Ultrahigh energy storage density and efficiency in AgNbO_3-based ceramics by percolating interaction between antipolar regions and defect pairs

Domain: physics
Published: 2026-01-10
Editorial outcome: accept

Abstract
A critical challenge for the application of lead-free antiferroelectrics in energy storage systems is their poor thermal stability and low efficiency when the superior energy storage density is attained, primarily due to the inherent first-order nature and narrow temperature window of antiferroelectric-to-ferroelectric transitions. Here, we elucidate a unique percolating interaction between antipolar regions in antiferroelectrics and engineered defect pairs using density functional theory and phase field calculations. Strategic distribution of the strongly coupled Li-Ta pairs in AgNbO3 fosters a percolating interaction that facilitates antipolar rotations, enabling a pronounced polarization change with minimal hysteresis. Guided by theoretical calculations, a large recoverable energy storage density of 12.8 J/cm3, with a high efficiency of 90%, is achieved at room temperature in Ag0.95Li0.05Nb0.35Ta0.65O3 ceramics. Moreover, the superior energy storage performance can remain stable within a wide temperature range from −70 to 170 °C, which paves the way for application in advanced energy capacitors.

Introduction
The rapid development of advanced pulse power systems and microelectronic devices, e.g., hybrid electric vehicles and miniaturized pulsed energy generators, drives a significant demand for high-performance energy-storage dielectric capacitors that exhibit both large energy storage density and efficiency1. To date, although most dielectrics can exhibit inherently fast charge-discharge rates and ultrahigh power density, it remains difficult to simultaneously achieve significant enhancements in both energy storage density and efficiency. This challenge is particularly evident as the energy storage density of dielectrics is still much inferior to that of electrochemical batteries, which is regarded as a key and long-standing bottleneck for energy storage dielectrics2–4.

The widely used estimation equation for recoverable energy storage density of dielectrics, i.e., Ue = ∫ Pmax Pr EdP, clearly suggests that antiferroelectrics hold significant prospective for substantial Ue due to the large polarization change (ΔP) by the field-induced phase transition from antiferroelectric (AFE) state displaying low remnant polarization (Pr) to resultant ferroelectric (FE) state exhibiting large maximum polarization (Pmax)5–8. Therefore, antiferroelectric systems are more conducive to achieve larger energy storage density than representative relaxor ferroelectric and superparaelectric systems if the driving field is set to the same as the threshold of AFE-FE transition8. The traditional antiferroelectrics for promising Ue are lead-based PbXO3 (X=Hf, Zr, etc.) systems. But the growing environmental and human health concerns associated with the use of Pb-based materials have driven significant efforts to develop high-performance lead-free AFEs for energy storage applications9,10.

Over the past few decades, AgNbO3 (AN)-based system has been regarded as one most promising lead-free antiferroelectric systems for energy storage capacitors. These systems can exhibit a large field-induced maximum polarization and achieve a relatively low remnant polarization after the removal of the electric field to zero. It is further understood that pure AgNbO3 shows an antiferroelectric-dominated ferrielectric phase near room temperature, owing to the low energy difference between antiferroelectric Pbcm and ferrielectric Pmc21 phases10,11. The Li doping transforms the antiferroelectric-dominated ferrielectric phase in AgNbO3 into a ferroelectric R3c phase12,13. In practice, by introducing dopants such as La, Bi, Nd, and Na to replace Ag at the A-site, the tolerance factor of AgNbO3-based systems will be reduced14–16. The enhanced stability of the antiferroelectric phase facilitates the boosts of the Ue up to ~8 J/cm3. But low efficiency (η) calculated by Ue/(Ue + Uloss), still remains lower than 80% due to the large electric hysteresis (ΔE) of antiferroelectric-ferroelectric transitions17–19, where the energy loss Uloss is simulated by the enclosed area of polarization–electric (P–E) field loops. The low η (i.e., the high loss) can generate excess heat, posing additional risks of material and device failure10. The design of relaxor antiferroelectrics via random chemical heterogeneity represents a viable strategy for enhancing η by suppressing the AFE-FE phase transition and stabilizing antiferroelectric nanodomains20–23. Combining relaxor antiferroelectric design with tolerance factor manipulation enhances the η of AgNbO3-based ceramics while maintaining relatively high Ue. Representative examples include AgNbO3-AgTaO3 ceramics (Ue of 6 J/cm3 and η of 90%)24, (Ag,Na,La)NbO3 ceramics (Ue of 11.4 J/cm3 and η of 80%)25, and (Ag,La)(Nb,Ta)O3 ceramics (Ue of 8.6 J/cm3 and η of 85%)26. However, the further optimization of energy storage efficiency by a stronger frustration of the AFE-FE phase transition leads to a sharp decrease in Pmax. Enhancing the recoverable energy storage density (Ue) necessitates increasing the applied electric field. Notably, over-elevating the applied electric field would generate an increase of conductive leakage current, easily leading to the occurrence of dielectric breakdown and degrading the device lifetime, especially with varying temperatures1,27. To date, achieving high η (>85%) in the AgNbO3-based ceramics is always accompanied by relatively low Ue (<9 J/cm3). It is also noteworthy that the high Ue of most reported lead-free antiferroelectric ceramics just appears within the temperature range from room temperature to 150 °C28, not covering the lower temperatures to expand the usability in the extreme climate conditions.

Recently, it has been revealed that the percolating electric field formed by incorporating dopants with different radius and valence into ABO3 ferroelectric matrix, can break the long-range-ordered transitions to nano-sized glassy transitions displaying low hysteresis29,30. Additionally, the interaction of the local percolating field will increase the driving electric field for the maximum polarization outputs near ferroelectric transitions30–34. Thus, it can be anticipated that the proper designed percolating field into AgNbO3 systems could not only decrease the scale of AFE-FE phase transition regions for low P–E field hysteresis (low ΔE, i.e., high energy storage efficiency), but also hinder the electrical domain wall motion to ascend the amplitudes of forward switching field (EAFE-FE) and backward switching field (EFE-AFE), which is beneficial for larger energy storage density. As shown in Supplementary Fig. 1, the evolution of the Landau free energy profile clearly illustrates the principle for the changes in EAFE-FE, EFE-AFE, and ΔE (EAFE-FE − EFE-AFE) with increasing the designed local field. Thus, if this designed approach enables simultaneous enhancements in both Ue and η. Moreover, the optimization of nano-sized domain structures and the strong percolating interaction energy in AgNbO3 could significant increase the thermal stability of electric domain configurations, which is important for optimizing the temperature stability of superior energy storage density and efficiency.

Motivated by this analysis, our multi-scale calculation reveals that the coordinated effect of Li+ and Ta5+ cations with adjacent oxygen octahedrons in AgNbO3 superlattice structures can lead to the percolating dipole interaction field in the antiferroelectric matrix for the simultaneous decrease of ΔE and increase of EAFE-FE due to the special rotated antipolar alignment, meanwhile remaining large polarization in the saturation state. Consequently, a remarkable Ue of 12.8 J/cm3 with a high η of 90% is achieved at room temperature in Ag0.95Li0.05Nb0.35Ta0.65O3 (ANLi-65Ta) ceramics. Intriguingly, the superior energy storage performance of ANLi-65Ta ceramics maintains the stability within the temperature range from −70 to 170 °C. To our best knowledge, this performance with remarkable thermal stability exceeds that of the most reported lead-free bulk ceramics, overcoming the long-standing bottleneck in lead-free energy storage dielectrics.

Results
Atomic-scale design of Li-Ta pairs within the antipolar regions of AgNbO3
In the antiferroelectric state of AgNbO3, the characteristic alignments are evidenced by the two adjacent antipolar states, i.e., antipolar region22,23. Under an adequate electric field, the antipolar alignment can be reoriented into the same direction, corresponding to the field-induced ferroelectric state. The polar state is used to describe each polarization variant within the lattice. Here, 2×2×1 supercell structures of the antiferroelectric phase (Pbcm) in AgNbO3 were built by using density functional theory (DFT) calculations. The representative positions of Li+ and Ta5+ cations within the AgNbO3 unit cell structure are illustrated in Fig. 1a, where different cations and anions are marked by spheres with distinct colors. Figure 1b shows the projection of the lattice structure in the y–z plane for AN, AN-Li, and ANLi-Ta, where AN-Li and ANLi-Ta represent Li+ cation-doped AgNbO3 superlattice and the composition with incorporation of Ta5+ cation into the AN-Li superlattice, respectively. The antipolar alignments in pure AgNbO3, as indicated in the upper and lower dashed blue rectangles, are determined by the displacement of Nb5+ cations in NbO6 octahedral units. The potential substitution sites for Li+ cations in AgNbO3 supercell structure can be classified into two types: Li1, located within the polarization region, and Li2, situated at the antiferroelectric boundary region, as indicated by the dashed yellow and black rectangles in Fig. 1b, respectively. Supplementary Fig. 2a–c reveal that when Li+ cations are placed at the low-energy polarization region (Site of Li1) rather than the high-energy boundary (Site of Li2), a larger additional position shift of Nb along the y-axis can be achieved, resulting in a larger local polarization. Such a localized mechanism is consistent with the previous experimental observations, which revealed that Li dopants can thermodynamically stabilize the R3c ferroelectric phases of AgNbO3 due to the A-site and B-site coordinating displacements, especially when the substitution level of Li for Ag reaches ≥5%12,35–37. In addition, the substitution of Li+ cations for Ag+ cations causes the decreased lattice parameters because of the smaller ionic radii (1.17 Å CN=12) of Li+ cation than that (1.48 Å CN=12) of Ag+ cation35. Additionally, the substitution of Ta for Nb results in stronger ionic bonding and compresses oxygen octahedrons9.

To systematically investigate the site-dependent energy of Ta substitution in the AN-Li superlattice, the possible substitution sites can be classified into 16 distinct types, based on the symmetry relation and the distance from the Li doping site (see Supplementary Fig. 2d). Supplementary Fig. 2e and Table 1 display the relative energies of the Ta doping sites (taking the lowest-energy Site3 as zero) and their position differences (i.e., the atomic displacement of B-site cations) along the z-direction. As shown in Supplementary Fig. 2e, Ta5+ cations preferentially substitute for Nb5+ cations at sites with lower relative energy. In such cases, the resulting atomic displacement remains minimal, leading to only a slight rotation of the antipolar polarization. However, with increasing Ta concentration, a growing fraction of Ta5+ cations randomly incorporates into sites adjacent to Li-doped sites, such as Sites 1, 2, 5, 6, and 10. These proximal substitutions correspond to a notable increase in relative energy, which reflects the enhanced local coupling between Li+ and Ta5+ cations. These strongly coupled Li-Ta configurations are conceptualized as defect pairs. Consequently, the atomic displacement along the z-axis is substantially enlarged, inducing a pronounced rotation of the antipolar polarization, as depicted in Fig. 1c. The rotation of polarization for antipolar regions is calculated and illustrated in Supplementary Fig. 3. With increasing Ta concentration, the enhanced interaction between strongly coupled Li-Ta pairs and antipolar regions will redistribute the local polarization and lead to the formation of high-percentage rotated antipolar regions (see Fig. 1c), referred to as the rotated antiferroelectric (RAFE) state, eventually forming a percolating network that partitions the long-range-order antiferroelectric states into coexisting nano-sized antipolar and polar regions.

Predicted energy storage properties of RAFE state by phase field simulations
To reveal the influence of percolating interaction between antipolar regions and defect pairs on theoretical Ue and η potentials, a phase-field model has been developed for the ANLi-xTa system before carrying out experiments for cost-effectiveness, where ANLi-xTa represents the detailed composition with the introduction of Ta into Li-doped AgNbO3, and x is the atomic percent of Ta. The detailed energy descriptions and thermodynamic parameters used in the simulations are given in the Methods section, where dipole interaction energy between antipolar regions in AgNbO3 and strongly coupled Li-Ta pairs governs the formation and growth of the rotated antipolar regions (see Supplementary Fig. 4). Only strongly coupled Li-Ta pairs with adequate dipole interaction energy can generate and expand the RAFE state. Notably, unlike previously reported relaxor antiferroelectrics24,38, the incorporation of strongly coupled Li-Ta pairs can greatly hinder the decrease of local polarization magnitude in the AgNbO3 system (see Supplementary Fig. 2c). Additionally, with increasing Ta concentration, a high interaction field between strongly coupled Li-Ta pairs with neighboring antipolar regions will lead to the enhanced stability of the antiferroelectric state. It will ascend the switching field for AFE-FE transitions as expected, resulting in a possible boost of Ue in ANLi-xTa antiferroelectrics. Owing to the fact that pure AgNbO3 ceramic possesses a breakdown strength (Eb) of ~180 kV/cm (see Supplementary Fig. 5) and the corresponding calculated strain is ~0.25% in our established phase-field modeling. Leveraging this correlation, a rational assumption for our designed systems is made that the Eb for each ANLi-xTa composition is determined by the electric field at which the system reaches the same critical strain of 0.25%39–41, while the detailed methodology for determining Eb is included in the Supplementary Information.

Figure 2a shows that the pure AgNbO3 exhibits an antiferroelectric-dominated state characterized by nearly zero remnant polarization and long-range-order antiferroelectric domain configurations in the microscale, consistent with the reported10. Upon the introduction of Li, the ferroelectric states emerge, resulting in the appearance of “butterfly” strain–electric (S–E) field curve and a classic P–E field loop of ferroelectrics under the Eb. With further increasing Ta concentration to gradually occupy the proximity position of Li, more rotated antipolar regions are produced as expected especially as the Ta concentration rises from approximately 45% to 65% and the associate S–E/P–E loop of each composition under applying the field along [100] as shown in Fig. 2b, c becomes significantly slimmer due to the miniaturized antipolar and polar regions and the decreased ΔE for AFE-FE transition. With increasing Ta content, the long-range-order antiferroelectric and ferroelectric domains have been progressively partitioned into the ferroelectric and antiferroelectric nanodomains. Concurrently, the formation of rotated antipolar regions with strong local dipole fields stabilizes ferroelectric and antiferroelectric nanodomains and hints at the domain wall motion. This structural evolution strongly delay the field-induced antiferroelectric-ferroelectric transition, resulting in low polarization under low electric fields. However, a sufficiently increased electric field eventually triggers the AFE-FE transition, leading to a substantial rise in polarization. As a result, the Pmax at field application direction [100] increases from 0.34 to 0.45 C/m2 under the respective Eb. The corresponding field-induced phase evolution is presented in Supplementary Fig. 6. For the composition with the highest proportion of RAFE state, the most antiferroelectric and ferroelectric nanoregions gradually transform into the RAFE state when the Eb field is applied. Figure 2d provides schematic representations of characteristic polarization vector mapping for ferroelectric, RAFE, and antiferroelectric states, illustrating that the RAFE state exhibits more disordered polarization directions, in contrast to the parallelly ordered polarization arrangement of the ferroelectric state and the completely antiparallel arrangement of the antiferroelectric state. Figure 2e illustrates that the phase fraction of the RAFE state significantly increases with higher Ta concentrations due to the ascending percolated interaction field. Additionally, it has been revealed that AgTaO3 may be quantum paraelectric state (R3c)42, rather than an antiferroelectric (Pbcm) state of AgNbO3. To clarify the microstructural basis of superior AgTaO3-abundant state (ANLi-65Ta), the formation energy difference between R3c and Pbcm phases of different Nb-doped AgTaO3 compositions at absolute zero (0 K) is calculated, as shown in Supplementary Fig. 7. The calculation results clearly show that the antiferroelectric phase is more stable than a quantum paraelectric phase when the atomic percent of Ta falls below 80%, verifying the antiferroelectric feature of ANLi-65Ta.

Figure 2f–h demonstrates that a simultaneous enhancement in Eb, Ue, and η can be achieved by forming more rotated antipolar regions, which is driven by a percolating interaction between strongly coupled Li-Ta pairs and the antipolar regions in the AgNbO3 antiferroelectric matrix. Notably, the theoretical Eb, η, and Ue are markedly increased from 180 kV/cm, 44.5%, and 1.8 J/cm3 at AgNbO3 to 820 kV/cm, 96.6%, and 15.7 J/cm3 for ANLi-65Ta, respectively, by inducing the large proportion of RAFE (~90%). The corresponding field-induced strain curves transition from a steep slope to a slanted slope (see Fig. 2b), enhancing the stability of materials and electromechanical breakdown properties40. After introducing Li into AgNbO3 (i.e., ANLi-0Ta), the formation of a long-range-order ferroelectric phase leads to a largely enhanced remnant polarization upon removal of the external electric field, further causing a sharp decrease in both η and Ue compared to the undoped AgNbO3 system, as shown in Fig. 2g, h. Furthermore, when the temperature increases, long-range-order ferroelectric structures of ANLi-0Ta gradually transform into long-range-order antiferroelectric structures in a narrow temperature window (see Supplementary Fig. 8). With continuously increasing Ta concentration, the rotated antipolar regions gradually restrict the growth and diminishment of antiferroelectric and ferroelectric nanoregions, being able to maintain the characteristic structure across a wide temperature range. It suggests the great potential for increasing the thermal stability of the boosted Ue and η.

Superior energy-storage performance in Li/Ta co-doped AgNbO3 ceramics
AgNbO3 ceramics doped with Li and Ta were fabricated according to the composition design in phase field simulation, (Ag0.95Li0.05)(Nb1−x/100Tax/100)O3 (abbreviated as ANLi-xTa) with x values of 0, 5, 25, 45, and 65. The measured mean densities of ANLi-xTa (x=0, 5, 25, 45, and 65) are 6.52, 6.71, 7.28, 7.78, and 8.03 g/cm3, respectively, by using Archimedes’ method. Figure 3a presents the P–E loops of AN, ANLi-xTa (x=0, 5, 25, 45, and 65), and AgTaO3 (AT) ceramics under the respective Eb. Compared to the computational results in the single crystal model, Pmax does not exhibit a similar significant enhancement in the experiment of ANLi-xTa polycrystalline ceramics. The Pmax slightly increases from 38.25 μC/cm2 at ANLi-0Ta to 40.39 μC/cm2 at ANLi-65Ta under Eb. Every P–E loop has been measured under Eb three times. The error value for the Pmax for all compositions is below ±0.1 μC/cm2. Under the same applied electric field, the Pmax evidently drops with increasing Ta concentration, as shown in Supplementary Fig. 9. In addition to the miniaturized domains and delayed AFE-FE transition with increasing Ta concentration, the continuous decrease in grain size from 3.92 μm (ANLi-0Ta) to 0.78 μm (ANLi-65Ta), as shown in Supplementary Fig. 10 further restricts polarization enhancement under the same electric field. In ferroelectric/antiferroelectric ceramics, the decreased grain size hinders domain wall motion and domain switching due to the enhanced clamping effects from grain boundaries and the absence of mobile domain wall43. ANLi-5Ta ceramics exhibit typical ferroelectric polarization hysteresis and current–electric field loops (see Supplementary Fig. 11a, b), indicating a predominant ferroelectric structure at room temperature due to the influence of Li on the microstructure of AgNbO3. In contrast, characteristic double hysteresis loops appear in the composition with x=25 (see Supplementary Fig. 11c). As shown in Supplementary Fig. 12a, with increasing Ta concentration, the value of room-temperature strain at the same field of 160 kV/cm sharply decreases from ~0.3% of ANLi-5Ta to ~0.02% of ANLi-65Ta. At the same time, the strain hysteresis also sharply decreases, resulting in slimmer strain loops with a slanted slope in ANLi-65Ta ceramics, agreeing well with calculated strain behavior and experimental slimmer P–E loop characteristics. As shown in Supplementary Fig. 12b, c, the forward and backward switching fields for the field-induced antiferroelectric-to-ferroelectric phase transition increase from 110 kV/cm and 16 kV/cm in ANLi-25Ta to 187 kV/cm and 170 kV/cm in ANLi-65Ta, respectively. This increase in the switching fields demonstrates the enhanced stability of the antiferroelectric phase with increasing Ta concentration from ANLi-25Ta to ANLi-65Ta at room temperature, consistent with the tendency of the established Ag(TaxNb1−x)O3 phase diagram44. The lowest ΔE of approximately 17 kV/cm is achieved for ANLi-65Ta due to the influence of RAFE state, in comparison with other representative AN-based systems (see Fig. 3b)9,24–26,45,46. Accordingly, the Ue and η simultaneously increase from 0.2 J/cm3 and 9% for ANLi-0Ta to 12.8 J/cm3 and 90% for ANLi-65Ta (see Supplementary Fig. 13), i.e., ~64 times and ~10 times enhancements in Ue and η respectively, surpassing almost all reported lead-free AgNbO3 and NaNbO3 (NN)-based antiferroelectric ceramics, as shown in Fig. 3c1,28,38,47–51. Such enhancement in energy storage performance arises not only from the increased Eb but also from the high polarization, which derives from a delayed field-induced antiferroelectric-to-ferroelectric transition enabled by the percolating interaction between antipolar regions and defect pairs.

Figure 3d displays the statistical breakdown strengths of ANLi-xTa and AT ceramics, analyzed using Weibull distribution fitting17,52, while the detailed methodology is included in the Supplementary Information. It is evident that the actual mean Eb significantly increases from approximately 212 kV/cm for ANLi-5Ta to approximately 760 kV/cm for ANLi-65Ta. This tendency is also consistent with the phase field predictions, providing solid verification for the rationality of Eb definition in phase field simulations. Figure 3e illustrates the temperature-dependent unipolar P–E loops of ANLi-65Ta under an electric field of 510 kV/cm. The Ue exhibits high thermal stability over a 240 °C temperature range, decreasing only from 6.7 J/cm3 at −70 °C to 6.2 J/cm3 at 170 °C. Figure 3f shows that ANLi-65Ta, exhibiting an average Ue of 5.3–6.5 J/cm3 over a temperature range (Tspan) of 240–255 °C under electric fields of 450–510 kV/cm (see Supplementary Fig. 14), surpasses that of most reported AN, NaNbO3, BaTiO3, K0.5Na0.5NbO3, and Bi0.5Na0.5TiO3-based lead-free bulk ceramics24,26–28,48,53–66. Here, Tspan is defined by the temperature range when the Ue is higher than 90% of the maximum under the same electric field.

Microstructural basis for the superior energy-storage properties in ANLi-xTa ceramics
Rietveld refinement results, shown in Fig. 4a and Supplementary Fig. 15, reveal the coexistence of the Pbcm and R3c phases in ANLi-xTa ceramics at room temperature46,67. The composition-dependent percentages and the fitted lattice parameters of Pbcm (M3/M2) and R3c phases are presented in Fig. 4b and Supplementary Table 2, respectively. With increasing Ta concentration, the phase fraction of the Pbcm antiferroelectric phase increases, indicating the enhancement of the switching field of the antiferroelectric-ferroelectric phase transition. In addition, the softening and hardening, appearance, and suppression of Raman-active phonons are sensitive to the nano-structural changes, especially for similar M2 and M3 phases68–70. The corresponding room-temperature Raman results shown in Supplementary Fig. 16, demonstrate that the breathing mode of Ag+ near 84 cm−1 is only observed in AgNbO3 and Ag0.97Li0.03Nb0.97Ta0.03O3 (AN-3LT) and not in compositions with higher Li/Ta co-doping. It is related to the happening of phase transition from antiferroelectric-dominated ferrielectric phase to ferroelectric phase near ANLi-5Ta ceramics13,71. The ν5 mode exhibits a distinct redshift from approximately 260 cm−1 in both AgNbO3 and Ag0.97Li0.03Nb0.97Ta0.03O3 to 221 cm−1 of ANLi-5Ta. Concurrently, the NbO6 octahedral vibrational modes shift from 96, 107 cm−1 of AgNbO3 to 94, 103 cm−1 of ANLi-5Ta. This systematic softening of both the ν5 and NbO6 phonon modes reflects progressive changes in the local octahedral structure. In addition, with further increasing Ta concentration, all Raman peaks become weaker and broader, due to the disruption of long-range-order electrical domains and the increased disorder or relaxor feature24. When the Ta content is over 40 mol%, the phase transition from M2 to M3 happens, resulting in the blue shift of the ν1 mode from 569 cm−1 of ANLi-25Ta to 591 cm−1 of ANLi-65Ta.

The temperature-dependent dielectric permittivity curves depicted in Fig. 4c, d and Supplementary Fig. 17 reveal the phase transitions of ANLi-xTa ceramics. With increasing Ta concentration, the temperature for phase transitions from AFEM3 to AFEM2 and from AFEM2 to FER both gradually decreases. Notably, the decrease of M3-M2 transition temperature is faster than the M2-R case. Consequently, the M3-M2 and M2-R phase transition lines converge together near ANLi-65Ta, being inclined to form the antiferroelectric and ferroelectric coexistent region (i.e., M3-M2-R) at ANLi-65Ta. In addition, the abrupt changes in dielectric loss curves during temperature variations are closely associated with the phase transitions. For the antiferroelectric (M2)-ferroelectric (R) phase transition, the dielectric loss peaks systematically shift toward higher temperatures with increasing measurement frequency. For the paraelectric AT ceramics, no dielectric anomaly indicative of a phase transition is observed. As shown in Supplementary Fig. 18, the increase in dielectric permittivity with decreasing frequency at elevated temperatures is attributed to the contribution of leakage current. The frequency dispersion of the M2 to R and M3 to R transitions is fitted using the Vogel-Fulcher relation to determine the freezing temperature (Tf)29,30. As shown in Fig. 4e, with increasing Ta concentration, the freezing temperature (Tf) gradually decreases. Above Tf, it is acknowledged that the polarization shows the ergodic polar dynamics, which has no clear frequency dependence in dielectric results, indicating a much shorter relaxation time and lower activation energy for polarization fluctuation72,73. In comparison with the Tf (−18.8 °C) of ANLi-45Ta ceramics, the freezing temperature has been much decreased to −121.5 °C of ANLi-65Ta ceramics. In other words, the temperature range for ergodic antiferroelectric (M2 and M3 with Pbcm symmetry) and ferroelectric coexistent nanostructures can remain stable above the freezing temperature of ANLi-65Ta.

To further investigate the rotation configuration of antipolar structures under different proportions of Li/Ta in AgNbO3, atomic-scale high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) was employed in the ANLi-5Ta and ANLi-65Ta ceramics. Figure 5a shows that the ANLi-5Ta sample generally exhibits a long-range-order antiferroelectric domain pattern with alternating polarization directions every two atomic layers. In comparison, the polarization vectors of ANLi-65Ta, presented in Fig. 5d, are more disordered and deviate from the primary antiferroelectric directions. The polarization angle mapping and corresponding histogram in Fig. 5b, e indicate that both ANLi-5Ta and ANLi-65Ta display a bimodal symmetric angle distribution, reflecting their average antiferroelectric characteristics. Distinct from ANLi-5Ta, the formation of a RAFE state with increased polar rotation in ANLi-65Ta results in a more dispersed angle distribution. Additionally, for ANLi-5Ta, Gaussian fitting of the polarization displacement distribution in Fig. 5c reveal two distinct peaks centered near 4.7 pm and 8.4 pm. This bimodal distribution indicates that the local polarization magnitudes are not random but are concentrated around these two specific values, which are attributed to the formation of the R3c ferroelectric state after Li doping into the AgNbO3 system. This highlights the prominent ferroelectric-like characteristic of ANLi-5Ta, consistent with the DFT results for AN-Li. With further increasing Ta concentration, Fig. 5f shows that ANLi-65Ta displays only a single peak in its polarization magnitude distribution, suggesting that ANLi-65Ta contains a substantial fraction of RAFE state due to the presence of abundant rotated antipolar regions, smearing the antiferroelectric boundary region. Furthermore, as shown in Supplementary Fig. 19, the polarization angle distribution in Ag(Ta0.8Nb0.2)O3 (ANT80) exhibits a distinct bimodal characteristic, which is the typical polarization state of the antiferroelectric structure. These results confirm that the antiferroelectric phase is stable even at Ta concentrations as high as 80 at.%, thereby corroborating the reliability and accuracy of the DFT calculations.

Methods
DFT calculations
Our DFT calculations were conducted by using the Vienna Ab-initio Simulation Package74. The spin-polarized Perdew–Burke–Ernzerhof exchange75–correlation functional and projector augmented wave method76 were adopted with the valence-electron configurations of 4d105s1 for Ag, 4p64d45s1 for Nb, 2s1 for Li, 2s22p4 for O, and 5d46s1 for Ta. The cut-off energy of 400 eV for all calculations. The 2×2×1 160-atom supercell of the Pbcm phase of AgNbO3 was adopted. The atomic positions and lattice constants were fully relaxed until the total energy difference, and forces were less than 10−7 eV and 0.01 eV/Å, respectively. The Monkhorst–Pack k-point mesh of 1×1×1 was adopted for geometrical optimization calculations for all structures77.

Phase field simulation
AgNbO3-based system is taken as a typical lead-free antiferroelectric system by solving the time-dependent Ginzburg-Landau (TDGL) equation:

∂P(x,t) / ∂t = −L δF / δP(x,t), (i=1,2,3) (1)

where L is the kinetic coefficient related to the domain mobility, t is time, P(x,t) is the polarization and F is the total free energy of the whole system, expressed as following78:

F = ∫ (flan + fgrad + felas + felec + flocalelec) dV (2)

where V is the volume of the system. The landau free energy flan can be calculated by

flan = α(P1^2+P2^2+P3^2) + α11(P1^4+P2^4+P3^4) + α12(P1^2P2^2+P2^2P3^2+P1^2P3^2) + α112(P1^4(P2^2+P3^2) + P2^4(P1^2+P3^2) + P3^4(P1^2+P2^2)) + α111(P1^6+P2^6+P3^6) + α113(P1^2P2^2P3^2) (3)

where α, α11, α12, α112, α111, and α113 are Landau coefficients.
The gradient free energy fgrad representing the energy from polarization inhomogeneity is described as79,80:

fgrad = Σ (i=1,2,3) [α (∂Pi/∂x)^2 + (∂Pi/∂y)^2 + (∂Pi/∂z)^2] + β [(∂^2Pi/∂x^2)^2 + (∂^2Pi/∂y^2)^2 + (∂^2Pi/∂z^2)^2], (i=1,2,3) (4)

where α is a negative coefficient representing the stability of AFE phase, β is a positive coefficient representing the stability of FE phase. The elastic strain energy felas can be expressed by
felas = 1/2 Cijkl eij ekl = 1/2 Cijkl (εij − εij0)(εkl − εkl0), where Cijkl is the elastic stiffness tensor. eij, εij, and εij0 are the elastic strain, total strain, and the spontaneous strain, respectively. The electrostatic energy felec can be calculated by felec = −1/2 Ei Pi − 1/2 Ei Pi, where Ei is the electric field component, including the dipole field, depolarization field, and applied electric field, Pi is the average polarization. The local random distribution electric field energy flocalelec related with dopant valence and concentration can be expressed as: flocalelec = Ei,localelec Pi, where Ei,localelec is the random distribution electric field. Additionally, the normalized nearest neighbor polar directions are averaged to distinguish the regions of AFE, RAFE, and FE. The simulations were carried out in two dimensions with cell sizes 256Δx×256Δy (Δx and Δy are the number of grid points, which are equal to 2 nm) with periodic boundary conditions.

Sample preparation
(Ag0.95Li0.05)(Nb1−x/100Tax/100)O3 ceramics were fabricated by the solid state reaction method with chemical powders of Ag2O (99.9%, Alfa Aesar), Li2CO3 (99%, Alfa Aesar), Nb2O5 (99.9%, Alfa Aesar), and Ta2O5 (99.9%, Alfa Aesar). The raw chemical powders were ball-milled in ethanol for 12 h in nylon cans with zirconium dioxide grinding beads using a planetary ball mill with a rotation rate of 700 r/min. Then the mixed powders were dried and calcined at 900 °C for 6 h in an oxygen atmosphere. The calcined materials were ground and then ball-milled again for 12 h. After drying, the powders were pressed into disks with a diameter of 8 mm under 200 MPa via cold isostatic pressing. The sintering was done at 1080 °C for 6 h in an oxygen atmosphere, where the heating and cooling rates are set as 3 and 5 °C/min, respectively. The ceramic samples were thinned and polished using an automatic metallographic grinding and polishing machine (YMPZ-1) at a rotation speed of 500 r/min. Final polishing was performed with an alumina-based slurry for 1 min. Pt electrodes were then deposited on both surfaces via a plasma magnetron sputtering system (VTC-16-D) with a deposition time of 80 s. Then, the ceramic samples were polished to a thickness of ~80 μm for energy-storage measurement. The diameter of silver electrodes is around 1.5 mm.

Characterization
The measurements of breakdown field and all P–E loops were characterized using a Radiant Premier II ferroelectric test station at room temperature, with an applied electric field frequency of 10 Hz. The P–E loops of AN and ANLi-5Ta were measured under Standard bipolar settings, and the P–E loops of ANLi-25Ta, ANLi-45Ta, and ANLi-65Ta were measured under Standard monopolar settings. Room-temperature Raman spectra from 50 to 1000 cm−1 were measured by using a Horiba Alimentation LabRAM spectrometer with a laser wavelength of 532.2 nm. The temperature-dependent dielectric permittivity of ANLi-xTa (x=5, 25, and 45) and ANLi-65Ta ceramics was measured from 400 to −100 °C with a cooling rate of 3 °C/min under different frequencies of 100 Hz, 1 kHz, 10 kHz, 100 kHz, and 500 kHz by using a dielectric temperature measurement system (CNOGTICAL DMS1000 with HIOKI 3532 LCR meter). XRD measurement was performed at Bruker D8 ADVANCE with the voltage of 40 kV and the current of 30 mA, where the XRD scanning range for samples is set from 20° to 90° with the rate of 1°/min and the step of 0.02°. Atomic HAADF images were obtained by a double spherical aberration (Cs) corrected STEM (Spectra 300, Thermo Fisher Scientific) equipped with probe and image correctors and operated at 300 kV. The Weibull distribution fitting was employed to evaluate breakdown strength.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Please see the attached file for more detailed review comments.\nUsing density functional theory (DFT) and phase-field simulations, the authors proposed a strategy to enhance energy storage properties in lead-free antiferroelectrics through a unique percolating interaction between antipolar regions and engineered defect dipoles. Based on the experimental results, the authors claimed the increasing percolating interaction between Li-Ta dipoles and antipolars in AgNbO3-based antiferroelectrics induced more rotated antipolar regions from the initial AFE state. This leads to a remarkable recoverable energy storage density of 12.8 J/cm3 with 90% efficiency, stable up to 255 °C, surpassing most lead-free ceramics.\nThe manuscript is interesting and could be considered for publication until all the raised major/minor comments are systematically addressed along with the additional experimental results. The comments are the following.\nComments:\n1) The role of Li substitution was not very clearly discussed when Li was introduced to AgNbO3, it disrupted the long-range antiferroelectric domain configuration and transformed the antiferroelectric state into a ferroelectric state. Theoretically, the ferroelectric state appeared upon Li substitution also noticed experimentally in polarization hysteresis loops. However, was it only due to the preferred Li1 to occupy the polarization region rather than the boundary or ionic radius, etc?\n2) It is understandable that the quantity of the Li was low and very challenging to atomically visualize in the STEM. Alternatively, Raman spectroscopy can lead to verifying the disruption of the long-range antiferroelectric domains and transformation into a ferroelectric state upon tilting the octahedra where phonon modes become softened appearing like other studies [J. Materiomics 10, 431 (2024); Phys. Rev. Materials 3, 084405 (2019); J. Alloys Compd. 667, 310 (2016)].\n3) In the phase field simulation results in Figure 2c, authors claimed a slim polarization-electric field (P-E) loops with an increase in the maximum polarization (Pmax increased from 0.34 C/m2 to 0.45 C/m2) upon the increasing Ta concentration, attributed to the due to the decreased ΔE for antiferroelectric-ferroelectric (AFE-FE) transition in the constructed rotated antiferroelectric (RAFE) matrix. On the contrary, the Pmax of the highly substituted (AL5NT65) composition at a much higher electric field (~750 kV/cm) was nearly comparable to the lower substituted (AL5NT5) composition at a lower electric field (~200 kV/cm). Can the author explain the reason?\n4) Was the unipolar P-E loop in Fig. 3(a) measured in the as-sintered state (before the poling process)? The bipolar P-E loop of AL5NT5 exhibits a hysteresis curve characteristic of ferroelectric behavior. In ferroelectric materials, if a unipolar P-E loop is measured in a poled state, the hysteresis observed between the Pr and Pmax paths is typically small, leading to a minor difference between the polarization value at E = 0 (Pr) and the polarization at Emax (Pmax). Additionally, the overall hysteresis should be minimal. However, in Fig. 3(a), the unipolar P-E loop of AL5NT5 shows a substantial difference between the initial polarization at E = 0 (P = 0 μC/cm2) and the final remnant polarization (Pr = ~28 μC/cm2) after measurement. Moreover, the loop exhibits significant hysteresis. The authors should provide a detailed explanation of the sample state in which the measurements for Fig. 3(a) were conducted.\n5) Is the unipolar P-E loop in Fig. 3(a) measured in the as-sintered (before poling process) state? The bipolar P-E loop of AL5NT5 shows a hysteresis curve close to the ferroelectric characteristic. In the case of a ferroelectric, if a unipolar P-E loop is measured in a poled state, the hysteresis curve that appears between the Pr and Pmax paths is measured, so the difference between the polarization value at the E = 0 state (Pr) and the polarization value at the Emax state (Pmax) is expected to be small and the hysteresis will also be small. However, the hysteresis curve of AL5NT5 shown in Fig. 3(a) shows a significant difference between the initial polarization value at E = 0 (P = 0 μC/cm2) and the final polarization value after measuring the unipolar P-E loop (Pr = ~28 μC/cm2), and it shows a significantly large hysteresis characteristic. The author needs to provide a detailed explanation of the sample state in which the results of Fig. 3(a) were measured.\n6) For comparison of the theoretical and experimental results, authors should provide P-E hysteresis loops of the pure AN in Figure 3a, demonstrating AFE-FE transitions to a higher level in (Ag0.95Li0.05)(Nb1-x/100Tax/100)O3, with x values of 5, 25, 45, and 65. Also, they should provide strain loops to strengthen their arguments showing a bipolar hysteresis response to slimmer loop characteristics.\n7) The authors claimed an ultrahigh energy storage density of 12.8 J/cm3 and an excellent efficiency of 90% for AL5NT65 at the applied electric field of ~750 kV/cm. However, the excellent thermal stability (ranging from 5.4 J/cm3 at -70 °C to 4.9 J/cm3 at 185 °C) of the corresponding composition was presented at a moderate electric field of 450 kV/cm rather than at a higher electric field. Authors must show the thermal stability of the AL5NT65 at the higher electric field.\n8) Based on the Rietveld refinement of the X-ray diffraction (XRD) data for the AL5NT5 to AL5NT65, it could be seen that extra diffraction peaks around the ~23o and 46o were noticed in the XRD spectra of AL5NT45 and AL5NT65 ceramics [Figure 4a and Supplementary Figure 11]. Also, these XRD peaks were not fitted by the provided Pbcm and R3c CIF files. Are these secondary peaks? Or showing the existence of another phase along with the Pbcm and R3c phases which only appeared at a higher doping level of Ta. Did authors fit XRD with other noncentrosymmetric (Pmc21) or cubic phases along with the current Pbcm and R3c phases (Z. Lu et al., Nano energy 79, 105423 (2021)? to get a better fit like S. Ali et al., Chemical Engineering Journal 485, 150087 (2024). Authors must verify the origin of these peaks.\n9) This sentence is confusing and the authors need to rewrite it “The transitions from AFE M3 to AFE M2 and from AFE M2 to FE R3c gradually converge together when the composition approaches to AL5NT65, suggesting the coexistence of AFE M3, M2 and FE R nanostructures.”\n10) The definition and explanation of 'Li-Ta dipoles' appear on line 169. However, since this term is introduced earlier in the text, readers may be confused about its meaning. For instance, 'Li-Ta defect dipoles' is mentioned on line 117 and 'Li-Ta dipoles' on line 119. The authors should define these terms earlier in the manuscript or consider using alternative wording in the initial mentions.\n11) The authors represented the recoverable energy storage density as follows:\nW_rec=∫_(P_r)^(P_max) EdP\nThis is an incorrect mathematical formula for Wrec. Although the positive integral of an electric field with respect to polarization from remnant polarization (Pr) to saturated polarization (Pmax) seems to be identical to the negative integral of an electric field with respect to polarization from Pmax to Pr mathematically, the positive integral cannot be equal to the negative integral due to the hysteretic characteristic of ferroelectrics/piezoelectrics in reality. As the authors probably know, the upward path in a hysteresis loop from Pr to Pmax is never identical to the downward path from Pmax to Pr. Hence, Wrec should be represented as shown in [Ceram. Inter. 47 (2021) 23488; Adv. Funct. Mater 29 (2019) 1807321]:\nW_rec=-∫_(P_max)^(P_r) EdP", "reviewer_2": "This manuscript reports a recoverable energy storage density of 12.8 J/cm3 with an efficiency of 90% achieved at room temperature in Ag0.95Li0.05Nb0.35Ta0.65O3 ceramics. This achievement is attributed by the authors to a rotated antiferroelectric (RAFE) state related to interaction between Li-Ta defect dipole and antipolars invented by them based on their simulation study. Therefore, the authors called their manuscript as “Ultrahigh energy storage density and efficiency in AgNbO3-based ceramics by percolating interaction between antipolars and defect dipoles”. However, this title has several incorrect or even misleading statements.\nFirst, the authors claim that the values obtained by them and shown in Fig. 3c are ultrahigh “surpassing all reported lead-free antiferroelectric ceramics”. However, comparable values of 12.6 J/cm3 and 94% were recently reported in Chem. Eng. J. 503 (2025) 158557 for multilayer ceramic capacitors with a simpler composition of AgNb0.5Ta0.5O3. When the composition is complicated, values up to 43.5 J/cm3 and 85% can be achieved in lead-free ceramics as reported in Adv. Energy Mater. 2024, 14, 2400821 and references therein. Therefore, if 12.6 J/cm3 is ultrahigh, how should one call 43.5 J/cm3?\nSecond, these values were obtained by the authors in ceramics having just 35% Nb. Therefore, claiming that these ceramics are based on AgNbO3 looks misleading as well. These ceramics are rather based on AgTaO3 that is not antiferroelectric but quantum paraelectric, according to works like Appl. Phys. Lett. 95, 242904 (2009). Thus, one should not invent the rotated antiferroelectric (RAFE) state but follow the explanations presented in the works mentioned above regarding turning the antiferroelectrics into quasi-linear dielectrics for high energy storage applications.\nThird, following the previous issue, DFT simulations done for Ta doping ions in AgNbO3 lattice do not look to be valid. One must consider instead an opposite situation with Nb doping of AgTaO3. Moreover, even presented simulations show that “the substitution site with lower energy, distant from the Li cations, should be occupied first”, contradicting the idea of Li-Ta dipole formation and its interaction with antipolars. When the Ta content is low there are no Li-Ta dipoles. When Ta content is high, the matrix is not antiferroelectric anymore. Furthermore, besides the RAFE state, the authors invented other terms like antipolars and polars without clear definition for them. That together with a lack of definition of symbols and abbreviations like E, FE, AN-Li, ANLi-Ta, AnLi-xTa, XRD and Tm at first mentioning or at all creates additional difficulties to understand the manuscript. Additionally, the authors wrongly call XRD data as spectrum, despite that there is no frequency dependence. On top of that, it is not clear why the authors call Li-Ta dipoles as defect dipoles, while no lattice defects like vacancies or even extra charge carriers are assumed to be originated by them. Thus, the manuscript title and manuscript itself look misleading from the beginning to the end.\nConcerning other issues, a site cannot be replaced as written in Fig. 1a or substituted as written in the corresponding text, just ions can. Fig. 2e-f misses Ta concentration values. According to the caption of comparative Fig. 3f, it is limited by the electric field lower than 450 kV/cm and η is higher than 85%, without explanation why these values are chosen. Based on Fig. 4, the authors claim on “the coexistence of AFE M3, M2 and FE R nanostructures”, whereas Fig. 4b contradictory shows not 3 but only 2 Pbcm and R3c phases. Moreover, Fig. 4c does not show any peak corresponding to the Tm point in Fig. 4f for x = 5. Similarly, Fig. 4c-d shows 4 curves each that does not correspond to 5 points in Fig. 4e. Furthermore, Vogel-Fulcher analysis represented in Fig. 4e must be done using angular frequency instead of ordinary one together with imaginary part of the dielectric permittivity data, whereas Fig. 4c-d shows only its real part. Besides the freezing temperatures, Vogel-Fulcher analysis must be also characterized by activation energies, which are not presented by the authors. Instead, the authors suggested some “enhanced polar dynamics with increasing Ta concentration even under lower temperatures” without any clearance what do they mean by enhanced dynamics. The density of the studied ceramics is not indicated as well.\nThere are also other examples of unclear sentences like “The further boost of Ue will greatly rely on the boost of breakdown strength (Eb), which will increase the failure risk especially with varying temperatures” or “The schematic formation of a rotated antiferroelectric state (RAFE) between ferroelectric structure (FE) with induced polar (P1) and normal antiferroelectric (AFE) after introducing Li/Ta elements in AN antiferroelectric structure. The existence of RAFE form a percolating field to divide and break the long-range order AFE and FE state, as marked in the formation of red network lines.” The manuscript is also full of scientifically ambiguous words like “excellent”, “improved/ing” or “outstanding” as well as by words “through” when they do not mean indeed through.\nFinally, there are many missing experimental conditions, like milling ball material and rotation rate, sintering heating and cooling rates, XRD range, rate and step, P-E loop measurement frequency and temperature range as well as the equipment used to control the temperature in this and dielectric measurements. Methods and equipment used to polish ceramics down to ~80 μm thickness and to deposit electrodes are also missing.\nThus, tis manuscript cannot be recommended for publication.", "reviewer_3": "Dear authors,\nthe comments on the manuscript are given in the attached file.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Responses to reviewers’ comments for manuscript NCOMMS-25-08527 (Title:\nUltrahigh energy storage density and efficiency in AgNbO -based ceramics by\n3\npercolating interaction between antipolars and defect dipoles)\nWe are grateful for the reviewers’ evaluations and constructive comments on our\nmanuscript entitled “Ultrahigh energy storage density and efficiency in AgNbO -based\n3\nceramics by percolating interaction between antipolars and defect dipoles”\n(NCOMMS-25-08527). The point-by-point responses to the reviewers’ comments are\nsummarized below and the detailed changes made in the manuscript are marked by blue\nfonts with yellow highlights.\nResponses to the comments of Reviewer # 1\nReviewer #1: Using density functional theory (DFT) and phase-field simulations, the\nauthors proposed a strategy to enhance energy storage properties in lead-free\nantiferroelectrics through a unique percolating interaction between antipolar regions\nand engineered defect dipoles. Based on the experimental results, the authors claimed\nthe increasing percolating interaction between Li-Ta dipoles and antipolars in AgNbO -\n3\nbased antiferroelectrics induced more rotated antipolar regions from the initial AFE\nstate. This leads to a remarkable recoverable energy storage density of 12.8 J/cm3 with\n90% efficiency, stable up to 255 °C, surpassing most lead-free ceramics. The\nmanuscript is interesting and could be considered for publication until all the raised\nmajor/minor comments are systematically addressed along with the additional\nexperimental results. The comments are the following.\nResponse: We greatly appreciate the reviewer’s positive evaluations for our work.\nTo address the major/minor comments from Reviewer 1, we have provided careful\nresponses and subsequently revised the manuscript accordingly.\nComments 1: The role of Li substitution was not very clearly discussed when Li was\nintroduced to AgNbO , it disrupted the long-range antiferroelectric domain\n3\nconfiguration and transformed the antiferroelectric state into a ferroelectric state.\nTheoretically, the ferroelectric state appeared upon Li substitution also noticed\nexperimentally in polarization hysteresis loops. However, was it only due to the\npreferred Li1 to occupy the polarization region rather than the boundary or ionic radius,\netc?\nResponse: Experimental results in previous references have revealed that Li+\ncations to replace Ag+ cations can stabilize the R3c ferroelectric phase of AgNbO\n3\nmatrix in thermal dynamics due to the A- and B-site coordinating displacements\nespecially when Li→Ag substitution percentage reaches ≥5% (J. Phys. Condens.\nMatter 23, 075901 (2011); J. Eur. Ceram. Soc. 41, 1236-1243 (2021); Inorg. Chem. 59,\n17, 12595-12607 (2020)).\nIn this work, we further utilized DFT calculations to make clear the in-depth\nphysical reasons for the appearance of ferroelectric state in Li-doped AgNbO .\ni.e., Li1 (polarization region) and Li2 (antiferroelectric boundary region) sites in the\nAgNbO antiferroelectric superlattice. As shown in Fig. R1c, when Li is placed at the\n3\nlow-energy polarization region (Site of Li1) rather than high-energy boundary (Site of\nLi2), the higher position shift along y axis will result in a larger local polarization output.\nTherefore, it is concluded that the emergence of the ferroelectric state in\nantiferroelectric state is associated with Li-induced significant ionic displacements\nalong y axis. We have added the key points of these discussions into the revised\nmanuscript.\nRevisions: The discussion sentences have been inserted into the Page 6 of\nmanuscript: “Supplementary Figs. 2a-c reveal that when Li+ cation is placed at the low-\nenergy polarization region (Site of Li1) rather than high-energy boundary (Site of\nLi2), the larger additional position shift of Nb along y axis can be achieved, resulting in a\nlarger local polarization. Such a localized mechanism is well consistent with the\nexperimental observations in previous references which revealed that Li dopants can\nstabilize the R3c ferroelectric phases of AgNbO in thermal dynamics due to the A-site\n3\nand B-site coordinating displacements especially when Li→Ag substitution percentage\nreaches ≥5%12,36-37.” And the related references have been set as Refs. 12, 36 and 37.\nIn addition, we have added Fig. R1 as Supplementary Fig. 2a-c.\nFig. R1 Li-doped AgNbO superlattice structures a. Antiferroelectric structure of AgNbO .\n3 3\nb. Li-doped AgNbO antiferroelectric structure c. The relative energy to Li1 Site (exhibiting\n3\nlowest energy and setting to zero in energy), and position shift along y axis for Li1 and Li2\nsubstitutions.\nComments 2: It is understandable that the quantity of the Li was low and very\nchallenging to atomically visualize in the STEM. Alternatively, Raman spectroscopy\ncan lead to verifying the disruption of the long-range antiferroelectric domains and\ntransformation into a ferroelectric state upon tilting the octahedra where phonon modes\nbecome softened appearing like other studies [J. Materiomics 10, 431 (2024); Phys.\nRev. Materials 3, 084405 (2019); J. Alloys Compd. 667, 310 (2016)].\nResponse: As suggested, we have further measured the Raman spectra of AgNbO\n3\n(AN), and (Ag Li )(Nb Ta )O (abbreviated as ANLi-xTa, x=5, 25, 45 and\n0.95 0.05 1-x/100 x/100 3\n65) where the abbreviation of ANLi-xTa to replace the origin abbreviation of AL5NTx\nin the revised manuscript according to another reviewer’s suggestion. To clarify the\nphase transition between AN and ANLi-5Ta, we have fabricated another in-between\ncomposition Ag Li Nb Ta O (AN-3LT) according to the reference (Phys. Rev.\n0.97 0.03 0.97 0.03 3\nB 104, 174104 (2021)). Fig. R2a displays the Raman spectra of above compositions\nwhere the phonon vibrational modes of Ag+ cation vibration, octahedral vibration\n(NbO ), bending mode (ν ) and stretching mode (ν ) are marked out to characterize the\n6 5 1\nmicrostructure changes.\nAs shown in Fig. R2b, the frequency of the ν mode exhibits an obvious redshift\n5\nfrom ~260 cm-1 of AgNbO and AN-3LT to 221 cm-1 of ANLi-5Ta while octahedral\n3\nvibration (NbO ) modes also shift from 96, 109cm-1 of AgNbO to 94, 106cm-1 of ANLi-\n6 3\n5Ta. Such softening of ν and NbO phonon modes is attributed to the gradual changes\n5 6\nin octahedral structures. With increasing Ta concentration from ANLi-5Ta to ANLi-\n65Ta, the frequencies of the ν and NbO mode continue to shift to lower values and all\n5 6\nRaman peaks become weaker and broader in comparison with AgNbO , due to the\n3\ndisruption of long-range-order electrical domains and the increased disorder degree to\nrelaxor feature (Nat. Commun. 11, 4824 (2020)).\nIn comparison, the breathing mode of Ag+ near 84 cm-1 could be only observed in\nAN and AN-3LT rather than ANLi-5Ta or higher Ta compositions. The appearance and\nsuppression of Raman-active phonon are ascribed to the structural transformation (Phys.\nRev. B 104, 174104 (2021)). The calculated lattice parameters from XRD data of AN\nand ANLi-5Ta in previous reference (J. Mater. Chem. C 7, 4403-4414 (2019)) and\nSupplementary Table 2 revealed that the structural change is related to the phase\ntransition from antiferroelectric-dominated ferrielectric phase to ferroelectric phase.\nWhen Ta content is over 40 mol%, the phase transition from M to M happens,\n2 3\nresulting in the blueshift of ν mode from 569 cm-1 of ANLi-25Ta to 591 cm-1 of ANLi-\n1\n65Ta.\nFig. R2 Room-temperature Raman spectra of AgNbO (AN), Ag Li Nb Ta O\n3 0.97 0.03 0.97 0.03 3\n(AN-3LT) and ANLi-xTa (x=5, 25, 45 and 65) ceramics. a. Room-temperature Raman spectra\nof different compositions. b. Composition-dependent frequency evolution of Ag+, octahedral\nvibration (NbO ), bending mode (ν ) and stretching mode (ν ).\n6 5 1\nRevisions: Fig. R2 has been added as Supplementary Fig. 15 in Supplementary\nInformation. The discussion sentences have been inserted into the Page 13-14 of\nmanuscript: “The softening and hardening, appearance and suppression of Raman-\nactive phonons are sensitive to the nano-structural changes, especially for similar M\n2\nand M phases65-67. The according room-temperature Raman results shown in\nonly observed in AgNbO and Ag Li Nb Ta O (AN-3LT)rather than higher\n3 0.97 0.03 0.97 0.03 3\nLi/Ta co-doped compositions. It is related to the happening of phase transition from\nantiferroelectric-dominated ferrielectric phase to ferroelectric phase near ANLi-5Ta\nceramics13,68. The frequency of the ν mode exhibits an obvious redshift from ~260 cm-\n5\n1 of AgNbO and Ag Li Nb Ta O to 221 cm-1 of ANLi-5Ta, while octahedral\n3 0.97 0.03 0.97 0.03 3\nvibration (NbO ) modes also shift from 96, 107cm-1 of AgNbO to 94, 103cm-1 of ANLi-\n6 3\n5Ta. Such softening of ν and NbO phonon modes are ascribed to the gradual changes\n5 6\nin octahedral structures. In addition, with further increasing Ta concentration, all Raman\npeaks become weaker and broader, due to the disruption of long-range-order electrical\ndomains and the increased disorder or relaxor feature25. When Ta content is over 40\nmol%, the phase transition from M to M happens, resulting in the blueshift of ν mode\n2 3 1\nfrom 569 cm-1 of ANLi-25Ta to 591 cm-1 of ANLi-65Ta.” And related references\nincluding the reviewer mentioned have been added as Refs. 65-67.\nComments 3: In the phase field simulation results in Figure 2c, authors claimed a slim\npolarization-electric field (P-E) loops with an increase in the maximum polarization\n(P increased from 0.34 C/m2 to 0.45 C/m2) upon the increasing Ta concentration,\nmax\nattributed to the decreased ΔE for antiferroelectric-ferroelectric (AFE-FE) transition in\nthe constructed rotated antiferroelectric (RAFE) matrix. On the contrary, the Pmax of\nthe highly substituted (AL5NT65) composition at a much higher electric field (~750\nkV/cm) was nearly comparable to the lower substituted (AL5NT5) composition at a\nlower electric field (~200 kV/cm). Can the author explain the reason?\nResponse: We are grateful for this rigorous question. Ta doping not only enhances\nthe stability of the antiferroelectric (AFE) state of AN-Li but also induces local dipole\nfields, both of which we have included in our phase-field simulations. These effects\ngive rise to the appearance of rotated antiferroelectric (RAFE) state that (1) increases\nthe forward and backward switching field required for the antiferroelectric-ferroelectric\n(FE) transition, (2) produces a low electric hysteresis (∆E) of successive\nAFE→FE→AFE transitions under applying and removing fields and (3) decreases\nfield-induced strain with a slanted slope, causing the enhancement in breakdown\nstrength E (Acta Mater. 257, 119186 (2023)). Accordingly, the slimmer P-E loops with\nb\nthe increased maximum polarization (P ) under E will be obtained in the phase field\nmax b\nsimulations when increasing Ta concentration.\nA similar trend was also observed in our experiments: the P under E increases\nmax b\nfrom 38.76 μC/cm2 (E ~210 kV/cm) at ANLi-5Ta to 40.39 μC/cm2 (E ~760 kV/cm)\nb b\nat ANLi-65Ta although the increase is not as significant as simulations. It is because\nthe simulations were carried out in a single crystal while the experiments were\nperformed in polycrystalline ceramics. The decrease of grain size from 3.2 μm of ANLi-\n5Ta ceramics to 0.78 μm of ANLi-65Ta ceramics (see Fig. R3), will restrict the actual\nenhancement of polarization amplitude (J. Am. Ceram. Soc. 97 1-27 (2014)).\nRevisions: To make the statement much clearer, the following sentences are\ninserted “owing to the enhancement of breakdown strength” and “Compared to the\ncomputational results in the single crystal model, P does not exhibit a similar\nmax\nsignificant enhancement in the experiment of ANLi-xTa polycrystalline ceramics. The\nP slightly increase from 38.76 μC/cm2 at ANLi-5Ta to 40.39 μC/cm2 at ANLi-65Ta.\nmax\nIt is because the continuously decreased grain size of ANLi-xTa polycrystalline\nceramics with the increase of Ta doping level (see Supplementary Fig. 9), will greatly\nrestrict the polarization enhancement, although the ascend trend of P can also been\nmax\nobserved.” into the Page 9 and Page 11 of the revised manuscript. Fig. R3 is inserted\ninto Supplementary Fig. 9 of Supplementary Information.\nFig. R3 SEM morphology images, grain size distribution analysis and Ta composition\ndependent average grain size of ANLi-xTa (x=5, 25, 45 and 65) ceramics. The average grain\nsize of ANLi-xTa ceramics continues to decrease with the increase of Ta concentration.\nComments 4: Was the unipolar P-E loop in Fig. 3(a) measured in the as-sintered state\n(before the poling process)? The bipolar P-E loop of AL5NT5 exhibits a hysteresis\ncurve characteristic of ferroelectric behavior. In ferroelectric materials, if a unipolar P-\nE loop is measured in a poled state, the hysteresis observed between the Pr and Pmax\npaths is typically small, leading to a minor difference between the polarization value at\nE = 0 (Pr) and the polarization at Emax (Pmax). Additionally, the overall hysteresis\nshould be minimal. However, in Fig. 3(a), the unipolar P-E loop of AL5NT5 shows a\nsubstantial difference between the initial polarization at E = 0 (P = 0 μC/cm2) and the\nfinal remnant polarization (Pr = ~28 μC/cm2) after measurement. Moreover, the loop\nexhibits significant hysteresis. The authors should provide a detailed explanation of the\nsample state in which the measurements for Fig. 3(a) were conducted.\nResponse: We would like to thank the reviewer’s comment. Firstly, the P-E loops\nwere measured in the as-sintered state of ANLi-xTa ceramics before the poling process.\nAs show in Fig. R4, the bipolar P-E loop of ANLi-5Ta was measured and unilateral\ndata (0→E →0) was used to display the ferroelectric characteristic features including\nb\nlarge P and P to make the comparison with pure AgNbO and high-level Ta-doped\nmax r 3\ncompositions. With further increasing Ta concentration, unipolar P-E loop of ANLi-\n25Ta, ANLi-45Ta and ANLi-65Ta were used to determine the optimization results of\nenergy storage performance.\nRevisions: In order to enhance the preciseness of manuscript, the measuring\nmethod of P-E loops has been added in the Method part of the revised manuscript: “The\nP-E loops of AN and ANLi-5Ta were measured under Standard bipolar setting and the\nP-E loops of ANLi-25Ta, ANLi-45Ta and ANLi-65Ta were measured under Standard\nmonopolar setting. The frequency for all P-E measurement is set as 10 Hz.”\nFig. R4 Polarization-electric field (P-E) loops of ANLi-xTa (x=5, 25, 45 and 65).\nComments 5: For comparison of the theoretical and experimental results, authors\nshould provide P-E hysteresis loops of the pure AN in Figure 3a, demonstrating AFE-\nFE transitions to a higher level in (Ag Li )(Nb Tax/100)O , with x values of 5,\n0.95 0.05 1-x/100 3\n25, 45, and 65. Also, they should provide strain loops to strengthen their arguments\nshowing a bipolar hysteresis response to slimmer loop characteristics.\nResponse: We are grateful for the reviewer’s kind suggestion. As shown in Fig.\nR5a, we have added the P-E loop of pure AN into the Fig.3a of revised manuscript,\nwhich is consistent with simulations in Fig. 2c. Fig. R5b gives the corresponding strain\nloops of ANLi-xTa (x=5, 25, 45 and 65) under the same field of 160 kV/cm. With\nincreasing Ta concentration, the value of room-temperature strain sharply decreases\nfrom ~0.3% of ANLi-5Ta to ~0.02% of ANLi-65Ta. Accordingly, the strain hysteresis\nalso sharply decreases, resulting in a slim strain loop of ANLi-65Ta ceramic. It agrees\nwell with the slim strain loop characteristics in the simulation results of Fig. 2b. Fig.\nR5c-d show that the forward and backward switching fields (E and E ) of\nAFE-FE FE-AFE\nantiferroelectric-ferroelectric phase transition slightly decrease and then increase to a\nhigher level at ANLi-65Ta. But the continuous decrease of electric hysteresis (ΔE=E\nAFE-\n-E ) is achieved, further confirming slimmer loop characteristics with Ta doping.\nFE FE-AFE\nRevisions: The discussion for strain behavior has been added in Page 12 of the\nrevised manuscript: “As shown in Supplementary Fig. 11a, with increasing Ta\nconcentration, the value of room-temperature strain at the same field of 160 kV/cm\nsharply decreases from ~0.3% of ANLi-5Ta to ~0.02% of ANLi-65Ta. At the same time,\nthe strain hysteresis also sharply decreases, resulting in slimmer strain loops with a\nslanted slope in ANLi-65Ta ceramics, agreeing well with calculated strain behavior and\nexperimental slimmer P-E loop characteristics.” Fig. 3a in the revised manuscript has\nbeen replaced by Fig.R5a. In addition, we have also added Fig. R5b-d in Supplementary\nFig. 11.\nFig. R5 Room-temperature Polarization and Strain properties. a. P-E loops of AN and\nANLi-xTa (x=5, 25, 45 and 65) ceramics. b. Strain loops of ANLi-xTa ceramics under 160\nkV/cm. c. Ta composition dependence of unipolar current-electric field loops. d. The obtained\nE , E , ΔE of ANLi-xTa ceramics.\nAFE-FE FE-AFE\nComments 6: The authors claimed an ultrahigh energy storage density of 12.8 J/cm3\nand an excellent efficiency of 90% for AL5NT65 at the applied electric field of ~750\nkV/cm. However, the excellent thermal stability (ranging from 5.4 J/cm3 at -70 °C to\n4.9 J/cm3 at 185 °C) of the corresponding composition was presented at a moderate\nelectric field of 450 kV/cm rather than at a higher electric field. Authors must show the\nthermal stability of the AL5NT65 at the higher electric field.\nResponse and revisions: We appreciate the reviewer’s kind suggestion. Indeed,\nwe reported the ultrahigh room-temperature energy storage density of 12.8 J/cm3 and\nan excellent efficiency of 90% for AL5NT65 at the applied electric field of ~760 kV/cm,\nrepresenting the highest storage potential for the AgNbO -based ceramics.\ndecrease of applied field is always used to make sure the reliability for the dielectric\ncapacitor, as reported in Science 5374, 100-104 (2021); Science 384, 185-189 (2024);\nScience 385, 204-209 (2024). As shown in Fig. R6a-b, we have further measured\ntemperature-dependent polarization-electric field (P-E) loops under the higher electric\nfield (510 kV/cm) than initial 450 kV/cm. When the applied electric field increases\nfrom 450 kV/cm to 510 kV/cm, the ANLi-65Ta exhibits an average U (~6.5 J/cm3)\ne\nwith a temperature range T ~240 °C, in comparison with the average U (~5.3 J/cm3)\nspan e\nwith a temperature range T ~255 °C under 450 kV/cm, surpassing most of reported\nspan\nstate-of-the-art lead-free bulk ceramics, especially lead-free AgNbO and NaNbO -\n3 3\nbased antiferroelectric ceramics when taking both U and T into consideration. We\ne span\nhave added these discussions into Page 13 of revised manuscript and replaced Fig. 3e-\nf by Fig. R6b-c. Fig. R6a has been moved into the Supplementary Fig. 13.\nFig. R6 Temperature-dependent polarization and energy storage performance of ANLi-\n65Ta. Temperature-dependent P-E loops of ANLi-65Ta under (a) 450 kV/cm and (b) 510\nkV/cm, respectively. c. Comparison of U and temperature range (T ) of ANLi-65Ta with\ne span\nother reported state-of-the-art lead-free bulk ceramics when the electric field and η are set as <\n510 kV/cm and >85%, respectively.\nComments 7: Based on the Rietveld refinement of the X-ray diffraction (XRD) data\nfor the AL5NT5 to AL5NT65, it could be seen that extra diffraction peaks around the\n~23o and 46o were noticed in the XRD spectra of AL5NT45 and AL5NT65 ceramics\n[Figure 4a and Supplementary Figure 11]. Also, these XRD peaks were not fitted by the\nprovided Pbcm and R3c CIF files. Are these secondary peaks? Or showing the existence\nof another phase along with the Pbcm and R3c phases which only appeared at a higher\ndoping level of Ta. Did authors fit XRD with other noncentrosymmetric (Pmc21) or\ncubic phases along with the current Pbcm and R3c phases (Z. Lu et al., Nano energy\n79, 105423 (2021)? to get a better fit like S. Ali et al., Chemical Engineering Journal\n485, 150087 (2024). Authors must verify the origin of these peaks.\nResponse: We are grateful for the reviewer’s careful comments. Rietveld\nrefinements for XRD data of ANLi-25Ta, ANLi-45Ta and ANLi-65Ta ceramics have\nbeen remade on the basis of lattice parameters from the mentioned references (Nano\nenergy 79, 105423 (2021), Chem. Eng. J. 485, 150087 (2024)). As shown in Fig. R7,\nthere is no secondary phase. The extra diffraction peaks around ~23° and 46° also\nbelong to the Pbcm and R3c phases. The fitting Rwp is lower than 5.5% indicative of\nthe refinement reliability. The refinement results of Fig. 4a-b and Supplementary Fig.\n14 have been substituted by Fig. R7 and the related references have been added as Refs.\n45 and 64.\nFig. R7 Rietveld refinement results for XRD data of ANLi-xTa ceramics. a. ANLi-65Ta\nceramics and evolution of phase fraction for ANLi-xTa ceramics at room temperature. b. XRD\nRietveld refinement results for ANLi-25Ta and ANLi-45Ta ceramics.\nComments 8: This sentence is confusing and the authors need to rewrite it “The\ntransitions from AFE M3 to AFE M2 and from AFE M2 to FE R3c gradually converge\ntogether when the composition approaches to AL5NT65, suggesting the coexistence of\nAFE M3, M2 and FE R nanostructures.”\nResponse and revisions: We appreciate this detailed suggestion from reviewer.\nWe have rewritten the mentioned sentence in the Page 15 of revised manuscript to\nclarify our description as following: “With increasing Ta concentration, the temperature\nfor phase transitions from AFE M to AFE M and from AFE M to FE R both gradually\n3 2 2\ndecreases. Notably, the decrease of M -M transition temperature is faster than M -R\n3 2 2\ncase. Consequently, the M -M and M -R phase transition lines converge together near\n3 2 2\nANLi-65Ta, being inclined to form the antiferroelectric and ferroelectric coexistent\nregion (i.e. M -M -R) at ANLi-65Ta.”\n3 2\nComments 9: The definition and explanation of 'Li-Ta dipoles' appear on line 169.\nHowever, since this term is introduced earlier in the text, readers may be confused about\nits meaning. For instance, 'Li-Ta defect dipoles' is mentioned on line 117 and 'Li-Ta\ndipoles' on line 119. The authors should define these terms earlier in the manuscript or\nconsider using alternative wording in the initial mentions.\nResponse and revisions: To make related statement much clearer, we have used\nalternative words to rewrite the earlier initial mentions on line 117 and 119 as following:\n“the coordinated effect of Li+ and Ta5+ cations with adjacent oxygen octahedrons in\nAgNbO superlattice structures can lead to the percolating dipole interaction field in\n3\nantiferroelectric matrix for the simultaneous decrease of ΔE and increase of E due\nAFE-FE\nto the special rotated antipolar alignment, meanwhile remaining large polarization in\nsaturation state.” We have added the corresponding modification to the revised\nmanuscript on Page 5.\nComments 10: The authors represented the recoverable energy storage density as\nP\nfollows: W  max EdP\nrec\nP\nr\nThis is an incorrect mathematical formula for W . Although the positive integral of an\nrec\nelectric field with respect to polarization from remnant polarization (P) to saturated\nr\npolarization (P ) seems to be identical to the negative integral of an electric field with\nmax\nrespect to polarization from P to P mathematically, the positive integral cannot be\nmax r\nequal to the negative integral due to the hysteretic characteristic of\nferroelectrics/piezoelectrics in reality. As the authors probably know, the upward path\nin a hysteresis loop from P to P is never identical to the downward path from P\nr max max\nto P. Hence, W should be represented as shown in [Ceram. Inter. 47 (2021) 23488;\nr rec\nP\nAdv. Funct. Mater 29 (2019) 1807321]: W  r EdP\nrec\nP\nmax\nResponse: We thank reviewer’s precise comment. In the manuscript, we indeed\nused the downward path from P to P to calculate the recoverable energy storage\nmax r\ndensity. To address this concern, we have modified the mathematical formula for the\nrecoverable energy storage density in the manuscript on Page 3 as following:\nP\nU  r EdP, based on the reviewer’s mentioned references, which have been also\ne\nP\nmax\nset as Ref. 6 and Ref. 7 in the revised manuscript.\nResponses to the comments of Reviewer # 2\nThis manuscript reports a recoverable energy storage density of 12.8 J/cm3 with an\nefficiency of 90% achieved at room temperature in Ag Li Nb Ta O ceramics.\n0.95 0.05 0.35 0.65 3\nThis achievement is attributed by the authors to a rotated antiferroelectric (RAFE) state\nrelated to interaction between Li-Ta defect dipole and antipolars invented by them\nbased on their simulation study. Therefore, the authors called their manuscript as\n“Ultrahigh energy storage density and efficiency in AgNbO -based ceramics by\n3\npercolating interaction between antipolars and defect dipoles”. However, this title has\nseveral incorrect or even misleading statements.\nResponse: We sincerely appreciate the reviewer’s taking time and effort in\nevaluating our manuscript. Over the past three months, we have conducted an additional\ncomprehensive review of recent publications in the field of energy storage density in\nlead-free antiferroelectric ceramics, including the references suggested by the reviewer.\nOur analysis confirms that the energy storage performance presented in our study\nremain the highest among the reported literature when taking energy storage density,\nefficiency, thermal stability and test conditions into comprehensive consideration. More\ndetailed justifications are provided in the following sections. Furthermore, we have\nthoroughly revised our manuscript to address the reviewer’s remaining concerns, as\noutlined below.\nComments 1: The authors claim that the values obtained by them and shown in Fig. 3c\nare ultrahigh “surpassing all reported lead-free antiferroelectric ceramics”. However,\ncomparable values of 12.6 J/cm3 and 94% were recently reported in Chem. Eng. J. 503\n(2025) 158557 for multilayer ceramic capacitors with a simpler composition of\nAgNb0.5Ta0.5O3. When the composition is complicated, values up to 43.5 J/cm3 and\n85% can be achieved in lead-free ceramics as reported in Adv. Energy Mater. 2024, 14,\n2400821 and references therein. Therefore, if 12.6 J/cm3 is ultrahigh, how should one\ncall 43.5 J/cm3?\nResponse: To the best of our knowledge, the energy storage density of 12.8 J/cm³\nwith an efficiency of 90% reported in our study represents one of the highest values\namong reported lead-free antiferroelectric ceramics. We have thoroughly examined the\ntwo references provided by the reviewer and determined that the reported works and\ntheir associated properties can not be directly comparable to our study. For a fair\ncomparison, all scientific discussions and property evaluations should be conducted\nunder similar working conditions. Assessing the significance of our results without\nconsidering the actual applied electric field and sample thickness would be unjust. First,\nthe applied electric fields in our work and the cited references differ significantly.\nP\nAccording to the equation for recoverable energy storage density U  r EdP,\nthe\ne\nP\nmax\nelectric field (E) plays a critical role in determining Uₑ. As shown in Fig. R8, if we\nrecalculate the recoverable energy storage density of the references mentioned by the\nreviewer (Chem. Eng. J. 503, 158557 (2025) and Adv. Energy Mater. 14, 2400821\n(2024)) under the same electric field (760 kV/cm) as in our work, the resulting Uₑ values\nare approximately 7.76 J/cm³ and 3.74 J/cm³, respectively, which are significantly lower\nthan the 12.8 J/cm³ achieved in our study. This demonstrates that, under identical\nconditions, our work exhibits superior performance compared to the referenced\nliterature.\nFig. R8 Polarization-electric field (P-E) loops of this work and the reviewer’s mentioned\nreferences under 760 kV/cm.\nSecondly, there is a substantial difference in sample thickness between our study\nand the cited works. The referenced studies report values obtained from multilayer\nceramic capacitors (MLCCs), where each layer exhibits an extremely small thickness.\nSince the breakdown strength (E ) and thickness (t) of materials follow an exponential\nb\n1\ndecay relationshipE  (as supported by Prog. Mater. Sci. 109 (2019) 72-108 and\nb\nt\nChem. Rev. 121 (2021) 6124-6172), the reported properties cannot be directly\ncompared.\nTherefore, we maintain that the use of the term \"ultrahigh\" in our original\nmanuscript is both reasonable and logically justified. Our results still represent the\nhighest energy storage density and efficiency among lead-free antiferroelectric\nceramics.\nComments 2: These values were obtained by the authors in ceramics having just 35% Nb.\nTherefore, claiming that these ceramics are based on AgNbO looks misleading as\n3\nwell. These ceramics are rather based on AgTaO that is not antiferroelectric but\n3\nquantum paraelectric, according to works like Appl. Phys. Lett. 95, 242904 (2009).\nThus, one should not invent the rotated antiferroelectric (RAFE) state but follow the\nexplanations presented in the works mentioned above regarding turning the\nantiferroelectrics into quasi-linear dielectrics for high energy storage applications.\nThird, following the previous issue, DFT simulations done for Ta doping ions in\nAgNbO lattice do not look to be valid. One must consider instead an opposite situation\n3\nwith Nb doping of AgTaO .\nwork, we not only identify the optimal ANLi-xTa composition at x=65, but also\nsystematically investigate how Ta content (x = 5, 25, 45 and 65) tunes the microstructure,\ndrives the antiferroelectric-ferroelectric transition, and impacts energy-storage\nperformance. As shown in Fig. R9 (Fig. 5e in the manuscript), the polarization angle\nmapping of superior of ANLi-65Ta displays the bimodal symmetric angle distribution,\nindicating that the matrix is the antiferroelectric-dominated state rather than the\nquantum paraelectric state.\nTo further address the reviewer’s concern, we have additionally constructed two\nsuperlattice structures for several Nb-doped AgTaO compositions in DFT calculation,\n3\ni.e., phase (quantum paraelectric state) and Pbcm phase (antiferroelectric state), as\nshow 𝑅 n 3̅ 𝑐 in Fig. R10a-b. Fig. R10c gives the associated fitted curves of formation energy\nevolution of and Pbcm phases with increasing Nb proportions in AgTaO .\nThe\n3\nformation ene\n𝑅\nrg 3̅y\\𝑐\ndifference between and Pbcm phases of different Nb-doped\nAgTaO\n3\ncompositions is described by𝑅E3̅𝑐\nPbcm\nE\nR3c\n. When the formation energy\ndifference is larger than zero, the phase is more stable than Pbcm phase;\non the\ncontrary, the Pbcm phase is more s\n𝑅\nta 3̅b\\𝑐\nle than phase. As shown in Fig. R10d, the\nstable state of pure AgTaO\n3\nis phase, co\n𝑅\nn 3̅si\\𝑐\nstent with the reviewer’s mentioned\nReferences (Appl. Phys. Lett. 95\n𝑅\n,\n3\n2̅4\\𝑐\n2904 (2009)), while pure AgNbO\n3\nshows the well-\nknown Pbcm antiferroelectric phase, further validating the accuracy of our simulations.\nNotably, when the substitution concentration of Nb exceeds 20% in AgTaO ,\nthe\n3\nantiferroelectric Pbcm phase starts to be more stable than phase. Therefore, the\n(Ag\n0.95\nLi\n0.05\n)(Nb\n0.35\nTa\n0.65\n)O\n3\nshould be also antiferroelectric\n𝑅\n-d 3̅o\\𝑐\nminated state in theory.\nFig. R9 Polarization angle mapping with the related statistical histogram of ANLi-65Ta.\nFig. R10 Phase stability of Nb-doped AgTaO . (a-b) The microstructure evolution of\n3\nand Pbcm superlattices of AgTa Nb O with increasing Nb percentage. c. The associated\n1-x x 3\n𝑅3̅𝑐\nformation energy variations of and Pbcm phases with Nb content and (d) the difference\nof formation energy between phase and Pbcm phase for selected AgTa Nb O\n𝑅3̅𝑐 1-x x 3\ncompositions.\n𝑅3̅𝑐\nRevisions: Fig. R10 have been inserted as Supplementary Fig. 7 to address the the\nreviewer’s concerns. The following sentences are also given on Page 9-10 of the revised\nmanuscript: “It has been revealed that AgTaO may be quantum paraelectric state\n3\n( )43, rather than antiferroelectric (Pbcm) state of AgNbO To make clear the\n3.\n𝑅3̅𝑐\nmicrostructural basis of superior AgTaO -abundant state (ANLi-65Ta), the formation\n3\nenergy difference between and Pbcm phases of different Nb-doped AgTaO\n3\ncompositions is calculated, as\n𝑅 3\ns̅h\\𝑐\nown in Supplementary Fig. 7. The calculation results\nclearly show that the antiferroelectric phase is more stable than quantum paraelectric\nphase when the atomic percent of Ta falls below 80%, verifying the antiferroelectric\nfeature of ANLi-65Ta.” In addition, the reviewer’s mentioned reference has been set as\nRef. 43.\nComments 3: Moreover, even presented simulations show that “the substitution site\nwith lower energy, distant from the Li cations, should be occupied first”, contradicting\nthe idea of Li-Ta dipole formation and its interaction with antipolars. When the Ta\ncontent is low there are no Li-Ta dipoles. When Ta content is high, the matrix is not\nantiferroelectric anymore.\nResponse: We would gently suggest that this comment might call for further\nconsideration to ensure its applicability here.\n1) As shown in Fig. R11, the system energy increases in general when the distance\nbetween Li+ and Ta5+ cations decreases, causing the increased coordinated effect of Li+\nand Ta5+ cations with adjacent oxygen octahedron in AgNbO . For example, Ta5+\n3\ncation replaces Nb5+ cation at Sites 1, 2, 5, 6, 10 of (Ag,Li)NbO (AN-Li) superlattice which\n3\nare close to Li+ sites.\nTa5+ cations have the tendency to firstly substitute the Nb5+ cations at the sites\ndistant from Li+ sites when low-doping level of Ta5+ cations is incorporated, which\nresults in the minimal shift along z-direction for the original antipolar i.e., the weak\nrotation of antiparallelly arranged polarization. In comparison, when the Ta content\nincreases to higher level, like 45-65%. there is a great possibility of the random\nsubstitution of Ta5+ cations at the nearest or next-nearest neighboring sites (Sites 1, 2,\n5, 6, 10 shown in Fig. R11) to the Li-doped site, causing the significant shift of\npolarization along z-direction i.e., the strong rotation of antiparallelly arranged\npolarization. This is the reason for the appearance of significant rotation in antiparallel\npolarization state of (Ag,Li)NbO ceramics with high Ta-doping level.\n3\n2) As stated in the responses for comment 2, the antiferroelectric state still remains\nstable at Ta composition of x=65% and acts as the dominant phase on the basis of\nrelative experimental and additional DFT calculation analysis.\nTo outline the best locations of Li+ and Ta5+ cations in AgNbO to achieve superior\n3\nenergy storage properties, we simplify the notations of the coordinated effect of Li+ and\nTa5+ with adjacent oxygen octahedron as Li-Ta pairs in the revised manuscript to replace\nLi-Ta dipoles and make the statement much clearer.\nRevisions: We have replaced Supplementary Fig. 2e by Fig. R11 and also revised\nthe discussions on Page 7-8 of the revised manuscript: “As shown in Supplementary\nFig. 2e, the system energy increases when the distances between Li+ and Ta5+ cations\ndecrease, especially for Ta5+ cations doped at Site1, 2, 5, 6 and 10, due to the\nstrengthened coordinated effect between Li+ and Ta5+ cations with adjacent oxygen\noctahedron (represented by Li-Ta pairs) in AgNbO structure. To minimize the system\n3\nenergy, the Ta5+ cations have the tendency to firstly substitute the Nb5+ cations distant\nfrom Li-doped sites, which results in the minimal shift along z-direction for the original\nantipolar. In comparison, when the Ta content increases to higher level like 45-65%,\nthere is a great possibility of the random substitution of Ta5+ cations at the nearest or\nnext-nearest neighboring sites (Sites 1, 2, 5, 6, 10 shown in Supplementary Fig. 2d) to\nthe Li-doped site, causing the significant z-direction shift for the polarization of\nantipolar regions i.e., the strong rotation of antipolar regions, as shown in Fig.1c.”\nFig. R11 The relative energy to Site3 (exhibiting lowest energy and setting to zero in\nenergy) of different Ta-doped cases and the corresponding position difference in the z-\ndirection.\nComments 4: Furthermore, besides the RAFE state, the authors invented other terms\nlike antipolars and polars without clear definition for them. That together with a lack of\ndefinition of symbols and abbreviations like E, FE, AN-Li, ANLi-Ta, AnLi-xTa, XRD\nand Tm at first mentioning or at all creates additional difficulties to understand the\nmanuscript. Additionally, the authors wrongly call XRD data as spectrum, despite that\nthere is no frequency dependence.\nResponse and revisions: We appreciate the reviewer’s comments and suggestions.\nThe definition of antipolar is to describe two adjacent antiparallel polar state of\nantiferroelectrics according to References (J. Am. Ceram. Soc.104, 3775-3810 (2021);\nNature 637, 1104-1110 (2025)). The definition of polar is widely used to describe the\npolarization variants within the lattice. The RAFE is the abbreviation of rotated\nantiferroelectric state. E is the electric field. FE is the ferroelectric state. The term of\nAN-Li describes the Li cation-doped AgNbO superlattice. ANLi-Ta represents the\n3\ncomposition with incorporation of Ta cation into the AN-Li superlattice, while ANLi-\nxTa represents the detailed composition with introduction of Ta into Li-doped AgNbO\n3\nand x is the molar percent of Ta. XRD is the abbreviation of X-ray diffraction. T is the\nm\ntemperature of maximum permittivity. We have defined all abbreviations upon their\nfirst appearance in the revised manuscript. In addition, the use frequency of these\nabbreviations is reduced in the revised manuscript to improve the readability. We are\nsorry for the mistake “XRD spectrum”. We have revised it to “XRD data” in the revised\nmanuscript on Page 14.\nComments 5: On top of that, it is not clear why the authors call Li-Ta dipoles as defect\ndipoles, while no lattice defects like vacancies or even extra charge carriers are assumed\nto be originated by them. Thus, the manuscript title and manuscript itself look\nmisleading from the beginning to the end.\nResponse: We are grateful for this comment and sorry for the generation of\nmisunderstanding. As shown in Fig. R11, significant antipolar rotation can be\nuniversally induced when Ta5+ cations are doped at the sites close to Li+ positions\nbecause the bond changes and local dipole field are formed through the coordinated\neffect of Li+ cation and Ta5+ cation with adjacent oxygen octahedrons. The substitution\nof Ta for Nb results in stronger ionic bonding and compresses oxygen octahedrons. And\nthe substitution of Li for Ag causes the decreased lattice parameters because of the\nsmaller ionic radii (1.17 Å CN=12) of Li+ cation than that (1.48 Å CN=12) of Ag+\ncation.\nRevisions: To enhance the accuracy of the statement in the revised manuscript, we\nhave not simply used the notation of Li-Ta dipole any more. We have substituted it with\nLi-Ta pairs to describe the coordinate effect of Li+ cation and Ta5+ cation with adjacent\noxygen octahedrons and then analyze the influence of Li-Ta pairs on the antipolar\nregions and associate energy storage properties of antiferroelectrics in the revised\nmanuscript.\nComments 6: Concerning other issues, a site cannot be replaced as written in Fig. 1a\nor substituted as written in the corresponding text, just ions can.\nResponse and revisions: We thank the reviewer very much for the suggestion. We\nhave replaced the Fig. 1a with below Fig. R12 and the relation of cation substitutions\nhave been written in the figure caption.\nFig. R12 The schematic AgNbO (AN)perovskite structure where Li+ cation substitutes\nComments 7: Fig. 2e-f misses Ta concentration values. According to the caption of\ncomparative Fig. 3f, it is limited by the electric field lower than 450 kV/cm and η is\nhigher than 85%, without explanation why these values are chosen.\nResponse and revisions: We are sorry for missing the Ta concentration values in\nFig.2e-f. The missing Ta concentration values have been added in updated Fig. 2 in the\nrevised manuscript, as shown in Fig. R13 below.\nIn practice for testing thermal stability of superior energy storage effect of\ndielectrics, the decrease of applied field E is always conducted to make sure the working\nsafety of the dielectric capacitor, as reported in References (Science 5374, 100-104\n(2021); Science 384, 185-189 (2024); Science 385, 204-209 (2024)). The experimental\nresults indicate that our energy storage ceramics can work well and stably under the\nelectric field 450 kV/cm within the temperature range of -70 °C-185 °C (T ~255 °C)\nspan\n(see Fig. R6a). In order to compare the temperature-dependent recoverable energy\nstorage density (U ) with other reported state-of-the-art lead-free bulk ceramics under\ne\ncomparable electric field strengths, we restricted the electric field lower than 450\nkV/cm. When the sample is heated up, the increased conducive leakage currents could\nresult in the degradation of energy storage efficiency (η). Thus, we define the effective\ntemperature range for recoverable energy storage density when the energy storage\nefficiency exceeds 85%.\nFig. R13 Phase-field calculations used for determining the energy-storage performance of\nformed RAFE. a. Phase fraction evolution of different microstructures with changing ANLi-\nxTa composition. (b-d). Breakdown strength (E ), Energy storage efficiency (η) and\nb\nRecoverable energy storage density (U ) variations of ANLi-xTa system with increasing Ta\ne\nconcentration.\nComments 8: Based on Fig. 4, the authors claim on “the coexistence of AFE M3, M2\nand FE R nanostructures”, whereas Fig. 4b contradictory shows not 3 but only 2 Pbcm\nand R3c phases.\nResponse and revisions: For AgNbO lattice structure, the antiferroelectric M\n3 3\nand M have the same space group (Pbcm) based on the references (J. Mater. Chem. A\n2\n8, 23724-23737 (2020), J. Mater. Chem. A 10, 14747-14787 (2022)). M and M only\n3 2\nshow the subtle differences in the cation displacement resulting in a broad peak of\ntemperature-dependent dielectric permittivity, which are difficult to distinguish by\nrefining conventional XRD data of the ceramic powders (J. Mater. Chem. A 8, 23724-\n23737 (2020)). Therefore, in this work, the only antiferroelectric space groups (Pbcm)\nand ferroelectric space group (R3c) of AgNbO are used in the Rietveld refinement of\nferroelectric (R3c) phases. The description “the coexistence of AFE M , M and FE R\n3 2\nnanostructures” is based on the phase diagram analysis, i.e., M -M and M -R transition\n3 2 2\nlines are converged together. To address the reviewer’s concern, the description of the\ncoexistence of AFE M , M and FE R nanostructures have been substituted by\n3 2\n“antiferroelectric (M and M with Pbcm symmetry) and ferroelectric coexistent\n3 2\nnanostructures” on Page 15 in the revised manuscript.\nComments 9: Fig. 4c does not show any peak corresponding to the T point in Fig. 4f\nm\nfor x = 5. Similarly, Fig. 4c-d shows 4 curves each that does not correspond to 5 points\nin Fig. 4e.\nResponse and revisions: We are sorry for this oversight. As shown in Fig. R14,\nwe have supplemented the omissive dielectric permittivity and dielectric loss data of\nANLi-xTa ceramics. The temperature-dependent dielectric permittivity was measured\nwithin the temperature range of -100-400 °C under five different frequencies of 100 Hz,\n1 kHz, 10 kHz, 100 kHz and 500 kHz respectively, in which the five points used in the\nVogel-Fulcher fitting of Fig. 4e were given. We have revised the Fig. 4c-d by Fig. Rb-\nc in the revised manuscript and Supplementary Fig. 16 in Supplementary Information.\nFig. R14 Dielectric permittivity of ANLi-xTa ceramics. The temperature- and frequency-\ndependent dielectric permittivity and loss (tan δ) for (a) ANLi-5Ta, (b) ANLi-25Ta, (c) ANLi-\n45Ta and (d) ANLi-65Ta ceramics.\nComments 10: Vogel-Fulcher analysis represented in Fig. 4e must be done using\nangular frequency instead of ordinary one together with imaginary part of the dielectric\npermittivity data, whereas Fig. 4c-d shows only its real part. Besides the freezing\ntemperatures, Vogel-Fulcher analysis must be also characterized by activation energies,\nwhich are not presented by the authors.\nResponse and revisions: We appreciate the reviewer’s comment. According to\nreferences (J. Appl. Phys. 68, 2916 (1990); Curr. Appl. Phys. 11, S14-S21 (2011)), the\nVogel-Fulcher relation for angular frequency (ω) and measurement frequency (f) can\nbe respectively described as following:\nE /k\na E /k\neT m T f lnln  a (1)\n0 0 T T\nm f\nE /k\na E /k\nf  f eT m T f ln f ln f  a (2)\n0 0 T T\nm f\nwhere ω=2πf, T is the freezing temperature/°C, E the activation energy/eV, k is the\nf a\nBoltzmann constant, ω the fitting angular frequency/rad•s-1, f the fitting frequency/Hz\n0 0\nand T the temperature of the maximum permittivity/°C.\nm\nWe have fitted Vogel-Fulcher relation based on the Equation 1 and Equation 2.\nThe fitting parameters are displayed in Table R1 and Table R2 respectively. As we can\nsee, the values of the freezing temperature T and activation energy E which are fitted\nf a\nby using angular frequency and measurement frequency are almost the same within the\nuncertainty of the fit. E represents the activation energy for the polarization fluctuation.\na\nWith increasing Ta concentration, the E of M to R phase transition gradually increases\na 2\nfrom 8.83 meV of ANLi-5Ta to 29.90 meV of ANLi-45Ta, as shown in Table R1. When\nthe composition is close to ANLi-65Ta, the M , M and R gradually merge at nearly\n3 2\none point, accompanying with sharply decreased E (9.03 meV) compared with the E\na a\nof ANLi-45Ta. As a result, ANLi-65Ta ceramics have the low activation energy for\npolarization fluctuation in nano scale indicative of high polar dynamics.\nWe have revised the fitting parameter of Fig. 4e and the freezing temperature of\nFig. 4f in the revised manuscript by using angular frequency to fit the Vogel-Fulcher\nrelation. And the Table R1 has been added as Supplementary Table 3 in the\nSupplementary Information. In addition, the imaginary parts of the dielectric\npermittivity data have been supplemented in the updated Fig. 4c-d in the revised\nmanuscript.\nTable R1. Fitting T, E and Adj. R-Square (R2) of ANLi-xTa (x=5, 25, 45 and 65) ceramics on\nf a\nthe basis of Vogel-Fulcher relation by using angular frequency.\nANLi-5Ta ANLi-25Ta ANLi-45Ta ANLi-45Ta ANLi-65Ta\nM2-R M2-R M3-M2 M2-R\nT (°C) -3.8±0.5 -94.6±0.5 -18.8±0.6 -103.1±1.6 -121.5±0.5\nf\nE (meV) 8.83±1.0 13.02±1.0 4.44±0.5 29.90±1 9.03±1\na\nR2 0.98907 0.98185 0.98610 0.99646 0.98087\nTable R2. Fitting T, E and Adj. R-Square (R2) of ANLi-xTa (x=5, 25, 45 and 65) ceramics on\nf a\nthe basis of Vogel-Fulcher relation by using measurement frequency.\nANLi-5Ta ANLi-25Ta ANLi-45Ta ANLi-45Ta ANLi-65Ta\nM2-R M2-R M3-M2 M2-R\nT (°C) -4.2±0.3 -95.0±1.0 -19.1±0.5 -105.0±2.0 -121.9±0.4\nf\nE (meV) 9.85±0.5 14.35±0.7 5.04±0.3 29.90±1.4 9.89±0.5\na\nR2 0.98907 0.98185 0.98610 0.99646 0.98087\nComments 11: The authors suggested some “enhanced polar dynamics with increasing\nTa concentration even under lower temperatures” without any clearance what do they\nmean by enhanced dynamics.\nResponse and revisions: As shown in Fig. R15, with increasing Ta concentration,\nthe freezing temperature (T) gradually decreases. Above T, it is acknowledged that the\nf f\npolarization shows the ergodic polar dynamics which has no clear frequency\ndependence in dielectric results, indicating much shorter relaxation time and lower\nactivation energy for polarization fluctuation (J. Appl. Phys. 68, 2916 (1990); Curr.\nAppl. Phys. 11, S14-S21 (2011)). In comparison with T (-18.8 °C) of ANLi-45Ta\nf\nceramics, the freezing temperature has been much decreased to -121.5 °C of ANLi-\n65Ta ceramics. That is to say, the temperature range for ergodic polarization state has\nbeen maintained to the much lower temperature. In addition, as shown in Table R1,\nANLi-65Ta ceramics exhibit much lower activation energy (E ) than that of ANLi-25Ta\na\nand ANLi-45Ta ceramics. Therefore, ANLi-65Ta ceramics exhibit the enhanced polar\ndynamics even under much lower temperatures. We have added these discussions in the\nrevised manuscript on Page 15 to clarify our expressions. And the related references\nhave been set as Ref. 69 and Ref. 70.\nFig. R15 Vogel-Fulcher fitting for the angular frequency dispersion versus the\ntemperature of maximum permittivity (T ) of ANLi-xTa (x=5, 25, 45 and 65) ceramics.\nm\nComments 12: The density of the studied ceramics is not indicated as well.\nResponse and revisions: According to the suggestions, we have determined the\ndensity of ANLi-xTa ceramics by using Archimedes’ method. The mean densities of\nANLi-5Ta, ANLi-25Ta, ANLi-45Ta and ANLi-65Ta ceramics are 6.71 g/cm3, 7.28\ng/cm3, 7.78 g/cm3 and 8.03 g/cm3, respectively. We have added these results in the\nrevised manuscript on Page 11.\nComments 13: There are also other examples of unclear sentences like “The further\nboost of Ue will greatly rely on the boost of breakdown strength (Eb), which will\nincrease the failure risk especially with varying temperatures” or “The schematic\nformation of a rotated antiferroelectric state (RAFE) between ferroelectric structure (FE)\nwith induced polar (P1) and normal antiferroelectric (AFE) after introducing Li/Ta\nelements in AN antiferroelectric structure. The existence of RAFE form a percolating\nfield to divide and break the long-range order AFE and FE state, as marked in the\nformation of red network lines.” The manuscript is also full of scientifically ambiguous\nwords like “excellent”, “improved/ing” or “outstanding” as well as by words “through”\nwhen they do not mean indeed through.\nResponse and revisions: We are grateful for the constructive feedback on\nimproving clarity and scientific precision of our work. We have carefully revised the\nmanuscript to address the issues raised. Firstly, for clarification of ambiguous sentences\nthe reviewer mentioned, we have revised related sentences as following: “Enhancing\nthe recoverable energy storage density (U ) necessitates increasing the applied electric\ne\nfield. Notably, over-elevating applied electric field would generate the increase of\nconductive leakage current, easily leading to the occurrence of dielectric breakdown\nand degrades the device lifetime, especially with varying temperatures.” on Page 4. And\nthe figure caption of Fig. 1c in the revised manuscript is updated as following: “The\npolarization distributions in ANLi-Ta superlattice show that the formation of Li-Ta pairs\ncould rotate the antipolar states, resulting in the transformation from normal antipolar\nof antiferroelectric (AFE) represented by antiparallel arranged blue lines to rotated\nantipolar of antiferroelectric (RAFE) represented by colored lines with various degrees\nof rotation.” on Page 7. Terms such as “excellent”, “improved/ing” “outstanding” and\nso on have been replaced with quantitative metrics or deleted. For example, for “an\nexcellent efficiency of 90%” on Page 2, the term “excellent” has been replaced by\n“high”. For “outstanding temperature stability within the range from -70 to 185 °C” on\nPage 5, the term “outstanding” has been deleted. For example, for “markedly improved\nfrom 180 kV/cm” on Page 10, the term “improved” has been replaced by “increased”.\nIn addition, the usage of “through” without clear mechanistic linkage has been modified\nin the revised manuscript. For example, for “the further optimization of efficiency\nthrough a stronger frustration of the AFE-FE phase transition” on Page 4 and “through\ninducing the large proportion of RAFE” on Page 10, the term “through” have been\nsubstituted with “by”.\nComments 14: Finally, there are many missing experimental conditions, like milling\nball material and rotation rate, sintering heating and cooling rates, XRD range, rate and\nstep, P-E loop measurement frequency and temperature range as well as the equipment\nused to control the temperature in this and dielectric measurements. Methods and\nequipment used to polish ceramics down to ~80 μm thickness and to deposit electrodes\nare also missing.\nResponse and revisions: We appreciate the reviewer’s comment. The milling ball\nmaterial is zirconium dioxide. The rotation rate for ball milling is set as 700 r/min. The\nsintering heating and cooling rate are set as 3 °C/min and 5 °C/min respectively. The\nXRD range for samples is set from 20° to 90° with the rate of 1°/min and the step of\n0.02°. The P-E loops are measured under 10 Hz. The temperature-dependent dielectric\npermittivity of ANLi-xTa (x=5, 25 and 45) and ANLi-65Ta ceramics was measured\nfrom 400 °C to -100 °C by using a dielectric temperature measurement system\n(CNOGTICAL DMS 1000). The automatic metallographic grinding and polishing\nmachine (YMPZ-1) was used to reduce the thickness of ceramics and then polish the\nbulk ceramics. The electrodes were deposited by a plasma magnetron sputtering\ndeposition system (VTC-16-D). We have added these detailed experimental conditions\nin the Method of the revised manuscript to address the concern of reviewer.\nResponses to the comments of Reviewer # 3\nThe manuscript titled “Ultrahigh energy storage density and efficiency in AgNbO -\n3\nbased ceramics by percolating interaction between antipolars and defect dipoles”\nreports on a chemical substitutionbased strategy to modify the perovskite structure of\nAgNbO to tailor its antipolar state and improve its energy density properties. The\n3\nstrategy is based on adding Li and Ta ions, respectively replacing Ag and Nb in\nAgNbO , leading to compositions of chemical formula (Ag Li )(Nb Ta )O\n3 0.95 0.05 1-x/100 x/100 3\nwith x=5, 24, 45, 65. The manuscript is undoubtedly interesting; however, it is still a\nquestion if it is suitable for Nature Communication or a minor journal.\nResponse: We greatly appreciate the reviewer’s acknowledgement for the novelty\nof our manuscript. To highlight the significance of this work, we have further carefully\npolished the manuscript and emphasized the innovation points based on the following\nreviewer’s comments.\nComments 1: Overall, the terminology is a bit inconsistent and perhaps slightly loose.\nThis refers to: i) Li-Ta dipoles vs Li-Ta defect dipoles. Is it really appropriate using Li-\nTa defect dipoles for Li-O and TaO dipoles? Also, I think it should be clearly specified\nwhy these are regarded/defined as defect dipoles, since Li is isovalent to Ag and Ta to\nNb; ii) antipolar regions vs antipolars vs rotated antipolars: I suggest sticking with\nantipolar regions and rotated antipolar regions.\nResponse: We greatly appreciate and agree with the reviewer’s valuable comments\nand suggestions. After careful consideration, we think it is not really appropriate using\nLi-Ta defect dipoles or Li-Ta dipoles for describing the role of Li+ and Ta5+ cations in\nAgNbO structures. And we have replaced the terms of Li-Ta defect dipoles and Li-Ta\n3\ndipoles by Li-Ta pairs in the revised manuscript. And we have used Li-Ta pairs to\nanalyze their interaction with neighboring antipolar regions as follows to make related\nstatement much clearer.\nThe substitution of Ta5+ cation for Nb5+ cation results in stronger ionic bonding for\nB-O bonds and compresses the oxygen octahedrons (Adv. Mater. 29, 1701824 (2017)).\nIn comparison, the substitution of Li+ cation for Ag+ cation causes the local dipole field\ndue to the decrease of lattice parameters, i.e., smaller ionic radii (1.17 Å CN=12) of Li\nthan that (1.48 Å CN=12) of Ag. Thus, the coordinated effect of Li+ cations and Ta5+\ncations with adjacent octahedrons represented by Li-Ta pairs will result in the shift\nalong z-direction of the polarization for original antipolar regions, i.e., the rotation of\nantiparallel arranged polarization, as shown in DFT calculations. In addition, we have\nreplaced the mentioned terms by using antipolar regions and rotated antipolar regions\nin the revised manuscript.\nComments 2: There is an ongoing discussion in the literature about AgNbO being\n3\nferrielectric rather than totally antipolar (as lately reviewed in Journal of Materials\nChemistry A 10 (28), 14747-14787), but this has not been taken into account or\nmentioned in the discussion.\nResponse: We agree with the reviewer’s comment. Pure AgNbO (AN) is the\n3\nantiferroelectric-dominated ferrielectric phase near room temperature due to the low\nenergy difference between antiferroelectric (Pbcm) and ferrielectric (Pmc2 ) phases as\n1\ngiven in the reviewer’s mentioned reference (J. Mater. Chem. A 10, 14747-14787\n(2022)). Thus, AgNbO displays a large maximum polarization under applied electric\n3\nfield and reaches a relatively low rather than zero remnant polarization after electric\nfield removal. Through doping Li+ cations into AgNbO , ferrielectric phase can be\n3\ntransformed to ferroelectric (R3c) phase as evidenced by the experimental results of\nReference (J. Phys. Condens. Matter 23, 075901 (2011); J. Eur. Ceram. Soc. 41, 1236-\n1243 (2021)).\nRevisions: We have added the related discussions in the introduction part of\nrevised manuscript on Page 3 based on related references (Refs. 10-13), which also\nincludes the reviewer’s mentioned reference as following: “It was further understood\nthat pure AgNbO shows the antiferroelectric-dominated ferrielectric phase near room\n3\ntemperature due to the low energy difference between antiferroelectric Pbcm and\nferrielectric Pmc2 phases10,11. Through doping Li cations into AgNbO , the\n1 3\nantiferroelectric-dominated ferrielectric phase can be transformed to ferroelectric R3c\nphase12,13.”\nComments 3: In relation to this, the RAFE units that the authors mention and depict in\nsome of the schemes presented in the figures, actually resemble ferrielectric units.\nIn this case, what is the real breakthrough of this paper for Nat Comm if the ferrielectric\nstate in AN-based materials is already known?\nResponse: We sincerely appreciate and respect the reviewer's divergent\nperspectives regarding the significance of this paper. Nevertheless, we would like to\nemphasize that this work represents a meaningful breakthrough in the promising lead-\nfree AgNbO ceramics due to its outstanding energy storage performance and the novel\n3\nphysical mechanism elaborated in the following paragraph.\nThe rotated antiferroelectric state (RAFE) in Li-Ta co-doped AgNbO ceramics is\n3\ndifferent from the initial ferrielectric state possibly existed in pure AgNbO material.\n3\ntransformed into the ferroelectric-dominated state when incorporating low-level Li into\nAgNbO , which shows the ferroelectric hysteresis behavior in\n3\n(Ag Li )(Nb Ta )O (see Supplementary Fig. 10a). In physics, it is related to\n0.95 0.05 0.95 0.05 3\nthe increase of one individual polar strength of antiferroelectric (AFE) unit (P→P+P ),\n1\nas revealed in Fig. 1b due to the coordinating A-/B-site cation displacements. The\nincrease of maximum polarization (2P+P ) will be achieved through antiferroelectric\n1\n(AFE)-ferroelectric (FE) transitions under adequate electric field, boosting the energy\nstorage density. More substitution of Ta for Nb causes stronger ionic B-O bonds and\ncompresses oxygen octahedrons, increasing the coordinated effect of Li+ and Ta5+\ncations with adjacent octahedrons and leading to the significant shift along z-direction\nof the polarization for surrounding antipolar regions. The consequent formation of\npercolating interaction field networks will miniaturize the ferroelectric and\nantiferroelectric regions, stabilize the initial antiferroelectric state and then delay the\nfield-induced AFE-FE transition, resulting in the larger forward and backward\nswitching field (E , E ) and lower electric hysteresis (ΔE= E -E ).\nAFE-FE FE-AFE AFE-FE FE-AFE\nTherefore, the large energy storage density with high energy storage efficiency can\nbe simultaneously achieved in this work, outperforming those of reported AgNbO -\n3\nbased ceramics, not relying the ferrielectric microstructure basis mentioned by reviewer.\nIn addition, density-functional theory (DFT) calculations and antiferroelectric phase-\nfield simulations have further revealed that the percolating networks composed by\nrotated antipolar regions is the key factor for this superior energy storage properties.\nBased on the aforementioned analysis here and in the manuscript, the\nbreakthrough of this paper is that the superior energy storage properties with excellent\nthermal stability is achieved in lead-free antiferroelectric ceramics by a designed\npathway of rotated antipolar regions in antiferroelectric state due to the dipole\ninteraction energy between Li-Ta pairs and surrounding antipolar regions. Thus, we\nbelieve that this paper is suitable for publication in Nature Communication from the\nperspective of outstanding energy storage properties and physical mechanism.\nComments 4: Is it that if these units become percolating the field-induced transition\ncan be delayed and energy density can be consequently enhanced? But what is the\nmechanisms by which this can happen?\nResponse: Fig. 1b displays that overall ferroelectric state appears in Li-doped\nAgNbO antiferroelectric units. As shown in Supplementary Fig. 2. only when more Ta\n3\ncations occupies the high-energy sites near the Li-doped sites, the increased coordinate\neffect of Li+ and Ta5+ cations with adjacent octahedrons, causing the strong rotation of\nsurrounding antiparallel arranged polarization. Thus, rotated antipolar regions with\nlarge local dipole field will be formed and percolated to stabilize ferroelectric and\nantiferroelectric nanodomains and hint the domain wall motion under applied electric\nfield. Consequently, the forward switching field (E ) and backward switching field\nAFE-FE\n(E ) are both increased, indicative of the delay of field-induced antiferroelectric-\nFE-AFE\nferroelectric transition. Therefore, the energy storage density can be enhanced.\nComments 5: In figure 1, it would be good if some additional details can be added to\nenhance the visualization of why the polarization experience exactly the rotation\ndepicted in the last configuration of the structure.\nResponse and revisions: We thank the reviewer’s constructive suggestion.\nWe\nhave redrawn the schematic superlattice structure at the left side of Fig. R16. For normal\nantipolar regions of antiferroelectric (AFE), the polarizations are represented by\nantiparallel arranged blue arrows. After doping Ta to the high-energy sites in AN-Li\nlattice for the formation of the desired Li-Ta pairs, cations of the A-/B-sites of the\nsurrounding AgNbO lattice structures shift and deviate from the initial positions,\n3\nresulting in oxygen octahedrons tilt and antipolar rotations. Thus, the polarizations\nundergo various degrees of rotation, represented by colored arrows. With additionally\nincreasing Ta concentration, more Li-Ta pairs are formed. The rotated antipolar regions\nare enlarged and percolated to divide and miniaturize the antiferroelectric regions. In\naddition, we have the key points of these discussions into the revised manuscript and\nreplaced Fig. 1c by Fig. R16 to enhance the visualization of polarization experience\nafter the formation of Li-Ta pairs.\nFig. R16 The polarization distributions in ANLi-Ta superlattice show that the formation\nof Li-Ta pairs could rotate the AFE antipolar states, resulting in the transformation from\nnormal antipolar of antiferroelectric (AFE) represented by antiparallelly arranged blue\nlines to rotated antipolar of antiferroelectric (RAFE) represented by colored lines with\nvarious degrees of rotation.\nComments 6: In figure S1, the ions should be labelled in structure scheme of the\nstructure and indicate the positions of Ta, in particular, the five positions which are\nenergy favourable indicated in the plot. Also, for the plot the definition of “relative\nenergy of Ta” should be given. Why is this a relative quantity?\nResponse and revisions: We thank the reviewer’s suggestion. As shown in Fig.\nR17a, we have used the number to label the positions of Ta in substituting Nb cations.\nWhen Ta cation replaces Nb cation at Site3, the formation energy is the lowest. We set\nthe energy of Site3 as zero. To enable a more intuitive comparison of the formation\nenergy differences, we calculated the relative energy of other Ta doping sites to Site3.\nAnd the five positions which have high relative energy and large antipolar rotations\nhave been labelled by red numbers (1, 2, 5, 6, 10) in Fig. R17a, which are the nearest\nor next-nearest positions to Li-doped site. In addition, we have added the definition of\n“relative energy of Ta” in the revised manuscript and Fig. R17a-b as Supplementary\nFig. 2d-e.\nFig. R17 The configurations and relative energy differences of Ta-doped AN-Li\nsuperlattice. a. The possible 16 Ta doping sites. b. The relative energy to Site3 (exhibiting\nlowest energy and setting to zero in energy) of different Ta-doped cases and the corresponding\nposition difference in the z-direction.\nComments 7: Specify how the data in figure 2e and supplementary Fig.6 have been\nobtained. For the latter, how was the temperature effect simulated?\nResponse: We are grateful for this comment. The phase field simulations in this\nwork were carried out within two-dimension grid scale of 2 nm where the number of\ngrid points is equal to 256×256. The polarization vector for each grid point have been\ncalculated, as denoted by the arrows. In order to distinguish the antiferroelectric (AFE),\nrotated antiferroelectric (RAFE) and ferroelectric (FE) states in each grid point, the\nnearest neighboring polarizations of every grid point were normalized and then\naveraged. The calculated value is zero for AFE while one is for FE state. In comparison,\nthe value of RAFE is between zero and one. By counting the values of all grid points,\nthe phase fraction of three states was obtained. And then we used gradient color range\nfrom blue to yellow representing the value of every grid point to plot out the distribution\nof AFE, RAFE and FE regions as shown in Supplementary Fig. 8 (Previous\nsupplementary Fig. 6). And the microstructural evolution of different Ta concentration\nwith temperature was calculated by using the phase field model described in Methods\npart. The gradient energy coefficients α and β control the influence of temperature effect\non the stability of antiferroelectric and ferroelectric phases.\nComments 8: The sentence “If a defect dipole with designed orientation can enhance\nthe polarization amplitude of initial AFE antipolars and slightly rotate the alignment of\nantipolars to facilitate the AFE-FE transitions, the polarization of the AN-based systems\nwill be increased with lowered polarization hysteresis, finally achieving the\nsimultaneous boosts in U and η” seems contradictory and unclear for the following\ne\nreasons. It seems to hint at the fact that the AFE-FE transition could be facilitated with\nincreasing Ta; however, the E seems to increase with increasing Ta, as shown in\nAFE-FE\nFig.3a and Fig. Suppl 8. Hence, the addition of Ta is not facilitating but hindering or\ndelaying this transition, and it is actually this that is beneficial to improve energy\ndensity, along the reduction of ΔE. But it is not the reduction of ΔE alone that leads to\nthe large energy density reported. Based on this, also the sentence: “In addition, the\nmodified electric interaction energy near Li-Ta dipoles in AN antipolar matrix through\nincorporating Ta into the neighboring position of Li, can also decrease the switching\nenergy barriers of AFE-FE transition” seems in contradiction with the results, because\nE increases with increasing Ta content.\nAFE-FE\nResponse: The reviewer’s careful comments are greatly appreciated. We\ncompletely agreed with the reviewer’s understanding and are sorry for this imprecise\ndescription. The increased interaction between Li-Ta pairs and neighboring oxygen\noctahedrons in antiferroelectric matrix will not only rotate the polarization direction\nand induce nano-sized ferroelectric state simultaneously, but also stabilize the initial\nrotated antiferroelectric state, especially hindering the antiferroelectric domain wall\nmotion. It will ascend the forward and backward switching field (E E ) of\nAFE-FE, FE-AFE\nantiferro"}]

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