Robust ferroelectricity in HfO2-based bulk crystals via polymorphic engineering

Robust ferroelectricity in HfO2-based bulk crystals via polymorphic engineering | 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 Physical Sciences - Article Robust ferroelectricity in HfO 2 -based bulk crystals via polymorphic engineering Haohai Yu, Shuxian Wang, Yihao Shen, Xiaoyu Yang, Pengfei Nan, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3803321/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The discovery of ferroelectricity in hafnium dioxide (HfO2) thin films over the past decade has revolutionized the landscape of ferroelectrics. HfO2-based ferroelectrics exhibit extraordinary switching capabilities and integrability in existing semiconductor chips, making them a promising candidate for next-generation ferroelectrics beyond the constraints of Moore’s law. However, the underlying mechanism of their ferroelectricity remains a topic of debate, possibly related to the presence of a metastable and volatile ferroelectric phase. Herein, we have achieved the successful growth of HfO2-based bulk crystals, revealing a remarkable remanent polarization of 26 μC/cm2 by a comprehensive understanding of the polymorphic engineering strategy. This result not only rivals the performances observed in extensively studied ultra-thin films but also underscores the universal feature of HfO2-based ferroelectricity. Our investigation has unveiled the intricate local structural transitions during the development of the ferroelectric phase in bulk crystals, clearly elucidating that the ferroelectric orthorhombic Pbc21 phase originates from the metastable tetragonal phase. This groundbreaking discovery clarifies the ferroelectric origin of HfO2 and provides a strategic approach for designing robust ferroelectricity. Our findings hold the potential to advance the comprehension of ferroelectric mechanisms in fluorite-structured materials, paving the way for significant strides in the subsequent development of HfO2-based nonvolatile electronic and photonic devices. Physical sciences/Materials science/Materials for devices/Electronic devices Physical sciences/Materials science/Materials for devices/Information storage Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction With scientific and technological advances, ferroelectric materials exhibiting excellent compatibility with the complementary metal-oxide semiconductor (CMOS) process have become the foundation of optoelectronic functional devices capable of integration and miniaturization 1–3 . Over the years, there has been a mounting interest in HfO 2 -based fluorite-structure ferroelectric materials. Of particular interest is that their switchable ferroelectric polarization capabilities endure, even when the film thickness is reduced to the atomic realm, typically ranging from 0.5 to 1 nm 4,5 . Consequently, HfO 2 -based ferroelectric materials have emerged as a class of promising candidates for the development of highly compact microelectronic devices, encompassing nonvolatile information memory and field-effect transistors, ushering in a new era beyond Moore’s law 6–8 . Regarding HfO 2 and its analog ZrO 2 , the temperature-dependent polymorphs manifest as cubic ( c , Fm -3 m ), tetragonal ( t , P 4 2 / nmc ), and monoclinic ( m , P 2 1 / c ) phases, while the pressure-induced polymorphs include orthorhombic-I ( o- AFE, Pbca ) and orthorhombic-II ( Pnma ) 9,10 . It is worth noting that none of these space groups can sustain any ferroelectric polarization due to their centrosymmetric (non-polar) nature. The intrinsic ferroelectric origin of HfO 2 -based materials has remained a mystery ever since its first discovery in an Si:HfO 2 thin film 11 . Several polar ferroelectric space groups have been proposed based on extensive theoretical and experimental studies, including the orthorhombic ( Pbc 2 1 and Pmn 2 1 ) and rhombohedral ( R 3 m ) phases 12–14 . Early research into HfO 2 -based ferroelectrics was largely confined to thin films, typically around 10 nm in thickness, because the captivating ferroelectricity rapidly degrades with increasing thickness. Numerous theoretical models have been proposed to explore the formation mechanism of the HfO 2 -based ferroelectric phase 15–17 . In the case of thin films, the primary stabilizing factor for ferroelectric phases is often attributed to the phase transformation originating from the metastable t phase. For colloidal HfO 2 nanocrystals, the m phase at the twinning boundary can evolve into the polarization phase, even in the absence of symmetry breaking 18 , 19 . Additionally, flat polar phonon bands are considered to be a contributing factor to ferroelectric switching in HfO 2 16 , while a moderate electrical stimulus can induce a transformation from the antipolar o -AFE phase to the polar o -FE phase 20 . Recently, Pbc 2 1 ( o- FE) ferroelectric polarization was also discovered in Y:HfO 2 bulk crystals, providing a fresh research perspective for understanding the ferroelectric origin in HfO 2 21 . Unfortunately, the resultant remanent polarization ( P r ) in Y:HfO 2 bulk ferroelectric crystals reaches only ~3 μC/cm 2 , approximately one order of magnitude lower than those of ultra-thin films (20–50 μC/cm 2 ) 22 – 24 . The proposed Curie phase transition in Y:HfO 2 bulk crystals ( o- FE → c ) differs from that observed in thin films ( o- FE → t ) 22 . The controversy surrounding the origin of ferroelectricity in HfO 2 -based materials is ascribed to the fact that their switchable spontaneous polarization mainly arises from the movement of oxygen ions rather than cation displacement within perovskite systems 6 . To gain a comprehensive understanding of the ferroelectric origin in HfO 2 -based materials, it is imperative to clarify the motion trajectories of oxygen atoms. However, the challenge lies in the small atomic number of oxygen, which complicates the atomic-scale characterization 24 ,25 . In this study, we report compelling evidence of robust ferroelectricity in HfO 2 -based (Lu:Hf 1− x Zr x O 2 ) bulk crystals. Our investigation highlights the pivotal roles played by Lu 3+ and Zr 4+ ions in the adjustment of polymorphic phases. Notably, we achieved an optimal P r value of up to 26 μC/cm 2 in these bulk crystals, a value comparable to those of HfO 2 -based epitaxial ferroelectric films. To gain insights into the structural aspects, we conducted a temperature-dependent X-ray diffraction (XRD) analysis and an integrated differential phase-contrast scanning transmission electron microscopy (iDPC-STEM) investigation. Through these analyses, we successfully identified the polymorphic phases present in Lu:Hf 1− x Zr x O 2 bulk crystals, including the o- FE, o- AFE, and t phases. Building upon this foundation, we further revealed the t - o phase evolution process, facilitated by the direct observation of the movement trajectory of Hf and O atoms near the phase boundary. These findings provide a clear understanding of the formation mechanism behind the o- FE polar phase and pave the way for the development of bulk-state fluorite-structure ferroelectric crystals. Crystal growth and structural characterization of Lu:Hf 1− x Zr x O 2 bulk crystals Leveraging rare-earth-doped HfO 2 (RE:HfO 2 ) has emerged as a feasible strategy to stabilize the relevant metastable polymorphs, such as c , t , o- FE, and o- AFE. To prevent the formation of the m phase within the RE:HfO 2 bulk crystals, it is important to meticulously consider the eutectoid reaction (occurring at ~1780°C, t → c + m ), especially when dealing with nearly pure HfO 2 (Supplementary Fig. 1) 25 . As shown in Supplementary Figs. 2–4, the XRD data for both the as-grown Gd:HfO 2 and Lu:HfO 2 crystals highlighted the importance of adhering to this selection rule. The phase evolution of RE:HfO 2 can be controlled by managing the oxygen vacancies that arise from the heterovalent substitution of rare-earth ions. Previous studies on RE:HfO 2 have indicated that the optimal stabilization range of the o- FE phase typically falls below 10 at.% of rare earth (RE) doping 26,27 . Among the various RE-doping scenarios, Lu:HfO 2 crystals possess a distinct advantage at lower concentrations (Supplementary Table 1) and thus were selected for an investigation into related polymorphic transformations. As shown in Supplementary Fig. 3, the obtained XRD data for Lu:HfO 2 crystals (10–11 at.%) suggested the existence of orthorhombic phases. Subsequent Raman spectroscopy revealed that the primary phase in the as-grown Lu:HfO 2 crystals was the o- AFE phase rather than the o- FE phase (Supplementary Fig. 6) 24 . In addition to the incorporation of RE 3+ ions, the introduction of Zr 4+ ions stands out as a feasible phase control method in high-temperature Hf 1− x Zr x O 2 metastable polymorphs. The ferroelectric phase can be maintained within a specific range of Zr doping, typically falling between 35 and 50 at.% 28–30 . Thus, we grew Lu:Hf 1− x Zr x O 2 crystals by concurrently optimizing the Lu or Zr doping concentrations. To begin, we held the Lu doping concentration constant at 9 at.% while adjusting the Zr doping concentration at 5 at.% increments. As shown in Supplementary Figs. 9 and 10, high-quality Lu:Hf 1− x Zr x O 2 crystals were successfully grown. The subsequent structural investigation confirmed the existence of orthorhombic phases ( o- AFE or o- FE). Furthermore, as shown in Supplementary Fig. 11, we observed the vibrational modes of the t phase within the Lu:Hf 1− x Zr x O 2 crystals, in addition to the distinct scattering response of the o- AFE phase. In general, the orthorhombic o- AFE phase or o- FE phases emerge as a result of the temperature-driven phase transition from the high-temperature t or c phase. According to their respective formation energies, these polymorphs rank in the descending order of c , t , o- FE, and o- AFE, with the o- AFE phase being the most energetically favorable 22,24 . The Raman vibrations shown in Fig. 1c and Supplementary Fig. 11 implied that the introduction of Zr 4+ ions could stabilize the metastable t and o- AFE phases within the Lu:Hf 1− x Zr x O 2 bulk crystals simultaneously. It is worth noting that the presence of the o- FE phase was also reasonable in the bulk crystals because its formation energy is between those of the t and o- AFE phases. The crystal doped with 40 at.% Zr exhibited superior machining characteristics, demonstrating a greater resilience to cracking than the other three Lu:Hf 1− x Zr x O 2 crystals (Supplementary Fig. 9a). Building upon this observation, we prepared a series of Lu:Hf 0.6 Zr 0.4 O 2 crystals with varying Lu doping concentrations. As shown in Fig. 1b, with an increase in the Lu doping level, the diffraction intensities at 38.7°, 53.5°, and 55.7° gradually diminished in comparison to the dominant Bragg peak at 30°. This trend suggested a growing prevalence of the t -phase component in the final crystal structure. The Raman spectroscopy results aligned with the structural characterization, revealing that the sample doped with 10.5 at.% Lu was mainly characterized by t -phase vibrational modes. The post-annealing experiment further highlighted the essential role played by RE 3+ ions in stabilizing the metastable phases to room temperature (Supplementary Figs. 12 and 13). Such a phenomenon coincides with the phase modulation behavior observed in RE:HfO 2 and RE:ZrO 2 , where larger RE doping concentrations tend to stabilize the metastable t phase with a higher formation energy 32,33 . Next, we conducted temperature-dependent XRD analysis on the Lu:Hf 0.6 Zr 0.4 O 2 (9.25 at.%) crystals to study the polymorphism transformation between different metastable phases as a function of temperature. A reversible phase transition was observed (Fig. 1d,e), with transformation temperatures occurring in the heating and cooling processes, located in ranges of 600–700°C during heating and 400–500°C during cooling. These phase-change temperatures were further confirmed by the differential scanning calorimetry (DSC) measurement (Supplementary Fig. 14). The transition temperatures of the DSC results were ~628°C during heating and ~483°C during cooling. Such a large thermal hysteresis (~145°C) reflected a large barrier of the activation energy between the high- and low-temperature phases owing to the rearrangement of the Hf and O atoms, e.g., 46.0 meV/f.u for t to o -FE and 68.8 meV/f.u for t to o -AFE 22 . The transition from the low-temperature orthorhombic phase to the high-temperature polymorph was marked by the disappearance of Bragg diffraction peaks at ~53.7°, ~55.9°, ~65.8°, and ~67.9°. This signified the complete transformation from the low-temperature phase to the high-temperature phase. Notably, the high-temperature phase possessed two distinct diffraction peaks around ~59.5 o (or ~73.7 o ), suggesting that the high-temperature metastable polymorph was the t phase rather than the c phase 19,34,35 . The above structural analyses highlight the polymorphic engineering within the Lu:Hf 1– x Zr x O 2 bulk crystals by describing the synergistic contributions from co - doping Lu 3+ and Zr 4+ ions. The presence of RE 3+ ions serves to address the challenges posed by the eutectoid reaction during the crystal growth and facilitates the phase evolution within the bulk crystals by leveraging oxygen vacancies (Supplementary Fig. 15), which are induced by heterovalent substitution 17 . By maintaining fixed optical floating zone growth conditions, the introduction of Zr 4+ ions plays an important role in fine-tuning the t - o transition temperature (Supplementary Fig. 25), benefiting the adjustment of the phase composition within the final bulk crystals. Dielectric and ferroelectric characterizations of Lu:Hf 1− x Zr x O 2 bulk crystals In this context, we investigated temperature-dependent dielectric constant ( ε r ) in Lu:Hf 0.6 Zr 0.4 O 2 bulk crystals. As exhibited in Fig. 2a, analogous to the aforementioned temperature dependences of structural and thermal results, an evident transition peak of ε r was observed at the Curie temperature (~661°C). This o - t transition behavior was consistent with that observed in HfO 2 -based ferroelectric films and aroused our research interest in the ferroelectric property within the as-grown bulk crystals 36 . Then, the related ferroelectric polarization in Lu:Hf 1− x Zr x O 2 bulk crystals was investigated using the positive-up-negative-down technique. As shown in Fig. 2b and Supplementary Fig. 16, pronounced polarization hysteresis was observed, confirming the existence of the ferroelectric phase 37 . For the Lu:Hf 0.6 Zr 0.4 O 2 bulk crystal, the coercive field ( E c ) of was determined to be 1.45 MV/cm, consistent with the values reported for HfO 2 -based ferroelectric thin films (1–2 MV/cm) 6,16,38 . The obtained saturation polarization ( P s ) attained a value of 48.6 μC/cm 2 , approaching the intrinsic polarization of HfO 2 -based ferroelectric materials (50–60 μC/cm 2 ) 15,23,31 . Notably, as shown in Fig. 2b and Supplementary Table 2, the measured remanent polarization P r reached 26 μC/cm 2 , which was comparable to those of HfO 2 -based epitaxial ferroelectric films (~10 nm in thickness) and surpassed the values reported for thick polycrystalline films (~17 μC/cm 2 , ~1 μm thick) as well as Y:HfO 2 bulk crystals (~3 μC/cm 2 , ~2.7 μm thick) 22,39 . Typically, the ferroelectric performance of HfO 2 -based films deteriorates with an increase in thickness. However, the as-grown Lu:Hf 0.6 Zr 0.4 O 2 bulk crystals could maintain excellent ferroelectric properties, even when the thickness was increased by three orders of magnitude. This result underscores the universal feature of HfO 2 -based ferroelectricity and eliminates the restriction that the excellent ferroelectric performance is confined solely to meticulously prepared HfO 2 -based epitaxial thin films. Additionally, the local piezoresponse force microscopy (PFM) analysis (Fig. 2c-f, Supplementary Fig. 18) showed an apparent change in the phase and amplitude when a voltage was applied. Clear contrast was observed by applying the same voltage magnitude with the opposite poling direction. The subsequent second harmonic generation (SHG) characterization further ascertained the presence of a polar phase within the as-grown bulk crystals (Supplementary Fig. 17). The remarkable ferroelectric performance of the Lu:Hf 0.6 Zr 0.4 O 2 crystals underscores the importance of understanding the local crystal structure, given the coexistence of multiple phases within the bulk crystals. Formation mechanism of o -FE phase in Lu:Hf 1− x Zr x O 2 bulk crystals We employed scanning transmission electron microscopy (STEM) to examine the local atomic arrangement within the bulk Lu:Hf 0.6 Zr 0.4 O 2 crystal. It is noteworthy that the HfO 2 -based ferroelectricity is intricately associated with the displacement of oxygen ions, in contrast to the more traditional perovskite ferroelectric materials, where the shift of cation plays a dominant role 40,41 . To gain deeper insight into the transformation mechanism between various phases in the bulk crystal, we utilized the iDPC-STEM technique owing to its heightened sensitivity to light elements, enabling a more comprehensive study of the phase transitions. Figure 3a-c and Supplementary Fig. 19 exhibit the crystal structures of the o- AFE and t phases, as well as the o- FE polar phase. Specifically, the t phase possesses a single type of oxygen site, located at the center of the four neighboring cation positions. In contrast, both the o- FE and o- AFE phases contain dual oxygen sites (O1 and O2), exhibiting an off-center behavior. Notably, the o- FE and o- AFE phases exhibit a significant distribution difference of O2 ions within the ac plane. To delve further into the microstructure, iDPC-STEM was employed along the b -axis direction of the o- FE and o- AFE phases, a strategic choice for precise phase identification 20,42 . Figure 3d-f unveils critical insights into the material composition. Apart from the Hf/Zr/Lu cations, the image clearly highlights the presence of oxygen ions, being instrumental to the phase identification at the atomic scale. This finding is in accordance with the structural and ferroelectric analyses discussed earlier, which confirmed that the bulk crystal simultaneously possessed the t , o- FE, and o- AFE phases. In the o- FE phase, the O2 ions in different polarization layers exhibited a uniform c -axis displacement direction, thus yielding robust ferroelectric polarization. The lattice parameters of the o- FE phase were measured at a = 5.17 Å and c = 5.41 Å, closely resembling those of HfO 2 -based ferroelectric films and bulk crystals 22,23 . In contrast, the o- AFE phase ( a = 5.16 Å and c = 5.11 Å), although possessing a similar cation distribution to that of the o- FE phase, exhibited a distinctive feature. The adjacent polarization layers exhibited reversed polarization directions, resulting in an antipolar nature. As shown in Fig. 3g, the o- FE and o- AFE phases coexisted in certain regions owing to the low free energy gap between these two phases (~10 meV/f.u) 43,44 . This observation coincides with the atomic-resolution phase identification in ZrO 2 and Hf 0.5 Zr 0.5 O 2 ferroelectric films, revealing that the disparity between the o- FE and o- AFE polymorphs relies on the displacement direction of the oxygen ions within the polarization layers 14,20,22 . Furthermore, as shown in Fig. 4a, we observed the local multiphase region within the Lu:Hf 0.6 Zr 0.4 O 2 bulk crystal, where the t , o- FE, and o- AFE phases coexisted. Notably, we identified distinct transitional phase regions between the t and o- FE or o- AFE phases, which differed from the steep t - o phase boundary observed in HfO 2 -based ferroelectric films 20,45 . The complete t - o phase transformation process contained two distinct stages, denoted as t ’ and t ”, corresponding to changes in the O and Hf sites, respectively (Supplementary Figs. 21 and 24). With Cluster 4 as an example, as illustrated in Fig. 4b, the Hf sites showed minimal position alteration, while the O sites within the polarization layers exhibited an evident atomic shift in the t ’ stage, leading to a reduction in d 3 compared to that of the t phase. In the adjacent t ” stage, the primary change occurred within the neighboring horizontal Hf atomic layers, giving rise to an increase in d 1 and a decrease in d 2 . The position change of the Hf atoms led to a slight vertical displacement of the O atoms, but the horizontal mirror symmetry m h remained unbroken. This observation delineated the concrete atomic shift trajectory during the t - o phase transformation, contributing to a more comprehensive understanding of the formation mechanism of the o- FE phase. According to the phase evolution shown in Fig. 4c, the movement of O atoms in the t ’ stage broke the centrosymmetric operation and transformed the space group from tetragonal non-polar P 4 2 / nmc to orthorhombic polar crystal systems. Through the t - o transition, the shift of the O sites ( d 3 ) reached the maximum distance and yielded robust intrinsic polarization in the o- FE phase. Additionally, the values of d 1 , d 2 , and d 3 in the o- FE phase remained relatively constant at approximately ~270 , ~240 , and ~75 pm, respectively. The apparent distance distinction between the o- FE and t phases ( d 1 = d 2 = ~259 pm, d 3 = ~130 pm) implied that the bulk crystal experienced a strong strain alteration during the t - o transition process. To assess the strain distributions within the Lu:Hf 1− x Zr x O 2 bulk crystals, we conducted a thorough analysis using geometric phase analysis (GPA). As shown in Fig. 4d and Supplementary Fig. 23, the crystal specimen manifested a significant normal strain and a relatively weak shear strain. The normal strain progressively increased throughout the t - o phase transformation (from the right to the left sides within Clusters 1–8), a phenomenon akin to the stabilization mechanism observed in epitaxial films for the o- FE phase via the strain effect 4,6,31,46 . In the case of two orthorhombic phases (as shown in Supplementary Figs. 22 and 23), the o- FE phase exhibited an apparent compressive strain within the spacer layers, while the o- AFE phase exhibited alternating strong tensile and compressive strains in the adjacent spacer layers. Notably, the strain fluctuations in the o- AFE phase were significantly more pronounced than those in the o- FE and t phases, suggesting that the presence of the o- AFE phase carried a higher risk of inducing cracks in the bulk crystals. The primary phase in the Lu:HfO 2 (10–11 at.%) and Gd:HfO 2 (15 at.%) bulk crystals was the o- AFE phase, and hence, these bulk crystals were easily broken during the machining process. In contrast, the introduction of Zr 4+ ions brought the t metastable phase as a buffer region into the Lu:Hf 1− x Zr x O 2 bulk crystals. This effectively accommodated the large local strain fluctuations caused by the o- FE and o- AFE phases and ensured the processing feasibility of the as-grown bulk crystals, even with a thickness as low as tens of micrometers (Fig. 2b). Discussion The puzzle surrounding the ferroelectric origin of HfO 2 -based materials poses a hurdle to the understanding of the intricate structure-property interplay between device manufacturing and their ferroelectric performances 1,6,47 . Although different ferroelectric crystal structures have been proposed over the past decade, the relevant research has predominantly revolved around phase identification. The direct observation of evidence for the evolution of the metastable ferroelectric phase at the atomic scale remains challenging due to the small grain size (~20 nm) inherent in nanoscale thin films 6,48 – 50 . Through composition optimization, we realized a controllable polymorphic adjustment in the fast growth process by understanding the mechanism of the relevant phase transformation, which effectively stabilized the metastable o- FE phase in the as-grown bulk crystals. On that basis, we achieved robust ferroelectric polarization within the fluorite-structure Lu:Hf 1− x Zr x O 2 bulk crystals, rivaling the performances observed in ultra-thin films. Of particular importance is that we uncovered the metastable phases within the bulk crystals and provided clear evidence of the t - o phase evolution pathway by directly tracking the movement of Hf and O atoms. These local structural changes were intricately related to the synergistic modulation from co-doped Lu 3+ and Zr 4+ ions. The Zr 4+ ions played a vital role in stabilizing the metastable t phase, and the Lu 3+ ions controlled the progress of the t - o phase transformation effectively (Fig. 1b,c). Notably, these results underscore the important role of the bulk-state perspective in deciphering the mechanisms that govern the phase transformation in HfO 2 -based materials. This approach also facilitates the exploration of the domain wall structure at a unit-cell-size level and the associated domain evolution. The significance of these findings greatly enhances our understanding of the ferroelectric mechanisms in HfO 2 -based materials. Furthermore, they facilitate the development of electronic and photonic functional devices with fluorite-structured materials that are compatible with CMOS technology. This echoes the functionalities observed in applications involving perovskite-based materials. In brief, our research represented a breakthrough in inducing robust ferroelectricity within Lu:Hf 1− x Zr x O 2 bulk crystals, achieved through a comprehensive understanding of the regulatory role played by Lu 3+ and Zr 4+ ions. The as-grown crystal exhibited an impressive P r value of 26 μC/cm 2 , even with a thickness three orders of magnitude higher than those of the extensively studied ultra-thin films. The main source of ferroelectricity in the Lu:Hf 1− x Zr x O 2 bulk crystals was attributed to the t - o phase transition, a finding consistent with the observations in thin films. Furthermore, we elucidated the intricate process of t - o phase evolution by directly observing the dynamic movement of Hf and O atoms, as well as the precise structural alterations. These findings bridge the gap between bulk and ultra-thin HfO 2 -based ferroelectric materials, providing profound insights into their ferroelectric origin. We anticipate that this study, serving as a paradigm for fabricating large-sized bulk HfO 2 -based ferroelectric crystals, will facilitate the understanding of the nanosized ferroelectric domain evolution in fluorite-structured materials, which will greatly benefit the development of CMOS-compatible devices in ferroelectrics, piezoelectrics, and pyroelectrics. Online content Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at. Methods Crystal growth The Lu:Hf 1- x Zr x O 2 bulk crystals were grown by the optical floating zone (OFZ) method with a four-ellipsoidal-mirror furnace (Crystal Systems Inc., FZ-T-12000-X-I-S-SU), which could realize the heating temperature to 3000 o C. For the optimal growth parameters, the feed and seed rod rotation rates were set at 10 rpm and 5 rpm, respectively, the growth rate was set at 20 mm/h, and the flow rate of O 2 was fixed at 150 ml/min. XRD, DSC, and dielectric measurements The as-obtained Lu:Hf 1- x Zr x O 2 bulk crystals were directly used for the related characterizations. The room-temperature XRD measurements were carried out on a Rigaku diffractometer (smartlab 3 kW) with a Cu Kα radiation source, and the step size was 0.01°. The temperature-dependent in-situ XRD measurements were analyzed by a Rigaku diffractometer (smartlab, 9 kW) with a Cu K α radiation source. The diffraction data were collected after a delay of 5 min to maintain thermal balance. The heating rate was 10 o C/min, and the scanning rate was 0.01°/step. The DSC data of Lu:Hf 1- x Zr x O 2 were measured by employing a TA DISCOVERY (SDT650) synchronous thermal analyzer. The whole process was in the air atmosphere, the surveyed temperature range was from 30 to 1000 o C. Both the heating and cooling rates were 5 o C/min. The temperature-dependent dielectric constant ε r was surveyed using an LCR meter (ZX8528A, Zhixin Precision Electronics) with a heating rate of 5 o C/min. XPS, Raman, and SHG characterizations The room-temperature X-ray photoelectron spectroscopy (XPS) was conducted with Thermo Fisher ESCALAB XI+ equipped with monochromatic Al-K α radiation. Room-temperature Raman spectra were surveyed with an iHR550 Raman spectrometer and a 632-nm He-Ne laser (5 mW). The room-temperature second harmonic generation (SHG) investigation was realized with an iHR550 Raman spectrometer and a femtosecond laser (1030 nm, 250 fs, 200 kHz). P – E and PFM measurements A pristine Lu:Hf 1- x Zr x O 2 crystal was mechanically polished into a piece with a thickness of 10-20 μm. The Au electrode with an area of 250000 µm 2 was made by sputtering. The P – E loop was measured by the positive-up-negative-down technique provided in a Ferroelectric Material Test System (aixACCT, TF Analyzer 2000) with V max =6000 V and f =1 Hz. The PFM sample was prepared by Helios 5 CX Dualbeam scanning electron microscopy. The sample was stuck with the silver epoxy to fix to gold-plated silicon wafers, followed by a reduction by a focused ion beam to the order of ~50 nm (observed by SEM, HITACHI S-4800). The samples were performed by MFP-3D-Origion+ Asylum Research. Dual-frequency resonance-tracking PFM was conducted using a conductive Ti/Ir-coated probe tip (25 nm radius, resonant frequency: 75 kHz, force constant: 2.8 N/m) to image written domain structures and measure switching-spectroscopy piezoelectric hysteresis loops. Contact was made to the bottom Ag electrode for grounding in PFM studies. PFM imaging was performed with the tip in direct contact with the sample surface. STEM analysis The direction of the as-grown crystal specimens was confirmed by EBSD based on Carl Zeiss crossbeam 550L FIB-SEM. The electron transparent sample for the STEM observation was prepared by a Carl Zeiss crossbeam 550L FIB-SEM using the conventional lift-out method. The integrated differential phase-contrast scanning transmission electron microscopy (iDPC-STEM) experiments were carried out at 300 kV using a ThermoFisher Scientific Themis Z microscope, equipped with a probe corrector, and a four-segment DF4 detector. The convergence angle was 25 mrad and the collection angle for iDPC-STEM imaging was 6-20 mrad. STEM-EDS mapping was carried out using a thermofisher Spectra 300 equipped with a Super X EDS probe. Fourier-filtered iDPC-STEM images were analyzed by CalAtom Software to extract the atomic position of Hf/Zr and nonpolar O ions by multiple-ellipse fitting. The positions of polarized O ions were extracted by line profile using Gatan Microscopy Suite Software (Version 3.22.1461.0). Declarations Data availability The data that supports the plots within this paper and other findings of this study are available from the corresponding authors on request. Acknowledgments We thank C.Wang for the useful discussion on the ferroelectric investigation. This work is supported by the National Key Research and Development Program of China (2021YFB3601504), the National Natural Science Foundation of China (52025021), the Natural Science Foundation of Shandong Province (ZR2022LLZ005), and the Future Plans of Young Scholars at Shandong University. Author contributions S.W., H.Y., S.Z., and H.Z. designed and conceived the research idea. S.W., Y.S., and H.Y. performed the crystal growth and related characterizations, including XRD, Raman, XPS, and SHG. Y.S. performed the polarization measurement and PFM investigations under the supervision of H.Z. S.W., X.Y., and P.N. performed the STEM observation and relevant analysis under the guidance of B.G. and H.Y. S.W. and Y.S. wrote the original manuscript, H.Y., S. Z., and H.Z. revised the manuscript. All authors contributed to the discussion of the results. 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Ferroelectric polarization-switching dynamics and wake-up effect in Si-doped HfO 2 . ACS Appl . Mater . Interfaces 11 , 3142–3149 (2019). Zhou, P. et al. Intrinsic 90° charged domain wall and its effects on ferroelectric properties. Acta Mater . 232 , 117920 (2022). Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryInformation.pdf Supplementary Information Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-3803321","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":265244307,"identity":"90311896-3c44-4643-9c09-896a34317b55","order_by":0,"name":"Haohai Yu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYBACAwYGNjDJDyYZmEnQItlAmhYQ4wCxWszZDx978KPgcOLm84e3STBUWCc2sJ89gFeLZU9aumGPweHEbTfSyiQYzqQnNvDkJeB32IEcMwkesBYeMwnGtsOJDUAufi3n35hJ/gFq2dx/BqjlHzFabuSYSYNs2cAAtI6xgSgtz9KkZQzSjWfcSCu2SDiWbtzGk0PIYcnHJN/8sZbt7z+88caHGiCD/Qx+LVDQDKESGGDRRBjUEaluFIyCUTAKRiQAABE+RXenskEFAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-2295-1400","institution":"State Key Laboratory of Crystal Materials, Shandong University","correspondingAuthor":true,"prefix":"","firstName":"Haohai","middleName":"","lastName":"Yu","suffix":""},{"id":265244308,"identity":"02aaf298-335b-402e-8716-34af3618852a","order_by":1,"name":"Shuxian Wang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Shuxian","middleName":"","lastName":"Wang","suffix":""},{"id":265244309,"identity":"edcb6140-13d6-4d8e-9659-e7ca6eb02071","order_by":2,"name":"Yihao Shen","email":"","orcid":"","institution":"Shandong University","correspondingAuthor":false,"prefix":"","firstName":"Yihao","middleName":"","lastName":"Shen","suffix":""},{"id":265244310,"identity":"c8a3b9cc-576b-49d4-bc14-36d415f4fe1f","order_by":3,"name":"Xiaoyu Yang","email":"","orcid":"","institution":"Anhui University","correspondingAuthor":false,"prefix":"","firstName":"Xiaoyu","middleName":"","lastName":"Yang","suffix":""},{"id":265244311,"identity":"ebd39031-0b7c-4441-9879-0deee8e6e2df","order_by":4,"name":"Pengfei Nan","email":"","orcid":"","institution":"Anhui University","correspondingAuthor":false,"prefix":"","firstName":"Pengfei","middleName":"","lastName":"Nan","suffix":""},{"id":265244312,"identity":"c258aa8d-1151-47a6-a403-0fbfe0a6790a","order_by":5,"name":"Binghui Ge","email":"","orcid":"https://orcid.org/0000-0002-6470-6278","institution":"Anhui University","correspondingAuthor":false,"prefix":"","firstName":"Binghui","middleName":"","lastName":"Ge","suffix":""},{"id":265244313,"identity":"8c8a077c-3835-4bdc-b658-983ac0eb8543","order_by":6,"name":"Shujun Zhang","email":"","orcid":"https://orcid.org/0000-0001-6139-6887","institution":"University of Wollongong, Australia","correspondingAuthor":false,"prefix":"","firstName":"Shujun","middleName":"","lastName":"Zhang","suffix":""},{"id":265244314,"identity":"32732f4e-8053-4844-90c7-44332e4f1b0e","order_by":7,"name":"Huaijin Zhang","email":"","orcid":"https://orcid.org/0000-0002-2118-5863","institution":"Shandong University","correspondingAuthor":false,"prefix":"","firstName":"Huaijin","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2023-12-25 07:20:50","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3803321/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3803321/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49243609,"identity":"223a2f2b-f5ce-4b9e-aa55-581bed8b374d","added_by":"auto","created_at":"2024-01-05 18:44:16","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1889991,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eBulk crystal, structural, and optical characterizations of Lu:Hf\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0.6\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eZr\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0.4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eO\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, Photograph of the as-grown Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e (9.25\u0026nbsp;at.\u0026nbsp;%) crystal with a dimension of \u003cem\u003eφ\u003c/em\u003e3 × 60 mm\u003csup\u003e3\u003c/sup\u003e. \u003cstrong\u003eb\u003c/strong\u003e, Room-temperature XRD data of the Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e crystals with different Lu doping concentrations. The standard cards of the \u003cem\u003eP\u003c/em\u003e4\u003csub\u003e2\u003c/sub\u003e/\u003cem\u003enmc\u003c/em\u003e (\u003cem\u003et\u003c/em\u003e) and \u003cem\u003ePbca\u003c/em\u003e (\u003cem\u003eo-\u003c/em\u003eAFE) phases correspond to ICSD Nos. 173966 and 79913, respectively, and the standard card of the \u003cem\u003ePbc\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e (\u003cem\u003eo-\u003c/em\u003eFE) phase is from Ref.(\u003cem\u003e31\u003c/em\u003e). \u003cstrong\u003ec\u003c/strong\u003e, Room-temperature Raman spectra of the Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e crystals. The theoretical Raman vibrational modes of the\u003cem\u003e Pbca \u003c/em\u003eand \u003cem\u003ePbc\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e phases are from Ref.(24).\u003cstrong\u003e d\u003c/strong\u003e,\u003cstrong\u003ee\u003c/strong\u003e, Temperature-dependent XRD data of the Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e (9.25\u0026nbsp;at.\u0026nbsp;%) sample over 30 to 1000\u003csup\u003eo\u003c/sup\u003eC range. Following the complete heating-cooling cycle, the specimen exhibits no discernible diffraction differences compared to its pristine state. The standard card of the \u003cem\u003ec\u003c/em\u003e phase corresponds to ICSD No. 173967.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-3803321/v1/0774a7d2369e2b68c9623471.png"},{"id":49243249,"identity":"14992050-4c7e-4fda-b1ea-7ff9dee3cc42","added_by":"auto","created_at":"2024-01-05 18:36:16","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":3159742,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDielectric and ferroelectric properties in Lu:Hf\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0.6\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eZr\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0.4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eO\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e (9.25\u0026nbsp;at.\u0026nbsp;%) crystal.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, Temperature-dependent dielectric behavior at 100\u0026nbsp;kHz. As shown in the inset, the related room-temperature dielectric constant \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e was approximately 23. \u003cstrong\u003eb\u003c/strong\u003e, Polarization versus electric field. The inset is the polished crystal with a thickness of ~17\u0026nbsp;μm. \u003cstrong\u003ec\u003c/strong\u003e,\u003cstrong\u003ed\u003c/strong\u003e, Switching loops for PFM measurement involving voltage-dependent phase and amplitude. \u003cstrong\u003ee\u003c/strong\u003e, Local PFM phase contrast under different voltages. \u003cstrong\u003ef\u003c/strong\u003e, Local PFM amplitude variation under different polarization states. For all the above PFM measurements, the sample thickness was reduced to ~50\u0026nbsp;nm via the FIB method, yielding an electric field of ~1.6\u0026nbsp;MV/cm for the measurement of switching loops (\u003cstrong\u003ec\u003c/strong\u003e,\u003cstrong\u003ed\u003c/strong\u003e) and ~2\u0026nbsp;MV/cm in the measurements of local phase (\u003cstrong\u003ee\u003c/strong\u003e) and amplitude (\u003cstrong\u003ef\u003c/strong\u003e).\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-3803321/v1/c503ade2a005c6f874b6201f.png"},{"id":49243251,"identity":"96ed7185-74f5-49b4-85a4-c828460d3276","added_by":"auto","created_at":"2024-01-05 18:36:16","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":4177499,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStructure schematics and detailed iDPC-STEM images of the bulk Lu:Hf\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0.6\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eZr\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0.4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eO\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e (9.25\u0026nbsp;at.\u0026nbsp;%) crystal. a-c\u003c/strong\u003e, Atomic arrangements of the\u003cem\u003e o-\u003c/em\u003eFE (\u003cem\u003ePbc\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003eo-\u003c/em\u003eAFE (\u003cem\u003ePbca\u003c/em\u003e), and \u003cem\u003et\u003c/em\u003e (\u003cem\u003eP\u003c/em\u003e4\u003csub\u003e2\u003c/sub\u003e/\u003cem\u003enmc\u003c/em\u003e) phases, respectively. The yellow, cyan, and red spheres denote the Hf/Zr/Lu, O1, and O2 ions, respectively. For \u003cem\u003eo-\u003c/em\u003eFE and \u003cem\u003eo-\u003c/em\u003eAFE, the O1 ions are located in the spacer layers (Layer Ⅱ) and the O2 ions belong to the remaining polarization layers (Layers Ⅰ and Ⅲ, rectangular light blue areas). The polarization directions are parallel in \u003cem\u003eo-\u003c/em\u003eFE (cyan arrows) and antiparallel in \u003cem\u003eo-\u003c/em\u003eAFE (cyan and orange arrows). \u003cstrong\u003ed-f\u003c/strong\u003e, The observed atomic arrangements of \u003cem\u003eo-\u003c/em\u003eFE, \u003cem\u003eo-\u003c/em\u003eAFE, and \u003cem\u003et\u003c/em\u003e phases, respectively. \u003cstrong\u003eg\u003c/strong\u003e, The iDPC-STEM image contains the \u003cem\u003eo-\u003c/em\u003eFE and \u003cem\u003eo-\u003c/em\u003eAFE phases simultaneously, and the local zoom-in region well matches the polar \u003cem\u003eo-\u003c/em\u003eFE and the antipolar \u003cem\u003eo-\u003c/em\u003eAFE phases. All the scale bars are 1\u0026nbsp;nm.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-3803321/v1/66da4384df84226f1f875eb2.png"},{"id":49243252,"identity":"348e3342-e7fa-486c-b90b-3f6a194eb05e","added_by":"auto","created_at":"2024-01-05 18:36:16","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":11663219,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePhase evolution within the Lu:Hf\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0.6\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eZr\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e0.4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eO\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e (9.25\u0026nbsp;at.\u0026nbsp;%) crystal.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, iDPC-STEM results that illustrate the transformation from the initial \u003cem\u003et\u003c/em\u003e (brown) phase to the transient \u003cem\u003et\u003c/em\u003e’ (pink) and \u003cem\u003et\u003c/em\u003e” (yellow), and the formation of \u003cem\u003eo\u003c/em\u003e-FE (green) and \u003cem\u003eo\u003c/em\u003e-AFE (blue) phases. \u003cstrong\u003eb\u003c/strong\u003e, Taking Cluster 4 as an example, the ion distances \u003cem\u003ed\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003ed\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, and \u003cem\u003ed\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e across different phase regions are displayed.\u003cem\u003e d\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003ed\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e represent the distances between the Hf sites within the polarization and spacer layers, respectively. \u003cem\u003ed\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e denotes the distance between the vertical Hf column and its corresponding O column on the right. \u003cstrong\u003ec\u003c/strong\u003e, Phase evolution mechanism from the \u003cem\u003et\u003c/em\u003e to \u003cem\u003eo-\u003c/em\u003eFE phases. The horizontal shift of O sites primarily occurs in the \u003cem\u003et\u003c/em\u003e’ stage while the change in the vertical Hf-Hf column is concentrated in the \u003cem\u003et\u003c/em\u003e” stage. The \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo \u003c/em\u003ephase transition breaks the 4-fold rotation symmetry along the [001] direction of the \u003cem\u003et\u003c/em\u003e phase but retains the mirror operation that is parallel to the (100) plane of the \u003cem\u003eo\u003c/em\u003e phases (\u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e). \u003cstrong\u003ed\u003c/strong\u003e, Overlapping profile of the iDPC-STEM image of the Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e (9.25\u0026nbsp;at.\u0026nbsp;%) sample shown in (a) and the normal strain (\u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003eyy\u003c/em\u003e\u003c/sub\u003e) calculated from GPA analysis.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-3803321/v1/5ffdf6b63bad9ddcfb92b867.png"},{"id":50655452,"identity":"aa61ef28-5d27-425d-b674-735573c5682e","added_by":"auto","created_at":"2024-02-05 10:10:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4592951,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3803321/v1/2d7e8f01-a238-449b-b8f5-25f64e9bb1a6.pdf"},{"id":49243253,"identity":"fffc6a90-1765-4896-b302-4cb374f25752","added_by":"auto","created_at":"2024-01-05 18:36:16","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3926664,"visible":true,"origin":"","legend":"Supplementary Information","description":"","filename":"SupplementaryInformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3803321/v1/4bd42baf65074ae5ddc8f5a5.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"\u003cp\u003eRobust ferroelectricity in HfO\u003csub\u003e2\u003c/sub\u003e-based bulk crystals via polymorphic engineering\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eWith scientific and technological advances,\u0026nbsp;ferroelectric materials exhibiting excellent compatibility with the complementary metal-oxide semiconductor (CMOS) process have become the foundation of\u0026nbsp;optoelectronic\u0026nbsp;functional devices capable of integration and miniaturization\u003csup\u003e1\u0026ndash;3\u003c/sup\u003e. Over the years, there has been a mounting interest in HfO\u003csub\u003e2\u003c/sub\u003e-based fluorite-structure ferroelectric materials.\u0026nbsp;Of particular interest is that\u0026nbsp;their switchable ferroelectric polarization capabilities endure, even when the film thickness is reduced to the atomic realm, typically ranging from\u0026nbsp;0.5 to\u0026nbsp;1\u0026nbsp;nm\u003csup\u003e4,5\u003c/sup\u003e.\u0026nbsp;Consequently, HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectric materials\u0026nbsp;have emerged as\u0026nbsp;a class of promising candidates for the development of highly compact microelectronic devices, encompassing nonvolatile information memory and field-effect transistors, ushering in a new era beyond Moore\u0026rsquo;s law\u003csup\u003e6\u0026ndash;8\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eRegarding HfO\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e\u0026nbsp;\u003c/sup\u003eand its analog ZrO\u003csub\u003e2\u003c/sub\u003e, the temperature-dependent polymorphs manifest as cubic (\u003cem\u003ec\u003c/em\u003e, \u003cem\u003eFm\u003c/em\u003e-3\u003cem\u003em\u003c/em\u003e), tetragonal (\u003cem\u003et\u003c/em\u003e, \u003cem\u003eP\u003c/em\u003e4\u003csub\u003e2\u003c/sub\u003e/\u003cem\u003enmc\u003c/em\u003e), and monoclinic (\u003cem\u003em\u003c/em\u003e, \u003cem\u003eP\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e/\u003cem\u003ec\u003c/em\u003e) phases, while the pressure-induced polymorphs include orthorhombic-I (\u003cem\u003eo-\u003c/em\u003eAFE, \u003cem\u003ePbca\u003c/em\u003e) and orthorhombic-II (\u003cem\u003ePnma\u003c/em\u003e)\u003csup\u003e9,10\u003c/sup\u003e. It is worth noting that none of these space groups can sustain any ferroelectric polarization due to their centrosymmetric (non-polar) nature. The intrinsic ferroelectric origin of HfO\u003csub\u003e2\u003c/sub\u003e-based materials has remained a mystery ever since its first discovery in an Si:HfO\u003csub\u003e2\u003c/sub\u003e thin film\u003csup\u003e11\u003c/sup\u003e. Several polar ferroelectric space groups have been proposed based on extensive theoretical and experimental studies, including the orthorhombic (\u003cem\u003ePbc\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003ePmn\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e) and rhombohedral (\u003cem\u003eR\u003c/em\u003e3\u003cem\u003em\u003c/em\u003e) phases\u003csup\u003e12\u0026ndash;14\u003c/sup\u003e. Early research into HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectrics was largely confined to thin films, typically around 10\u0026nbsp;nm in thickness, because the captivating ferroelectricity rapidly degrades with increasing thickness. Numerous theoretical models have been proposed\u0026nbsp;to explore the\u0026nbsp;formation mechanism of the HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectric phase\u003csup\u003e15\u0026ndash;17\u003c/sup\u003e. In the case of thin films, the primary stabilizing factor for ferroelectric phases is often attributed to the phase transformation originating from the metastable \u003cem\u003et\u003c/em\u003e phase.\u0026nbsp;For\u0026nbsp;colloidal HfO\u003csub\u003e2\u003c/sub\u003e nanocrystals, the \u003cem\u003em\u003c/em\u003e phase at the twinning boundary can evolve into the polarization phase, even in the absence of symmetry breaking\u003csup\u003e18\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e\u003csup\u003e19\u003c/sup\u003e.\u0026nbsp;Additionally, flat polar phonon bands are considered to be a contributing factor to ferroelectric switching in HfO\u003csub\u003e2\u003c/sub\u003e\u003ca href=\"#_ENREF_16\" title=\"Lee, 2020 #1073\"\u003e\u003csup\u003e16\u003c/sup\u003e\u003c/a\u003e, while a\u0026nbsp;moderate electrical stimulus can induce a transformation from the antipolar \u003cem\u003eo\u003c/em\u003e-AFE phase to\u0026nbsp;the\u0026nbsp;polar \u003cem\u003eo\u003c/em\u003e-FE phase\u003csup\u003e20\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eRecently, \u003cem\u003ePbc\u003c/em\u003e2\u003csub\u003e1\u003c/sub\u003e (\u003cem\u003eo-\u003c/em\u003eFE) ferroelectric polarization was also discovered in Y:HfO\u003csub\u003e2\u003c/sub\u003e bulk crystals, providing a fresh\u0026nbsp;research perspective for understanding the\u0026nbsp;ferroelectric origin in HfO\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e21\u003c/sup\u003e. Unfortunately,\u0026nbsp;the resultant\u0026nbsp;remanent\u0026nbsp;polarization (\u003cem\u003eP\u003csub\u003er\u003c/sub\u003e\u003c/em\u003e) in Y:HfO\u003csub\u003e2\u003c/sub\u003e bulk ferroelectric crystals reaches only\u0026nbsp;~3\u0026nbsp;\u0026mu;C/cm\u003csup\u003e2\u003c/sup\u003e, approximately one order of magnitude lower than those of ultra-thin films (20\u0026ndash;50\u0026nbsp;\u0026mu;C/cm\u003csup\u003e2\u003c/sup\u003e)\u003csup\u003e22\u003c/sup\u003e\u003csup\u003e\u0026ndash;\u003c/sup\u003e\u003csup\u003e24\u003c/sup\u003e.\u0026nbsp;The proposed\u0026nbsp;Curie phase transition in Y:HfO\u003csub\u003e2\u003c/sub\u003e bulk crystals (\u003cem\u003eo-\u003c/em\u003eFE \u0026rarr; \u003cem\u003ec\u003c/em\u003e) differs from that observed in thin films (\u003cem\u003eo-\u003c/em\u003eFE \u0026rarr;\u003cem\u003e\u0026nbsp;t\u003c/em\u003e)\u003csup\u003e22\u003c/sup\u003e.\u0026nbsp;The controversy surrounding the origin of ferroelectricity in HfO\u003csub\u003e2\u003c/sub\u003e-based materials is ascribed to the fact that their switchable spontaneous polarization mainly arises from the movement of oxygen ions rather than cation displacement within perovskite systems\u003csup\u003e6\u003c/sup\u003e. To gain a comprehensive understanding of the ferroelectric origin in HfO\u003csub\u003e2\u003c/sub\u003e-based materials, it is imperative to clarify the motion trajectories of oxygen atoms. However, the challenge lies in the small atomic number of oxygen, which complicates the atomic-scale characterization\u003csup\u003e24\u003c/sup\u003e\u003csup\u003e,25\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn this study, we report compelling evidence of robust ferroelectricity in\u0026nbsp;HfO\u003csub\u003e2\u003c/sub\u003e-based\u0026nbsp;(Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e)\u0026nbsp;bulk\u0026nbsp;crystals. Our investigation highlights the pivotal roles played by Lu\u003csup\u003e3+\u003c/sup\u003e and Zr\u003csup\u003e4+\u003c/sup\u003e ions in the adjustment of polymorphic phases. Notably, we achieved an optimal \u003cem\u003eP\u003csub\u003er\u003c/sub\u003e\u003c/em\u003e value of up to 26\u003csup\u003e\u0026nbsp;\u003c/sup\u003e\u0026mu;C/cm\u003csup\u003e2\u003c/sup\u003e in these bulk crystals, a value comparable to those of HfO\u003csub\u003e2\u003c/sub\u003e-based epitaxial\u0026nbsp;ferroelectric films. To gain insights into the structural aspects, we conducted a temperature-dependent X-ray diffraction (XRD) analysis and an\u0026nbsp;integrated differential phase-contrast scanning transmission electron microscopy (iDPC-STEM) investigation. Through these analyses, we successfully identified the polymorphic phases present in Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk crystals, including the \u003cem\u003eo-\u003c/em\u003eFE, \u003cem\u003eo-\u003c/em\u003eAFE, and \u003cem\u003et\u003c/em\u003e phases. Building upon this foundation, we further revealed the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase evolution process, facilitated by the direct observation of the movement trajectory of Hf and O atoms near the phase boundary. These findings provide a clear understanding of the formation mechanism behind the \u003cem\u003eo-\u003c/em\u003eFE polar phase and pave the way for the development of bulk-state fluorite-structure ferroelectric crystals.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCrystal growth and structural characterization of\u003c/strong\u003e \u003cstrong\u003eLu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003ebulk\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;crystals\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eLeveraging rare-earth-doped HfO\u003csub\u003e2\u003c/sub\u003e (RE:HfO\u003csub\u003e2\u003c/sub\u003e) has emerged as a feasible strategy to stabilize the relevant metastable\u0026nbsp;polymorphs, such as\u0026nbsp;\u003cem\u003ec\u003c/em\u003e, \u003cem\u003et\u003c/em\u003e, \u003cem\u003eo-\u003c/em\u003eFE, and \u003cem\u003eo-\u003c/em\u003eAFE.\u0026nbsp;To prevent the formation of the\u0026nbsp;\u003cem\u003em\u003c/em\u003e phase within the RE:HfO\u003csub\u003e2\u003c/sub\u003e bulk crystals, it is important to meticulously consider the eutectoid reaction (occurring at ~1780\u0026deg;C,\u003cem\u003e\u0026nbsp;t\u003c/em\u003e \u0026rarr; \u003cem\u003ec\u003c/em\u003e + \u003cem\u003em\u003c/em\u003e), especially when dealing with nearly pure HfO\u003csub\u003e2\u003c/sub\u003e (Supplementary\u0026nbsp;Fig. 1)\u003csup\u003e25\u003c/sup\u003e. As shown in Supplementary Figs. 2\u0026ndash;4, the XRD data for both the as-grown Gd:HfO\u003csub\u003e2\u003c/sub\u003e and Lu:HfO\u003csub\u003e2\u003c/sub\u003e crystals highlighted the importance of adhering to this selection rule.\u0026nbsp;The phase evolution of RE:HfO\u003csub\u003e2\u003c/sub\u003e can be controlled by managing the oxygen vacancies that arise from the heterovalent substitution of rare-earth ions. Previous studies on RE:HfO\u003csub\u003e2\u003c/sub\u003e have indicated that the optimal stabilization range of the \u003cem\u003eo-\u003c/em\u003eFE phase typically falls below 10\u0026nbsp;at.% of rare earth (RE) doping\u003csup\u003e26,27\u003c/sup\u003e. Among the various RE-doping scenarios, Lu:HfO\u003csub\u003e2\u003c/sub\u003e crystals possess a distinct advantage at lower concentrations (Supplementary Table 1) and thus were selected for an investigation into related polymorphic transformations. As shown in Supplementary Fig. 3, the obtained XRD data for Lu:HfO\u003csub\u003e2\u003c/sub\u003e crystals (10\u0026ndash;11 at.%) suggested the existence of orthorhombic phases. Subsequent Raman spectroscopy revealed that the primary phase in the as-grown Lu:HfO\u003csub\u003e2\u003c/sub\u003e crystals was the \u003cem\u003eo-\u003c/em\u003eAFE phase rather than the \u003cem\u003eo-\u003c/em\u003eFE phase (Supplementary Fig. 6)\u003csup\u003e24\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eIn addition to the incorporation of RE\u003csup\u003e3+\u003c/sup\u003e ions, the introduction of Zr\u003csup\u003e4+\u003c/sup\u003e ions stands out as a feasible phase\u0026nbsp;control\u0026nbsp;method in high-temperature\u0026nbsp;Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e metastable polymorphs. The ferroelectric phase can be\u0026nbsp;maintained\u0026nbsp;within a specific range of Zr doping, typically falling between 35 and 50\u0026nbsp;at.%\u003csup\u003e28\u0026ndash;30\u003c/sup\u003e. Thus, we grew Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e crystals by concurrently optimizing the Lu or Zr doping concentrations. To begin, we held the Lu doping concentration constant at\u0026nbsp;9\u0026nbsp;at.%\u0026nbsp;while adjusting the Zr doping concentration at 5\u0026nbsp;at.% increments.\u0026nbsp;As shown in Supplementary Figs. 9 and 10, high-quality\u0026nbsp;Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e crystals were successfully grown. The subsequent\u0026nbsp;structural investigation confirmed the existence of\u0026nbsp;orthorhombic phases (\u003cem\u003eo-\u003c/em\u003eAFE or \u003cem\u003eo-\u003c/em\u003eFE). Furthermore, as shown in Supplementary Fig. 11, we observed the vibrational modes of the \u003cem\u003et\u003c/em\u003e phase within the\u0026nbsp;Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e crystals, in addition to\u0026nbsp;the distinct scattering response of the \u003cem\u003eo-\u003c/em\u003eAFE phase. In general, the orthorhombic \u003cem\u003eo-\u003c/em\u003eAFE phase or \u003cem\u003eo-\u003c/em\u003eFE phases emerge as a result of the temperature-driven phase transition from the high-temperature \u003cem\u003et\u003c/em\u003e or \u003cem\u003ec\u003c/em\u003e phase. According to their respective formation energies, these polymorphs rank in the descending order of\u003cem\u003e\u0026nbsp;c\u003c/em\u003e, \u003cem\u003et\u003c/em\u003e, \u003cem\u003eo-\u003c/em\u003eFE, and \u003cem\u003eo-\u003c/em\u003eAFE, with the \u003cem\u003eo-\u003c/em\u003eAFE phase being the most energetically favorable\u003csup\u003e22,24\u003c/sup\u003e.\u0026nbsp;The\u0026nbsp;Raman vibrations shown in Fig. 1c\u0026nbsp;and\u0026nbsp;Supplementary Fig.\u0026nbsp;11 implied that the introduction of Zr\u003csup\u003e4+\u003c/sup\u003e ions could stabilize\u0026nbsp;the metastable \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo-\u003c/em\u003eAFE phases within the\u0026nbsp;Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk\u0026nbsp;crystals simultaneously.\u0026nbsp;It is worth noting that the presence of the \u003cem\u003eo-\u003c/em\u003eFE phase was also reasonable in the bulk crystals because its formation energy is between those of the \u003cem\u003et\u0026nbsp;\u003c/em\u003eand \u003cem\u003eo-\u003c/em\u003eAFE phases.\u003c/p\u003e\n\u003cp\u003eThe crystal doped with 40 at.% Zr exhibited superior machining characteristics, demonstrating a greater resilience to cracking than the other three\u0026nbsp;Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e crystals (Supplementary Fig. 9a). Building upon this observation, we prepared\u0026nbsp;a series of Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e crystals with varying Lu doping concentrations. As shown in Fig. 1b, with an increase in the Lu doping level, the diffraction intensities at 38.7\u0026deg;, 53.5\u0026deg;, and 55.7\u0026deg; gradually diminished in comparison to the dominant\u0026nbsp;Bragg peak at 30\u0026deg;. This trend suggested a growing prevalence of\u003cem\u003e\u0026nbsp;\u003c/em\u003ethe\u003cem\u003e\u0026nbsp;t\u003c/em\u003e-phase component in the final crystal structure. The Raman spectroscopy results aligned with the structural characterization, revealing that the sample doped with 10.5\u0026nbsp;at.%\u0026nbsp;Lu was mainly characterized by\u0026nbsp;\u003cem\u003et\u003c/em\u003e-phase\u0026nbsp;vibrational modes. The post-annealing experiment further highlighted the essential role played by RE\u003csup\u003e3+\u003c/sup\u003e ions in stabilizing the metastable phases to room temperature (Supplementary Figs. 12 and 13). Such a phenomenon coincides with the phase modulation behavior observed in RE:HfO\u003csub\u003e2\u003c/sub\u003e and RE:ZrO\u003csub\u003e2\u003c/sub\u003e, where larger RE doping concentrations tend to stabilize the metastable \u003cem\u003et\u003c/em\u003e phase with\u0026nbsp;a\u0026nbsp;higher formation energy\u003csup\u003e32,33\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNext, we conducted temperature-dependent\u0026nbsp;XRD analysis\u0026nbsp;on the Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e (9.25 at.%) crystals to study the polymorphism transformation between different metastable phases as a function of temperature. A reversible phase transition was observed\u0026nbsp;(Fig. 1d,e), with transformation temperatures occurring in the heating and cooling processes, located in ranges of 600\u0026ndash;700\u0026deg;C during heating and 400\u0026ndash;500\u0026deg;C during cooling. These phase-change temperatures were further confirmed by the differential scanning calorimetry (DSC) measurement\u0026nbsp;(Supplementary Fig. 14). The transition temperatures of the DSC results were ~628\u0026deg;C during heating and ~483\u0026deg;C during cooling. Such a large thermal hysteresis (~145\u0026deg;C) reflected a large barrier of the activation energy between the high- and low-temperature phases owing to the rearrangement of the Hf and O atoms, e.g.,\u0026nbsp;46.0\u0026nbsp;meV/f.u for \u003cem\u003et\u003c/em\u003e to \u003cem\u003eo\u003c/em\u003e-FE and\u0026nbsp;68.8\u0026nbsp;meV/f.u for \u003cem\u003et\u003c/em\u003e to \u003cem\u003eo\u003c/em\u003e-AFE\u003csup\u003e22\u003c/sup\u003e. The transition from the low-temperature\u0026nbsp;orthorhombic phase\u0026nbsp;to the high-temperature polymorph was marked by the disappearance of Bragg diffraction peaks at ~53.7\u0026deg;, ~55.9\u0026deg;, ~65.8\u0026deg;, and ~67.9\u0026deg;. This signified the complete transformation from the low-temperature phase to the high-temperature phase. Notably,\u0026nbsp;the high-temperature phase possessed two distinct diffraction peaks around\u0026nbsp;~59.5\u003csup\u003eo\u003c/sup\u003e (or\u0026nbsp;~73.7\u003csup\u003eo\u003c/sup\u003e), suggesting that the high-temperature metastable\u0026nbsp;polymorph was\u0026nbsp;the \u003cem\u003et\u003c/em\u003e phase rather than the \u003cem\u003ec\u003c/em\u003e phase\u003csup\u003e19,34,35\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe above structural analyses highlight the polymorphic engineering within the\u0026nbsp;Lu:Hf\u003csub\u003e1\u0026ndash;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk\u0026nbsp;crystals by describing the synergistic contributions from co\u003cem\u003e-\u003c/em\u003edoping Lu\u003csup\u003e3+\u003c/sup\u003e and Zr\u003csup\u003e4+\u003c/sup\u003e ions. The presence of RE\u003csup\u003e3+\u003c/sup\u003e ions serves to address the challenges posed by the eutectoid reaction during the crystal growth and facilitates the phase evolution within the bulk crystals by leveraging oxygen vacancies (Supplementary Fig. 15), which are induced by heterovalent substitution\u003csup\u003e17\u003c/sup\u003e. By maintaining fixed optical floating zone growth conditions, the introduction of Zr\u003csup\u003e4+\u003c/sup\u003e ions plays an important role in fine-tuning the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e transition temperature (Supplementary Fig. 25), benefiting the adjustment of the phase composition within the final bulk crystals.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDielectric and ferroelectric\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003echaracterizations of Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003ebulk\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;crystals\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn this context, we investigated temperature-dependent\u0026nbsp;dielectric constant (\u003cem\u003e\u0026epsilon;\u003csub\u003er\u003c/sub\u003e\u003c/em\u003e) in Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e bulk\u0026nbsp;crystals. As exhibited in Fig. 2a, analogous to the aforementioned temperature dependences of structural and thermal results, an evident transition peak of \u003cem\u003e\u0026epsilon;\u003csub\u003er\u003c/sub\u003e\u003c/em\u003e was observed\u0026nbsp;at the Curie temperature (~661\u0026deg;C). This\u0026nbsp;\u003cem\u003eo\u003c/em\u003e-\u003cem\u003et\u003c/em\u003e transition behavior was consistent with that observed in\u0026nbsp;HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectric films and aroused our research interest in the ferroelectric property within\u0026nbsp;the as-grown bulk crystals\u003csup\u003e36\u003c/sup\u003e. Then,\u0026nbsp;the related ferroelectric polarization in Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk\u0026nbsp;crystals was investigated using the positive-up-negative-down technique. As shown in Fig. 2b and\u0026nbsp;Supplementary Fig.\u0026nbsp;16, pronounced polarization hysteresis was observed, confirming the existence of the ferroelectric phase\u003csup\u003e37\u003c/sup\u003e. For the Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e bulk\u0026nbsp;crystal, the\u0026nbsp;coercive field (\u003cem\u003eE\u003csub\u003ec\u003c/sub\u003e\u003c/em\u003e) of was determined to be 1.45\u0026nbsp;MV/cm, consistent with the values reported for HfO\u003csub\u003e2\u003c/sub\u003e-based\u0026nbsp;ferroelectric\u0026nbsp;thin\u0026nbsp;films (1\u0026ndash;2\u0026nbsp;MV/cm)\u003csup\u003e6,16,38\u003c/sup\u003e.\u0026nbsp;The obtained saturation polarization (\u003cem\u003eP\u003csub\u003es\u003c/sub\u003e\u003c/em\u003e) attained a value of 48.6\u0026nbsp;\u0026mu;C/cm\u003csup\u003e2\u003c/sup\u003e, approaching the intrinsic\u0026nbsp;polarization of HfO\u003csub\u003e2\u003c/sub\u003e-based\u0026nbsp;ferroelectric materials (50\u0026ndash;60\u0026nbsp;\u0026mu;C/cm\u003csup\u003e2\u003c/sup\u003e)\u003csup\u003e15,23,31\u003c/sup\u003e.\u0026nbsp;Notably, as shown in Fig. 2b and\u0026nbsp;Supplementary\u0026nbsp;Table 2, the measured remanent polarization \u003cem\u003eP\u003csub\u003er\u003c/sub\u003e\u003c/em\u003e reached 26 \u0026mu;C/cm\u003csup\u003e2\u003c/sup\u003e, which was comparable to those of HfO\u003csub\u003e2\u003c/sub\u003e-based epitaxial\u0026nbsp;ferroelectric films (~10\u0026nbsp;nm in thickness)\u0026nbsp;and\u0026nbsp;surpassed the values reported for\u0026nbsp;thick\u0026nbsp;polycrystalline films (~17\u0026nbsp;\u0026mu;C/cm\u003csup\u003e2\u003c/sup\u003e,\u0026nbsp;~1\u0026nbsp;\u0026mu;m thick) as well as Y:HfO\u003csub\u003e2\u003c/sub\u003e bulk crystals (~3 \u0026mu;C/cm\u003csup\u003e2\u003c/sup\u003e,\u0026nbsp;~2.7\u0026nbsp;\u0026mu;m thick)\u003csup\u003e22,39\u003c/sup\u003e. Typically,\u0026nbsp;the\u0026nbsp;ferroelectric performance\u0026nbsp;of HfO\u003csub\u003e2\u003c/sub\u003e-based\u0026nbsp;films\u0026nbsp;deteriorates with an increase in thickness. However, the as-grown Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e bulk crystals could maintain excellent\u0026nbsp;ferroelectric properties, even when the thickness was increased by three orders of magnitude. This result underscores the universal feature of HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectricity and eliminates the restriction that the excellent ferroelectric performance is confined solely to meticulously prepared HfO\u003csub\u003e2\u003c/sub\u003e-based epitaxial thin films. Additionally,\u0026nbsp;the local piezoresponse force microscopy (PFM) analysis (Fig. 2c-f,\u0026nbsp;Supplementary Fig.\u0026nbsp;18) showed an apparent change in the phase and amplitude when a voltage was applied. Clear contrast was observed by applying the same voltage magnitude with the opposite poling direction. The subsequent second harmonic generation (SHG) characterization further ascertained the presence of a polar phase within the as-grown bulk crystals (Supplementary Fig.\u0026nbsp;17).\u0026nbsp;The remarkable ferroelectric performance of the\u0026nbsp;Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e crystals\u0026nbsp;underscores the importance of understanding the local crystal structure, given the coexistence of multiple phases within the bulk crystals.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFormation mechanism of \u003cem\u003eo\u003c/em\u003e-FE phase in Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003ebulk\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;crystals\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe employed scanning transmission electron microscopy (STEM) to examine the local atomic arrangement within the bulk Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e crystal. It is noteworthy that the HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectricity is intricately associated with the displacement of oxygen ions,\u0026nbsp;in contrast to\u0026nbsp;the more traditional perovskite ferroelectric materials, where the shift of cation plays a dominant role\u003csup\u003e40,41\u003c/sup\u003e. To gain deeper insight into the transformation mechanism between various phases in the bulk crystal, we utilized the iDPC-STEM technique owing to its heightened sensitivity to light elements, enabling a more comprehensive study of the phase transitions.\u003c/p\u003e\n\u003cp\u003eFigure 3a-c and\u0026nbsp;Supplementary Fig.\u0026nbsp;19 exhibit the crystal structures of the\u0026nbsp;\u003cem\u003eo-\u003c/em\u003eAFE and \u003cem\u003et\u003c/em\u003e phases, as well as the \u003cem\u003eo-\u003c/em\u003eFE polar phase.\u0026nbsp;Specifically, the \u003cem\u003et\u003c/em\u003e phase possesses a single type of oxygen site,\u0026nbsp;located at the center of the four neighboring cation positions. In contrast,\u0026nbsp;both the\u0026nbsp;\u003cem\u003eo-\u003c/em\u003eFE and \u003cem\u003eo-\u003c/em\u003eAFE phases contain dual\u0026nbsp;oxygen sites (O1 and O2), exhibiting\u0026nbsp;an off-center behavior. Notably,\u0026nbsp;the\u003cem\u003e\u0026nbsp;o-\u003c/em\u003eFE and \u003cem\u003eo-\u003c/em\u003eAFE phases\u0026nbsp;exhibit a significant distribution difference of O2\u0026nbsp;ions within the \u003cem\u003eac\u003c/em\u003e plane. To delve further into the microstructure, iDPC-STEM was employed along the \u003cem\u003eb\u003c/em\u003e-axis direction of the\u0026nbsp;\u003cem\u003eo-\u003c/em\u003eFE and \u003cem\u003eo-\u003c/em\u003eAFE phases, a strategic choice for precise phase identification\u003csup\u003e20,42\u003c/sup\u003e. Figure 3d-f unveils critical insights into the material composition. Apart from the\u0026nbsp;Hf/Zr/Lu cations,\u0026nbsp;the image clearly highlights the presence of\u0026nbsp;oxygen ions, being instrumental to the phase identification\u0026nbsp;at the atomic scale. This finding is in accordance with the structural and\u0026nbsp;ferroelectric analyses discussed earlier, which confirmed that the bulk crystal simultaneously possessed the \u003cem\u003et\u003c/em\u003e,\u003cem\u003e\u0026nbsp;o-\u003c/em\u003eFE, and \u003cem\u003eo-\u003c/em\u003eAFE\u0026nbsp;phases. In the\u0026nbsp;\u003cem\u003eo-\u003c/em\u003eFE phase, the O2 ions in different polarization layers exhibited\u0026nbsp;a uniform\u0026nbsp;\u003cem\u003ec\u003c/em\u003e-axis\u0026nbsp;displacement direction, thus yielding robust\u0026nbsp;ferroelectric polarization.\u0026nbsp;The lattice parameters of the \u003cem\u003eo-\u003c/em\u003eFE phase were measured at \u003cem\u003ea\u003c/em\u003e = 5.17 Å and \u003cem\u003ec\u003c/em\u003e = 5.41 Å, closely resembling those of HfO\u003csub\u003e2\u003c/sub\u003e-based\u0026nbsp;ferroelectric\u0026nbsp;films and bulk crystals\u003csup\u003e22,23\u003c/sup\u003e. In contrast, the\u003cem\u003e\u0026nbsp;o-\u003c/em\u003eAFE phase (\u003cem\u003ea\u003c/em\u003e = 5.16 Å and \u003cem\u003ec\u003c/em\u003e = 5.11 Å), although possessing a similar cation distribution to that of the\u003cem\u003e\u0026nbsp;o-\u003c/em\u003eFE\u003cem\u003e\u0026nbsp;\u003c/em\u003ephase, exhibited a distinctive feature. The adjacent polarization layers exhibited reversed polarization directions, resulting in an antipolar nature. As shown in Fig. 3g, the \u003cem\u003eo-\u003c/em\u003eFE and \u003cem\u003eo-\u003c/em\u003eAFE phases coexisted in certain regions owing to the low free energy gap between these two phases (~10\u0026nbsp;meV/f.u)\u003csup\u003e43,44\u003c/sup\u003e. This observation coincides with the atomic-resolution phase identification in ZrO\u003csub\u003e2\u003c/sub\u003e and\u0026nbsp;Hf\u003csub\u003e0.5\u003c/sub\u003eZr\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e ferroelectric\u0026nbsp;films, revealing that the disparity between the \u003cem\u003eo-\u003c/em\u003eFE and \u003cem\u003eo-\u003c/em\u003eAFE polymorphs relies on the displacement direction of the oxygen ions within the polarization layers\u003csup\u003e14,20,22\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eFurthermore, as shown in Fig. 4a, we observed the local multiphase region within the Lu:Hf\u003csub\u003e0.6\u003c/sub\u003eZr\u003csub\u003e0.4\u003c/sub\u003eO\u003csub\u003e2\u003c/sub\u003e bulk crystal,\u0026nbsp;where the\u0026nbsp;\u003cem\u003et\u003c/em\u003e, \u003cem\u003eo-\u003c/em\u003eFE, and \u003cem\u003eo-\u003c/em\u003eAFE phases coexisted. Notably, we identified\u0026nbsp;distinct transitional phase regions between the \u003cem\u003et\u003c/em\u003e and \u003cem\u003eo-\u003c/em\u003eFE or\u003cem\u003e\u0026nbsp;o-\u003c/em\u003eAFE phases, which differed from the steep \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase boundary observed in HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectric films\u003csup\u003e20,45\u003c/sup\u003e. The complete \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase transformation process contained two distinct stages, denoted as \u003cem\u003et\u003c/em\u003e\u0026rsquo; and \u003cem\u003et\u003c/em\u003e\u0026rdquo;, corresponding to changes in the O and Hf sites, respectively (Supplementary Figs. 21 and 24). With Cluster 4 as an example, as illustrated in Fig. 4b, the Hf sites showed minimal position alteration, while the O sites within the polarization layers exhibited an evident atomic shift in\u0026nbsp;the \u003cem\u003et\u003c/em\u003e\u0026rsquo; stage, leading to a reduction in \u003cem\u003ed\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e compared to that of the \u003cem\u003et\u003c/em\u003e phase. In the adjacent \u003cem\u003et\u003c/em\u003e\u0026rdquo; stage, the primary change occurred within the neighboring horizontal Hf atomic layers, giving rise to an increase in \u003cem\u003ed\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e and a decrease in \u003cem\u003ed\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e. The position change of the Hf atoms led to a slight vertical displacement of the O atoms, but the horizontal mirror symmetry \u003cem\u003em\u003csub\u003eh\u003c/sub\u003e\u003c/em\u003e remained unbroken. This observation delineated the concrete atomic shift trajectory during the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase transformation, contributing to a more comprehensive understanding of the formation mechanism of the \u003cem\u003eo-\u003c/em\u003eFE phase. According to the phase evolution shown in Fig. 4c, the movement of O atoms in the \u003cem\u003et\u003c/em\u003e\u0026rsquo; stage broke the centrosymmetric operation and transformed the space group from tetragonal non-polar \u003cem\u003eP\u003c/em\u003e4\u003csub\u003e2\u003c/sub\u003e/\u003cem\u003enmc\u003c/em\u003e to orthorhombic polar crystal systems. Through the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e transition, the shift of the O sites (\u003cem\u003ed\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e) reached the maximum distance and yielded robust\u0026nbsp;intrinsic\u0026nbsp;polarization\u0026nbsp;in the \u003cem\u003eo-\u003c/em\u003eFE phase. Additionally, the values of \u003cem\u003ed\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003ed\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, and \u003cem\u003ed\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e in the \u003cem\u003eo-\u003c/em\u003eFE phase remained relatively constant at approximately ~270 , ~240 , and ~75 pm, respectively. The apparent distance distinction between the \u003cem\u003eo-\u003c/em\u003eFE and \u003cem\u003et\u003c/em\u003e phases\u0026nbsp;(\u003cem\u003ed\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e =\u0026nbsp;\u003cem\u003ed\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e =\u0026nbsp;~259 pm, \u003cem\u003ed\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e =\u0026nbsp;~130\u0026nbsp;pm) implied that\u0026nbsp;the bulk crystal experienced a strong strain alteration\u0026nbsp;during the\u0026nbsp;\u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e transition\u0026nbsp;process.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo assess the strain distributions within the\u0026nbsp;Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk crystals, we conducted a thorough analysis using geometric phase analysis (GPA). As shown in Fig. 4d and Supplementary Fig. 23, the crystal specimen manifested a significant normal strain and a relatively weak shear strain. The normal strain progressively increased throughout the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase transformation (from the right to the left sides within Clusters 1\u0026ndash;8), a phenomenon akin to the stabilization mechanism observed in epitaxial films for the \u003cem\u003eo-\u003c/em\u003eFE phase via the strain effect\u003csup\u003e4,6,31,46\u003c/sup\u003e. In the case of two orthorhombic phases (as shown in Supplementary Figs. 22 and\u0026nbsp;23), the \u003cem\u003eo-\u003c/em\u003eFE phase exhibited an apparent compressive strain within the spacer layers, while the \u003cem\u003eo-\u003c/em\u003eAFE phase exhibited alternating strong tensile and compressive strains in the adjacent spacer layers. Notably, the strain fluctuations in the \u003cem\u003eo-\u003c/em\u003eAFE phase were significantly more pronounced than those in the \u003cem\u003eo-\u003c/em\u003eFE and \u003cem\u003et\u003c/em\u003e phases, suggesting that the presence of the \u003cem\u003eo-\u003c/em\u003eAFE phase carried a higher risk of inducing cracks in\u0026nbsp;the\u0026nbsp;bulk\u0026nbsp;crystals. The primary phase in the Lu:HfO\u003csub\u003e2\u003c/sub\u003e (10\u0026ndash;11 at.%)\u0026nbsp;and\u0026nbsp;Gd:HfO\u003csub\u003e2\u003c/sub\u003e (15\u0026nbsp;\u0026nbsp;at.%) bulk crystals\u0026nbsp;was the \u003cem\u003eo-\u003c/em\u003eAFE phase, and hence, these bulk crystals were easily\u0026nbsp;broken during the machining process. In contrast, the introduction of Zr\u003csup\u003e4+\u003c/sup\u003e ions brought the \u003cem\u003et\u003c/em\u003e metastable phase\u0026nbsp;as a buffer region\u0026nbsp;into the\u0026nbsp;Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk crystals. This effectively accommodated the large local strain fluctuations caused by the\u0026nbsp;\u003cem\u003eo-\u003c/em\u003eFE\u003cem\u003e\u0026nbsp;\u003c/em\u003eand \u003cem\u003eo-\u003c/em\u003eAFE phases and ensured the processing feasibility of the as-grown bulk crystals, even with a thickness as low as tens of micrometers (Fig. 2b).\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe puzzle surrounding the ferroelectric origin of HfO\u003csub\u003e2\u003c/sub\u003e-based\u0026nbsp;materials poses a hurdle to the understanding of the intricate structure-property interplay between device manufacturing and their ferroelectric performances\u003csup\u003e1,6,47\u003c/sup\u003e. Although different ferroelectric crystal structures have been proposed over the past decade, the relevant research has predominantly revolved around phase identification. The direct observation of evidence for the evolution of the metastable ferroelectric phase at the atomic scale remains challenging due to the small grain size (~20\u0026nbsp;nm) inherent in nanoscale thin films\u003csup\u003e6,48\u003c/sup\u003e\u003csup\u003e\u0026ndash;\u003c/sup\u003e\u003csup\u003e50\u003c/sup\u003e. Through composition optimization, we realized a controllable polymorphic adjustment in the fast growth process by understanding the mechanism of the relevant phase transformation, which effectively stabilized the metastable \u003cem\u003eo-\u003c/em\u003eFE\u0026nbsp;phase\u0026nbsp;in the as-grown bulk crystals. On that basis, we achieved robust ferroelectric polarization within the\u0026nbsp;fluorite-structure\u0026nbsp;Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk crystals, rivaling the performances observed in ultra-thin films. Of particular importance is that we uncovered the metastable phases within the bulk crystals and provided clear evidence of the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase evolution pathway by directly tracking the movement of Hf and O atoms. These local structural changes were intricately related to the synergistic modulation from co-doped Lu\u003csup\u003e3+\u003c/sup\u003e and Zr\u003csup\u003e4+\u003c/sup\u003e ions. The Zr\u003csup\u003e4+\u003c/sup\u003e ions played a vital role in stabilizing the metastable \u003cem\u003et\u003c/em\u003e phase, and the Lu\u003csup\u003e3+\u003c/sup\u003e ions controlled the progress of the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase transformation effectively (Fig. 1b,c). Notably, these results underscore the important role of the bulk-state perspective in deciphering the mechanisms that govern the phase transformation in HfO\u003csub\u003e2\u003c/sub\u003e-based materials.\u0026nbsp;This approach also facilitates the exploration of the domain wall structure\u0026nbsp;at a unit-cell-size level\u0026nbsp;and the associated domain evolution. The significance of these findings\u0026nbsp;greatly enhances our understanding of\u0026nbsp;the\u0026nbsp;ferroelectric\u0026nbsp;mechanisms in\u0026nbsp;HfO\u003csub\u003e2\u003c/sub\u003e-based materials. Furthermore, they\u0026nbsp;facilitate the development of electronic and photonic functional devices\u0026nbsp;with fluorite-structured materials that are compatible with\u0026nbsp;CMOS technology. This echoes the functionalities observed in applications involving perovskite-based materials.\u003c/p\u003e\n\u003cp\u003eIn brief,\u0026nbsp;our research represented a breakthrough in inducing robust ferroelectricity within\u0026nbsp;Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk crystals, achieved through a comprehensive understanding of the regulatory role played by Lu\u003csup\u003e3+\u003c/sup\u003e and Zr\u003csup\u003e4+\u003c/sup\u003e ions. The as-grown crystal exhibited an impressive \u003cem\u003eP\u003csub\u003er\u003c/sub\u003e\u003c/em\u003e value of 26\u003csup\u003e\u0026nbsp;\u003c/sup\u003e\u0026mu;C/cm\u003csup\u003e2\u003c/sup\u003e, even with a thickness\u0026nbsp;three orders of magnitude higher than those of the extensively studied ultra-thin films. The main source of ferroelectricity in the\u0026nbsp;Lu:Hf\u003csub\u003e1\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk crystals was attributed to the \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase transition, a finding consistent with the observations in thin films. Furthermore, we elucidated the intricate process of \u003cem\u003et\u003c/em\u003e-\u003cem\u003eo\u003c/em\u003e phase evolution by directly observing the dynamic movement of Hf and O atoms, as well as the precise structural alterations. These findings bridge the gap between bulk and ultra-thin HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectric materials, providing profound insights into their ferroelectric origin. We anticipate that this study, serving as a paradigm for fabricating large-sized bulk HfO\u003csub\u003e2\u003c/sub\u003e-based ferroelectric crystals, will facilitate the understanding of the nanosized ferroelectric domain evolution in fluorite-structured materials, which will greatly benefit the development of CMOS-compatible devices in ferroelectrics, piezoelectrics, and pyroelectrics.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eOnline content\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAny methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eCrystal growth\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe Lu:Hf\u003csub\u003e1-\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk crystals were grown by the optical floating zone (OFZ) method with a four-ellipsoidal-mirror furnace (Crystal Systems Inc., FZ-T-12000-X-I-S-SU), which could realize the heating temperature to\u0026nbsp;3000\u003csup\u003eo\u003c/sup\u003eC. For the\u0026nbsp;optimal growth\u0026nbsp;parameters,\u0026nbsp;the feed and seed rod rotation rates were set at 10\u0026nbsp;rpm and 5\u0026nbsp;rpm, respectively, the growth rate was set at 20\u0026nbsp;mm/h, and the flow rate of O\u003csub\u003e2\u003c/sub\u003e was fixed at 150 ml/min.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eXRD, DSC, and dielectric measurements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe as-obtained Lu:Hf\u003csub\u003e1-\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e bulk crystals were directly used for the related characterizations. The room-temperature XRD measurements were carried out on a Rigaku diffractometer (smartlab 3 kW) with a Cu K\u0026alpha; radiation source, and the step size was 0.01\u0026deg;. The temperature-dependent in-situ XRD measurements were analyzed by a Rigaku diffractometer (smartlab, 9 kW) with a Cu K\u003cem\u003e\u0026alpha;\u003c/em\u003e radiation source. The diffraction data were collected after a delay of 5 min to maintain thermal balance. The heating rate was 10\u003csup\u003eo\u003c/sup\u003eC/min, and the scanning rate was 0.01\u0026deg;/step.\u0026nbsp;The DSC data of\u0026nbsp;Lu:Hf\u003csub\u003e1-\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u0026nbsp;\u003c/sub\u003ewere measured by employing a TA DISCOVERY (SDT650) synchronous thermal analyzer. The whole process was in the\u0026nbsp;air\u0026nbsp;atmosphere, the surveyed temperature range was from\u0026nbsp;30\u0026nbsp;to\u0026nbsp;1000\u003csup\u003eo\u003c/sup\u003eC. Both the heating and cooling rates were 5\u003csup\u003eo\u003c/sup\u003eC/min. The temperature-dependent dielectric constant \u003cem\u003e\u0026epsilon;\u003csub\u003er\u003c/sub\u003e\u003c/em\u003e was surveyed using an LCR meter (ZX8528A,\u0026nbsp;Zhixin Precision Electronics) with a heating rate of 5\u003csup\u003eo\u003c/sup\u003eC/min.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eXPS, Raman, and SHG characterizations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe room-temperature\u0026nbsp;X-ray photoelectron spectroscopy (XPS) was conducted with Thermo Fisher ESCALAB XI+ equipped with monochromatic Al-K\u003cem\u003e\u0026alpha;\u0026nbsp;\u003c/em\u003eradiation.\u0026nbsp;Room-temperature Raman spectra were surveyed with\u0026nbsp;an iHR550 Raman\u0026nbsp;spectrometer\u0026nbsp;and a 632-nm He-Ne laser (5 mW).\u0026nbsp;The\u0026nbsp;room-temperature\u0026nbsp;second harmonic generation (SHG) investigation was realized with\u0026nbsp;an iHR550 Raman\u0026nbsp;spectrometer and a\u0026nbsp;femtosecond laser (1030 nm, 250 fs, 200 kHz).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eP\u003c/em\u003e\u003c/strong\u003e\u003cstrong\u003e\u0026ndash;\u003c/strong\u003e\u003cstrong\u003e\u003cem\u003eE\u003c/em\u003e\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;and PFM measurements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA pristine\u0026nbsp;Lu:Hf\u003csub\u003e1-\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eZr\u003cem\u003e\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e crystal was mechanically polished into a piece with a thickness of 10-20\u0026nbsp;\u0026mu;m. The Au electrode with an area of 250000\u0026nbsp;\u0026micro;m\u003csup\u003e2\u003c/sup\u003e was made by\u0026nbsp;sputtering.\u0026nbsp;The\u0026nbsp;\u003cem\u003eP\u003c/em\u003e\u0026ndash;\u003cem\u003eE\u003c/em\u003e loop was measured by the positive-up-negative-down technique provided in a\u0026nbsp;Ferroelectric Material Test System\u0026nbsp;(aixACCT, TF Analyzer 2000) with\u0026nbsp;\u003cem\u003eV\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e=6000\u0026nbsp;V and\u0026nbsp;\u003cem\u003ef\u003c/em\u003e=1\u0026nbsp;Hz.\u0026nbsp;The PFM sample was prepared by\u0026nbsp;Helios 5 CX Dualbeam scanning electron microscopy.\u0026nbsp;The sample was stuck with the silver epoxy\u0026nbsp;to\u0026nbsp;fix\u0026nbsp;to gold-plated silicon wafers, followed by a reduction by a focused ion beam to the order of ~50\u0026nbsp;nm (observed by SEM, HITACHI S-4800). The samples were\u0026nbsp;performed by MFP-3D-Origion+\u0026nbsp;Asylum Research.\u0026nbsp;Dual-frequency resonance-tracking PFM was conducted using a conductive Ti/Ir-coated probe tip\u0026nbsp;(25\u0026nbsp;nm radius, resonant frequency: 75\u0026nbsp;kHz, force constant: 2.8\u0026nbsp;N/m)\u0026nbsp;to image written domain structures and measure switching-spectroscopy piezoelectric hysteresis loops. Contact was made to the bottom Ag electrode for grounding in PFM studies. PFM imaging was performed with the tip in direct contact with the sample surface.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSTEM analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe direction of the as-grown crystal specimens was confirmed by EBSD based on Carl Zeiss crossbeam 550L FIB-SEM. The electron transparent sample for the STEM observation was prepared by a Carl Zeiss crossbeam 550L FIB-SEM using the conventional lift-out method. The integrated differential phase-contrast scanning transmission electron microscopy (iDPC-STEM) experiments were carried out at 300 kV using a ThermoFisher Scientific Themis Z microscope, equipped with a probe corrector, and a four-segment DF4 detector. The convergence angle was 25 mrad and the collection angle for iDPC-STEM imaging was 6-20 mrad. STEM-EDS mapping was carried out using a thermofisher Spectra 300 equipped with a Super X EDS probe. Fourier-filtered iDPC-STEM images were analyzed by CalAtom Software to extract the atomic position of Hf/Zr and nonpolar O ions by multiple-ellipse fitting. The positions of polarized O ions were extracted by line profile using Gatan Microscopy Suite Software (Version 3.22.1461.0).\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that supports the plots within this paper and other findings of this study are available from the corresponding authors on request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe thank C.Wang for the useful discussion on the ferroelectric investigation. This work is supported by the National Key Research and Development Program of China (2021YFB3601504), the National Natural Science Foundation of China (52025021), the Natural Science Foundation of Shandong Province (ZR2022LLZ005), and the Future Plans of Young Scholars at Shandong University.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eS.W., H.Y., S.Z., and H.Z. designed and conceived the research idea. S.W., Y.S., and H.Y. performed the crystal growth and related characterizations, including XRD, Raman, XPS, and SHG. Y.S. performed the polarization measurement and PFM investigations under the supervision of H.Z. S.W., X.Y., and P.N. performed the STEM observation and relevant analysis under the guidance of B.G. and H.Y. S.W. and Y.S. wrote the original manuscript, H.Y., S. Z., and H.Z. revised the manuscript. All authors contributed to the discussion of the results.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e The authors declare no competing interests.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary information\u0026nbsp;\u003c/strong\u003eThe online version contains supplementary material available at.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrespondence and requests for materials\u003c/strong\u003e should be addressed to Haohai Yu or Huaijin Zhang.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eKang, S. et al. 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Intrinsic 90\u0026deg; charged domain wall and its effects on ferroelectric properties. \u003cem\u003eActa Mater\u003c/em\u003e. \u003cstrong\u003e232\u003c/strong\u003e, 117920 (2022).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3803321/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3803321/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The discovery of ferroelectricity in hafnium dioxide (HfO2) thin films over the past decade has revolutionized the landscape of ferroelectrics. HfO2-based ferroelectrics exhibit extraordinary switching capabilities and integrability in existing semiconductor chips, making them a promising candidate for next-generation ferroelectrics beyond the constraints of Moore’s law. However, the underlying mechanism of their ferroelectricity remains a topic of debate, possibly related to the presence of a metastable and volatile ferroelectric phase. Herein, we have achieved the successful growth of HfO2-based bulk crystals, revealing a remarkable remanent polarization of 26 μC/cm2 by a comprehensive understanding of the polymorphic engineering strategy. This result not only rivals the performances observed in extensively studied ultra-thin films but also underscores the universal feature of HfO2-based ferroelectricity. Our investigation has unveiled the intricate local structural transitions during the development of the ferroelectric phase in bulk crystals, clearly elucidating that the ferroelectric orthorhombic Pbc21 phase originates from the metastable tetragonal phase. This groundbreaking discovery clarifies the ferroelectric origin of HfO2 and provides a strategic approach for designing robust ferroelectricity. Our findings hold the potential to advance the comprehension of ferroelectric mechanisms in fluorite-structured materials, paving the way for significant strides in the subsequent development of HfO2-based nonvolatile electronic and photonic devices.","manuscriptTitle":"Robust ferroelectricity in HfO2-based bulk crystals via polymorphic engineering","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-05 18:36:11","doi":"10.21203/rs.3.rs-3803321/v1","editorialEvents":[{"type":"communityComments","content":1}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1e8e1ee2-06e1-4d11-a424-28b38d1338f7","owner":[],"postedDate":"January 5th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":27966954,"name":"Physical sciences/Materials science/Materials for devices/Electronic devices"},{"id":27966955,"name":"Physical sciences/Materials science/Materials for devices/Information storage"}],"tags":[],"updatedAt":"2024-02-05T10:02:33+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-05 18:36:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3803321","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3803321","identity":"rs-3803321","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}