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[Kantaro Murayama](https://orcid.org/0000-0003-0993-0215), [Ryota Masuki](https://orcid.org/0000-0002-5407-844X), [Cédric Tassel](https://orcid.org/0000-0002-8867-4813), [Hideaki Sakai](https://orcid.org/0000-0001-9839-1377), [Tatsuya Yanagisawa](https://orcid.org/0000-0003-4558-8824), Keito Yoshida, [Hiroshi Oike](https://orcid.org/0000-0001-6866-7774), [Suguru Yoshida](https://orcid.org/0000-0002-1016-5031), Xiangyu Gu, [Kohdai Ishida](https://orcid.org/0000-0002-9824-6388), [Morito Namba](https://orcid.org/0000-0002-0118-9832), [Ksenia Denisova](https://orcid.org/0000-0001-8019-2126), Valérie Dupray, [Simon Clevers](https://orcid.org/0000-0002-1377-1141), [Olivier Mentré](https://orcid.org/0000-0002-1822-6003), [Takuya Nomoto](https://orcid.org/0000-0002-4333-6773), [Terumasa Tadano](https://orcid.org/0000-0002-8132-2161), [Craig M. Brown](https://orcid.org/0000-0002-9637-9355), [Peter Lemmens](https://orcid.org/0000-0002-0894-3412), [Ryotaro Arita](https://orcid.org/0000-0001-5725-072X), [Hiroshi Takatsu](https://orcid.org/0000-0001-5792-0113), [Hiroshi Kageyama](https://orcid.org/0000-0002-3911-9864)

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[Lattice softening and diffusive dynamics in the polar metal LiReO                    <sub>3</sub>](https://mdr.nims.go.jp/datasets/31d91e09-30e2-4ee1-b34e-5c3ecb0155b2)

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Lattice softening and diffusive dynamics in the polar metal LiReO3Murayama et al., Sci. Adv. 12, eadt3886 (2026)     3 April 2026S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e1 of 9M AT E R I A L S  S C I E N C ELattice softening and diffusive dynamics in the polar metal LiReO3Kantaro Murayama1†, Ryota Masuki2†, Cédric Tassel1‡, Hideaki Sakai3, Tatsuya Yanagisawa4,  Keito Yoshida4, Hiroshi Oike2,5§, Suguru Yoshida1, Xiangyu Gu1, Kohdai Ishida1, Morito Namba1, Ksenia Denisova6, Valérie Dupray7, Simon Clevers7, Olivier Mentré8, Takuya Nomoto9,10,  Terumasa Tadano11, Craig M. Brown12,13, Peter Lemmens6, Ryotaro Arita9,14*,  Hiroshi Takatsu1*, Hiroshi Kageyama1*Polar metals, characterized by the nontrivial coexistence of metallicity and polar structural order, define an emerg-ing frontier in quantum materials research. However, the interplay between their structural phase transitions and fluctuation dynamics remains poorly understood. Here, we reveal distinct diffusive dynamics in metallic lithium rhenium trioxide (LiReO3) associated with its polar-to-nonpolar transition. Unlike isostructural lithium niobate (LiOsO3) and related systems, LiReO3 exhibits pronounced phase fluctuations both above and below Ts. Thermo-electric, Raman, and ultrasound measurements demonstrate a probe-dependent thermal hysteresis, while ultra-sound data further show lattice softening and persistent resonant absorption at low temperatures across a broad timescale (1 to 100 microseconds). These observations indicate a multiscale spatiotemporal dynamics governed by a shallow anharmonic potential stabilized by itinerant electrons, as supported by finite-temperature first-principles calculations. By mapping the fluctuation landscape shaped by itinerant electrons, this work offers a previously unexplored perspective for exploiting fluctuation-driven phenomena in polar metals.INTRODUCTIONFerroelectric oxides are indispensable for both fundamental studies and technological applications (1). Among them, LiNbO3 (LN)–type structures are widely used because of their strong piezoelectricity, py-roelectricity, and nonlinear optical properties (2, 3). These materials undergo polar-nonpolar (P-NP) structural phase transitions driven by symmetry breaking (4–6). Beyond these well-established proper-ties, relaxor ferroelectrics exhibit nanoscale phase inhomogeneity upon cooling, manifested as polar nanoregions (7), a phenomenon attributed to the Anderson localization of ferroelectric phonons (8). The incorporation of transition metals has further broadened LN-type materials, enabling multiferroicity, as exemplified by MnTiO3 (9) and FeTiO3 (10).In contrast to these insulating materials, polar metals were long considered improbable since their theoretical proposal in the 1960s (11), primarily because conduction electrons were expected to screen out polar instabilities and suppress P-NP transitions. This view was overturned five decades later by the discovery of LiOsO3, an LN-type compound that undergoes a P-NP transition at Ts = 140 K while re-taining metallicity, thus recognized as the first polar metal undergoing a P-NP structural phase transition (12). Since then, the coexistence of polarity and metallicity has attracted growing attention (13–16). Ultrafast spectroscopy studies suggest that the transition in LiOsO3 involves a decoupling between itinerant electrons and transverse op-tical polar phonons (17), whereas high-pressure experiments attri-bute this decoupling to a local Li-O coordination instability (18). Recent second-harmonic generation (SHG) measurements further identified short-range polar correlations persisting above Ts (Ts < T  < ~230 K) (19), indicating the presence of a critical region and an order-disorder–type second-order transition, reminiscent of the sce-nario proposed for LiNbO3 (4, 5, 20–24).Despite these observations, the underlying driving force remains elusive, particularly regarding how the polar metallic state relates to its insulating counterparts. The intricate interplay between P-NP phase transitions and fluctuation dynamics, governed by the unique electronic states of polar metals, remains poorly understood. Fur-thermore, the functional exploitation of such fluctuations represents an emerging yet largely unexplored direction.In this work, we report that LiReO3 is a polar metal undergoing a P-NP transition at a slightly higher temperature (Ts = 170 K) than LiOsO3 (Fig. 1A) but with a fundamentally different character. Un-like LiOsO3, which exhibits precursor phenomena only above Ts (19, 25), LiReO3 undergoes a first-order transition marked by dif-fusive lattice dynamics and persistent spatiotemporal fluctuations 1Department of Energy and Hydrocarbon Chemistry, Graduate School of Engineer-ing, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan. 2Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan. 3Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan. 4De-partment of Physics, Hokkaido University, Sapporo 060-0810, Japan. 5PRESTO, Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan. 6Institute for Condensed Matter Physics, Technische Universität Braunschweig, Braunschweig 38106, Germany. 7SMS. UR 3233, Univ Rouen Normandie, Normandie Univ, Rouen F-76000, France. 8Université Lille Nord de France, UMR 8181 CNRS, Unité de Catalyse et de Chimie du Solide (UCCS USTL), Villeneuve d’Ascq F-59655, France. 9Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan. 10Depart-ment of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan. 11CMCM, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan. 12Chemical and Biomolecular Engineering, University of Delaware, Newark, DE 19716, USA. 13National Institute of Standards and Technolo-gy, Center for Neutron Research Gaithersburg, MD 20899-6102, USA. 14RIKEN Cen-ter for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.*Corresponding author. Email: arita@​riken.​jp (R.A.); takatsu@​scl.​kyoto-u.​ac.​jp (H.T.); kage@​scl.​kyoto-u.​ac.​jp (H.K.)†These authors contributed equally to this work.‡Present address: Univ. Bordeaux, CNRS, Bordeaux INP, ICMCB, UMR 5026, Pessac F-33600, France.§Present address: Research Center for Materials Nanoarchitectonics (MANA), Na-tional Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan.Copyright © 2026 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY). Downloaded from https://www.science.org at National Institute for Materials Science on April 06, 2026mailto:arita@​riken.​jpmailto:takatsu@​scl.​kyoto-u.​ac.​jpmailto:kage@​scl.​kyoto-u.​ac.​jphttp://crossmark.crossref.org/dialog/?doi=10.1126%2Fsciadv.adt3886&domain=pdf&date_stamp=2026-04-03Murayama et al., Sci. Adv. 12, eadt3886 (2026)     3 April 2026S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e2 of 9that extend well below Ts, accompanied by probe-dependent hyster-esis spanning a wide temperature range. The suppression of the polar phase in the insulating-to-metal crossover of LiRe1–xNbxO3 highlights the role of mobile electrons in screening the internal electric field. In addition, first-principles calculations reveal an exceptionally small energy difference between polar and nonpolar states, resulting in a shallow potential landscape that stabilizes a biphasic regime over an extended temperature range. These findings provide insights into the interplay between polarity and metallicity, as it enlarges its exis-tence and demonstrates a pathway to accessing and controlling emer-gent low-temperature functionalities in polar metals.RESULTSPolar metallic LiReO3Previous structural analyses of LiReO3 were limited to room tempera-ture and assumed a polar (R3c) structure without direct confirmation of polarity (26). The authors also noted possible lithium nonstoichi-ometry or inhomogeneity, potentially resulting from a topochemi-cal reaction from ReO3 (26). To obtain stoichiometric samples, we used high-pressure synthesis, which effectively suppresses defects commonly present under ambient-pressure conditions (27–29). The synchrotron x-ray diffraction (SXRD) pattern at 300 K was indexed using a rhombohedral cell [a = 5.09984(1) Å, c = 13.39810(4) Å] (fig. S1), consistent with previous reports (26). However, SHG mea-surements showed no signal at 293 K, while a clear peak emerged at 143 K (Fig. 1B and fig. S2), indicating the breaking of centrosym-metry below room temperature.Rietveld refinements of the SXRD data at 300 and 100 K were performed using the centrosymmetric (R-3c) and noncentrosym-metric (R3c) space groups, respectively (fig. S1 and tables S1 and S2), with both models yielding regular ReO6 octahedra. To further in-vestigate the low-temperature structure, neutron powder diffraction (NPD) at 6 K was conducted, which revealed off-centering of Li+ ions (fig. S3 and table S3), as observed in canonical polar oxides such as LiNbO3 and LiTaO3 (4, 30–33). These results collectively confirm the emergence of a polar phase in LiReO3 below room temperature, consistent with SHG observations.In situ SXRD measurements (fig. S4) revealed a P-NP structural phase transition, characterized by anomalous thermal expansion between 160 and 190 K (Fig. 1C, top). This observation is consistent with Raman spectroscopy, which shows additional phonon modes within the same temperature range (160 to 180 K; figs. S5 and S6 and tables S4 and S5). The temperature dependence of the lattice param-eters initially suggests a second-order–like transition, further sup-ported by a λ-shaped anomaly in the specific heat at Ts = 170 K (Fig. 1C, middle). Furthermore, the electrical resistivity ρ exhibits a kink at Ts while maintaining metallic behavior (dρ/dT > 0; Fig. 1C, Fig. 1. P-NP transition and electronic property of LiReO3. (A) Crystal structures of LiReO3 in the polar (R3c; left) nonpolar (R-3c; right) phases. Spheres and polyhedra represent Li+ ions and ReO6 octahedra, respectively. (B) Difference in emission intensity (ΔI = I143 K′ – I293 K′) as a function of emission wavelength under 1300-nm excita-tion, highlighting peaks at 650 nm and 433 nm corresponding to second- and third-harmonic generation (SHG and THG), respectively. The corrected intensities I143 K′ and I293 K′ were obtained by scaling the data at 143 and 293 K to normalize the fluorescence background in the 400- to 700-nm region, as shown in Fig. 1B (inset; see also the Supplementary Materials). The pronounced SHG signal at 650 nm confirms the noncentrosymmetric structure below Ts despite strong fluorescence background. a.u., ar-bitrary units. (C) Temperature dependence of (top) lattice parameters normalized to 300 K; (middle) specific heat at 0 T (open) and 7 T (closed), with the black line indicat-ing a fit excluding the transition region; and (bottom) electrical resistivity measured during cooling. All results consistently demonstrate the P-NP transition near 170 K.Downloaded from https://www.science.org at National Institute for Materials Science on April 06, 2026Murayama et al., Sci. Adv. 12, eadt3886 (2026)     3 April 2026S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e3 of 9bottom). These results confirm that LiReO3 is a metallic system un-dergoing a P-NP phase transition at 170 K, a temperature higher than that of LiOsO3 (140 K).Polar phase instabilityThe transition temperature (Ts) of LiReO3 (170 K) is markedly sup-pressed to just 12% of that in the isostructural insulating compound LiNbO3 (Ts = 1480 K) (4). While this suppression is presumably re-lated to the presence of conduction electrons, the underlying mech-anism is unclear. To explore this, we synthesized solid solutions of LiRe1–xNbxO3. The SXRD patterns show sharp peaks and a gradual shift in peak positions with increasing x, indicating high crystallin-ity and the successful formation of an entire solid solution (fig. S7).The unit cell volume (V) increases linearly with x, following Vegard’s law. In contrast, the individual lattice parameters (a, c) exhibit non-linear variations (Fig. 2A), likely reflecting electronic effects, as ob-served in other solid solutions (34–37). Ts also evolves nonlinearly: On the Re-rich side, samples with x = 0.1 and 0.2 exhibit nearly the same Ts as the parent compound (x = 0), as evidenced by anomalies in the lattice constants (fig. S8) and specific heat (fig. S9). With in-creasing x, Ts gradually rises and tracks a minimum in the c-axis length (Fig. 2B), a trend empirically observed in LiOsO3 as well (12). For x  ≥ 0.7, in situ SXRD measurements up to 1100 K show no sig-nature of a phase transition, suggesting that Ts continues to increase toward x = 1, where it reaches 1480 K in LiNbO3 (4).The resulting phase diagram, constructed from structural and specific heat measurements, delineates the evolution from polar me-tallic to polar insulating phases across the solid solution series (Fig. 2C). While the continuity of the P-NP transition with respect to Nb content x remains to be clarified, Ts shows a strong correlation with the electronic transport properties. As the Nb content decreas-es from x = 1 to 0.75, the resistivity (ρ) drops sharply (Fig. 2, D and E), and the temperature coefficient dρ/dT switches from negative to positive, signaling an insulator-to-metal crossover around x = 0.7 (Fig. 2, C and E). These observations suggest that the instability of the polar phase originates from a crossover in electronic character, from localized to itinerant electrons, accompanied by enhanced screening of internal electric fields. The nearly flat Ts region between x = 0 and x = 0.2 (Fig. 2C) indicates sufficient screening that effec-tively suppresses variations in Ts. Thus, this systematic investigation of LiRe1–xNbxO3 offers clear experimental evidence for the suppres-sion of polar order via conduction-electron screening, reinforcing the pivotal role of itinerancy in destabilizing the polar phase (11, 12).Extensive thermal hysteresis of LiReO3As discussed earlier, LiReO3 exhibits second-order–like behavior in both specific heat and lattice parameters (Fig. 1C). However, an in-triguing feature emerges in its thermodynamic and structural respons-es: pronounced thermal hysteresis, whose onset temperature and width vary depending on the experimental probe (Fig. 3). Thermo-electric measurements, which are sensitive to thermal fluctuations near P-NP structural instabilities (38) and detect direct changes in electronic states near the Fermi level (S ∝ �D/�E |E = EF), reveal weak but extended hysteresis spanning a wide temperature range (100 to 370 K) across Ts (Fig. 3A). Ultrasonic experiments show marked softening of the transverse elastic constants, with a hysteresis ob-served between 60 and 240 K (Fig. 3B). These probes, sensitive to quadrupolar and strain susceptibilities, capture lattice dynamics on Fig. 2. Itinerancy-induced polar phase instability in LiRe1–xNbxO3. (A) Lattice parameters a, c, and cell volume V at 100 K as a function of Nb content x in LiRe1–xNbxO3 (0 ≤ x ≤ 1). (B) Temperature dependence of the c axis for selected compositions, normalized at 100 K. (C) P-NP phase diagram of LiRe1–xNbxO3. Open circles represent Ts values estimated from lattice parameters (a, c) and specific heat measurements. The filled circle corresponds to earlier reported data (4). Dotted lines at x = 0.7, 0.8, and 0.9 represent the possible Ts region with the maximum measurement temperature as the lower bound and 1470 K (the Ts of LiNbO3) as the upper boundary because no distinct changes appeared in measurements for these compositions up to 1000 to 1100 K. The dashed curve connecting the Ts values at x = 0 and x = 1 is a guide to the eye. (D) Temperature-dependent resistivity of LiRe1–xNbxO3 measured during cooling from 300 to 2 K. (E) Room-temperature resistivity as a function of x, showing a cross-over from itinerant to localized electronic behavior upon electron doping. The (C) and (E) show a notable change near x = 0.6 to 0.75 in the polar structure, suggesting the presence of a metal-insulator crossover.Downloaded from https://www.science.org at National Institute for Materials Science on April 06, 2026Murayama et al., Sci. Adv. 12, eadt3886 (2026)     3 April 2026S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e4 of 9shorter timescales than those accessed by thermal relaxation process-es in specific heat, thus offering complementary insights into elec-tronic and structural fluctuations.Additional evidence for these exceptional dynamics and fluctua-tions comes from electrical resistivity and Raman spectroscopy, both of which show persistent hysteresis during heating and cooling cy-cles (figs. S10 and S11), with signatures extending up to 300 K. The observation of hysteresis in these microscopic or local measurements supports the first-order nature of the P-NP transition in LiReO3. While SHG probes the presence of a polar structure, its signal is a time-integrated ensemble of snapshots defined by the ultrafast in-teraction timescale (~100 fs) and thus cannot distinguish whether the polar structure is static or slowly fluctuating. In contrast, combi-nations of slower probes such as thermoelectric, ultrasonic, and Ra-man scattering experiments reveal persistent fluctuations on longer time scales. The variation in hysteresis width among different probes suggests that the underlying dynamics span multiple time and length scales, indicative of microscopic phase coexistence and spa-tiotemporal fluctuations. This method-dependent behavior is remi-niscent of complex dynamical phenomena in other systems, including local instabilities in rattling compounds (e.g., PrOs4Sb12) (39) and spin fluctuations in geometrically frustrated magnets (e.g., NiGa2S4) (40). Given the broad and probe-dependent nature of the hysteresis, determining a single, well-defined transition temperature is not straightforward. In this study, we define Ts as the temperature at which the specific heat or the c-axis lattice parameter reaches a maximum or minimum, thereby characterizing the transition on slower, mac-roscopic timescales.First-principles calculations at finite temperaturesWe investigated the phase transitions of metallic LiReO3 and insu-lating LiNbO3 using first-principles calculations at finite temperatures. To capture the effects of lattice anharmonicity, we used a recently developed approach based on self-consistent phonon (SCP) theory (41–45), which explicitly incorporates anharmonic lattice vibrations (46, 47). This method successfully reproduces both the transition tem-peratures and thermal hysteresis behavior in the two compounds. The calculated transition temperatures, Ts,calc = 267 K for LiReO3 and 1350 K for LiNbO3, are in reasonable agreement with the experi-mental values (170 and 1480 K, respectively) (4), demonstrating that our model effectively captures the essential features of the P-NP transitions.The calculations reveal a notable contrast in thermal hysteresis. LiReO3 exhibits an extended hysteresis window of ΔTcalc = 145 K (165 to 310 K; Fig. 4A), while LiNbO3 shows a much narrower hys-teresis of ~40 K (fig. S12). This difference stems from their distinct potential energy landscapes (Fig. 4B): LiNbO3 has a deep potential well, resulting in a high transition temperature and minimal hyster-esis. In contrast, LiReO3 exhibits a shallow double-well potential that amplifies thermal fluctuations and facilitates phase competition over a broad temperature range. These features are qualitatively con-sistent with experimental observations, namely, a lower Ts and broader hysteresis in LiReO3, suggesting that the shallow potential, likely stabilized by conduction electrons, plays a central role in its first- order–like transition behavior. While SCP calculations also predict a first-order phase transition for LiOsO3 (Ts = 207 K, ΔTcalc = 120 K), experimental studies (12,  19,  25,  48–50) report a continuous, second-order phase transition without any detectable signatures of hysteresis (12, 19, 25, 48–50).Although shallow potential wells (~50 meV) are also present in conventional insulating ferroelectrics such as BaTiO3 (51, 52), they do not give rise to the extended thermal hysteresis observed in LiReO3 (53), highlighting the critical role of electron itinerancy. Moreover, ex-perimental signatures such as two-phase coexistence and short-range fluctuations in LiReO3 point to complexities that are inherently diffi-cult to capture within current first-principles frameworks, posing a substantial challenge for further theoretical developments.Fluctuations in the low-temperature regimeUnlike LiOsO3, LiReO3 exhibits persistent and unconventional fluc-tuations well below Ts. A clear macroscopic manifestation appears in the electrical resistivity, which displays a broad hump below Ts (Fig. 1B). This behavior contrasts with the valley-like drop observed in LiOsO3 (12), which is characteristic of coherent long-range or-dering in a Fermi liquid state (54–56). On a microscopic scale, the Raman spectrum of LiReO3 at 4 K remains unusually broad and dif-fuses over a wide frequency range (fig. S6). This spectral profile sug-gests that dynamic fluctuations persist on the timescale of optical phonons, indicative of an unresolved P-NP state. This behavior re-sembles quasielastic scattering associated with correlated or coop-erative disorder, as reported in martensitic precursors (57), ice-rule systems (58), and mixed-anion compounds (59). Additional evidence Fig. 3. Thermal hysteresis in LiReO3. Temperature dependence of (A) thermo-power Q for LiRe1–xNbxO3 (x = 0, 0.2) determined through thermoelectric measure-ments and (B) transverse elastic constants of LiReO3, normalized at 300 K, probed by ultrasonic measurements, showing distinct softening below Ts. The prior increase of the elastic constant above Ts may arise from reduced phonon anharmonicity (61, 100, 101) or embryonic domain formation typically observed in first-order phase transitions (102–104).Downloaded from https://www.science.org at National Institute for Materials Science on April 06, 2026Murayama et al., Sci. Adv. 12, eadt3886 (2026)     3 April 2026S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e5 of 9comes from elastic measurements: The transverse elastic constants exhibit continuous softening well below Ts (Fig. 3B), deviating from conventional structural transitions where softening typically occurs near the critical point and is followed by rapid hardening (60). This anomaly highlights an unusual mechanical “softness” in the low-temperature phase, likely associated with spatial modulations due to the proximity of competing polar and nonpolar states.A central highlight of this study arises from ultrasonic echo measurements. Echo signals spanning a wide temporal range (1 to 100 μs; Fig. 5A) reveal exceptionally slow and complex spatiotemporal fluctuations that persist down to 10 K, well below Ts. Unlike typical structural transitions, where ultrasonic absorption diminishes be-cause of reduced anharmonic phonon scattering (61), LiReO3 exhibits anomalous absorption behavior, suggesting that acoustic waves re-main resonantly coupled to the polar phase or fluctuations. This be-havior indicates a diffusive and dynamically fluctuating lattice state, driven by the small energy separation between the polar and nonpo-lar phases. These results underscore a strong coupling between acous-tic and electronic degrees of freedom mediated by phonon-electron interactions, presenting a compelling case of itinerancy-enhanced lattice dynamics. Moreover, they suggest that such fluctuations in soft polar metals may serve as memory elements, enabling spatially localized and temporally delayed electrical responses to acoustic stimuli.Together, the probe-dependent hysteresis, broad Raman features, and anomalous ultrasonic responses indicate a highly diffusive lat-tice environment, consistent with a first-order phase transition ac-companied by persistent fluctuations well below Ts. These findings establish LiReO3 as a rare polar metal that exhibits multiscale dy-namical behavior, bridging characteristics of both displacive and order-disorder transitions.DISCUSSIONPhase transition mechanisms in LiReO3 and LiOsO3Despite having identical crystal structures and itinerant electronic states, LiReO3 and LiOsO3 undergo fundamentally different P-NP transitions: first-order in LiReO3 and second-order in LiOsO3 (12, 19, 25, 48–50). This contrast is not captured by the current theo-retical models (see above), suggesting that additional effects, such as short-range ordering and thermal disorder of Li displacements, play essential roles beyond current approximations. Raman scattering experiments reveal that LiReO3 exhibits softened phonon modes in the 340- to 400-cm−1 range compared to LiOsO3 (table  S4 and4 fig. S5) (48–50). Density functional theory (DFT) calculations show that these modes correspond to octahedral vibrations involving shear displacements of Li ions, in contrast to the axial Li motion Fig. 4. Theoretical calculations for metallic LiReO3 and insulating LiNbO3. (A) Calculated atomic displacements in LiReO3 as a function of temperature based on inter-atomic force constants (IFCs), showing a dispersive hysteresis when only the long-range order is considered. (B) Calculated energy per unit cell for LiRe1–xNbxO3 (x = 0, 1) as a function of the polar mode amplitude, normalized to the Li displacement. For both LiReO3 and LiNbO3, the circles and lines represent results from density functional theory (DFT)– and IFC-based calculations, respectively.Fig. 5. Dynamic fluctuations in polar metallic LiReO3. (A) Temperature-dependent ultrasonic echo profiles of LiReO3 from 10 to 335 K, collected upon heating using a 17-MHz transverse wave. (B) Schematic illustration of the P-NP transition in LiReO3 and LiOsO3, depicting potential curves for the first-order transition in LiReO3 versus the second-order transition in LiOsO3. The shallow potential in LiReO3, attributed to screening effects of conduction electrons (as indicated by theoretical calcula-tions in Fig. 4), facilitates phase fluctuations. These fluctuations are schematically depicted in a bar diagram with red (polar) and gray (nonpolar) regions illustrating their temperature evolution. LiOsO3 undergoes a second-order phase transition likely influenced by more pronounced Li thermal disorder (represented by dashed lines; discussed in detail in the main text), with its corresponding bar diagram showing fluctuations present only in the critical region around and above Ts.Downloaded from https://www.science.org at National Institute for Materials Science on April 06, 2026Murayama et al., Sci. Adv. 12, eadt3886 (2026)     3 April 2026S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e6 of 9typically observed in polar transitions of LN-type compounds. In LiReO3, the coupling between these soft shear modes and the polar-active mode likely stabilizes a collective lattice distortion, suppress-ing Li disorder and promoting a first-order phase transition.Recent SHG measurements on LiOsO3 have revealed a polar phase with short-range correlations within the nonpolar phase (Ts < T <  ~230 K) (19), indicating a critical region and suggesting an order- disorder–type second-order transition (Fig. 5B, bottom), similar to the scenario proposed for LiNbO3, although the mechanism remains under debate (4–6, 20–24, 62, 63). The Raman frequency of the Li shear mode in LiNbO3, responsible for coupling with the polar-active axial Li vibrations, closely matches that in LiOsO3 (24, 64, 65). This fact implies that Li thermal disorder plays a similar role in those compounds. In contrast, the softer Li shear mode in LiReO3 likely acts to suppress such disorder, resulting in a first-order transition primarily driven by a displacive-type mechanism (Fig. 5B, top). This soft shear mode may also amplify phase fluctuations through fur-ther shallowing of the potential energy surface, reinforcing the first-order nature of the transition.Figure 5B schematically illustrates these contrasting phase tran-sition pathways in LiReO3 and LiOsO3. In LiOsO3, strong Li order-disorder effects dominate, leading to second-order behavior (Fig. 5B, bottom). In LiReO3, these effects are less pronounced, allowing a first-order transition to emerge, stabilized by a shallow potential en-ergy landscape (Fig. 5B, top). The nature of P-NP phase transitions in LiNbO3-type compounds has long been debated, particularly re-garding the competition between displacive and order-disorder mechanisms. Our results provide what is likely the first compelling experimental evidence of a first-order transition within this class of materials.The slightly higher Ts in LiReO3 (170 K) compared to LiOsO3 (140 K) also merits serious consideration. This difference likely re-flects variations in their d-electron counts: The higher d-electron oc-cupancy in LiOsO3 enhances conduction electron screening, which suppresses polar distortions and lowers Ts. However, transition tem-peratures are ultimately governed by a complex interplay between elec-tronic and lattice degrees of freedom, including interatomic force constants (IFCs), and remain an active topic of investigation.Final remarks and outlookFluctuations above the critical temperature (Tc) are observed across a wide range of materials and are often characterized by inhomoge-neous nanoregions (66). These include pseudogaps and electronic nematic phases in unconventional superconductors (67–69), as well as pretransitional behavior in martensitic transformations of inter-metallic compounds (57, 70–73) and oxides such as LaNbO4 (74) and Pb3(PO4)2 (75), where nucleation and growth processes are mediat-ed by “ghost lattices” or “embryonic fluctuations.” Similar phenomena occur in ferroelectric BaTiO3 (76–82) and in first-order electronic transitions in Mott insulators and charge-ordered systems (83–89).While most studies focus on phase fluctuations above transition temperatures, our work on LiReO3 reveals a rare case in which a first- order phase transition coexists with persistent dynamical fluctua-tions both above and below Ts. This unusual behavior, driven by a shallow energy landscape and facilitated by electron itinerancy in conjunction with the P-NP transition, represents a major advance in our understanding of fluctuating states in quantum materials. Un-like conventional systems that respond uniformly to external fields, materials with inherent fluctuations may exhibit nonlinear, delayed, or selective responses to stimuli such as heat, light, or acoustic per-turbations (90–92).This insight advances the emerging concept of “fluctuation-based materials science,” which recognizes dynamic structural and electronic fluctuations as valuable resources rather than defects to be eliminated. These fluctuations can drive emergent spin and elec-tronic functionalities while producing nonlinear responses that re-main unattainable in statically ordered systems. By repositioning fluctuations from sources of noise to active design parameters and harnessing external stimuli such as ultrasound as control mecha-nisms, promising opportunities emerge for energy conversion and adaptive electronic technologies. The unique dynamical behavior observed in LiReO3 thus provides a compelling platform for explor-ing fluctuation evolution in polar metals and for developing materi-als design principles that leverage dynamic degree of freedom to achieve emergent electronic and structural functionalities.MATERIALS AND METHODSSample preparationPolycrystalline samples of LiRe1–xNbxO3 (0 ≤ x ≤ 1) were synthe-sized via high-pressure and high-temperature solid-state reactions using stoichiometric NbO2 (Rare Metallic; 99.9%), ReO2 and a 20% molar excess of Li2O2 (Sigma-Aldrich; 90%). ReO2 powder was pre-pared using Re (Sigma-Aldrich; 99.995%) and Re2O7 (Sigma-Aldrich; 99.99%) in an evacuated silica tube ~ 5 Pa at 300°C and then 650°C for 1 day each at a heating rate of 200°C hour−1. The chemicals for high-pressure reactions were ground, pelletized, and wrapped in platinum foils of 0.02-mm thickness and inserted into boron nitride (BN) sleeves. After sealing both ends of the sleeve with BN lids, the sample cell was loaded into a graphite tube and introduced into py-rophyllites. These assembly procedures were conducted in an N2-filled glovebox due to the air-sensitive precursors. After pressurization to reach 8 to 9 GPa, the samples were heated to 1100° to 1400°C for 1 hour and quenched down to room temperature within 5 min, and then the pressure was slowly released to the ambient atmosphere. The pellets were crushed into powders and washed with water to remove residual lithium-related by-products and unreacted precursors. As-prepared pellets were used for resistivity, thermoelectric, and ultra-sonic measurements.Characterization of samplesSXRD experiments for LiRe1–xNbxO3 were performed at the BL02B2 beamline in SPring-8. The wavelength of the incident beam was λ = 0.420150 and 0.420391 Å, and the temperature was changed in the range from 100 to 1100 K. NPD measurements of LiReO3 (x = 0) were performed at 6 K using the high-resolution powder diffrac-tometer BT-1 at the National Institute of Standards and Technology (NIST) Center for Neutron Research. Incident neutrons of wave-length λ = 1.5400 Å monochromated by vertical-focused Cu(311) monochromator were used. These diffraction data were analyzed by the JANA2006 software (93). SHG measurements were performed using a TCS SP8 MP confocal microscope (Leica Microsystems, Wetzlar, Germany) coupled to a tunable InSight X3 single laser (Spectra-Physics, USA) emitting femtosecond pulse (100 fs/80 MHz). For this experiment, an excitation wavelength of 1300 nm for a laser power of 0.25 W was chosen. The sample was placed in a computer-controlled heating/cooling state (Linkam THMS600) and cooled be-tween 293 and 143 K at a cooling rate of 5 K min−1. The SHG intensity Downloaded from https://www.science.org at National Institute for Materials Science on April 06, 2026Murayama et al., Sci. Adv. 12, eadt3886 (2026)     3 April 2026S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e7 of 9was measured as digital counts (0 to 255 levels) from the multipho-ton microscope detectors, averaged over all pixels in the acquired image. To clarify the temperature-dependent component associated with SHG, the spectrum at 293 K was subtracted from the low tem-perature spectrum at 143 K after appropriate scaling (see the Sup-plementary Materials). The acquisitions of the spectral emission of the sample were performed between 380 and 780 nm.Physical property measurementsSpecific heat measurements were carried out using a commercial calo-rimeter (Quantum Design, PPMS) with a thermal relaxation meth-od. Entropy changes near the phase transition were also determined through specific heat measurements (fig. S13). Resistivity measure-ments were performed using the physical property measurement sys-tem (Quantum Design, PPMS). Magnetic susceptibility (M/H) was measured with a SQUID magnetometer (Quantum Design, MPMS; fig. S14). Thermoelectric measurements were performed by a steady- state method with a temperature difference (ΔT) of less than 1 K (typically 2 to 4% of the measurement temperature below 50 K) be-tween the voltage contacts. Raman scattering experiments were per-formed with a HORIBA Jobin Yvon model HR800 micro Raman spectrometer using a 50× objective. The spectra were collected in quasi-backscattering geometry using a λ = 532 nm laser line of a Nd:YAG laser with a power of P = 0.4 mW. Low-temperature data were sampled with single crystals inserted in a CRYOVAC, He-cooled micro-cryostat in the temperature range between 4 and 300 K. The energy range of the experiments is 20 to 500 cm−1. Ultrasound mea-surements were conducted on as-synthesized LiReO3 pellets in a temperature range from 2 to 335 K and in magnetic fields at 0 T. To generate and detect ultrasonic waves, piezoelectric plates of LiNbO3 transducers were attached to the samples using epoxy glue.Theoretical calculationsThe electronic state of polar LiReO3 was calculated using the projected- augmented plane-wave (PAW) method implemented in the Quan-tum ESPRESSO package (94–96). We used Perdew-Burke-Ernzerhof functional of generalized gradient approximation as an exchange-correlation functional. The calculations used pseudopotentials Li.rel- pbe-s-kjpaw_psl.1.0.0.UPF, Re.pbe-spn-kjpaw_psl.1.0.0.UPF, and O.pbe-n-kjpaw_psl.1.0.0.UPF. Because the used Li pseudopotential is “hard” and requires a high cutoff energy (suggested minimum: 103 Ry) for precision, we used the cutoff energy of 120 Ry. The k-point mesh was set to 14 by 14 by 14, and the Gaussian smearing was used with width of 0.003 Ry. The total energy was minimized until the convergences fell to less than 10−7 eV during self-consistent cy-cles, and the lattice relaxations were conducted until the atomic forces became smaller than 0.02 eV Å−1. Density of states (DOS) (fig. S15) were evaluated without Hubbard U correction.The calculations of the P-NP transition were performed using the finite-temperature structural optimization based on SCP theory (46, 47). The temperature dependence of the crystal structure was calculated by optimizing the structure-dependent free energy, which was obtained using the SCP theory. SCP theory is a commonly used method for quantitative calculations of strongly anharmonic mate-rials because the phonon anharmonicity is nonperturbatively treated (41–45). The SCP calculation and the finite-temperature structural optimizations were performed using ALAMODE package (42, 97, 98). We used the Vienna Ab initio Simulation Package (99) for the DFT calculations. In calculating the temperature dependence of the crystal structure, we fixed the shape of the unit cell because the lattice con-stants showed only small changes (around 0.2%) below and above Ts. The anharmonic IFCs, which we truncated at the fourth-order, were obtained using the compressive sensing method from the displacement-force data. For more details on the theoretical calculations, including DFT-based phonon calculations for Raman scattering anal-ysis and Gibbs free energy (fig. S16), see “Details of theoretical cal-culations” in the Supplementary Materials.Certain commercial equipment, instruments, or materials are iden-tified in this document. This identification does not imply recom-mendation or endorsement by the NIST or does it imply that the products identified are necessarily the best available for the purpose.Supplementary MaterialsThis PDF file includes:Supplementary TextFigs. S1 to S16Tables S1 to S5ReferencesREFERENCES  1.  P. S. Halasyamani, K. R. 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Funding: This study was supported by the CREST program (JPMJCR1421 to H.K.; JPMJCR2543 to H.K. and T.Y.); the JSPS Grant-in-Aid for Specially Promoted Research “Hydrogen Ion Ceramics” (JP22H04914 to H.K., H.T., and C.T.); the Scientific Research on Innovative Areas “Mixed anion” (JP16H06439 to H.K.); the Transformative Research Areas (A) of “Hyper-Ordered Structures Science” (JP21H05561 to H.T.), “Supra-ceramics” (JP22H05143 to C.T.), and “Asymmetry Quantum Matters” (JP23H04868 to T.Y.); the Scientific Research (JP22H01777 and JP24K01583 to C.T. and H.T.); the JSPS Core-to-Core Program (A) Advanced Research Networks (grant JSPSCCA20200004 to H.K.); the JST Adopting Sustainable Partnerships for Innovative Research Ecosystem (JPMJAP2408 to H.K. and S.Y.); and the Nippon Sheet Glass Foundation for Materials Science and Engineering (R6-25 to H.T.). We also acknowledge support by the Deutsche Forschungsgemeinschaft, DFG EXC-2123 QuantumFrontiers – 390837967. K.M. and R.M. were supported by the JSPS Research Fellowships for Young Scientists (JP23KJ1395 and JP22KJ1028). Author contributions: K.M. and R.M. contributed equally to this work. H.K., H.T., C.T., and R.A. designed this study. The manuscript was written by K.M., H.T., H.O., P.L., and H.K. with advice from all other authors. K.M., K.I., and X.G. synthesized the materials. K.M. and C.T. measured the SXRD and analyzed the structures from SXRD data. K.M., H.T., C.T., and C.M.B. performed NPD experiments and analyzed the structures from NPD data. K.M., M.N., and H.T. performed specific heat and electrical resistivity measurements. H.S. performed thermoelectric measurements. T.Y. and K.Y. carried out the ultrasonic experiments. V.D., S.C., and O.M. conducted SHG measurements. K.D. and P.L. performed Raman scattering. S.Y. conducted phonon calculations and analysis of Raman scattering data. K.M. conducted partial density of states calculations. Theoretical calculations of temperature dependence were conducted by R.A., T.N., T.T., and A.R. All the authors discussed the results of this work. Competing interests: The authors declare that they have no competing interests. Data, code, and materials availability: All data and code needed to evaluate and reproduce the results in the paper are present in the paper and/or the Supplementary Materials. There were no new materials generated in the study.Submitted 24 September 2024 Accepted 2 March 2026 Published 3 April 2026 10.1126/sciadv.adt3886Downloaded from https://www.science.org at National Institute for Materials Science on April 06, 2026Lattice softening and diffusive dynamics in the polar metal LiReO3Kantaro Murayama, Ryota Masuki, Cédric Tassel, Hideaki Sakai, Tatsuya Yanagisawa, Keito Yoshida, Hiroshi Oike,Suguru Yoshida, Xiangyu Gu, Kohdai Ishida, Morito Namba, Ksenia Denisova, Valérie Dupray, Simon Clevers, OlivierMentré, Takuya Nomoto, Terumasa Tadano, Craig M. Brown, Peter Lemmens, Ryotaro Arita, Hiroshi Takatsu, and HiroshiKageyamaSci. Adv. 12 (14), eadt3886.  DOI: 10.1126/sciadv.adt3886View the article onlinehttps://www.science.org/doi/10.1126/sciadv.adt3886Permissionshttps://www.science.org/help/reprints-and-permissionsUse of this article is subject to the Terms of serviceScience Advances (ISSN 2375-2548) is published by the American Association for the Advancement of Science. 1200 New York AvenueNW, Washington, DC 20005. The title Science Advances is a registered trademark of AAAS. Copyright © 2026 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claimto original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).Downloaded from https://www.science.org at National Institute for Materials Science on April 06, 2026https://www.science.org/content/page/terms-service Lattice softening and diffusive dynamics in the polar metal LiReO3 INTRODUCTION RESULTS Polar metallic LiReO3 Polar phase instability Extensive thermal hysteresis of LiReO3 First-principles calculations at finite temperatures Fluctuations in the low-temperature regime DISCUSSION Phase transition mechanisms in LiReO3 and LiOsO3 Final remarks and outlook MATERIALS AND METHODS Sample preparation Characterization of samples Physical property measurements Theoretical calculations Supplementary Materials This PDF file includes: REFERENCES Acknowledgments