Introduction

Ferroelectric materials often exhibit ultrahigh electrical and electromechanical responses near phase boundaries where competing ground states coexist. A notable example is the morphotropic phase boundary (MPB) in lead zirconium titanate (PbZr1-xTixO3, PZT), a transition region in the composition-temperature phase diagram marked by an abrupt change in crystal symmetry1,2,3,4,5,6. The flattening of the free energy profile at the MPB facilitates polarization rotation among different phases under external fields, leading to remarkable dielectric and piezoelectric performance2,7,8. However, despite these advantages, the presence of toxic lead in PZT raises significant environmental and health concerns, particularly for implantable bio-micro-electromechanical systems (bio-MEMS) and in vivo piezoelectric sensors9,10. Thus, there is an urgent need for lead-free alternatives with comparable or superior performance.

Among lead-free ferroelectrics, potassium sodium niobate ((K,Na)NbO3, KNN) has emerged as a promising candidate, attracting substantial research interest over the past two decades11,12. Most research efforts have focused on enhancing susceptibilities in KNN-based bulk ceramics by constructing multi-phase boundaries through chemical substitutions13,14,15,16,17,18,19. However, with the increasing demand for device miniaturization, developing lead-free thin films with ultrahigh electrical and electromechanical susceptibilities is crucial for applications such as micro- and nano-electromechanical systems (MEMS and NEMS)20. Chemically-driven phase boundaries, however, often introduce compositional complexity, leading to structural disorder and heterogeneity that degrade thin-film crystallinity21,22. Moreover, the high volatility of alkali metals makes precise chemical tuning of KNN-based thin films particularly challenging. To overcome these limitations, alternative approaches beyond chemical methods are essential for constructing phase boundaries in lead-free ferroelectric thin films.

Epitaxial strain, arising from lattice mismatch between thin films and substrates, offers a promising alternative approach for creating MPB-like phase boundaries in lead-free ferroelectrics. For instance, under compressive strain larger than −4%, BiFeO3 undergoes a phase transition to a highly distorted tetragonal-like phase, forming a mixed-phase structure comprising tetragonal-like and rhombohedral-like phases, which results in ultrahigh electromechanical responses23,24,25,26,27,28. Additionally, recent studies have demonstrated improved dielectric and piezoelectric properties in epitaxially BaTiO3 films, arising from a strain-induced bridging phase29 and a slush-like polar structure composed of coexisting phases with varying symmetries30. Despite the promise of strain-engineered phase boundaries, this approach remains underexplored in KNN-based thin films. To explore strain-induced MPB-like structures in these materials, we focus on sodium niobate (NaNbO3), a key end-member of the KNN family, known for its rich structural polymorphism and numerous phase transitions. The small energy barriers between nearly degenerate phases in NaNbO3 allow for structural modulation through a small thermal, electrical, or mechanical perturbations, providing possibility for enabling multi-phase boundaries with enhanced functionalities31. While NaNbO3 bulk ceramics have been extensively studied for decades as promising lead-free electroceramics for energy storage applications32,33,34,35,36, research on NaNbO3 thin films remains in its early stages but is rapidly gaining attention37,38,39,40,41,42,43,44. Recent advances in thin-film synthesis have enabled the growth of high-quality NaNbO3 films, unlocking their potential for ultrahigh electromechanical responses45,46. Furthermore, electron ptychography has recently revealed an unconventional microscopic picture in NaNbO3 films, where ferroelectricity is dominated by the anion displacements relative to the niobium sublattice47.

Here, combining epitaxial ab initio simulations, epitaxial thin-film synthesis, electrical measurements, and detailed structural characterizations via scanning probe microscopy, synchrotron X-ray diffraction, and electron ptychography, we design and construct strain-induced MPB-like polymorphic structures with enhanced dielectric and ferroelectric properties in NaNbO3 heterostructures. Our strategy is to leverage a slight strain perturbation from the substrate to manipulate structural instabilities among nearly degenerate phases in NaNbO3 thin films, thereby inducing a multi-phase boundary. The coexisting polymorphs near the phase boundary facilitate continuous polarization rotation, resulting in a multi-state switching pathway and large enhancements in dielectric susceptibility and tunability across a broad frequency range.

Results and Discussion

Design and synthesis of strain-induced multi-phase boundary in NaNbO3 films

Bulk NaNbO3 exhibits a complex phase diagram with multiple temperature-dependent phase transitions48. At room temperature, it typically adopts an orthorhombic antiferroelectric Pbcm phase, which can be irreversibly switched into a ferroelectric Pmc21 phase under an electrical field. Our density functional theory (DFT) simulations (Fig. 1a) further reveal additional competing ferroelectric polymorphs in NaNbO3 thin films that are energetically favorable near the bulk lattice of NaNbO3 (a ~ 3.88 − 3.915 Å). This suggests the possibility of phase transitions or polymorph coexistence in NaNbO3 thin films under small strain. These polymorphs include phases with space group symmetries Cm, Pc, and Cc, each exhibiting distinct polarization configurations and oxygen octahedral tilts (Fig. 1b and Supplementary Fig. 1). Given the intricate energy balance among these competing phases, we aim to experimentally realize MPB-like structures with coexisting ferroelectric polymorphs in NaNbO3 heterostructures to enable giant enhancements in dielectric and ferroelectric properties via strain engineering.

Fig. 1: Structural phase and topography evolution of NaNbO3/SrTiO3 (001) heterostructures with varying film thickness.
figure 1

a Total energy as a function of lattice parameter for the Cc, Cm, and Pc phases in (001)-oriented epitaxial NaNbO3 thin films. The inset provides a magnified view of the energy curve in the range of 3.76–3.94 Å. b Schematic representations of the atomic structures of the Cc, Cm, and Pc phases in (001)-oriented epitaxial NaNbO3 thin films. c X-ray θ-2θ diffraction patterns of NaNbO3/SrTiO3 (001) heterostructures as a function of film thickness, measured near the pseudocubic (001) diffraction condition. d–g Atomic force microscopy (AFM) images of NaNbO3 films with thicknesses of d 25 nm, e 80 nm, f 125 nm, and g 185 nm. The 25 nm films exhibit atomically smooth surfaces, while labyrinthine topographical patterns emerge with increasing film thickness.

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To induce varying strain states in the thickness series via strain relaxation, we synthesize epitaxial NaNbO3 films with thicknesses ranging from 25 to 185 nm on (001)-oriented single crystalline SrTiO3 substrates, with atomically smooth interfaces (Supplementary Fig. 2) using pulsed laser deposition (PLD). X-ray reflectivity (XRR) is employed to calibrate the thickness of 25 nm films and determine the growth rate for thicker films (Supplementary Fig. 3a). The thickness-dependent structural evolution of the NaNbO3 films is further examined through high-resolution X-ray θ−2θ scans (Fig. 1c and Supplementary Fig. 3b, c). The presence of Laue fringes indicates the high crystalline quality of the films. Notably, films with a thickness t \(\ge\) 80 nm exhibit a broadened peak near the NaNbO3-001 diffraction condition, suggesting the presence of multiple diffraction peaks in NaNbO3 films, potentially associated with either distinct structural phases or different structural domain variants (Fig. 1c). To further explore this structural evolution, we study the film topography using atomic force microscopy (AFM). While 25 nm films exhibit atomically smooth surfaces, intriguing labyrinthine topography emerge in films with t\(\ge\)80 nm (Fig. 1d-g). These patterns, consisting of stripe-like features oriented along the pseudocubic [100] and [010], exhibit increasing ordering as thickness increases. The labyrinthine structures introduce regions of elevated “walls” and lowered “pathways” in the film topography, which possibly contributes to the broadening of diffraction peaks observed in θ−2θ scans. These labyrinthine patterns may arise from the coexistence of either structural phases with varying symmetries or domain variants with the same symmetry.

Ferroelectric domain structure characterization

To further elucidate the structural nature of the labyrinthine pattern, we examine the ferroelectric domain structures of NaNbO3 films using piezoresponse force microscopy (PFM) (Supplementary Fig. 4). PFM imaging reveals that the “walls” and the “pathways” of the labyrinthine pattern correspond to two distinct sets of ferroelectric polydomain structures, both exhibiting ultra-fine nanoscale domains and a high density of domain walls. These polydomain regions exhibit different PFM amplitude responses: the “walls” show a stronger vertical response than the “pathways”, indicating a larger out-of-plane polarization component (Fig. 2a, c, e), while the “pathways” display a stronger lateral response, suggesting a larger in-plane polarization component (Fig. 2b, d, f). Detailed analysis of vertical and lateral PFM amplitude and phase signals, performed by varying the relative orientation between the PFM cantilever and sample (Supplementary Fig. 5), suggests that the “pathways” exhibit an in-plane polarization component along the pseudocubic [110] or [1-10] (Fig. 2g), whereas the “walls” possess an in-plane polarization component along the pseudocubic [100] or [010] (Fig. 2h). Combining both the in-plane and out-of-plane signals as well as the projected domain wall orientation, we propose the following polarization configurations: the “pathways” adopt a polydomain structure with polarizations along [xxz] or [x-xz] (where x > z, given the stronger in-plane response; Fig. 2g), and the “walls” possess polarizations along [x0z] or [0xz] (where x < z, given the stronger out-of-plane response; Fig. 2h). Following established nomenclature used for similar polarization configurations in MPB PZT49, we designate these phases as “MC” and “MB”, respectively. Each phase allows four possible polarization variants (eight if considering out-of-plane inversion), forming various polydomain configurations with (010)- or (100)-type domain walls. Here we provide illustrations for charge-neutral configurations with oppositely aligned out-of-plane polarization in adjacent domains (Fig. 2g, h), Additionally, we also probe the potential presence of polydomain structures with charged domains walls in the films, where adjacent domains exhibit identical out-of-plane polarization direction. Based on PFM vertical amplitude contrast, we further analyze the areal fraction evolution of these phases as a function of thickness. The MB phase increases from 14% in 25 nm films to 73% in 185 nm films, with the MC phase following the opposite trend (Fig. 2i). These observations suggest that thinner films favor the MC phase with a larger out-of-plane polarization, whereas thicker films favor the MB phase with a larger in-plane polarization. This phenomenon is likely driven by the thickness-dependent strain evolution in NaNbO3 films: the compressive strain in thinner films stabilizes a phase with enhanced out-of-plane distortion, whereas strain relaxation in thicker films stabilizes a phase with increased in-plane distortion.

Fig. 2: Ferroelectric domain structure evolution of NaNbO3/SrTiO3 (001) heterostructures with varying film thickness.
figure 2

a, c, e Vertical and b, d, f lateral piezoresponse force microscopy (PFM) amplitude imaging, along with corresponding schematic representations of the MC (red) and MB (blue) phases for NaNbO3 films with thicknesses of a, b 25 nm, c, d 80 nm, and e, f 185 nm, respectively. Schematic representations of the polarization configurations with charge neutral domain walls for g MB and h MC phases, respectively, with corresponding in-plane projection schematics for the possible polydomain configurations. i Areal fraction of the MB phase as a function of thickness, showing an increase in MB phase and a decrease in Mc phase with increasing film thickness.

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Characterizing mixed-phase via synchrotron X-ray diffraction and electron ptychography

Given the nanoscale domain sizes approaching the resolution limit of PFM, we perform additional structural characterizations to further verify these phases and uncover additional structural details. First, we conduct second harmonic generation (SHG) polarimetry measurements to characterize the symmetry of the coexisting phases. Electric dipole SHG is a nonlinear optical process where incident light at a fundamental frequency, ω, is converted into second harmonic light at frequency, 2ω, by the interacting material owing to its broken inversion symmetry (Supplementary Fig. 6a). SHG polar plots are measured by rotating the polarization of the incident fundamental light while measuring the reflected SHG intensities corresponding to both polarization directions (p- and s-polarized) for each film thickness (Supplementary Fig. 6b-d). Following PFM observations, the polar plots are fitted using a multi-domain model assuming the coexistence of MC and MB phases, each consisting of four domain variants. It is important to note that, while our measurements are well fitted by this monoclinic multi-domain model, other structural models like multi-domain orthorhombic or rhombohedral models can also be used to fit the polar plots.

To further confirm the monoclinic distortion, we conduct X-ray reciprocal space mapping (RSM) to resolve the structural details of the coexisting phases. RSM has been applied in previous studies as a powerful method for identifying and differentiating monoclinic symmetries in oxide ferroelectrics50,51,52. We conduct RSMs around the NaNbO3-002 diffraction condition using both lab-source and synchrotron-based XRD (Fig. 3a and Supplementary Figs. 7a and 8). Diffraction peaks corresponding to NaNbO3 appear at higher and lower Qy positions with respect to SrTiO3-002. Based on peak positions, the calculated c-lattice parameters are ~ 3.891 Å and ~3.944 Å, corresponding to the MB and MC phases with lower and higher topographic heights, respectively. The intensity of these peaks evolves with thickness, with MC being more pronounced in 25 nm films and MB dominating at greater thickness, consistent with the trend observed in PFM imaging (Supplementary Fig. 7a). Based on the shift of the 002-diffraction peak, we quantify the thickness-dependent evolution of out-of-plane strain for each phase and estimate the average out-of-plane strain in the mixed-phase state by weighting the strain of each phase according to its areal fraction, as extracted from PFM imaging (Supplementary Fig. 7b, c). The corresponding in-plane compressive strain is estimated by converting the out-of-plane strain using the Poisson effect under biaxial strain conditions (Supplementary Fig. 7d). These results reveal a gradual decrease in both out-of-plane tensile strain and in-plane compressive strain with increasing film thickness, consistent with strain relaxation. To further investigate potential compositional effects, we perform X-ray photoelectron spectroscopy (XPS) on NaNbO3 films with varying thicknesses. While the XPS results show that the films are sodium deficient, there is no significant variation in Na/Nb ratio across the thickness series (Supplementary Fig. 9), indicating that the structural evolution is not driven by changes in sodium stoichiometry. Instead, it is governed directly by strain evolution: in thinner films, compressive strain stabilizes the MC-dominated mixed-phase state with a larger c-lattice parameter, whereas strain relaxation in thicker films reduces the c-axis distortion, favoring the MB-dominated mixed-phase state.

Fig. 3: Elucidating the microstructure of mixed phases in NaNbO3/SrTiO3 heterostructures.
figure 3

Synchrotron X-ray reciprocal space map (RSM) near the 002-diffraction condition for an 80 nm NaNbO3/SrTiO3 heterostructure, revealing two distinct peaks corresponding to the MB and MC phases, along with surrounding satellite peaks from the triclinic phase in the a HL-plane, b HK-plane at L = 2.013, and c HK-plane at L = 1.995. Zoomed-in RSMs near the 103-diffraction condition for the d MB and e MC phases of an 80 nm NaNbO3 film show peak splitting, as highlighted in Supplementary Fig. 10. f Scanning diffraction X-ray microscopy (SDXM) dark-field imaging depicts the coexistence of MB (blue), MC (red), and bridging Triclinic 1 (Tri-1, orange) phases. g Schematic illustration of the polarization rotation pathway between the MC and MB phases, facilitated by intermediate triclinic phases. h HAADF-STEM image of the NaNbO3/SrTiO3 heterostructure. i Nanoscale spatial distribution of two distinct phases in the NaNbO3 film, identified in red and blue via segmentation of nanobeam electron diffraction data. j, k Average diffraction patterns from the two segmented regions, showing the presence (j) or absence (k) of half-order diffraction spots indicative of in-phase and anti-phase octahedral tilts, respectively. l, m Ptychographic images of a 2 × 2 pseudo-cubic unit-cell region of the two phases, illustrating (l) in-phase and (m) anti-phase octahedral tilting. These tilt modes are distinguished by singular or split oxygen sites, highlighted with yellow ovals.

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Further insights into monoclinic distortion were obtained from the NaNbO3-103 diffraction condition. The 103-diffraction peak splits into two adjacent peaks for the MB phase (Fig. 3d) and three adjacent peaks for the MC phase (Fig. 3e and Supplementary Fig. 10), indicative of four-domain configuration in each phase45,51. These characteristic peak splitting confirms the presence of monoclinic distortion of the coexisting phases. Beyond these monoclinic features, we also observe four-fold symmetric satellite peaks surrounding the MB and MC in 002-diffraction, exhibiting similar L but opposite H values (Fig. 3b, c). The first set, with L ~ 2.013, corresponds to a triclinic phase (Tri-1, Fig. 3a, b) with a c-lattice parameter of ~3.885 Å and a tilt angle of 0.43° along [100] relative to the substrate normal. Similarly, another set, with L ~ 1.995, corresponds to a second triclinic phase (Tri-2, Fig. 3a, c) with a c-lattice parameter of ~3.951 Å and a tilt angle of 0.29° along [100]. These triclinic phases, previously also observed in other mixed-phase systems52, act as bridging phases between MB and MC (Fig. 3g). To directly visualize the real-space distribution of monoclinic and triclinic phases, we perform scanning diffraction X-ray microscopy (SDXM). This technique employs a focused, coherent synchrotron X-ray beam to scan point by point across the sample, enabling phase mapping by selecting specific diffraction peaks including those satellite peaks. Using this approach, we map the distributions of MB, MC, and Tri-1 phases (Fig. 3f), where the triclinic phases appear near the MB–MC boundary region. These observations further corroborate the bridging phase nature for these triclinic phases, with the polarization rotating between the MB and MC phases (Fig. 3g).

To further elucidate the spatial distribution of the coexisting phases across the film thickness, we perform scanning transmission electron microscopy (STEM) studies on mixed-phase NaNbO3 (Fig. 3h). We observe the segmentation of two phases (Fig. 3i and Supplementary Fig. 11), differentiated by the presence (Fig. 3j) and absence (Fig. 3k) of half-order satellite spots in the diffraction patterns, corresponding to in-phase and anti-phase oxygen octahedra tilts, respectively. Electron ptychography further resolves these tilt modes in real space, where in-phase and anti-phase tilts manifest as single (Fig. 3l and Supplementary Fig. 12a) and double (Fig. 3m and Supplementary Fig. 12b) oxygen columns in projection, respectively. Combining these findings with DFT simulations (Supplementary Fig. 1), we identify the in-phase tilted structures as Pc (a+b+c−) or Cm (a+b+c−) and the anti-phase tilted structure as Cc (a−a−c−). The simulated polarization profiles for Pc/Cm and Cc are also consistent with the polarization configurations for the MC and MB phases analyzed from PFM characterizations. These results further confirm the coexistence of monoclinic Pc/Cm (MC) and Cc (MB) phases in the mixed-phase NaNbO3 films.

Multi-state polarization switching

To understand how mixed-phase states influence macroscale properties, we conduct electrical measurements to examine the ferroelectric switching behavior of NaNbO3 films using a vertical capacitor geometry with symmetric La0.7Sr0.3MnO3 electrodes (Methods). Well-defined, fully saturated polarization-electric field (P-E) hysteresis loops were measured over a broad frequency range from 1 Hz to 10 kHz, exhibiting low leakage in the synthesized films (Fig. 4a and Supplementary Fig. 13). Both the saturated and remanent polarizations are significantly enhanced compared to previous studies on NaNbO344,45,53,54,55,56, due to the presence of MC phase with enhanced out-of-plane polarization. Maximum values of 53 µC/cm2 in saturated polarization and 40 µC/cm2 in remanent polarization were observed in 80 nm films. To further investigate the switching kinetics, we employ the positive-up negative-down (PUND) method, probing switched remanent polarization as a function of pulse voltage at varying pulse widths (Fig. 4b and Supplementary Fig. 14). Notably, the films exhibit multi-state polarization switching, with the intermediate-state polarization increasing from 28.05 µC/cm2 in 80 nm films to 54.10 µC/cm2 in 185 nm films (Fig. 4b). To elucidate the structural mechanism underlying this multi-state switching behavior, we perform local-scale PFM imaging by applying a DC bias within a defined region of the NaNbO3 films. By characterizing the evolution of film topography under increasing applied bias, we identify the following switching pathway: Initially, at a pre-poled bias of -6V, the film exhibits a uniform elevated topography (Fig. 4c). Upon applying a positive bias, a labyrinthine pattern emerges, exhibiting elevated “walls” and lowered “pathways”, indicative of mixed-phase formation (Fig. 4d). Further increasing the bias transforms the labyrinthine pattern back into a uniform elevated topography (Fig. 4e). These observations suggest a field-driven phase evolution in NaNbO3 films. Initially, the films are uniformly switched into the negatively poled MC phase. Upon applying a positive bias, the MC phase first transitions into an intermediate state, consisting of coexisting negatively poled MC and positively poled MB phases, before fully switching into a positively poled Mc phase at higher bias (Fig. 4f). The polarization evolution of these intermediate states aligns with the net polarization calculated for the mixed phase at each film thickness (Supplementary Table 1). These results confirm that the observed multi-state switching in mixed-phase NaNbO3 originates from phase transitions between monoclinic phases in NaNbO3. Moreover, we evaluate the endurance of stability of both the fully switched and intermediate polarization states. Our results demonstrate that the films exhibit minimal fatigue after more than 108 writing cycles, with less than a 10% change in remanent polarization (Supplementary Fig. 15a, b). Retention tests further confirm the long-term stability of both the fully switched and intermediate polarization states (Supplementary Fig. 15c). These results highlight the robustness of the multi-state switching behavior and demonstrate the potential of mixed-phase NaNbO3 films for reliable non-volatile multi-state memory and logic applications.

Fig. 4: Ferroelectric switching properties of NaNbO3 films with varying thickness.
figure 4

a Polarization-electric field (P-E) hysteresis loops as a function of film thickness, measured at 1 kHz. b Thickness-dependent positive-up, negative down (PUND) measurements of NaNbO3 films with varying thickness. The switched remanent polarization (ΔPr) is measured as a function of applied voltage at a pulse width of 0.1 ms and a pulse delay of 1 s. The pulse switching results indicate a multi-state switching pathway, with the presence of an intermediate polarization state, arising from a mixture of negatively poled MC and positively poled MB phases. c-e AFM topography evolution of 80 nm-thick NaNbO3 film after poling at c −6 V, d 2 V, and e 6 V, revealing the emergence of a labyrinthine pattern upon the intermediate poling voltage. f Corresponding schematic representations illustrate the field-driven phase evolution in NaNbO3 films: the negatively poled MC phase initially transitions into an intermediate state, where the negatively poled MC and positively poled MB phases coexist under the reversal field, before fully switching into a positively poled MC phase.

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Enhanced dielectric susceptibility and tunability

With the presence of mixed phases and multi-state switching in NaNbO3, how do these structural features influence the dielectric properties? Could they enhance susceptibility similarly to MPB PZT films? To explore this, we further investigate the dielectric properties of mixed-phase NaNbO3 films. First, we perform Rayleigh analysis by measuring dielectric permittivity under increasing AC excitation fields (Supplementary Fig. 16a). Using the Rayleigh law (\({\varepsilon }^{{\prime} }={\varepsilon }_{{init}}^{{\prime} }+{\alpha }^{{\prime} }{E}_{0}\))57, we extract the reversible Rayleigh coefficient (\({\varepsilon }_{{init}}^{{\prime} }\)) in the linear regime, which accounts for contributions from intrinsic lattice and reversible domain wall motion, as well as the irreversible Rayleigh coefficient (α’) in the nonlinear regime, which describes the extrinsic contribution from irreversible domain wall motion. Notably, the Rayleigh coefficients peak in 80 nm films, consistent with the thickness-dependent domain wall density observed in PFM imaging (Supplementary Fig. 16b and 17). These results indicate that the extrinsic contribution from both reversible and irreversible domain wall motion to dielectric permittivity correlates with domain wall line density in NaNbO3 films. The high density of domain walls in mixed-phase NaNbO3 leads to a significant enhancement in extrinsic domain wall contributions, resulting in increased domain wall mobility.

To further investigate the dielectric performance in the linear regime, we measure dielectric permittivity and loss tangent under low AC excitation fields across a frequency range of 20 Hz to 10 kHz (Fig. 5a). The results reveal an ultra-low loss tangent increasing with frequency, ranging from 0.021 to 0.067 in 185 nm films. Meanwhile, the measured permittivity exhibits a slight decrease with frequency, with a peak value of 977 observed in 80 nm films at 20 Hz. Among the examined thicknesses, the 80 nm films exhibit the highest permittivity, followed by 25 nm, 125 nm, and 185 nm films, consistent with the trend in domain wall density. Notably, even the 185 nm films show a high permittivity of up to 637. This enhancement arises from both intrinsic and extrinsic mechanisms. Intrinsically, the coexistence of monoclinic and triclinic phases facilitates continuous rotation of polarization under an applied electric field, thereby increasing dielectric susceptibility. Extrinsically, the high density of domain walls enhances reversible domain wall motion, which further contributes to enhanced susceptibility. Notably, this enhancement is comparable to, or even exceeds, previously reported values for MPB PZT films58,59,60,61 (600 - 1300 depending on film thickness, processing, and crystallographic orientation in polycrystalline films).

Fig. 5: Thickness-dependent dielectric property evolution of NaNbO3 thin films.
figure 5

a Dielectric permittivity and loss tangent measured as a function of frequency (20 Hz–10 kHz) at an AC excitation voltage of 5 mV for NaNbO3 films with varying thickness. Normalized dielectric permittivity as a function of DC field (b) up to 220 kV/cm (below the coercive field), and as a function of DC bias (c) up to 8 V (above the coercive field), with tunability (Δεr(bias)/εr(0)) extracted for each thickness. Measurements in b and c were performed on vertical capacitor structures with symmetric La0.7Sr0.3MnO3 electrodes at 1 kHz. The unconventional tunability behavior shown in (c) is attributed to the multi-state switching pathway in mixed-phase NaNbO3, where an intermediate mixed phase state (i.e., coexistence of negatively poled MB and positively poled MC or vice versa) maintains minimal permittivity change under a DC field. The direction of DC bias application is indicated for the 80 nm-thick film. d Normalized capacitance and loss tangent measured at 18 GHz using an in-plane interdigital capacitor geometry on NaNbO3/SrTiO3 heterostructures with varying film thickness. A maximum tunability of 54% was observed in 185 nm films, exhibiting unconventional tunability behavior due to the presence of an intermediate polarization state.

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Finally, we demonstrate how the mixed-phase structure enables exotic and highly tunable dielectric properties, which are critical for electronically tunable filters, antennas, resonators, and phase shifters in wireless communication systems. Upon applying a DC electric field, we observe enhanced tunability at room temperature across a broad frequency range, from 1 kHz to microwave frequencies (5–18 GHz). At low frequencies and under DC fields below the coercive field, we measure a hysteresis-free tunability ranging from 45% to 82%, with a peak value of 82% in 80 nm films (Fig. 5b). When increasing the DC field beyond the coercive field, tunability is further enhanced, ranging from 75% to 92%, again peaking at 92% in 80 nm films while maintaining a low loss tangent (Fig. 5c). Intriguingly, unlike conventional negative tunability, where permittivity continuously decreases with increasing DC field, mixed-phase NaNbO3 exhibits an unconventional tunability response with a plateau in dielectric permittivity at low fields, remaining stable until a higher field induces further dielectric suppression (Fig. 5c). This unconventional behavior is attributed to the multi-state switching pathway in mixed-phase NaNbO3, where an intermediate mixed phase state (i.e., coexistence of negatively poled MB and positively poled MC or vice versa) maintains minimal permittivity change under a DC field. This unconventional tunability extends into microwave frequencies. Using an interdigital capacitor geometry, we observe tunability ranging from 26% to 54% across 5–18 GHz, while maintaining a low loss tangent (Fig. 5d and Supplementary Fig. 18). The relatively lower capacitance modulation in this in-plane geometry, compared to the vertical capacitor geometry used for low-frequency measurements, is attributed to the underlying SrTiO3 substrate, which contributes significantly to the total capacitance but remains non-tunable under applied fields (Methods). Despite this substrate effect, the mixed-phase NaNbO3 still exhibits highly tunable dielectric properties at microwave frequencies. Future work will explore alternative device architectures designed to mitigate substrate effects and further elucidate the high-frequency tunability mechanisms in mixed-phase NaNbO3.

Outlook

Our work highlights a strain-induced phase boundary in chemically simple, lead-free ferroelectric thin films. We demonstrate strain-induced MPB-like polymorphic nanodomain structures composed of coexisting monoclinic and bridging triclinic phases, which drive significant enhancements in dielectric susceptibility and tunability. These enhancements are comparable to or even surpass those of PZT films near MPB compositions, arising from both continuous polarization rotation among the coexisting polymorphs and extrinsic contributions due to the motion of a high density of domain walls. Additionally, we uncover field-driven transitions between monoclinic phases that enable multi-state polarization switching and unconventional tunability behavior across a broad frequency range. Notably, NaNbO3 exhibits a unique ability to undergo allotropic modifications at a much lower strain level than other lead-free perovskite oxides such as BiFeO3, due to its structural richness. This advantage allows the use of a broader range of commercially accessible substrates that provide modest strain to induce and tune the phase boundary. Beyond the MPB-like boundary, the structural complexity of NaNbO3 also allows for the creation of various multi-phase boundaries involving different crystal symmetries and ferroic orders via strain engineering. Moreover, mixed-phase NaNbO3 exhibits significantly lower leakage currents compared to mixed-phase BiFeO3, enabling direct measurement of its intrinsic ferroelectric and dielectric properties near the strain-induced phase boundary. However, the underlying leakage mechanism requires further investigation in future studies. Additionally, the ultrahigh low-frequency tunability (up to 92%) observed in mixed-phase NaNbO3 suggests the promise of enhanced microwave tunability using alternative device architectures that minimize substrate effects. This positions NaNbO3 as a potential alternative to conventional tunable dielectrics such as (Ba,Sr)TiO3 (BST). More broadly, our findings open new opportunities for strain-engineered mixed-phase states in other lead-free perovskites, particularly in underexplored KNN-based thin films, for next-generation dielectric and ferroelectric applications.

Methods

Thin-film synthesis

Epitaxial heterostructures consisting of NaNbO3 films and La0.7Sr0.3MnO3 electrode layers were synthesized on (001)-oriented single-crystalline SrTiO3 substrates via pulsed laser deposition. The synthesis of 10 nm thick La0.7Sr0.3MnO3 bottom electrode layer was conducted in a dynamic oxygen pressure of 190 mTorr, at a growth temperature of 730 °C, a laser fluence of 1.6 J/cm-2, and a repetition rate of 3 Hz, using a 3.7 mm² imaged laser spot. The synthesis of NaNbO3 films with thicknesses ranging from 25 nm to 185 nm was conducted in a dynamic oxygen pressure of 210 mTorr, at a growth temperature of 660 °C, a laser fluence of 2.1 J cm-2, and a repetition rate of 2 Hz, using a 4.58 mm2 imaged laser spot. For fabricating NaNbO3 capacitor structures, a 60 nm thick La0.7Sr0.3MnO3 top electrode layer was synthesized right after the growth of NaNbO3 to form a tri-layer heterostructure. The synthesis of the top electrode layer was conducted in a dynamic oxygen pressure of 190 mTorr, at a growth temperature of 660 °C, a laser fluence of 1.6 J cm-2, and a repetition rate of 3 Hz, using a 3.7 mm2 imaged laser spot. Following synthesis, all samples were cooled down to room temperature at a rate of 5 °C min-1 under a static oxygen pressure of 2.5 Torr.

X-ray diffraction

A high-resolution X-ray diffractometer (Rigaku SmartLab) was used to perform θ–2θ line scans and X-ray reflectometry. A high-resolution X-ray diffractometer (Malvern Panalytical Empyrean) equipped with a 2D area detector was used to conduct 2D reciprocal space maps measurements. Synchrotron X-ray 3D reciprocal space mapping (3D-RSM) measurement was performed using a six-circle Huber diffractometer configured with Psi-C geometry at the beamline 7-ID-C of the APS at Argonne National Laboratory, utilizing X-rays with energies of 17.5 KeV (wavelength λ = 0.70846 Å). A Si (111) double-crystal monochromator with an energy resolution of ΔE/E = 1 × 10-4 was employed to fine-tune the X-ray energy. The X-ray beam at 7-ID-C, with a total flux of 3 × 1012 photons per second at 17.5 keV, was optically focused by using Kirkpatrick-Baez (K-B) mirrors, resulting in a beam profile of 30 µm (Vertical) × 50 µm (Horizontal). Scattering signals were recorded using a Eiger2 X 500 K 2D area detector, and the 2D images were subsequently processed. Geometric corrections were applied to all 3D-RSM data, which was further analyzed using the RSMap3D software developed at APS.

Scanning diffraction X-ray microscopy

Scanning diffraction X-ray microscopy (SDXM) measurement was performed at the Center for Nanoscale Materials’ Hard X-ray Nanoprobe Beamline 26-ID at the upgraded Advanced Photon Source (APS) at Argonne National Laboratory. The X-ray beam energy was set to 10 keV, with a focused beam size of 40 nm full width at half-maximum (FWHM) achieved using a Fresnel zone plate. Diffraction patterns were collected by an Eiger2 X 1 M detector positioned 1 meter from the sample, with a pixel size of 75 µm. SDXM tilt series were acquired at three sample angles, 18.3°, 18.5°, and 18.7°. Large field-of-view maps were obtained by stitching together eight SDXM maps, each covering an area of 6 \(\times\) 6 µm2 with a step size of 60 nm.

Piezoresponse force microscopy

Dual AC Resonance Tracking (DART) piezoresponse force microscopy was conducted to image the domain structure with an MFP-3D Origin+ AFM (Asylum Research) using a conductive Pt/Ir coated conductive tip (Nanosensor, PPP-EFM, force constant ≈ 2.8 N m-1).

Electrical measurements

Capacitor structures with symmetric La0.7Sr0.3MnO3 electrodes were fabricated using photolithography followed by a wet etching process. After patterning the photoresist in circular shapes with diameters of 15, 25, 50, and 75 μm on the as-grown heterostructure, the sample was immersed in a diluted phosphoric acid solution (1 part acid: 5 parts deionized water) at 70 °C for 15 s to selectively etch away the La0.7Sr0.3MnO3 top electrode regions that were not protected by the patterned photoresist. Eventually, the samples were immersed in acetone at 70 °C to remove the photoresist. Dielectric property measurements were conducted on at least 8 capacitors for each sample at room temperature. Dielectric permittivity and loss tangent were measured using an E4980A LCR meter (Agilent Technologies). PUND measurements were performed using a Precision Multiferroic Tester (Radiant Technologies). The capacitor structure was first pre-poled with a -VMax pulse to initialize its negative polarization state. The second pulse, +VMax, switched the polarization, and the switched polarization (P*) was measured. Following this, the sample was allowed to settle at 0 V before a second measurement was taken to account for non-remanent polarization contributions. The third pulse (+VMax) applied without switching, provided a measurement of the total non-remanent polarization (P^), followed by another 0 V measurement. The sequence was then mirrored for the negative voltage direction to complete the measurement. The P* represents switched polarization including both remanent and non-remanent polarization components. In contrast, the P^, measured during non-switching pulses, accounts only for the non-remanent contribution. Subtracting the P^ term from the P* term results in a measure of remanent-only polarization which is represented in (Fig. 4b and Supplementary Fig. 14). For this experiment, a pulse delay of 1 s and a pulse width of 0.01, 0.1, and 1 ms were used.

Microwave measurements were conducted on a gold interdigital capacitor (IDC) geometry fabricated using a lithographic process. A Keysight N5222B programmable network analyzer (PNA) was used to collect scattering parameters, while a Keithley 2612 A source meter unit (SMU) supplied the bias voltage. The sample was probed using an MPI TS150 probe station equipped with FormFactor Infinity probes and SHF bias tees. Each two-port measurement began with a 0 V bias applied to the probes. The bias voltage was then incrementally increased, alternating between positive and negative polarity. At each step, half of the total bias voltage was applied to each probe in opposite polarities. For instance, the first measurement applied 0 V to both probes, followed by +2.5 V and -2.5 V for a 5 V bias, then -2.5 V and +2.5 V for a -5 V bias, continuing this pattern until the maximum bias voltage was reached. A custom Python script automates data collection by controlling both the PNA and SMU. The acquired data includes a complete set of two-port scattering parameters for each bias condition. A MATLAB script was used to compute key parameters such as capacitance and tunability from the acquired data.

Scanning transmission electron microscopy

The cross-sectional lamellae were prepared using a Thermo Fisher Helios G4 UX focused ion beam with the standard lift-out method. The HAADF-STEM images and 4D-STEM data for ptychographic reconstructions were acquired on a Thermo Fisher Spectra 300 X-CFEG STEM operated at 300 kV in nanoprobe mode with a semi-convergence angle of 30 mrad and probe current of 60 pA. The 4D-datasets for ptychography were collected on an EMPAD-G2 detector62 operated at 2–10 kHz, with a probe overfocus of 10 nm and step-size of 0.42 Å. The ptychographic reconstructions used the least-squares maximum likelihood (LSQ-ML) multislice algorithm63,64,65 in the fold-slice package66,67 with 4 probe modes and slice thickness of 1-2 nm.

4D-STEM datasets for nanobeam diffraction were acquired on the EMPAD-G2 detector in microprobe mode with a semi-convergence angle of 1 mrad. We first performed cepstral transformation68,69,70 on the 4D-data to reduce the impact of sample mistilts across the lamella. The phase-segmentation was done on the cepstral-transformed data through k-means clustering.

Second harmonic generation

Second harmonic generation (SHG) polarimetry was done with femtosecond pulses at λ = 800 nm fundamental light from a regeneratively amplified SpectraPhysics Ti:Sapphire laser system (1 kHz, 80 fs). The schematic of the setup used for measurements is shown in Supplementary Fig. 6. Linearly polarized light incident on the sample at 45° generate second harmonic light at λ = 400 nm reflected off the sample. The p-polarized and s-polarized SHG intensities were spectrally filtered and measured by a photomultiplier tube through lock-in amplifier (SR830) detection. SHG Polar plots were generated by rotating the polarization angle (φ) of the incident fundamental light by a half-wave plate.

X-ray photoelectron spectroscopy

X-ray photoelectron spectroscopy (XPS) analyses were conducted using a PHI VersaProbe 4 equipped with a monochromatized Al Kα source. Spectra calibration was performed by aligning the adventitious carbon peak at 284.8 eV. The elemental stoichiometric ratios were quantified using the MultiPak software.

Density functional theory

Density functional theory (DFT) calculations were conducted on a (001)-oriented NaNbO3 epitaxial film, using the generalized gradient approximation, within the Perdew-Burke-Ernzerhof functional for solids (PBEsol) as implemented in the Vienna Ab initio Simulation Package (VASP). The projector augmented wave approach is employed to treat the valence electrons, which account for 7 electrons for Na (2p63s1), 13 electrons for Nb (4s24p64d45s1), and 6 electrons for O (2s22p4). A plane-wave basis with a kinetic energy cutoff of 550 eV is used. The NaNbO3 films are subject to a misfit strain ηmisfit, ranging from ≃ − 4% to ≃+4%, defined as ηmisfit = \(\frac{{a-a}_{0}}{{a}_{0}}\)×100%, where a represents the in-plane lattice constant of the substrate and a0 is the in-plane lattice constant resulting from the energy minimization of the Cc phase.

To model perfect epitaxy on a cubic substrate, the strain tensor in Voigt notation has three elements that are frozen during each simulation: η1 = η2 =ηmisfit and η6 = 0. Meanwhile, η3, η4, and η5 are allowed to relax, along with all internal atomic coordinates, until the Hellmann-Feynman force on each atom is converged to below 0.001 eV/Å for each considered misfit strain. For the NaNbO3 epitaxial film, the Cm symmetry used in the ref. 47 was rotated clockwise by 90° to perform the DFT calculations.

Reporting Summary

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