Introduction

Actuation is critical to modern technologies such as micro-positioning systems, robotic operation and ultrasonic motors, where shape memory alloys, electrostrictive materials and piezoelectric materials have attracted the most attention. The shape memory alloys exhibit large strains with pronounced hysteresis and energy loss, while the electrostrictive materials enable huge but intrinsic nonlinear electrostrain1,2. For high-precision positioning and manufacturing, the piezoelectric actuators are alternatively the most suitable due to their superior performance in terms of response time, displacement precision, and operational endurance3,4,5. Piezoelectric actuators hold the lion’s share of the global piezoelectric materials market, which is expected to reach USD 35.4 billion by 20266. Among all the material properties relevant to the actuation, large electrostrains are the most important. In recent decades, numerous high-performance perovskite piezoelectric materials have been developed, in particular lead-based ferroelectric (1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) and (1−x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-xPT) single crystals, which achieve an optimal electrostrain of ~1.7% in certain crystallographic directions5,7. Polycrystalline ceramic materials, on the other hand, have long been subject to a drop in performance due to the average of various crystal orientations. One way to boost the electrostrains of piezoceramics is to fabricate textured samples to create a unique high-performance direction, similar to single crystals. A high strain of over 0.5% was achieved in textured Pb(Zr,Ti)O3 (PZT) without additional chemical doping8. Ceramics exhibit advantages such as low cost, ease of fabrication and excellent repeatability, making them ideal materials for piezoelectric actuators.

The intrinsic and extrinsic contributions are known to contribute to the electrostrains of piezoceramics. The intrinsic contribution generally refers to the lattice strains (piezoelectricity), while the extrinsic contribution involves the movement of ferroelectric domains walls and/or field-induced phase transformations9,10,11,12. Defect engineering has been proposed to significantly increase the extrinsic contribution to electrostrains by aligning the defect dipoles to ferroelastic domains or by tailoring the mesoscale heterostrain13. This design strategy leads to electrostrains exceeding 1% in lead-free piezoelectric ceramics, such as 1.05% in (K,Na)NbO3 and 1.5% in (Bi,Na)TiO313,14. Unfortunately, achieving such large extrinsic electrostrains requires a high driving field (typically above 6 kV/mm), which poses a challenge for practical actuation applications due to induced non-linearity, remarkable hysteresis and potential electrical breakdown15. As a result, the desirable electrostrains at low driving fields are extremely important for improving control and durability in various actuation applications.

The nature of the monoclinic phase across the morphotropic phase boundary (MPB) of PZT has been widely studied, wherein the general advantage of a monoclinic distortion can be utilized for high piezoelectricity under electric field16,17,18,19. Theoretically, the flattening of the thermodynamic energy profiles results in ultrahigh piezoelectricity20. However, the ferroelectric phase transition for MPB compositions is first-order in nature and thus limits the achievement of an ideal flat energy landscape. To solve this challenge, local structural heterogeneity, i.e., polar nanoregions (PNRs), is utilized to manipulate the interfacial energies, i.e., the electrostatic and elastic energies associated with the interfaces21. The relaxor Pb(Mg1/3Nb2/3)O3 (PMN), with a nano polar structure and a higher degree of local structural heterogeneity, contributes to lowering the switching energy barrier of other ferroelectrics, which has been confirmed for the rare-earth-doped relaxor Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN-PT)22. Therefore, the incorporation of relaxor components into the MPB matrix can serve as an alternative design strategy to further improve electromechanical performance at low driving fields. For example, a large strain of 0.165% can be achieved in Ta-doped Pb(Ni1/3Nb2/3)O3-Pb(Zr0.3Ti0.7)O3 under an electric field of only 1.5 kV/mm23. A thermally stable strain of 0.17% was achieved under an electric field of 2 kV/mm in Sm-doped Pb(Mg1/3Nb2/3)O3-PbZrO3-PbTiO3 (PMN-PZ-PT) system24. A piezoelectric coefficient \({d}_{33}^{*}\) of over 1000 pm/V was achieved in textured PMN-PZ-PT ceramics doped with copper oxide at a maximum field of 3 kV/mm25. All these results indicate that the combination of relaxor ferroelectrics with piezoelectrics of MPB composition can improve the electrostrains of piezoceramics at low driving fields. Nevertheless, deeper insights into the mechanisms of high piezoresponse are still required, especially into the low-field-driven electrostrains in such complex compositions.

In this work, the relaxor-substituted MPB composition 0.9Pb(Zr0.5Ti0.5)O3−0.1Pb(Mg1/3Nb2/3)O3 (abbreviated as PZT-PMN) was systematically investigated, together with the commercial soft PZT ceramic PIC151, which was used as a comparison to show the advantage of relaxor substitution. It is revealed that PZT-PMN exhibits a larger electrostrain (~0.14% at 1 kV/mm) and a lower coercive field (<0.5 kV/mm) compared to PIC151. To unravel the structural origin of the low-field-driven electrostrain, in situ synchrotron X-ray diffraction (XRD) was employed to analyze domain switching dynamics, complemented by microsecond-resolved domain switching measurements and piezoresponse force microscopy (PFM) to understand the kinetics of domain wall motion26. The comprehensive microscopic and macroscopic characterizations reveal that the presented solid solution is featured with reduced lattice distortion and domain size, lowering the energy barrier for domain switching, and consequently promoting electrostrains at low electric fields.

Results and discussion

Crystal structure

The crystal structure of PZT-PMN was analyzed through transmission electron microscopy (TEM) and XRD analysis, as shown in Fig. 1. Corrugated domain structures are observed in Fig. 1a due to the presence of relaxor-like polarized nanodomains and/or mesoscopic chemical inhomogeneity27,28. Electron probe micro analysis (EPMA) was employed to evaluate the elemental distribution of PZT-PMN, and good chemical homogeneity was found (Fig. S1, Supplementary Information)29. The selected area electron diffraction (SAED) patterns recorded along the [111]pc zone axis reveal that all (hh0)pc planes have similar d-spacing values since all diffraction spots corresponding to (hh0)pc are distributed on the same lavender-colored circle, suggesting a pseudo-cubic structure of PZT-PMN. The enlarged areas in Fig. 1b show the relative position of the diffraction spots corresponding to the circle and indicate the slight deviation from perfect cubic symmetry, which is due to the lattice parameter β of the monoclinic lattice deviating from the ideal value of 90°.

Fig. 1: Structural and compositional information of the samples.
Fig. 1: Structural and compositional information of the samples.The alternative text for this image may have been generated using AI.
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a Domain morphology of PZT-PMN. The inset is the high-resolution transmission electron microscopy (HRTEM) image corresponding to this region. b The SAED image of PZT-PMN along <111>pc direction. Lavender-colored concentric circles are added to show the discrepancy in the distance between the center transmission spot and different {220}pc diffraction spots. Two regions marked by yellow and red squares are magnified to demonstrate the relative positions of the circle and diffraction spots. c The synchrotron XRD results, along with the Rietveld refinement of PZT-PMN and PIC151 samples under ambient conditions, where the insets are the magnification of the symbolic {200}pc diffraction peak and high-angle diffraction peaks56. The horizontal axis is represented by the scattering vector \({{{\boldsymbol{Q}}}}{{{=}}}\left(4\pi \sin \theta \right)/\lambda\). d The dielectric constant and loss of PZT-PMN and PIC151 samples as a function of temperature tested at frequency between 1 kHz to 1 MHz.

The Rietveld refinement of the high-energy XRD profiles reveals the pseudo-cubic structure of PZT-PMN (Fig. 1c), which can be described by a coexistence of cubic (space group Pmm) and monoclinic (space group C1m1) phases, in agreement with the TEM study. The pseudo-cubic structure is also evidenced by the single peak of the {200}pc reflections, as can be seen in the inset of Fig. 1c. According to the ternary phase diagram of PMN-PT-PZ system given by Ouchi et al., the PZT-PMN composition in the present study is located in tetragonal phase region and quite close to the tetragonal-rhombohedral-pseudo-cubic triple phase point30. As a result, the coexistence of C and M phase can adequately describe the structure and the reduced lattice distortion of the PZT-PMN ceramic. In contrast, the structure of PIC151 sample is characterized by a phase coexistence of rhombohedral (space group R3m) and tetragonal (space group P4mm) phases. An obvious peak splitting is noticed for the {200}pc reflections. The refined structural parameters of the two materials are listed in Table S1, Supplementary Information.

As featured in Fig. 1d, a strong frequency dispersion is observed for the temperature-dependent dielectric properties of PZT-PMN, while the temperature of the maximum permittivity Tm of PIC151 remains almost unchanged at different frequencies. Frequency dispersion is a characteristic feature of relaxor ferroelectrics31,32, and it is found that the dielectric behavior of PZT-PMN can be well described by the Vogel-Fulcher relationship33:

$$f={f}_{0}\exp \frac{-{E}_{a}}{k\left({T}_{m}-{T}_{f}\right)}$$
(1)

where \(f\) and \({f}_{0}\) are the measured frequency and the characteristic relaxation frequency (Debye frequency), respectively. \({E}_{a}\) and \({T}_{f}\) refer to the activation energy and freezing temperature of polarization fluctuation, respectively, and k is a constant. The fitting results for the frequencies ranging from 100 Hz to 1 MHz (Fig. S2, Supplementary Information) are listed in Table 1, with the parameters of a canonical relaxor system PMN-PT as a reference. The comparable activation energies (Ea) hint at facile domain wall activity and thus the possible existence of polar nanoregions (PNRs). The higher freezing temperature of the investigated PZT-PMN system indicates a higher nonergodic-ergodic phase transition temperature and thus improved thermal stability34,35. The above results indicate that the relaxor behavior is successfully realized by incorporating the relaxor compound PMN into the ferroelectric PZT matrix.

Table 1 Comparison of the Vogel-Fulcher fitting parameters of PZT-PMN and PMN-PT systems
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Electrostrains

The electrostrains of PZT-PMN and PIC151 are compared shown in Fig. 2a. A unipolar strain of 0.14%, corresponding to a large-signal piezoelectric coefficient \({d}_{33}^{*}\) of 1380 pm/V, is achieved at 1 kV/mm (Fig. 2b), which is 60% higher than a \({d}_{33}^{*}\) value of 850 pm/V of PIC151. A unipolar strain of 0.20% and 0.17% is obtained for PZT-PMN and PIC151, which corresponds to a \({d}_{33}^{*}\) value of 980 pm/V and 850 pm/V, respectively. The electrostrains of PZT-PMN and PIC151 at higher electric fields are shown in Fig. S3, Supplementary Information, where the electrostrain of PIC151 at 4 kV/mm (0.28%) is larger than that of PZT-PMN (0.26%). The nonlinearities can be quantified using the hysteresis value H36:

$$H=\frac{{S}_{{{{\rm{f}}}}}-{S}_{{{{\rm{r}}}}}}{{S}_{\max }}\times 100\%\,$$
(2)

where \({S}_{{{{\rm{f}}}}}\) and \({S}_{{{{\rm{r}}}}}\) are the strain measured at half of the maximum field in the falling and rising branches of the hysteresis loop, respectively, and \({S}_{\max }\) is the maximum strain measured in one cycle. PZT-PMN exhibits a lower hysteresis value than PIC151 for both small and large fields. In particular, a hysteresis value of 11.5% (at 1 kV/mm) and 3.0% (at 4 kV/mm) is calculated for PZT-PMN, while a hysteresis value of 15.5% and 9.5% is measured for PIC151 at the same electric fields (Fig. S3b). The electrostrains of piezoceramics are composed of intrinsic contribution from lattice deformation and extrinsic contributions, including movement of domain walls37, PNRs38, and field-induced phase transformation11,12. Among these, the intrinsic piezoelectricity is characterized by a linear field-dependent strain response, while the extrinsic ones are usually associated with nonlinearities before reaching saturation at high electric fields. Conventional approaches to increasing the electrostrains focus on reinforcing the contribution of the extrinsic domain switching and movement of domain walls, which inevitably increases the hysteresis. By forming the PZT-PMN solid solutions, a large electrostrain is harvested while maintaining a low hysteresis. Since nonlinearities are undesirable for piezoelectric actuators, the lower hysteresis of PZT-PMN makes this material a promising candidate for precise actuators39,40. In addition, low driving fields are preferred for piezoelectric actuators. As demonstrated in Fig. 2c, actuation performance of PZT-PMN at low fields is compared with other representative material systems. It is evident that the electrostrain performance of PZT-PMN outperforms that of other lead-based piezoelectric materials at a low field of 1 kV/mm, further emphasizing its excellent actuation capabilities at low fields. Here, the field of 1 kV/mm is selected based on the information given by the PI company (Physik Instrumente GmbH & Co. KG), a globally leading manufacturer of piezoelectric actuators, that the maximum allowable external field for a piezoelectric actuator is between 1 to 2 kV/mm along the polarization direction.

Fig. 2: Electrical properties of PZT-PMN and PIC151.
Fig. 2: Electrical properties of PZT-PMN and PIC151.The alternative text for this image may have been generated using AI.
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a Unipolar strain hysteresis curves measured under the maximum electric field of 1 kV/mm and 2 kV/mm at 0.1 Hz, b the large-signal piezoelectric coefficient \({d}_{33}^{*}\) and the hysteresis value \(H\) measured under 1 kV/mm and 2 kV/mm, and c comparison of electrostrain performance under 1 kV/mm among PZT-PMN and some representative ferroelectric systems57,58,59,60,61,62,63.

In situ structural characterization

To understand the structural change of the materials under electric fields, in situ field-dependent synchrotron XRD was conducted on both PZT-PMN and PIC151 samples. The schematic diagram of the measurement setup and the scattering geometry of the incident beam are illustrated in Fig. 3a. The X-ray beam travels through the sample, and diffraction patterns were collected from the Debye rings. These patterns were then sliced into several cakes with different scattering vectors with respect to the applied field and were integrated to produce one-dimension diffraction patterns as a function of electric field (Fig. S4, Supplementary Information). Here, we mainly focus on the data collected in the direction parallel to the electric field as they clearly reflect the effect of electric field on the structural change.

Fig. 3: In situ field-dependent structural characterization.
Fig. 3: In situ field-dependent structural characterization.The alternative text for this image may have been generated using AI.
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a Schematics of the measurement setup and the scattering vectors with respect to the applied field. Contour plots of b {111}pc and c {200}pc reflections of PIC151 and PZT-PMN. d Schematic of the center of mass (the average 2θ position weighted according to their intensities) of {200}pc reflections for the calculation of field-dependent electrostrains12. The calculated electrostrains based on the e {111}pc and f {200}pc reflections using the center of mass method.

Contour plots of the {111}pc and {200}pc reflections as a function of electric field are presented in Fig. 3b, c41. The field-induced lattice strain can be evaluated from the change of the reflection position of the {111}pc reflection, and non-180° domain switching induces the intensity interchange of the {200}pc and {002}pc reflections. The larger lattice distortion of PIC151 is reflected in a larger splitting of the {200}pc reflection (Fig. 3c). Note that the slight increase in intensity in the middle of the 2θ positions of the {200}pc and {002}pc reflections is due to the presence of a field-induced phase transformation11. To quantify the electrostrains contributed by a combination of piezoelectricity, domain switching, and the possible presence of field-induced phase transformation, the center of mass of the {200}pc reflection and its evolution with electric field are calculated12,17,42, as featured in Fig. 3d. The center of mass is essentially the average 2θ position weighted according to the intensity, and its field dependence represents the structural change of materials under electric fields. The calculated electrostrains based on {111}pc and {200}pc planes are depicted in Fig. 3e and Fig. 3f, respectively. It can be seen that PZT-PMN reaches saturation at 0.5 kV/mm and then shows a hysteresis-free behavior. Despite the slightly lower electrostrains of PZT-PMN than that of PIC151 at 2 kV/mm, PZT-PMN exhibits excellent actuation capabilities at low fields. The negative strains of PZT-PMN and PIC151 maximize at 0.35 kV/mm and 0.85 kV/mm, respectively, and are close to the coercive fields obtained from macroscopic characterization (0.4 kV/mm and 1.1 kV/mm, respectively), as shown in Fig. S5, Supplementary Information. The slight deviation between the synchrotron and macroscopic measurements could be attributed to the different frequencies. The frequency of the bipolar electric field during the synchrotron measurement is 0.025 Hz, while a frequency of 0.1 Hz was used for the macroscopic measurements.

Domain wall dynamics analysis

The field dependence of dielectric permittivity under subcoercive fields is quantified using the Rayleigh model43, as illustrated in Fig. 4a. Despite the similar initial permittivity values (εinit) at zero field, the Rayleigh coefficient, αε, of PZT-PMN (1.78) is twice as high as that of PIC151 (0.86), indicating a stronger contribution of the extrinsic domain wall motion to permittivity. The field-dependent dielectric permittivity of the two materials at large fields is compared in Fig. 4b, where the samples were exposed to a low-frequency, large-signal waveform modulated by a high-frequency, small-signal waveform. PZT-PMN exhibits a 22% higher permittivity at the coercive field and a 27% lower permittivity at the maximum electric field of 2 kV/mm. The higher dielectric tunability of PZT-PMN shows that the domain walls are more responsive at small fields and are easier to saturate at large fields, which can be attributed to facilitated movement of domain walls. The facilitated domain-wall motion can be attributed to a reduced lattice distortion. In La-doped (1−x)BiFeO3–xPbTiO3 solid solution, a threshold of tetragonal distortion, i.e., c/a ratio has been identified, below which the electric-field-induced domain mobility increases significantly, as inferred from the polarization and strain hysteresis44. Similar correlation is also validated in (1−x)Ba(Zr0.2Ti0.8)O3–x(Ba0.7Ca0.3)TiO3 composition, where an increase in 90˚ domain switching was observed with a decrease in the tetragonal distortion45.

Fig. 4: Domain switching dynamics analysis.
Fig. 4: Domain switching dynamics analysis.The alternative text for this image may have been generated using AI.
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a Subcoercive dielectric Rayleigh analysis and b permittivity—electric field curves of PZT-PMN and PIC151 samples. Time dependence of the c switched polarization ΔP and the d strain S of PZT-PMN and PIC151 under 420 V and 840 V.

Characterization of the dynamics of domain walls of PZT-PMN and PIC151 was performed using a customized high-voltage pulse setup, which enables simultaneous measurement of time-resolved polarization and strain changes over a wide range of electric fields (Fig. S6, Supplementary Information)46,47,48. Three-regime switching behavior can be recognized for both materials, consisting of initial rapid movement of non-180° domain walls (regime 1), main switching phase with 180° and non-180° switching events (regime 2), and creep-like non-180° domain wall motion (regime 3). The time-resolved polarization and strain changes of PZT-PMN and PIC151 at 420 V/mm and 840 V/mm are compared in Fig. 4c and Fig. 4d, respectively. At 420 V/mm, the strain of both materials decreases first, reaching the maximum negative strain, and increases (Fig. 4d). The observation of the maximum negative strain marks the transition from regime 1 to regime 2, indicating that both materials have entered the main switching regime. The slightly larger negative strain observed in PZT-PMN at 420 V/mm suggests enhanced activation of non-180° domain wall motion at this electric field. Additionally, the polarization of PZT-PMN exhibits a gradual increase below a duration of 1 ms, followed by a significantly accelerated rate of increase as it approaches the main switching regime. The polarization change of PZT-PMN at 10 s is 35 μC/cm2, 84% higher than that of PIC151. At 840 V/mm, PZT-PMN exhibits a faster increase in polarization below 10−5 s, reaching a large polarization change of 36 μC/cm2, and enters the third regime. In contrast, PIC151 is characterized by a slow increase in polarization in the investigated time period, reaching a polarization change of 44 μC/cm2 at 10 s. The above results reveal a faster switching behavior of PZT-PMN over PIC151 in the investigated field ranges, which can be described by using the Merz law49:

$$\tau \left({E}_{{{{\rm{Sw}}}}}\right)={\tau }_{0}\exp \left({E}_{a}/{E}_{{{{\rm{Sw}}}}}\right)$$
(3)

where the parameter τ0 is the time constant, Ea is the activation field, ESw is the magnitude of the applied field, and τ(ESw) is defined as the time when the switched polarization reaches half the maximum and is extracted from the field-dependent switching data shown in Fig. S646. The activation field is determined as 11.0 kV/mm and 34.9 kV/mm for PZT-PMN and PIC151, respectively (Fig. S7, Supplementary Information). A value of 11.0 kV/mm is smaller than 23.5 kV/mm of lanthanum-doped MPB composition PZT, validating easier and facilitated movement of domain walls in PZT-PMN materials47.

The dynamics of domain switching is accompanied by evolution of domain structures, which can be directly visualized by piezoresponse force microscopy (PFM)50. As shown in Fig. 5a, the fragmented domain structures are found in PZT-PMN, suggesting the possible existence of PNRs in PZT-PMN51. Low contrast is discernible within the out-of-plane signals of the PZT-PMN samples (Fig. S8a, Supplementary Information), indicating a predominance of non-180° domains. On the contrary, PIC151 features micron-sized ferroelectric 180° domains (Fig. 5b and Fig. S8b). These miniaturized ferroelastic domains in PZT-PMN are believed to be the origin of its high piezoelectric response under low electric field52.

Fig. 5: Local domain switching ability characterized by PFM.
Fig. 5: Local domain switching ability characterized by PFM.The alternative text for this image may have been generated using AI.
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The original in-plane phase image of a PZT-PMN and b PIC151. The lithography results when different electric field is applied on c PZT-PMN and d PIC151. The switching spectroscopy PFM (SS-PFM) results of e PZT-PMN and f PIC151.

Domain switching behavior at mesoscopic scale is further analyzed using a DC electric lithography technique and switching spectrum within PFM (SS-PFM). All domains in the test area (5 × 5 μm) were first aligned in the same direction under a sufficient external field (−20 V). Then, different reverse voltages were applied on different regions of the samples, as denoted by Fig. 5c, d. PZT-PMN demonstrates a strong domain switching ability as evidenced by the complete polarization reversal at a small voltage of 6 V represented by the red square, while the domains in PIC151 are only partially switched at twice the applied voltage. These results are in accordance with the minimal activation energy of PZT-PMN via switching dynamic analysis. Additionally, SS-PFM results measured on random points of both samples further support that PZT-PMN can yield larger electrostrain and reversed polarization than PIC151 (Fig. 5e, f).

The strategy to enhance the electrostrains of piezoelectric ceramics at low-driving electric fields by incorporating relaxor compositions is proposed and validated in this work with a comprehensive comparison with the commercial PIC151 ceramics. The relaxor-substituted PZT-PMN ceramics not only exhibit enhanced electrostrain (0.14%, equal to an ultrahigh d33* of 1380 pm/V) but also a smaller hysteresis (11.5%) at 1 kV/mm, which is crucial for practical actuator applications. Moreover, the role of the reduced lattice distortion and miniaturized domain structures modulated by the relaxor modification was investigated in multiple scales and found to benefit superior domain wall mobility and increased proportion of switchable ferroelastic domains. These findings confirm the potential of relaxor incorporation in low-field-driven exceptional performance of piezoelectric materials, thereby advancing the development of piezoelectric actuators toward enhanced output with reduced loss.

Methods

Specimen preparation

0.9Pb(Zr0.5Ti0.5)O3−0.1Pb(Mg1/3Nb2/3)O3 (abbreviated as PZT-PMN) ceramics were prepared using the columbite method. Columbite MgNb2O6 was synthesized by mixing stoichiometric MgO (99.9%, Sinopharm, China) and Nb2O5 (99.9%, Sinopharm, China) raw chemicals using planetary ball milling method with ethanol as the solvent for 24 h. The mixed powders were calcined at 1100 °C for 4 h. The MgNb2O6 powders were then ball milled with PbO (99%, Sinopharm, China), ZrO2 (99%, Sinopharm, China) and TiO2 (98.5%, Sinopharm, China) for 24 h. The mixed powders were then calcined at 1050 °C for 4 h to obtain PZT-PMN solid solutions. The PZT-PMN powders were then mixed with PVA binder before being pressed into pellets of 10 mm in diameter and 1.5 mm in thickness under uniaxial stress of 60 MPa. The green pellets were buried in sacrificial powder and sintered in an alumina crucible at a temperature of 1160–1200 °C for 3 h. Commercial PIC151 ceramics with the nominal composition of Pb0.99(Zr0.45Ti0.47(Ni0.33Sb0.67)0.08)O3 (PI Ceramics, Lederhose, Germany) were selected in this study for comparison53. Both sintered PZT-PMN ceramics and commercial PIC151 ceramics were cut and polished to the dimension of 5.0 × 5.0 × 0.5 mm3 for conventional electrical and strain measurements and time-resolved domain wall dynamics measurements. Another sample dimension of 5.0 × 1.0 × 1.0 mm3 was adopted for In situ synchrotron analysis.

Electrical characterization

The investigated ceramic samples were sputtered with platinum as electrodes for macroscopic electrical characterization. The polarization hysteresis loops were measured using a modified Sawer-Tower circuit, which is equipped with an optical displacement sensor (D63, Philtec Inc., USA) for the measurement of strain. The field-dependent dielectric permittivity was measured using a commercial ferroelectric analyzer (aixACCT TF Analyzer 2000, Germany), where a triangular signal (superimposed by an AC voltage of 0.04 kV/mm with a frequency of 1000 Hz) of 2 kV/mm with a frequency of 1 Hz was applied on samples. Measurement results under subcoercive electric field <0.5 kV/mm were described by the Rayleigh model. Both the Rayleigh coefficient \({\alpha }_{\varepsilon }\) and zero-field value of the permittivity \({\varepsilon }_{{{{\rm{init}}}}}\) were extracted by linear fitting using the data in subcoercive region. The temperature-dependent dielectric permittivity and loss tangent with a frequency of 100 Hz–1 MHz were measured using an impedance analyzer (TH2827, Changzhou Tonghui Electronic Co) combined with a temperature controller. The experimental setup to measure the time-dependent polarization and strain changes consists of a buffer capacitor, a commercial fast HV transistor switch (HTS 41-06-GSM, Behlke GmbH, Kronberg, Germany) and a function generator (Agilent 33220A, Santa Clara, USA), which was used to apply a high voltage within 115 ns without overshooting. Detailed information could be found in ref. 46. Prior to the switching measurements, the annealed samples were cycled 20 times at 0.5 Hz and 4 kV/mm to remove any unstable electric contributions. All samples were poled at 3 kV/mm for 20 s, followed by a relaxation time of 30 s. The switching field pulse, Esw, varying in the range of 0.2–2.0 times the coercive field, was applied in the opposite direction of the poling field.

Structural characterization

In situ synchrotron X-ray diffraction (XRD) experiments were performed at the P02.1 beamline at the Deutsches Elektronen-Synchrotron (DESY, Hamburg, Germany) with a monochromatic X-ray beam of 60 keV. The diffraction data were collected in transmission geometry using a 2D detector (1621 NES Series, PerkinElmer, USA). Instrument parameters, including the sample distance, position of beam center and detector tilts, were calibrated using the National Institute of Standards and Technology (NIST) standard (SRM674b) CeO2 sample under an identical experimental setup. For in situ electric field-dependent measurements, a bipolar electric field of 2 kV/mm was applied to the sample. The exposure time was set to be 0.5 s for each pattern. The two-dimensional XRD pattern was analyzed using software Fit2D to obtain the one-dimensional intensity-2θ patterns with different azimuthal angles (the angle between the scattering vector Q and the applied electric field E ) The detailed data processing can be found in Fig. S4. Field-dependent electrostrain based on structural analysis was calculated from the synchrotron XRD data collected in the azimuthal angle of 0° based on the center of mass method12.

Microstructure characterization

Determination and refinement of ambient crystal structure were performed using Cu Kα radiation on lab XRD (Rigaku, D/Max2500, Tokyo, Japan). GSAS-II is used to perform Rietveld refinement54,55. For Transmission electron microscopy (TEM) and SAED, the specimen was first mechanically polished to around 20 μm in thickness, followed by argon-ion beam milling (Gatan PIPS 695, Gatan Inc., USA) with an operating voltage of 0.1–6 kV to reach electron transparency. The characterization was then carried out using a high-resolution transmission electron microscope (JEOL 2100F, JEOL, Japan) operating at 200 kV. Local piezoelectric response of polished ceramic samples was characterized with PFM (MFP-3D, Asylum Research). For compositional analysis, the samples were first polished to achieve a surface roughness of less than 10 nm to minimize the influence of surface morphology. Afterward, EPMA was conducted using a JXA8230 ( JEOL, Japan) in an area of 30 × 30 µm, with 300 × 300 points measured.