectric property. The Lu:HZO bulk crystals experience a series of phase transitions during the crystal growth process. The crystallization from the melt will form the \u003cem\u003ec\u003c/em\u003e phase first. Then, following the downward movement across the transition temperature (above 2500\u003csup\u003eo\u003c/sup\u003eC)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, the \u003cem\u003ec\u003c/em\u003e phase rapidly transforms into the \u003cem\u003et\u003c/em\u003e-phase by expanding its (220) interplanar spacing and contraction of its (004) interplanar spacing (Supplementary Fig. 3). Subsequently, the steep temperature gradient along the growth direction further brings a partial \u003cem\u003et\u003c/em\u003e-phase section into the \u003cem\u003eo\u003c/em\u003e-AFE phase once the location temperature falls below the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e transition threshold. The rapid quenching process following growth benefits the stabilization of different phase distributions within the bulk crystal, providing an opportunity to obtain a well-defined \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE interface and permitting exploration of its MPB influence.\u003c/p\u003e\n \u003cp\u003eTo further analyze the phase difference between the pure \u003cem\u003et\u003c/em\u003e and mixed \u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE regions with as-grown Lu:HZO crystals, we took \u003cem\u003eCrystal\u003c/em\u003e 2 as a representative case and collected XRPD data from the \u003cem\u003et\u003c/em\u003e-phase (\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e) and \u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE (\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et+o\u003c/em\u003e\u003c/sub\u003e) regions. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb, the XRPD pattern from \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e region matches well with the standard \u003cem\u003et\u003c/em\u003e-phase reference, showing no evidence of \u003cem\u003eo\u003c/em\u003e-phase diffraction peaks. By comparison, the \u003cem\u003eo\u003c/em\u003e-phase diffraction peaks around 53\u003csup\u003eo\u003c/sup\u003e and 56\u003csup\u003eo\u003c/sup\u003e are observed in \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et+o\u003c/em\u003e\u003c/sub\u003e region. This result coincides with the above-mentioned Raman analysis that \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e-AFE phases coexist in the \u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE region. On that basis, we surveyed the element distribution of \u003cem\u003eCrystal\u003c/em\u003e 2 using electron probe microanalysis (EPMA) from the \u003cem\u003et\u003c/em\u003e-phase to \u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE regions. As exhibited in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec, the selected zone with different phases demonstrates uniform element distribution, indicating that the phase variation mainly stems from the modulation role of the OFZ growth strategy rather than compositional gradients. The detailed structural difference between \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et+o\u003c/em\u003e\u003c/sub\u003e was analyzed by performing Rietveld refinement characterization (Supplementary Figs. 3 and 4). As shown in Supplementary Table 1, the \u003cem\u003et\u003c/em\u003e-phase \u003cem\u003ec\u003c/em\u003e/(2\u003csup\u003e0.5\u003c/sup\u003e\u003cem\u003ea\u003c/em\u003e) of \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e is determined to be 1.010, a value smaller than that of the theoretically standard \u003cem\u003et\u003c/em\u003e-phase (1.028) but larger than that within \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et+o\u003c/em\u003e\u003c/sub\u003e (1.007)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. This phenomenon reveals that the as-obtained \u003cem\u003et\u003c/em\u003e-phase in Lu:HZO bulk crystals shows a weak structural anisotropy in contrast to the ideal \u003cem\u003et\u003c/em\u003e-phase, with position located at a lower-temperature region prior to quenching, displaying further reduced lattice distortion.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eDielectric characterization and\u003c/strong\u003e \u003cstrong\u003et\u003c/strong\u003e\u003cstrong\u003e/\u003c/strong\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003cstrong\u003e-AFE MPBs in Lu:HZO bulk crystals\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eIn the subsequent context, we conducted the frequency-dependent dielectric characterization of as-grown Lu:HZO crystals and compared the dielectric properties across various phase components, involving \u003cem\u003em\u003c/em\u003e, \u003cem\u003eo\u003c/em\u003e, \u003cem\u003et\u003c/em\u003e, \u003cem\u003ec\u003c/em\u003e, and different MPB-engineered configurations (Supplementary Figs.\u0026nbsp;5 and 6). All bulk crystalline samples exhibit low dielectric loss (\u0026lt;\u0026thinsp;0.02), comparable to those reported in thin films\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. Nevertheless, their \u003cem\u003e\u0026kappa;\u003c/em\u003e-values show notable variation. As elucidated in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ed, m-phase HfO\u003csub\u003e2\u003c/sub\u003e (~\u0026thinsp;14) and HZO (~\u0026thinsp;15) show low \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e values in contrast to other polymorphs, being in good agreement with the theoretical calculations\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. The \u003cem\u003eo\u003c/em\u003e-AFE sample exhibits an \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e value of 33, which is slightly higher than those of \u003cem\u003ec\u003c/em\u003e-HfO\u003csub\u003e2\u003c/sub\u003e (~\u0026thinsp;28) and \u003cem\u003ec\u003c/em\u003e-ZrO\u003csub\u003e2\u003c/sub\u003e (~\u0026thinsp;29)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. By contrast, the \u003cem\u003et\u003c/em\u003e-phase sample exhibits a clear dielectric advantage with a value on the order of 40, aligning well with the experimental results achieved in HfO\u003csub\u003e2\u003c/sub\u003e-based films\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Next, we compared the dielectric performances of three different MPB configurations, corresponding to \u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE, \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE, and \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE interfaces. The \u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE and \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE samples present a slight reduction in \u003cem\u003e\u0026kappa;\u003c/em\u003e compared to the pure \u003cem\u003et\u003c/em\u003e-phase, indicating that the simple phase mixing within the MPB structure does not inherently enhance the dielectric property. It is worth noting that the sample around the \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE interface demonstrates an \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e value of 57, comparable to those of the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE MPB films (Supplementary Fig. 7, Supplementary Table 2), representing a 43% increase over the pure \u003cem\u003et\u003c/em\u003e-phase sample. Additionally, the temperature-dependent dielectric measurements (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee,f and Supplementary Fig. 8) reveal a significantly higher \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e (~\u0026thinsp;670 \u003csup\u003eo\u003c/sup\u003eC) in the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs compared to their \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE counterparts (~\u0026thinsp;425\u003csup\u003eo\u003c/sup\u003eC). This marked increase is attributed to the larger energy barrier for the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition inherent in the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Consequently, when heated from room temperature to 200\u0026deg;C, the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs exhibit minimal variation in \u003cem\u003e\u0026kappa;\u003c/em\u003e\u003cstrong\u003e\u0026mdash;\u003c/strong\u003eonly 7%, compared to the 17% change observed in \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE MPBs\u003cstrong\u003e\u0026mdash;\u003c/strong\u003edirectly reflecting their superior dielectric thermal stability. This finding highlights the universality of the MPB role in modulating the dielectric properties of HfO\u003csub\u003e2\u003c/sub\u003e-based materials, ranging from thin films to bulk crystals. The manipulation of MPB distribution of HfO\u003csub\u003e2\u003c/sub\u003e-based materials remains challenging owing to various influencing variables, such as ion doping, interface engineering, and post-processing\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Thus, an in-depth understanding of the interplay between the crystal structure of MPB and dielectric response becomes crucial. The robust \u003cem\u003e\u0026kappa;\u003c/em\u003e observed at the \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE interface in the Lu:HZO crystal provides a valuable paradigm to clarify the MPB effects, benefiting from the absence of \u003cem\u003em\u003c/em\u003e-phase interference and the larger grain size in contrast to film counterparts\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n \u003cp\u003eThe enhanced dielectric properties observed at the \u003cem\u003et\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eo\u003c/em\u003e-AFE phase boundary in Lu:HZO bulk crystals are intricately linked to the microstructural characteristics of the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE phase boundaries. This underscores the critical role of analyzing the coherent interfaces at the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs and their associated strain distribution to elucidate the underlying enhancement mechanisms. As summarized in Supplementary Table 1, the refined lattice parameters of the \u003cem\u003eo\u003c/em\u003e-AFE phase (\u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;10.1365 \u0026Aring;, \u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.2135 \u0026Aring;, and \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.0833 \u0026Aring;) exhibit apparent differences compared to those of the \u003cem\u003et\u003c/em\u003e-phase (\u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.6015 \u0026Aring;, and \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.1431 \u0026Aring;), indicating the presence of strain near the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e MPB caused by the martensitic transformation characteristic in the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e transition\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e. To assess the potential strain effect on the \u003cem\u003et\u003c/em\u003e-phase induced by the adjacent \u003cem\u003eo\u003c/em\u003e-AFE phase near the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e MPB, we theoretically modeled the strain variations across various coherent interfaces between the \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e-AFE phases. Combined with the reported \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e transformation routes, the possible coherent interfaces at the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e MPB were identified and are presented in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea-i, focusing on the {001} and {110} planes of the \u003cem\u003et\u003c/em\u003e-phase. Among the investigated strain configurations on the \u003cem\u003et\u003c/em\u003e-phase, \u003cem\u003eCase\u003c/em\u003e-(1) and \u003cem\u003eCase\u003c/em\u003e-(2) induce tensile strain, whereas the other four cases result in compressive strain. \u003cem\u003eTypes\u003c/em\u003e Ⅰ, Ⅲ, Ⅶ, and Ⅷ coherent interfaces exhibit the maximum tensile strain, reaching 2.36% (\u003cem\u003eCase\u003c/em\u003e-(1)). In contrast, the largest compressive strain is observed in \u003cem\u003eTypes\u003c/em\u003e Ⅶ and Ⅷ coherent interfaces, with a value of -1.45% (\u003cem\u003eCase\u003c/em\u003e-(6)). \u003cem\u003eType\u003c/em\u003e Ⅶ demonstrates the most pronounced horizontal and vertical in-plane strain difference at the coherent interface (\u003cem\u003eCase\u003c/em\u003e-(1) and \u003cem\u003eCase\u003c/em\u003e-(6)), while \u003cem\u003eType\u003c/em\u003e Ⅱ displays the minimal in-plane strain disparity (\u003cem\u003eCase\u003c/em\u003e-(3) and \u003cem\u003eCase\u003c/em\u003e-(4)).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003eMicrostructural survey and local strain analysis in Lu:HZO bulk crystals\u003c/h2\u003e\n \u003cp\u003eAccurate identification of MPB configurations and their associated local strain fields in Lu:HZO bulk crystals necessitates atomic-scale structural characterization, particularly focusing on the interfacial strain mechanism by precise mapping of anion or cation distributions near the phase boundaries. To investigate these atomic-scale structural characteristics, we utilized integrated differential phase contrast scanning transmission electron microscopy (iDPC-STEM). This advanced technique was selected for its exceptional ability to simultaneously resolve both light (e.g., oxygen) and heavy (e.g., Hf/Zr/Lu) elements with high contrast (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea and Supplementary Fig. 9, the \u003cem\u003eb\u003c/em\u003e-axis serves as the optimal observation direction for identifying the \u003cem\u003eo\u003c/em\u003e-phase, as it clearly reveals the characteristic oxygen displacement patterns within polarization layers\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. Specifically, the \u003cem\u003eo\u003c/em\u003e-AFE and \u003cem\u003eo\u003c/em\u003e-FE phases can be distinguished by their antiparallel and parallel polarization vector alignments, respectively. In \u003cem\u003eCrystal\u003c/em\u003e 2 (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ee), the \u003cem\u003eo\u003c/em\u003e phase exhibits \u003cem\u003eo\u003c/em\u003e-AFE behavior, with antiparallel polarization along the \u003cem\u003ec\u003c/em\u003e-axis, in full agreement with the prior structural and optical characterization results. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb and Supplementary Fig. 9, the atomic arrangements along the \u003cem\u003ec\u003c/em\u003e-axis exhibit no major structural differences between \u003cem\u003eo\u003c/em\u003e-FE and \u003cem\u003eo\u003c/em\u003e-AFE phases. Key identifiers of the \u003cem\u003eo\u003c/em\u003e-phase include periodic variations in vertical Hf-Hf projected distances and horizontal displacements of O atoms, facilitating the \u003cem\u003eo\u003c/em\u003e-phase identification within the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e MPB regions. Our observation reveals a trapezoidal arrangement of Hf atoms (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ef), which shows excellent agreement with the predicted \u003cem\u003ec\u003c/em\u003e-axis atomic distribution of the \u003cem\u003eo\u003c/em\u003e phase. Given the predominance of the \u003cem\u003et\u003c/em\u003e-phase at the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e MPBs, we aligned the imaging orientation with the \u003cem\u003et\u003c/em\u003e-phase crystal structure. As exhibited in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec,d, observations along the \u003cem\u003ec\u003c/em\u003e-axis or \u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;directions of the \u003cem\u003et\u003c/em\u003e-phase are vital for defining subsequent \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e phase coherent interfaces. The atomic arrangements of the \u003cem\u003et\u003c/em\u003e-phase appear similar along both observation directions, making them difficult to distinguish in STEM characterization. To quantitatively characterize the \u003cem\u003et\u003c/em\u003e-phase observation direction, we introduced the \u003cem\u003eR\u003c/em\u003e-value, defined as (\u003cem\u003eh\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eh\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e)/(\u003cem\u003ev\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003ev\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e), which directly reflects tetragonality in the Hf atomic sublattice, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eg. Theoretically, \u003cem\u003eR\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1 represents the \u003cem\u003ec\u003c/em\u003e-axis orientation, while \u003cem\u003eR\u003c/em\u003e\u0026thinsp;\u0026ne;\u0026thinsp;1 signifies the \u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;orientation due to the anisotropic lattice parameter (\u003cem\u003ec\u003c/em\u003e \u0026ne; \u0026radic;2\u003cem\u003ea\u003c/em\u003e) in the \u003cem\u003et\u003c/em\u003e-phase structure\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. \u003cem\u003eR\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;1 and \u003cem\u003eR\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;1 reflect the \u003cem\u003ec\u003c/em\u003e-axis alignment of the associated \u003cem\u003et\u003c/em\u003e-phase crystalline grains along the horizontal and vertical directions, respectively. To verify the \u003cem\u003et\u003c/em\u003e-phase observation direction, we analyzed the observed \u003cem\u003et\u003c/em\u003e-phase \u003cem\u003eR\u003c/em\u003e-value distribution corresponding to the original image (Supplementary Fig. 10a,c). In Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eh and Supplementary Fig. 10a,b, the \u003cem\u003eR\u003c/em\u003e-value peaks at 1 with a range of 0.96\u0026ndash;1.05, confirming observation along the \u003cem\u003ec\u003c/em\u003e-axis direction of the \u003cem\u003et\u003c/em\u003e-phase. Conversely, statistical analysis in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ei and Supplementary Fig. 10c,d reveals \u003cem\u003eR\u003c/em\u003e values spanning from 0.95 to 1.045, with dominant peaks at 1.005 and 0.985, strongly indicating the \u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;observation direction of the \u003cem\u003et-\u003c/em\u003ephase.\u003c/p\u003e\n \u003cp\u003eAfter confirming the coexistence of crystalline phases within \u003cem\u003eCrystal\u003c/em\u003e 2, we systematically investigated the local structural evolution at the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e MPBs. Our analysis focused on MPBs aligned with either the \u003cem\u003eb\u003c/em\u003e- or \u003cem\u003ec\u003c/em\u003e-axis of the \u003cem\u003eo\u003c/em\u003e-AFE phase, corresponding to the \u003cem\u003ec\u003c/em\u003e-axis or \u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;direction of the \u003cem\u003et\u003c/em\u003e-phase, respectively. The \u003cem\u003ea\u003c/em\u003e-axis orientation of the \u003cem\u003eo\u003c/em\u003e-AFE phase was excluded due to the dense arrangement of O atoms, which obscures a clear structural interpretation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. As demonstrated in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea,b, Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ea,c, and Supplementary Figs. 11 and 12, several different coherent interfaces between the \u003cem\u003et\u003c/em\u003e-phase and \u003cem\u003eo\u003c/em\u003e-AFE phases were observed, suggesting the different \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e transformation pathways. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea, we systematically analyzed the local structural characteristics of a representative \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e coherent interface within the Lu:HZO bulk crystal. The upper-right region displays characteristic \u003cem\u003ec\u003c/em\u003e-axis-oriented \u003cem\u003eo\u003c/em\u003e-phase features, whereas the lower-left region exhibits distinct \u003cem\u003et\u003c/em\u003e-phase structural signatures\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. To determine the crystallographic orientation of the \u003cem\u003et\u003c/em\u003e-phase, we performed a statistical analysis of the \u003cem\u003eR\u003c/em\u003e values within the \u003cem\u003et\u003c/em\u003e-phase region based on the iDPC-STEM data presented in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea, as summarized in Supplementary Fig. 13. The dominant \u003cem\u003eR\u003c/em\u003e values peak at 0.985 and 1.01, providing compelling evidence for the \u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;zone-axis alignment in the observed \u003cem\u003et\u003c/em\u003e-phase region\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. We then established the projected Hf-Hf distance variation as a quantitative metric to track the structural phase evolution from the \u003cem\u003et\u003c/em\u003e-phase to the \u003cem\u003eo\u003c/em\u003e-AFE phase (Supplementary Fig. 14). In the \u003cem\u003et\u003c/em\u003e-phase region, the Hf-Hf distances remain nearly constant, while in the \u003cem\u003eo\u003c/em\u003e-AFE phase region, they exhibit periodic fluctuations between odd and even columns. This variation allowed us to identify three distinct phase regions during the structural evolution, corresponding to the \u003cem\u003et\u003c/em\u003e, transitional (\u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e), and \u003cem\u003eo\u003c/em\u003e-AFE phases. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec, \u003cem\u003eRow\u003c/em\u003e 8 predominantly exhibits \u003cem\u003et\u003c/em\u003e-phase characteristics, with only a localized right-side region developing the disparities of odd-even-column Hf-Hf distances indicative of the onset of the \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e-phase. \u003cem\u003eRow\u003c/em\u003e 22 captures a complete phase evolution sequence from the \u003cem\u003et\u003c/em\u003e-phase to the \u003cem\u003eo\u003c/em\u003e-AFE phase, where the Hf-Hf distances progressively diverge in the \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e-phase region before settling into characteristic values of ~\u0026thinsp;319 pm (odd columns) and ~\u0026thinsp;221 pm (even columns) in the \u003cem\u003eo\u003c/em\u003e-AFE phase. In contrast, \u003cem\u003eRow\u003c/em\u003e 38 presents a simple two-region distribution, where the \u003cem\u003eo\u003c/em\u003e-AFE phase dominates with minimal \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e-phase presence. Overall, Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb summarizes the systematic variation in Hf-Hf distances across different \u003cem\u003eRows\u003c/em\u003e, clearly delineating the spatial distributions of the \u003cem\u003et\u003c/em\u003e, \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eo\u003c/em\u003e-AFE phases.\u003c/p\u003e\n \u003cp\u003eBuilding on these structural observations, we quantitatively analyzed strain evolution at the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs. For this analysis, we first selected the coherent \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e interface configuration shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea,b to track strain variations through the complete \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition pathway. For strain calculations, we defined the reference state using the average Hf-Hf distance across the entire \u003cem\u003et\u003c/em\u003e-phase region. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb,d, we selected three different regions to systematically evaluate the local vertical strain variations throughout the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition, corresponding to \u003cem\u003eRows\u003c/em\u003e 2\u0026ndash;9, \u003cem\u003eRows\u003c/em\u003e 16\u0026ndash;23, and \u003cem\u003eRows\u003c/em\u003e 34\u0026ndash;41. To quantify strain evolution, we analyzed eight rows in each selected region, computing their average Hf-Hf distances relative to the reference \u003cem\u003et\u003c/em\u003e-phase state. During the phase transition process in \u003cem\u003eRows\u003c/em\u003e 2\u0026ndash;9, the \u003cem\u003et\u003c/em\u003e-phase region exhibits minor vertical strain fluctuations (-0.7% to 0.3%) attributed to different grain orientations caused by the rapid quenching process. As the transformation progresses into the \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e-phase region, a pronounced vertical tensile strain becomes evident. In \u003cem\u003eRows\u003c/em\u003e 16\u0026ndash;23, the vertical strain remains near zero (-0.8% to 0.6%) in the \u003cem\u003et\u003c/em\u003e-phase region, then undergoes a substantial increase when transitioning to the \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e-phase region. Upon complete transformation into the \u003cem\u003eo\u003c/em\u003e-AFE phase, the vertical strain stabilizes at ~\u0026thinsp;2%, as determined by averaging the strain values across the \u003cem\u003eo\u003c/em\u003e-AFE phases in the selected eight \u003cem\u003eRows\u003c/em\u003e. A similar strain evolution is observed in \u003cem\u003eRows\u003c/em\u003e 34\u0026ndash;41, where vertical strain increases from ~\u0026thinsp;1.05% (\u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e-phase) to ~\u0026thinsp;2.3% (\u003cem\u003eo\u003c/em\u003e-AFE phase). Additionally, we selected the \u003cem\u003et\u003c/em\u003e-phase and \u003cem\u003eo\u003c/em\u003e-AFE phase regions in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb to quantify the average vertical strain across the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition, obtaining a value of 2.53%. The measured vertical strain shows excellent agreement with the theoretical prediction for \u003cem\u003eCase\u003c/em\u003e-(1) in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ej (2.36%). The complementary horizontal strain analysis of the iDPC-STEM data (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea,b) reveals distinct behavior. The observed average compressive strain of -0.83% occupies an intermediate position between the theoretical values for \u003cem\u003eCase\u003c/em\u003e-(4) (-0.5%) and \u003cem\u003eCase\u003c/em\u003e-(6) (-1.45%). This critical comparison of experimental and theoretical strain values provides compelling evidence for the non-uniform spatial distribution of \u003cem\u003et\u003c/em\u003e-phase grains along both \u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;and \u003cem\u003ec\u003c/em\u003e-axis orientations, strongly supporting the proposed nanoscale disorder in \u003cem\u003et\u003c/em\u003e-phase grain arrangement\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n \u003cp\u003eUsing the coherent interface featuring \u003cem\u003eCase\u003c/em\u003e-(1) as a model system, we analyzed strain generation during the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition. As illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ee, the transition involves antiparallel displacement of Hf atoms within each row, contrasting with adjacent columns. Moreover, the Hf columns present periodic expansion and contraction of horizontal Hf-Hf distances along the \u003cem\u003ec\u003c/em\u003e-axis of the \u003cem\u003et\u003c/em\u003e-phase. Simultaneously, the sublattice of O atoms reorganizes, exhibiting antiparallel displacements between neighboring rows. Specifically, O atoms in the spacer layers progressively overlap along the observation direction, while those in the polarization layers separate vertically, reflecting the structural differences between these two distinct atomic configurations. The atomic rearrangement during the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition leads to distinct lattice configurations between the two phases. While the \u003cem\u003et\u003c/em\u003e-phase exhibits its maximum lattice parameter along the \u003cem\u003ec\u003c/em\u003e-axis, the \u003cem\u003eo\u003c/em\u003e-AFE phase maximizes along the \u003cem\u003eb\u003c/em\u003e-axis instead. This structural reorganization generates substantial tensile strain along the \u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;direction of the original \u003cem\u003et\u003c/em\u003e-phase lattice.\u003c/p\u003e\n \u003cp\u003eAdditionally, as illustrated in Supplementary Fig. 11, we observed another \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE coherent interface viewed along the \u003cem\u003eo\u003c/em\u003e-AFE \u003cem\u003ec\u003c/em\u003e-axis direction. For the \u003cem\u003et\u003c/em\u003e-phase, this interfacial configuration generates tensile strain along its \u003cem\u003ec\u003c/em\u003e-axis (1.56%) and compressive strain along its\u0026thinsp;\u0026lt;\u0026thinsp;110\u0026gt;(-0.42%) direction, consistent with the strain states described for \u003cem\u003eCase\u003c/em\u003e-(2) (\u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e // \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;AFE\u003c/sub\u003e ) and \u003cem\u003eCase\u003c/em\u003e-(4) (\u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e // \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u0026minus;AFE\u003c/sub\u003e ) in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ej. Regarding the \u003cem\u003ec\u003c/em\u003e-axis observation direction of the \u003cem\u003eo\u003c/em\u003e-AFE phase, another \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e coherent interface is also observed (Supplementary Fig. 12). The \u003cem\u003eR\u003c/em\u003e-value comparative analysis highlights a distribution anisotropy of the \u003cem\u003et\u003c/em\u003e-phase, with a predominance of \u003cem\u003ec\u003c/em\u003e-axis-aligned regions over those oriented along the \u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;direction. Building on the previously described phase identification methodology, the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e phase boundary can be unambiguously resolved through atomic-scale analysis of Hf atom arrangements\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. STEM imaging confirms the \u003cem\u003ec\u003c/em\u003e-axis orientation of the \u003cem\u003et\u003c/em\u003e-phase in the right region, as evidenced by its \u003cem\u003eR\u003c/em\u003e value centered near 1, while the left region aligns with the \u003cem\u003ec\u003c/em\u003e-axis orientation of the \u003cem\u003eo\u003c/em\u003e-AFE phase. The average strain calculation reveals a vertical tensile strain of 2.34% in the \u003cem\u003et\u003c/em\u003e-phase relative to the \u003cem\u003eo\u003c/em\u003e-AFE region, closely matching the theoretical prediction for \u003cem\u003eCase\u003c/em\u003e-(1) in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ej. In contrast, the horizontal strain analysis yields an average compressive strain of -0.72%, located in the theoretical range between \u003cem\u003eCase\u003c/em\u003e-(4) (-0.5%) and \u003cem\u003eCase\u003c/em\u003e-(6) (-1.45%).\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ea,b reveals a \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE coherent interface, with structural analysis confirming the \u003cem\u003eb\u003c/em\u003e-axis alignment of the \u003cem\u003eo\u003c/em\u003e-AFE phase through antiparallel polarization vector arrangements\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. \u003cem\u003eR\u003c/em\u003e-factor quantification (Supplementary Fig. 15) identifies the \u003cem\u003ec\u003c/em\u003e-axis orientation in the \u003cem\u003et\u003c/em\u003e-phase region, while horizontal Hf-Hf bond length analysis deciphers the clear \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e transformation pathways. This interfacial configuration drives weak average compressive strain (-0.17%) in the \u003cem\u003et\u003c/em\u003e-phase along the vertical direction, aligning with the theoretical \u003cem\u003eCase\u003c/em\u003e-(3) value (-0.2%) given in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ej. Besides, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ec,d, another \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e coherent interfacial configuration viewed along the \u003cem\u003eo\u003c/em\u003e-AFE \u003cem\u003eb\u003c/em\u003e-axis direction induces average compressive strains in the \u003cem\u003et\u003c/em\u003e-phase of approximately 0% (horizontal) and \u0026minus;\u0026thinsp;1.27% (vertical). The weak horizontal strain matches \u003cem\u003eCase\u003c/em\u003e-(3) (-0.2%) in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ej, while the stronger vertical strain lies between \u003cem\u003eCase\u003c/em\u003e-(4) (-0.5%) and \u003cem\u003eCase\u003c/em\u003e-(6) (-1.45%). This observation suggests a potential crystallographic match between the \u003cem\u003eb\u003c/em\u003e-axis of the \u003cem\u003eo\u003c/em\u003e-AFE phase and either the \u003cem\u003ec\u003c/em\u003e-axis or \u0026lt;\u0026thinsp;110\u0026thinsp;\u0026gt;\u0026thinsp;direction of the \u003cem\u003et\u003c/em\u003e-phase.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eEnhancement mechanism of dielectric constant at\u003c/strong\u003e \u003cstrong\u003et\u003c/strong\u003e\u003cstrong\u003e/\u003c/strong\u003e\u003cstrong\u003eo\u003c/strong\u003e\u003cstrong\u003e-AFE MPBs\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eSystematic nanoscale strain mapping at the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e MPBs in Lu-doped HZO bulk crystals reveals the strain-driven mechanisms governing \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transitions. Through microscopic characterization, five distinct strain configurations (\u003cem\u003eCase\u003c/em\u003e-(1), \u003cem\u003eCase\u003c/em\u003e-(2), \u003cem\u003eCase\u003c/em\u003e-(3), \u003cem\u003eCase\u003c/em\u003e-(4), and \u003cem\u003eCase\u003c/em\u003e-(6)) have been identified. By correlating these configurations with strain distribution statistics, we propose detailed interfacial connectivity models (Supplementary Fig.\u0026nbsp;17 and Supplementary Table\u0026nbsp;3). Our analysis shows that variations in the coordinate matching relationships between the \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e-AFE phases lead to differential strain states in the \u003cem\u003et\u003c/em\u003e-phase. Notably, the maximum observed average tensile and compressive strains in the \u003cem\u003et\u003c/em\u003e-phase reach 2.53% and \u0026minus;\u0026thinsp;1.27%, respectively, demonstrating a pronounced dominance of tensile strain effects over compressive strain contributions. These structural insights provide a solid foundation for understanding how strain mediates dielectric response modulation within Lu-doped HZO bulk crystals.\u003c/p\u003e\n \u003cp\u003eThe static dielectric constant (\u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e) mainly contains the electronic contribution (\u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e\u0026infin;\u003c/em\u003e\u003c/sub\u003e) and the ion contribution (\u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003eion\u003c/em\u003e\u003c/sub\u003e). Although different HfO\u003csub\u003e2\u003c/sub\u003e-based polymorphs exhibit a similar \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e\u0026infin;\u003c/em\u003e\u003c/sub\u003e value (~\u0026thinsp;5), they show an evident discrepancy in \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003eion\u003c/em\u003e\u003c/sub\u003e originating from distinct infrared-active phonon vibrational modes\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. The calculation of \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e can be expressed as,\u003c/p\u003e\n \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"EquationNumber\"\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere \u003cem\u003ee\u003c/em\u003e, \u003cem\u003eM\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e, and \u003cem\u003eV\u003c/em\u003e correspond to the electronic charge, a reference mass, and the lattice volume, respectively. \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003eTO\u003c/sub\u003e represents the vibration frequency of infrared-active transverse optical (TO) phonons, and \u003cem\u003eZ*\u003c/em\u003e denotes the relevant mode Born effective charge. Note that the \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003eion\u003c/em\u003e\u003c/sub\u003e contribution is positively proportional to the \u003cem\u003eZ*\u003c/em\u003e/\u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003eTO\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e, implying that the variation of \u003cem\u003e\u0026omega;\u003c/em\u003e\u003csub\u003eTO\u003c/sub\u003e can seriously affect the associated dielectric property. The vibrational modes of HfO\u003csub\u003e2\u003c/sub\u003e-based materials are inherently connected to the alteration of their crystal structures. Strain serves as an effective modulation strategy for controlling crystal phases in HfO\u003csub\u003e2\u003c/sub\u003e-based materials\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e53\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e, enabling precise modulation of lattice vibration frequencies across different phonon modes and potentially inducing phase transitions between polymorphs. In the \u003cem\u003et\u003c/em\u003e-phase HfO\u003csub\u003e2\u003c/sub\u003e, the three infrared-active TO vibrational modes consist of two distinct \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e modes (~\u0026thinsp;129 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and ~\u0026thinsp;460 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and an \u003cem\u003eA\u003c/em\u003e\u003csub\u003e2\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e mode (~\u0026thinsp;321 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003csup\u003e38\u003c/sup\u003e. Notably, the low-frequency \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e mode exhibits exceptional strain sensitivity compared to the other two vibrational modes, demonstrating a negative correlation with applied strain\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. Experimental characterization at the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs in Lu:HZO bulk crystals reveals substantially enhanced tensile lattice strain in the \u003cem\u003et\u003c/em\u003e-phase compared to compressive strain, establishing tensile strain dominance in the underlying mechanism. This experimental finding aligns with first-principles predictions for HfO\u003csub\u003e2\u003c/sub\u003e-based systems that tensile strain can give rise to the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase transition\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. The application of tensile strain induces pronounced softening of the low-frequency \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e phonon mode (~\u0026thinsp;129 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) in the \u003cem\u003et\u003c/em\u003e-phase, ultimately driving the martensitic phase transition from the \u003cem\u003et\u003c/em\u003e to \u003cem\u003eo\u003c/em\u003e-AFE phases\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e. The comparable magnitudes of \u003cem\u003eZ\u003c/em\u003e* among the three infrared-active TO vibrational modes suggest that the frequency blueshift of the \u003cem\u003et\u003c/em\u003e-phase \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e phonon mode at ~\u0026thinsp;129 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e will significantly enhance the \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003eion\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. This enhancement originates from the dominant contribution of the low-frequency \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e mode to \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003eion\u003c/em\u003e\u003c/sub\u003e, which is typically two-fold greater than that of the \u003cem\u003eA\u003c/em\u003e\u003csub\u003e2\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e mode and five-fold larger than the high-frequency \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e mode. These findings elucidate the dielectric enhancement mechanism at \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e MPBs in Lu:HZO bulk crystals, while underscoring the critical need for interface engineering in tailoring dielectric responses by selectively modulating specific phonon modes.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe MPB engineering paradigm brings the transformative potential for HfO\u003csub\u003e2\u003c/sub\u003e-based dielectric systems, delivering exceptional performance enhancement beyond conventional single-phase configurations\u003csup\u003e5,26\u003c/sup\u003e. While current research on HfO\u003csub\u003e2\u003c/sub\u003e-based MPB systems predominantly targets \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE coherent interfaces, insufficient study of the microstructural enhancement mechanism obscures fundamental structure-property correlations, leaving the intrinsic origin poorly understood. Furthermore, electric-field cycling or high-temperature operation often induces a phase transition between the \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo\u003c/em\u003e-FE phases, destabilizing the optimal phase composition and degrading dielectric properties\u003csup\u003e17,31\u003c/sup\u003e. In contrast, the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPB configuration offers an alternative pathway for optimizing HfO\u003csub\u003e2\u003c/sub\u003e-based dielectric performance, owing to its higher energy barrier relative to the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e-FE transition.\u0026nbsp;This enhanced energy barrier promotes long-term functional stability by preserving phase content and phase interface during operation.\u0026nbsp;A major challenge, however, lies in the thermodynamically driven coexistence of \u003cem\u003eo\u003c/em\u003e-AFE and \u003cem\u003eo\u003c/em\u003e-FE phases in HfO₂-based systems, resulting from their comparable free energies. This coexistence complicates both the establishment and characterization of exclusive \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs\u003csup\u003e33,34\u003c/sup\u003e.\u0026nbsp;In this study, we address this challenge by employing an integrated composition-growth strategy in Lu:HZO bulk crystals. We achieved controlled fabrication of \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs via optimized dopant design and OFZ processing. Crucially, the synergistic application of a large temperature gradient and rapid quenching enables deterministic regulation of \u003cem\u003et-o\u003c/em\u003e phase evolution by kinetically trapping \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e phase interfaces. Comprehensive dielectric characterization confirms that the formed \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs within\u0026nbsp;HfO₂-based bulk crystal\u0026nbsp;exhibit a comparable \u003cem\u003e\u0026kappa;\u003c/em\u003e-value to reported \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE MPBs (Supplementary Table 2). The subsequent microstructural characterization\u0026nbsp;deciphers that the \u003cem\u003et\u003c/em\u003e-phase near these\u003cem\u003e\u0026nbsp;t\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE interfaces experiences pronounced tensile strain.\u0026nbsp;The strain modifies the infrared-active phonon modes in the \u003cem\u003et\u003c/em\u003e-phase,\u0026nbsp;influenced by the adjacent \u003cem\u003eo\u003c/em\u003e-AFE phase, which directly governs the dielectric properties at \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs. Given the well-defined interplay relationship\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003c/p\u003e\n\u003cp\u003ethe tensile-strain-induced softening of the low-frequency\u003cem\u003e\u0026nbsp;E\u003csub\u003eu\u003c/sub\u003e\u003c/em\u003e phonon mode can drive a more substantial dielectric enhancement than that of \u003cem\u003eA\u003c/em\u003e\u003csub\u003e2\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e and high-frequency \u003cem\u003eE\u003csub\u003eu\u003c/sub\u003e\u003c/em\u003e modes\u003csup\u003e42,46\u003c/sup\u003e. This study elucidates the fundamental dielectric enhancement mechanisms in \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs by establishing how strain states at coherent \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e interfaces directly govern the \u003cem\u003e\u0026kappa;\u003c/em\u003e-value. Among the examined configurations, the \u003cem\u003eCase\u003c/em\u003e-(1) strain configuration is more suitable for dielectric enhancement in contrast to other coherent interfaces due to its remarkable tensile strain (2.36%). Moreover, the larger energy barrier for the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e transformation in \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs compared to \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE MPBs underpins their superior dielectric thermal stability (Fig. 2e,f)\u003csup\u003e32\u003c/sup\u003e. This establishes the application potential of the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPB design for the simultaneous optimization of both \u003cem\u003e\u0026kappa;\u003c/em\u003e and dielectric thermal stability in HfO₂-based systems. These results validate the superior feasibility of \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs for optimizing HfO₂-based dielectrics and provide a blueprint for enhancing properties through precise control of interfacial strain states. Building on the insights gained from Lu-HZO bulk crystals, we can extend these principles to HfO₂-based films\u003cstrong\u003e\u0026mdash;a system widely studied for CMOS compatibility\u003c/strong\u003e.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eWhile Zr⁴⁺ doping readily stabilizes the \u003cem\u003et\u003c/em\u003e-phase in such films\u003csup\u003e10\u003c/sup\u003e, the key challenge lies in promoting the formation of \u003cem\u003eo\u003c/em\u003e-AFE domains at coherent \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPB interfaces. One promising strategy involves RE doping, which has already proven effective in modulating phase stability during the development of HfO₂-based ferroelectrics\u003csup\u003e32\u003c/sup\u003e. Furthermore, precise control over rapid thermal annealing kinetics can provide a viable pathway to mediate the \u003cem\u003et\u003c/em\u003e-to-\u003cem\u003eo\u003c/em\u003e phase transition, enabling the tailored design of \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPB in thin-film systems. Collectively, this work lays the foundation for high-performance, miniaturized HfO₂-based devices essential for next-generation CMOS technologies. Furthermore, it introduces a bulk-crystal design framework for tailoring fluorite-structured materials, enabling the optimization of dielectric, piezoelectric, and ferroelectric functionalities, beyond just HfO₂-based systems, across diverse fields including data storage, energy harvesting, sensors, and photonic chips.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study demonstrates a controlled preparation of \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs in Lu-doped HZO bulk crystals and elucidates the origin of their dielectric enhancement. The pronounced thermal gradients and rapid quenching rates inherent to the OFZ growth strategy enable precise control of \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs. Dielectric characterization reveals that samples rich in \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs exhibit superior performance compared to their single-phase or multiphase-mixed counterparts. Atomic-scale structural analysis identifies a predominant tensile strain over compressive strain within the \u003cem\u003et\u003c/em\u003e-phase localized near \u003cem\u003et/o\u003c/em\u003e phase boundaries. This tensile strain reduces the low-frequency infrared \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e vibrational mode frequency, thereby enhancing the dielectric response. Moreover, \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs exhibit superior dielectric thermal stability than the extensively studied \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE MPBs. The multimodal characterization approach developed herein elucidates the atomic-scale mechanisms responsible for the significant dielectric enhancement at \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs in HfO\u003csub\u003e2\u003c/sub\u003e-based systems. These findings establish a foundation for understanding structure-property relationships in fluorite-structured oxides, providing key insights for the rational design of high-\u003cem\u003eκ\u003c/em\u003e components in next-generation CMOS-compatible electronics.\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\u003c/p\u003e\n\u003cp\u003eWe thank C.Wang and Q.Wang (Shandong University) for the\u0026nbsp;dielectric survey and thank Z.Ye and J.Wu (University of Jinan) for the structural refinement. 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.).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eS.W., H.Y., S.Z. and H.Z. conceived the research idea of this study. Y.S., H.W., X.M., Y.L., F.L. and S.W. conducted the crystal growth and related characterizations, including XRD, Raman, EPMA, and dielectric measurement. 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.S., H.W. and S.W. wrote the original manuscript. H.Y., S.Z. and H.Z. revised the manuscript. All authors contributed to the discussion of the experimental results.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSalahuddin S, Ni K, Datta S (2018) The era of hyper-scaling in electronics. 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Nature 634:1080\u0026ndash;1085\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"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-7347248/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7347248/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCMOS-compatible HfO\u003csub\u003e2\u003c/sub\u003e-based high-\u003cem\u003eκ\u003c/em\u003e dielectrics are pivotal for next-generation electronics in the post-Moore’s Law era. However, establishing coherent interfaces via morphotropic phase boundaries (MPBs) across the tetragonal (\u003cem\u003et\u003c/em\u003e) and orthorhombic (ferroelectric, \u003cem\u003eo\u003c/em\u003e-FE or antiferroelectric, \u003cem\u003eo\u003c/em\u003e-AFE) phases—a key strategy for enhancing dielectric properties—remains challenging due to unclear atomic-scale mechanisms and inherent thermal instability, which compromises long-term stability and reliability. To address this, we leverage metallurgical quenching principles to stabilize \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs in HfO\u003csub\u003e2\u003c/sub\u003e-based (Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e) bulk crystals. Through precise composition tuning and growth optimization, we stabilize these metastable\u003cem\u003e t\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPBs at the\u003cem\u003e t\u003c/em\u003e/\u003cem\u003et\u003c/em\u003e+\u003cem\u003eo\u003c/em\u003e-AFE interface at room temperature, achieving a comparable \u003cem\u003eκ\u003c/em\u003e-value (57) to actively studied \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE MPBs. Microstructural characterization reveals how tensile strain within the \u003cem\u003et\u003c/em\u003e-phase drives dielectric enhancement through softening of the low-frequency \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eu\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e \u003c/sub\u003ephonon mode. Critically, the \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-AFE MPB demonstrates a ~58% reduction in \u003cem\u003eκ\u003c/em\u003e variation rate over 30–200°C relative to \u003cem\u003et\u003c/em\u003e/\u003cem\u003eo\u003c/em\u003e-FE MPBs, signifying superior thermal stability. Our study establishes a generalizable design paradigm for developing high-\u003cem\u003eκ\u003c/em\u003e dielectrics in fluorite-structured materials, advancing next-generation CMOS-integrated functional devices for data storage, energy harvesting, sensing, and integrated photonics.\u003c/p\u003e","manuscriptTitle":"Beyond morphotropic phase boundaries: Atomic-scale mechanism unlocks thermal-stable high-κ performance in HfO2 via coherent interfaces","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-01 11:36:22","doi":"10.21203/rs.3.rs-7347248/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":"October 1st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":55628087,"name":"Physical sciences/Materials science/Condensed-matter physics/Structure of solids and liquids"},{"id":55628088,"name":"Physical sciences/Materials science/Condensed-matter physics/Phase transitions and critical phenomena"}],"tags":[],"updatedAt":"2026-02-19T08:11:44+00:00","versionOfRecord":{"articleIdentity":"rs-7347248","link":"https://doi.org/10.1038/s41467-026-68496-z","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2026-01-16 05:00:00","publishedOnDateReadable":"January 16th, 2026"},"versionCreatedAt":"2025-10-01 11:36:22","video":"","vorDoi":"10.1038/s41467-026-68496-z","vorDoiUrl":"https://doi.org/10.1038/s41467-026-68496-z","workflowStages":[]},"version":"v1","identity":"rs-7347248","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7347248","identity":"rs-7347248","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}