Oriented diffusion tailors interfacial strain-polarization coupling for broadband electromagnetic absorption

Domain: biology
Published: 2026-03-28
Editorial outcome: minor_revision

Abstract
Repurposing the interfacial strain from a hindrance to synergism empowers critical advances for magnetoelectric composites in the application of next-generation energy storage and electromagnetic devices, by reconstructing the interfacial activity and local field distributions. However, its deterministic creation, pivotal for optimizing interfacial electron transport and emergent functionality, is impeded by the uncontrollable atomic distortion and arrangement. Here, we report an oriented-diffusion strategy that tailors interfacial strain by orchestrating atomic migration within a carbon-confined Fe3C/ZnO magnetoelectric heterointerface. Engineering the outward effusion of dielectric ZnO generates a progressive strain gradient, driving a transition in the interfacial strain from compressive to tensile prior to eventual relaxation. This programmed strain state reconfigures atomic-scale electric fields at the heterointerface, thereby enhancing electron transports and interfacial polarization properties. Consequently, this enhancement enables the strain-mediated metamaterial outperforms conventional electromagnetic absorbers, exhibiting an ultrabroad effective absorption bandwidth covers the wireless communication and radar stealth spectra (2.0-18.0 GHz) with an over 95% radiation reduction. These findings provide a novel perspective on deciphering strain-polarization coupling mechanism and guide the development of advanced broadband magnetoelectric functional materials.

Introduction
With the rapid advancement and widespread adoption of Internet of Things (IoT), artificial intelligence (AI), and smart mobile devices, the societal demand of wireless communication technologies has escalated to unprecedented heights1,2. However, less than 30% electromagnetic (EM) waves are utilized in telecommunication, the rest are largely ignored and wasted, constituting severe EM pollution in the surrounding environment and causing health concern and signal interference in electrical equipment3. EM absorption materials provide an effective solution to this issue by harvesting the EM wave and dissipating it into thermal energy. This fundamental energy-dissipation mechanism endows them with EM protection capability as functional fillers, enabling versatile applications that span from micro-nano high-precision electronics (such as on-chip components and integrated modules)4 to large-scale architectural infrastructures5, 6 (such as hospitals, laboratories, and transportation hubs) for industrial interference suppression and environmental shielding. Theoretically, the EM attenuation mechanism is mainly originated from the dielectric and/or magnetic dipoles of a material that interact with the radiation. To pursue superior absorption properties, considerable effort has been devoted to ingeniously integrating dielectric and magnetic components to achieve magnetic-dielectric coupling7. However, current research of magnetic/dielectric composites-based absorber attributes their synergistic effect to merely superimposing magnetic/dielectric contributions, ignoring the intrinsic interaction across the combined components8,9. Deciphering the potential magnetoelectric coupling mechanism for EM dissipation is heavily influenced by numerous factors (e.g., reasonable selection of materials system and systematical characterization), posing significant difficulty.

Designing magnetoelectric heterojunction is an effective approach to maximize the interaction between dielectric and magnetic components through a stable bonding at their contacted interface10. The heterogeneous interface, serves as a key mediator for magnetoelectric coupling, triggering distinctive interfacial effect such as built-in electric field, further contributing interfacial11, or dipoles polarization, internal scattering for EM dissipation12,13. Interfacial strain commonly exists in the magnetoelectric heterointerface owing to the formation of chemical bonds and electrostatic absorption across the interface14. Most reports roughly ascribe the contribution of strain for EM loss to dipole polarization induced by lattice defects and interfacial atoms rearrangement, while ignoring strain modulation towards the intrinsic electronic structure15. In certain dielectrics (e.g., piezoelectric, ferroelectric materials), residual static stress can trigger intrinsic electric polarization16, leading to energy band bending, barrier height modulation, and electron-hole compensation17. Zinc oxide (ZnO) exemplifies this class of functional dielectrics, exhibiting inherent piezoelectric and semiconductor properties18,19. Its pronounced high-temperature thermodynamic instability, which drives distinctive thermal diffusion behavior20, offers a practical pathway to leverage component rearrangement in designing interfacial interaction in the heterostructure systems. These findings establish magnetoelectric heterostructures as promising candidate materials for advanced electronic and spintronic applications, where interfacial strain can be regulated and potentially affect carrier transport efficiency. However, precise strain modulation at heterointerfaces, especially at the atomic scale, remains challenging. The difficulty mainly stems from the inherent lattice mismatch21, thermal expansion incompatibility22, and dynamic stress relaxation23 during material synthesis, compounded by a lack of visualized analysis regarding strains-induced electronic structure transitions at the heterointerface. These inabilities impose huge obstacles on understanding the relationships between microscale interfacial strain and macroscale EM properties, severely restricting the deterministic strain regulation (including strain types and gradient) and the development of advanced EM functional heterostructures.

In this study, we demonstrated a programmed strain-polarization coupling mechanism and fabricated strain-controllable magnetoelectric interfaces by controlling oriented diffusion in carbon confined heterostructures. The interfacial strain transitioned sequentially from compressive to tensile and finally to a relaxed state during the outward diffusion of ZnO. This strain evolution mediated a volcano-type profile in interfacial coupling strength by reconstructing the electronic field distribution. Remarkably, engineering tensile strain at the magnetoelectric heterointerface effectively enhanced the electron transport and amplified the built-in electric fields, boosting interfacial polarization relaxation to dissipate the incident EM wave. The strain-polarization coupled magnetoelectric metamaterial exhibits full-bandwidth (2-18 GHz) effective EM energy absorption, establishing it as a promising candidate for diverse applications in wide-frequency wireless communications and EM protection. Therefore, our work provided a novel method for designing magnetoelectric heterostructure with strong polarization responsiveness by leveraging interfacial strain, demonstrating significant potential for dual-use military and civilian applications.

Results
Synthesis of confined magnetoelectric heterostructures
Confined ZnO/Fe3C magnetoelectric heterostructures were fabricated by precisely diffusing ZnO nanoparticles to a specific depth within carbon frameworks (Supplementary Fig. 1). As shown in Fig. 1a, this process initiated with the transformation of carbonaceous substrate tethered Zn/Fe oxide (ZFO) hybrids into carbon encapsulated ZnO/Fe3C yolk-shell nano-units through high-temperature carbothermal reduction, followed by manipulating the Zn source content for guiding the derivate ZnO effusion outwards the carbon nanocage. The carbon framework conversion from solid to yolk-shell was triggered by the Kirkendall cavitation effect24, causing the creation of limited nanovoid, as evident by scanning electron microscopy (SEM) and transmission electron microscopy (TEM) images (Supplementary Fig. 2). As Zn source content increased, excess ZnO gradually filled the surrounding voids, eventually breached the carbon cages confinement, and diffused outward to form continuous ZnO layers. Consequently, the ZnO/Fe3C (ZFC) heterostructure evolved through sequential confinement, penetration and separation stages with increasing ZnO content, as identified by high-resolution TEM (HRTEM), high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and energy-dispersive X-ray spectroscopy (EDS) elemental mapping (Fig. 1b and Supplementary Fig. 3), with the corresponding specimens termed ZFC-1, ZFC-2, and ZFC-3, respectively. Additionally, the augmented ZnO content enhanced the carbothermal reaction, as evident by the thermal gravity analysis (TGA) and Raman spectra (Supplementary Fig. 4), further boosting the gradient outward diffusion process.

In addition to morphology analysis, we performed in-situ argon ion sputtering to progressively etch the outer ZnO layers of ZFC-3 to depths of up to 400 nm, thereby characterizing the outward diffusion affected component arrangements. X-ray photoelectron spectroscopy (XPS) depth profiling recorded both a gradual decrease in the intensity of characteristic Zn 2p peaks and an opposite trend in the Fe 2p signals (Fig. 1c), confirming the separation of ZnO and Fe3C during the enhanced effusion process. Concurrently, the reaction between carbon substrates and ZFO induced the chemical transformation from ZnFe2O4 into ZnO and Fe3C, resulting in the formation of an interface between ZnO and Fe3C within the magnetoelectric heterostructures. The phase evolution and chemical state variation was verified by X-ray diffraction (XRD), X-ray absorption near edge structure (XANES), extended X-ray absorption fine structure (EXAFS), and XPS analysis (Fig. 1d-e, Supplementary Fig. 5-8 and Table 1). The absorption edge of Fe k-edge of ZFO and ZFC samples were close to that of Fe3O4 and Fe, respectively. In the Fe k-edge EXAFS of ZFO, a shift towards higher radial distance was detected in the peak of characteristic Fe-O-Fe, further identifying the formation of ZnFe2O4 in ZFO25. Meanwhile, the EXAFS of ZFC also confirmed the presence of Fe3C (via Fe-Fe and Fe-C peaks)26 and indicated the formation of interfacial chemical bonds in Fe3C/ZnO heterojunctions, as evident from emerging Fe-O peaks with a shift towards increased radial distance.

To reveal the configuration of the magnetoelectric interface built by semiconductor ZnO and ferromagnetic Fe3C, an aberration-corrected HAADF-STEM was employed to capture the ZnO/Fe3C heterostructures (Fig. 1f). Atomic arrangement of ZnO/Fe3C revealed a feature of coherent heterointerface, where the ZnO presented the (101) crystal plane and Fe3C exhibited the (211) crystal facet, thereby confirming atomically interactive connectivity across the interface. To minimize potential inaccuracies caused by closely spaced lattice, integrated differential phase contrast (iDPC) STEM was carried out. Detection of Fig. 1g presented a strong quantitative agreement between the crystalline structure and STEM results, accurately verifying the formation of magnetoelectric heterointerface between Fe3C (211) and ZnO (101). Additionally, the distribution of the intrinsic atomic-scale electric fields within Fe3C and ZnO were visualized using differential phase contrast (DPC) STEM27, with color vector wheels indicating the direction of the electric field (Fig. 1h). A uniform yet asymmetrical distribution of the local atomic electric field within each component reveals different potentials28, potentially inducing built-in electric field at the magnetoelectric interface.

Diffusion-regulated interfacial strain in confined ME heterostructures
To provide insights into the correlation between ZnO diffusion and magnetoelectric interface contact, molecular dynamics (MD) simulation (Supplementary Note 1) was employed to elucidate the ZnO content affected effusion process. The observations of recorded diffusion state indicated that at lower concentrations, ZnO molecules were largely hindered from penetrating the carbon layers (Fig. 2a). Conversely, with a higher initial concentration, the confinement imposed by the carbon layers was progressively overwhelmed, leading a pronounced outward diffusion. Continuous increase of the number density of penetrated ZnO (Fig. 2b and Supplementary Fig. 9) and the mean-square displacement (MSD, Fig. 2b) with the augmented concentration further proved the controllability of the ZnO gradient effusion process. In addition, ZnO oriented migration process inevitably affected the interface state, inducing potential reconfiguration of interfacial strain at the heterointerface. The interfacial stress field resulted from the ZnO gradient diffusion was characterized using geometric phase analysis (GPA) of STEM, complemented by strain distribution statistics (Fig. 2c-d and Supplementary Fig. 10). At the primary stage of magnetoelectric interface formation (ZFC-1), about 10.2% compression strains were detected at the ZFC interface, which was originated from the bonding effect of heterostructure formation. Upon initiation of ZnO outward diffusion (ZFC-2), the excess ZnO filled the original nanovoid within the carbon nanocages and tended to separate out, thereby inducing traction from the outer carbon layers on the penetrated ZnO. Concurrently, the upcoming separation of ZnO was also constrained by Fe3C owing to the interfacial bonding at the ZnO/Fe3C coherent heterojunctions and the static absorption, resulting in significant tension strain (16.8%) at their atoms contacted interface. The enhanced outward diffusion of ZnO overcame the constrains of both carbon shells and the interfacial bonding, thereby triggering the dissociation of the original ZnO/Fe3C heterointerface, as evident by the disappearance of Fe-O bond in Fe k-edge EXAFS of ZFC-3 (Supplementary Fig. 11). Seldom residual strain (0.5%) remained at the emerging Fe3C-C-ZnO triple-phase interface. Thus, the gradient-oriented diffusion process effectively governed a programmatic progression of the interfacial strain state from compressive to tensile, ultimately leading to its relief. The same interfacial strain states, with comparable quantitative values, was consistently observed in ZFC-x specimens across different batches (Supplementary Fig. 12), confirming the reproducibility and controllability of the oriented diffusion strategy.

To decipher the strain affected interfacial electronic structure, the distributions of interfacial electric field under different strain state were analyzed by the DPC-STEM technique (Fig. 2e). Unlike the uniform atomic electric fields in a homogenous component, pronounced distortion and mutual interaction were observed between neighboring Fe and Zn atoms across the interface, providing direct evidence of electric field couplings at the magnetoelectric heterointerface29. This atomic-level interfacial electric coupling was more pronounced as the compression strain converted to the tensile strain at the interface, which could accelerate the carriers transport across the interface and enhanced interfacial polarization. In contrast, only continuous and symmetrical atomic electric fields was observed within the separated ZnO, with no detectable electric field reconfigurations at the interface, implying the interfacial decoupling in ZFC-3 owing to the extinction of magnetoelectric heterojunction. In addition, the strain-mediated evolution of the interfacial coupling was analyzed using vector field distribution30 reconstructed from the atomic electric field maps (Fig. 2f). Characteristic gradients in the electric field vector rotation were detected at the magnetoelectric interfaces, confirming the strain-induced interfacial coupling. This coupling phenomenon was remarkably enhanced under tensile strain yet vanished upon interface separation. By precisely controlling ZnO diffusion to introduce interfacial strain, effectively programming the atomic electric field arrangement and the polarization capability at the magnetoelectric heterointerface.

Interfacial strain regulated electrical properties
The interfacial strain evolution guided by the gradient diffusion reconstructed the atomic interaction at the magnetoelectric heterointerface, varying the electrons motion in the interfacial built-in electric field (BIEF), thereby affecting the related electrical properties. Dielectric dispersion, manifested in frequency-dependent permittivity, fundamentally originated from the dynamic dielectric loss of absorbers to an external alternating electric field31. The variation of permittivity revealed that the interfacial strain enhanced dielectric dispersion properties, as verified by a steeper decline in permittivity with increasing frequency (Supplementary Fig. 13a-b) and a broader variation range across the 2–18 GHz band (Fig. 3a). This enhancement was mainly due to the strain-induced reconstruction of the local electronic structure via interfacial coupling (Fig. 2e-f), which accelerated realignment of interfacial potentials across the interface in response to the altering electric field, thereby improving interfacial polarization responsiveness32. The enhanced polarization relaxation could be characterized by the decreased real permittivity (ε′) and a more intense dielectric resonance peak in the imaginary part (ε″) for the strain-involved specimen (Supplementary Fig. 13a-b). According to the non-ideal Debye relaxation model33, the ε″, referred to the dielectric loss ability, was divided into conduction loss (ε″c) and polarization relaxation (ε″p) based on the tested electronic conductivity (Supplementary Table 2 and Supplementary Fig. 13c-d). Multiple polarization peaks were identified in the strain-involved ZFC heterostructures, and both of the peak intensity and width were increased as the interfacial state evolved from the relieved to compressive and tensile. This enhancement was also confirmed by the loss tangent of complex permittivity (tanδ = ε″/ε′), where the increased tanδ indicated the strain-improved dielectric loss ability (Fig. 3b). In addition, the interfacial strain affected polarization relaxation variation were analyzed by Cole-Cole plots. As the interfacial strain evolved from a relieved state to compressive and tensile states, the maximum relaxation peak shifted to higher frequencies (Fig. 3b), along with a broadened peak width (Fig. 3c). Theoretically, polarization relaxation peaks occurred when the frequency of the external electric field coincides with the intrinsic response rate (the reciprocal of the relaxation time) of the polarization mechanism within the absorbers34. Thus, this trend of relaxation peaks varied by the interfacial strain suggested a shortened relaxation time with a widened distribution35, demonstrating a sensitive yet broadband dielectric loss capability in the strain-involved magnetoelectric heterostructure.

To reveal the strain state-regulated interfacial polarization loss capability, off-axis electron holograms and projected charge density maps are conducted (Fig. 3d and Supplementary Fig. 14). The red and bule regions in charge maps corresponded to the electronic depletion and accumulation, respectively, and the color depth reflected the charge density. The 3D charge density distribution of the strain-relieved interface exhibited flat distribution with weak intensity, ascribing to the decouple of the magnetoelectric interaction (Fig. 2f). In contrast, remarkable fluctuation characterized by the uneven arrangement of positive and negative charge were detected in the ZFC heterointerface with compression and tension strain. The increased potential differences implied the augmented absolute electronegativity across these coupled interfaces, which promoted interfacial polarization and its associated electric field energy dissipation. After a sequential process of Fast Fourier Transform (FFT), Inverse FFT (IFFT), filter method, the electron wave phases in the holograms were converted into electric potentials, finally the localized polarization intensity could be calculated based on the Poisson’s equations29. Fig. 3e illustrated that interfacial strain effectively elevated the polarization intensity, which could be further enlarged by the tensile strain owing to the accelerated electrons transport by the enhanced interfacial coupling. Additionally, the ε″p/ε″c value could reflect the contribution of polarization loss within the tested frequency range. As shown in Fig. 3f, the values of ε″p/ε″c ratio rise with increasing frequency, indicating that polarization loss played a more dominant role at higher frequencies. Notably, this frequency dependent enhancement was most significant in the ZFC-2 specimen with interfacial tensile strain, highlighting the controllability of polarization loss through strain engineering.

To deeply decipher the regulation mechanism of the polarization loss, the reconfigured electronic structures in the ZnO gradient diffusion controlled ZFC-based heterointerfaces were further theoretically analyzed by density functional theory (Supplementary Note 2). The projected density of state (PDOS) analysis revealed a gradient diffusion-induced reconstruction of interfacial electronic structures (Fig. 3g) and BIEF, consistent with the observation from the DPC and electron holography. As tensile strain was formed on the ZFC heterointerface, more pronounced orbits overlaps were detected, assigning to the enhanced interfacial coupling interaction, thereby boosting electron transports of the external electric field across the interface. As the interfacial strain state evolved from the relieved to compressive and tensile, the reduced work function (Φ) suggested the lowered energy barriers for charge migration (Fig. 3h and Supplementary Fig. 15), which improved the electron mobility and activity36. This improvement facilitated the supply of polarizable charges, thereby promoting the response of interfacial dipoles to external alternating electric fields. In additional, the differential charge density distribution revealed pronounced and inhomogeneous charge accumulation and depletion at these coupled magnetoelectric interfaces (Supplementary Fig. 16), forming multiple localized space-charge regions34. This result indicated the generation of robust interfacial dipole layers with a wide distribution37, which could account for broadening the distribution of polarization relaxation. Thus, these combined experimental results and theoretical analyses revealed a tunable strain-polarization coupling mechanism. The interfacial strain evolution, tailored by oriented diffusion, effectively orchestrated a reconfiguration of interfacial electronic properties via constructing interfacial coupling. This process created intense and wide-ranging polarization responsiveness, thereby significantly enhancing the dielectric loss performance in response to the external EM wave.

Application in EM wave absorption
Owing to the strain-tailored interfacial electric coupling effects and enhanced electric properties, the Fe3C/ZnO magnetoelectric heterostructures exhibited significant dielectric loss ability, showing potential application in efficient EM wave absorption. The strain-regulated EM absorption performance of the as-fabricated magnetoelectric heterostructures was evaluated, indexed by reflection loss (RL) and effective absorption bandwidth (EAB, frequency range of RL≤-10)38. In Fig. 4a and Supplementary Fig. 17, both the minimum RL (RLmin) and maximum EAB (EABmax) exhibited the optimum when the magnetoelectric interface was subjected to tensile strain. A detail analyses of the EM parameters and magnetic response properties evolution (Supplementary Fig. 18-22 and Note 3) attributed this improvement to the increased dielectric loss ability caused by the strain-enhanced interfacial polarization and optimized impedance matching. The Fe3C/ZnO heterostructure within tensile strain exhibited a broad EAB of 7.38 GHz, covering entire Ku-band (from 12 to 18 GHz, the primary application band for radar stealth39), outperforming most reported EM absorption materials (Fig. 4b and Supplementary Table 3-4). Furthermore, we employed finite element analysis to simulate the surface current density and radar cross section (RCS) of a perfectly electric conducting (PEC) plate coated with ZFC-based magnetoelectric composites layers (Fig. 4c, Supplementary Fig. 23 and Note 4). Uniform distribution of surface current density40 and significant RCS reduction41 demonstrated the superior impedance matching and effective absorption properties of the strain-enhanced ZFC heterostructure in the simulated practical EM environment.

Widespread adoption of wireless communication techniques in civilian escalated the societal demand of absorbers with ultrawide EAB for addressing EM interference (produced by e.g., base stations, wireless routers and electronic devices)42,43. According to the equivalent medium theory, the periodic structure at subwavelength produced uniform EM response44. To achieve full-band absorption, an EM metamaterial was fabricated by mixing the strain-mediated Fe3C/ZnO heterostructures with resin and molding it into an 18 × 18 cm periodic metastructure (Supplementary Fig. 24 and Table 5), and the design principle of the metastructure were detailed in Supplementary Note 4. This hierarchical architecture, which featured pyramid-shaped units with internal perforation, could generate additional multiple resonances through impedance gradient matching and spatial dispersion. Fig. 4d showed the practical photos of the magnetoelectric metamaterial under the far-field testing environment. Remarkably, ultrawide EAB performance across the entire 2–18 GHz band was achieved, attributing to the synergistic effect between intrinsic excellent magnetoelectric coupling loss from heterostructures and diffraction resonances supplied by the metastructure.

To verify the application potential, we tested the absorption attenuation of the metamaterial against EM waves emitted by a 5G wireless router. Positioned as a shield in front of the WiFi router, the metamaterial remarkably reduced the detected radio frequency (RF) signals to the qualified levels (Fig. 4e). And the pronounced surface temperature elevation of the ZFC-2 metamaterials after radiation under a solid-state microwave source confirms the involved dissipation process from absorbed EM energy to heat (Supplementary Fig. 25 and Fig. 4f). Time dependent radiation values variation revealed that over 95% reduction of RF signals could be continuously achieved by this magnetoelectric metamaterials (Fig. 4g). In contrast, both control samples (the all-resin metastructure and the ZFC-2/resin plate) failed to achieve effective EM attenuation (Supplementary Fig. 26), further demonstrating that the impressive EM protection arises from the synergistic contribution between the strain-mediated magnetoelectric absorbers and the designed metastructure. Additionally, the corresponding dissipation mechanism was investigated via finite element simulation45. The frequencies (5.8 and 14.0 GHz) of characteristic resonance peaks identified from the RL results were selected to elucidate the EM field response behaviors. As shown in Fig. 4h, the attenuation of low-frequency EM energy occurred primarily through magnetic field dissipation, while at high frequencies it is dominated by electric field dissipation. This frequency-dependent behavior was confirmed by the spatial overlap of electric/magnetic field distributions and energy loss profiles46. These inspiring findings demonstrated that the tensile strain-enhanced magnetoelectric heterostructure provided a promising sustainable solution to address the elevating EM interference.

In conclusion, we have successfully fabricated carbon confined ZnO/Fe3C magnetoelectric heterostructures, and precisely tailored the interfacial strain by controlling the oriented diffusion gradient. As the strain of the magnetoelectric heterointerface evolved from the compressive to the tensile and relieved, the interfacial atomic electric fields exhibited an evolution from the enhanced interfacial coupling to the decoupling. Furthermore, the strain-driven coupling effect reconfigured the electronic structures across the atomic heterointerface, effectively accelerating the interfacial electrons transport and broadening the distribution of interfacial dipoles, thereby enhancing the polarization relaxation response ability. Eventually, the tensile strain-enhanced magnetoelectric heterostructure performed impressive EMA properties with a broad EAB covered 7.38 GHz; and its derivate metamaterials achieved full-band efficient absorption (2-18 GHz) and over 95% radiation attenuation efficiency, exhibiting significant potential for dual-use civilian and military application. Our results proposed a novel mechanism of interfacial strain engineering in regulating electronic properties and broaden the design paradigm of advanced EM functional materials.

Methods
General
The chemicals, electromagnetic parameters measurement, molecular dynamics simulation, and density functional theory are given in the Supplementary Methods and Notes.

Synthesis of ZnO/Fe3C@C-x (ZFC-x)
ZFC-x microspheres were prepared by continuous spray drying and annealing treatment. First, 3.0 g PVP-K30 and 0.9 g TMA was dissolved in of a 60 mL solution composed of isometric DI water, anhydrous ethanol, and DMF under vigorous stirring to obtain a homogenous solution. Then, 2.0 mmol Fe(NO3)3∙9H2O, x mmol Zn(NO3)2∙6H2O were simultaneously added into the solution and stirring until dissolution. The final obtained yellow spray solution was fed into a spray dryer, and the spray drying parameters were an inlet temperature of 180 °C, outlet temperature of 90 °C, feed rate of 1500 mL h−1, and an atomization pressure of 0.4 bar. The collected spray dried precursors were pre-treated at 300°C for 60 min to obtain solid ZFO@C hybrids, followed by pyrolyzing at 600 °C under N2 atmosphere for 300 min at a heating rate of 2 °C/min to obtain the ZFC-x. In addition, the ZFC-x samples prepared at the Zn(NO3)2∙6H2O amount of 1.0, 3.0, and 5.0 mmol were denoted as ZFC-1, ZFC-2, and ZFC-3, respectively.

Fabrication of ZFC based EM metamaterials
ZFC-based metamaterials with a size of 18 × 18 cm within periodic aligned units were prepared via a moulding process, the geometric parameters of the as-designed metamaterial unit were listed in Supplementary Table 5. First, a rubber inverted mold template was obtained via 3D printing. Then, a certain amount of ZFC powders were added into a fresh prefab resin mixture (the added weight ratios of resin E51, curing agent, and accelerator were 14:5:1) with a weight ratio of 2:3 and violently stirred for 30 min. The as-obtained ZFC/resin mixtures were poured into the 3D-printed inverted mold template and degassed for 60 min under the vacuum ambient. The inverted mold template with the degassed ZFC/resin mixtures were transferred to an oven and cured under 80 ºC for 12h. After the completion of curing, the final ZFC-based EM metamaterial was obtained.

Characterization
Field-emission SEM images were obtained using a Hitachi S-4800 microscope. TEM, HRTEM, EDS mapping results and off-axis electronic holography results were obtained on a on a dual spherical aberration correction field-emission STEM (Thermo Fisher Scientific, Spectra 300 TEM, American) operated at 300 kV, equipped with STEM-iDPC detector, STEM-HAADF detector, and Super-X EDS. X-ray diffraction (XRD) patterns were recorded on a Bruker-Axe X-ray diffractometer equipped with a Cu Kα radiation source (λ = 1.5406 Å, 40.0 kV, 40.0 mA). X-ray photoelectron spectroscopy (XPS) results were analysed on a Thermo Scientific ESCALAB 250Xi spectrometer equipped with a monochromatic X- ray source and argon etching system. X-ray absorption fine structure spectra were collected at the RapidXAFS 2M (Anhui Absorption Spectroscopy Analysis Instrument Co., Ltd.) by transmission mode at 20 kV and 40 mA. All spectra were collected in ambient conditions. Raman spectroscopy measurement was performed on a Renishaw inVia spectrometer under a 633 nm laser excitation. Thermogravimetric analysis (TGA, PerkinElmer) was performed in an air atmosphere to evaluate the content variation. The conductivity of the samples was tested by analysis of a four-point probe surface resistance tester.

Data Availability
Source data are provided with this paper. The data that support the findings of this study are available from the corresponding author upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript titled “Oriented atomic diffusion tailors strain–polarization coupling for broadband electromagnetic absorption” presents a technically robust strategy to modulate interfacial strain for achieving broadband electromagnetic (EM) wave absorption. The authors construct ZnO/Fe₃C@C microspheres (ZFC–x) featuring gradient tensile–compressive strain fields induced by controlled outward ZnO diffusion during annealing. The study effectively integrates advanced characterization techniques such as aberration-corrected STEM, electron holography, and XANES/EXAFS with multiscale simulations to elucidate the correlation between atomic-scale strain evolution, polarization relaxation, and interfacial charge transfer.\n\nThe central innovation lies in transforming interfacial strain from a passive structural feature into an active tuning parameter for dielectric and magnetic losses, thereby achieving a high effective absorption bandwidth of 7.38 GHz at 2.2 mm, further extendable to full 2–18 GHz coverage in a resin composite. The work is scientifically sound and presents clear potential for practical applications in EM interference mitigation. It can be considered suitable for publication in Nature Communications after the authors satisfactorily address the following critical points.\n1. The rationale for selecting ZnO in the heterostructure should be clearly mentioned.\n2. In the DFT methodology, the DFT+U approach is generally required for Fe-containing systems, but the manuscript does not specify the Hubbard U parameter; this should be clarified.\n3. The authors should specify whether a high-spin or low-spin configuration and what kind of magnetic interactions were considered in the DFT simulations.\n4. The choice of (211) and (101) crystal planes for Fe₃C and ZnO, respectively, in the DFT models should be justified.\n5. In the XPS analysis, O 1s and C 1s spectra should be included alongside Fe and Zn, and the Fe 2p spectrum should be deconvoluted to show multiplet splitting.\n6. The Fe 2p XPS (Fig. 1c) and Raman (Supplementary Fig. 4b) spectra exhibit a relatively low signal-to-noise ratio; improved data quality is recommended.\n7. Supplementary Figures 10 and 12 can be merged for conciseness.\n8. The Cole–Cole plots should be fitted using an appropriate equivalent circuit model to substantiate relaxation behaviour.\n9. Extracted parameters from Rietveld refinement should be provided to validate structural claims.\n10. The synthesis relies on precise ZnO outward diffusion and strain balancing; therefore, the manuscript should discuss reproducibility across batches and potential challenges in scaling up the process for industrial production.\n11. Long-term stability under cyclic heating or humid conditions should be examined, as Fe₃C and carbon shells may degrade upon oxidation.\n12. While qualitative relationships between strain, dielectric loss, and absorption are established, quantitative correlations would greatly strengthen the mechanistic understanding.\n13. A comparison table contrasting EAB, reflection loss, and filler loading with representative Fe-, Co-, and Ni-based hybrid absorbers would help contextualize the performance gains.\n14. The introduction briefly discusses EM pollution, but a more concrete discussion of practical applicability, such as the feasibility of large-scale EM shielding in industrial or architectural contexts, would make the work more relevant.", "reviewer_2": "In the manuscript \"Oriented Atomic Diffusion Tailors Strain-Polarization Coupling for Broadband Electromagnetic Absorption,\" the authors explore interfacial strain engineering to enhance the electronic properties of electromagnetic materials. They created a carbon-confined Fe3C/ZnO magnetoelectric heterointerface, where varying Zn precursor content influences the effusion of ZnO through the interface, leading to carbon-encapsulated yolk-shell nanostructures. The strain transition from compressive to tensile alters interfacial atomic electric fields, shifting from enhanced to decoupled coupling. This strain effect modifies the electronic structures, improving polarization relaxation and electron transport. The resulting heterostructure exhibited impressive electromagnetic absorption properties, with a broad effective absorption bandwidth of 7.38 GHz and an over 95% radiation attenuation efficiency from 2 to 18 GHz.\nThis work significantly expands the design framework for advanced electromagnetic functional materials. The authors have thoroughly studied their samples and provided both theoretical simulation and application-based evidence to support their claims.\nHowever, there are a few questions to consider before publication.\n1. With the increase of ZnO diffusion, a variation in carbon shell thickness from ~635 nm to ~860 nm to ~270 nm is observed in the ZFC-x samples. Please explain why this large variation is observed.\n2. The x-axis in Fig. 3f represents discrete ZnO samples; however, the graph displays a continuous 2D plot. Please clarify how this graph is created.\n3. The authors state in lines 339-340 that they tested the electron conductivity (σ) of the samples using a four-probe measurement. Based on this conductivity (σ), they categorized the dielectric loss (ε′′) into conduction loss (ε ′′) and polarization relaxation (ε ′′). However, they did not provide any details or data regarding this measurement.\n4. The VNA typically provides S-parameters. What method is used for converting these S-parameter data into intrinsic sample parameters, such as permittivity and permeability?\n5. Additionally, in the equations for input impedance and reflection (Equations 6 and 7 in the supplementary materials, lines 46 and 47), it appears that a constant term related to the free space impedance (Z ) is absent.\n6. The authors developed an electromagnetic (EM) metamaterial by combining a strain-mediated Fe C/ZnO heterostructure with resin, molding it into an 18 × 18 cm periodic metastructure to achieve full-band absorption. However, the rationale behind selecting this specific metastructure and how its dimensions were determined remains unclear. A brief explanation of the reasoning behind this choice would be beneficial for the article.\nThere are also a few typing and grammatical errors in both the main article and the supplementary article. The annotated documents highlighting these errors are attached for consideration.", "reviewer_3": "In this paper, the authors propose a new method for designing yolk-shell composite nanoparticles with controllable interfacial strain between the two components. They demonstrate it by synthesizing ZnO/Fe3C nanoparticles, where magnetoelectric interface forms through the outward diffusion of the ZnO species from the Zn + Fe + O + C precursor mix. Further, they investigate the evolution of the microstructure and macroscopic properties of these nanoparticles with the change of Zn/Fe precursor ratio. With theoretical calculations (molecular dynamics) and experimental data, the authors show, that the strain at the interfaces changes from compressive to tensile and then to neutral (relaxed) with increasing Zn content, and that the interfaces with tensile strains can be efficiently used as a GHz radiation absorber.\nOverall, the article presents a very comprehensive and topical study with clear applications and therefore can be published in Nature Communications. However, several issues should be addressed before publication:\n1. SEM images (supplementary Fig 2) show, that the size of the nanoparticles vary greatly, but I could not find any information about the average size or the size distribution for different ZFC powders. Fig 1b also features spherical particles of different size. Particle size is directly related to the magnetoelectric interface area to volume ratio, so it may skew the measured macroscopic parameters of the samples. I would like the authors to provide some statistical data on the ZFC powders morphological parameters and to comment on the relations between these parameters and the measured permittivity and GHz absorbing capabilities.\n2. The comparison (Fig 4b and supplementary Table 1) with other microwave absorbing materials is lacking. For example, there are articles, reporting materials with better EAB at lower or similar thickness, such as FeCo-Ti3C2 MXene (EAB – 8.8 GHz at 1.6 mm thickness, https://doi.org/10.1016/j.jmmm.2019.165639), ZF/rGO aerogels (EAB – 8.4 GHz at 2.1 mm thickness, https://dx.doi.org/10.2139/ssrn.4414816) and SiO2@FCIP + MWCNT (EAB – 7.9 GHz at 1.9 mm thickness, https://doi.org/10.1016/j.compositesa.2025.108719). While the parameters, obtained in the current manuscript are impressive, they can not be called record-breaking. I would like the authors to expand the comparison with these and/or other reports to make it more balanced.\n3. Vertical axis break and change of scale in Figure 4b is misleading. I can not find a good reason to make it this way. Please, remove the line break or explain why it is necessary.\n4. Figures 4e and 4f show, that GHz radiation from a consumer grade WiFi router heats the shielding resin metastructure up to 45 oC in one minute. It is hard to believe, considering very low peak RF power density of 150 mW/m2 (Fig 4g). By my estimations even if the metastructure dissipates all of the RF radiation into the thermal energy, in one minute it could only heat up by less than 1 oC (or heat up a very thin < 1 mkm surface layer by 20 degrees). I would like the authors to clarify the thermal balance of this experiment.\n5. I could not find detailed information about the molecular dynamics simulation neither in the main text, nor in the supplementary notes. I would like the authors to provide a description of the initial state used in the simulations and how different ZnO concentrations were implemented.\n6. How the statistical data on Supplementary Fig. 8 were gathered? From the text it is not clear, if it is a strain distribution within a single heterointerface or a distribution of average strains of several interfaces? In my understanding, big part of the theoretical considerations in the manuscript rely on the results, presented in Supplementary Fig. 8, so I would like the authors to provide evidence, that these strain distributions are representative.", "reviewer_4": "A magnetoelectric Fe3C/ZnO composite and its heterointerface were analyzed in detail, showing the redistribution of interfacial strain and polarization fields. It is shown that the polarization fields are strong when interfacial strain is large and that this causes high dielectric loss. The authors demonstrate the properties of the strained heterointerface in an EM absorption experiment, showing wideband absorption. The authors use a suite of advanced analysis tools to demonstrate the interfacial properties of the heterointerface but the basic theory and physical principles behind the wideband absorption is not immediately clear.\nWhile the results are nice, polarization control for EM absorption has already been extensively studied in all types of forms of 2D TMCs, nanoparticles, composites, defects, etc. In this context, the novelty of the work is not remarkably persuasive. The physical aspects how it can be differentiated from those of other works should be elucidated very clearly.\n1. Please add classic references that link interfacial polarization to EM wave absorption.\n2. Pg. 6 Clarify which ZnO crystal plane is being analyzed. In one place it says (101). In another it says (111).\n3. In Figures, it is hard to tell without labels which figure refers to ZFC1, 2 and 3. (Figure 1b, 2a, 2c, etc)\n4. It’s hard to understand the plot in Figure 3a. The text says that this is a dispersion curve, but there is no spectral data. What do the range of values refer to?\n5. Pg. 8 “THe dielectric dispersions arise from an electronic reconfirugration triggered by atomic-level stress regulated interfacial potential difference”. This is a general statement and can apply to any variation in the dielectric dispersion. Can the authors be more specific?\n6. Pg. 8, In the loss tangent plot, the authors describe a polarization relaxation peak. Specify its location. Can its origin be clarified using the analysis before (eg. Why does it occur at the specified frequency. What is the physical reason?)\n7. Pg.9 ‘THe polarization enhancement, becoming more remarkable as the frequency moved to the higher band’. This sentence is hard to understand\n8. If the goal is to show the properties of the composite in the EM absorption demonstration, it would be more convincing to perform the experiment on a film instead of a metasurface. Otherwise, it is hard to tell if the performance enhancement and wide-band absorption properties is due to the metasurface or the intrinsic properties of the composite. The relative contributions of the two effects are not explained in the current form.\n9. Please clarify the physical principles that link the unique interface strain engineering to wide-band absorption."}, "author_response": "General Response: We thank the reviewer for their careful reading of our manuscript and for noting that our work presents clear potential for practical applications in EM interference mitigation.\nQ1: The rationale for selecting ZnO in the heterostructure should be clearly mentioned.\nResponse 1: We wish to clarify that the core rationale for selecting ZnO in our Fe C/ZnO magnetoelectric heterostructure is fundamentally rooted in its exceptional and tunable dielectric properties and thermal diffusion behaviors. On the one hand, its dielectric behavior is mainly originated from the wurtzite crystal structure of ZnO, which features alternating layers of Zn2+ and O2- ions stacked along the c-axis, creating an intrinsic dipole moment and superior response ability toward external electric field [Ref. R1-2]. This unique atomic arrangement facilitates multiple polarization mechanisms [Ref. R3-4]: electronic polarization from its wide bandgap, strong ionic displacement polarization due to the charged sublattices, and defect-related relaxation polarization, which makes it as a promising dielectric candidate for electromagnetic wave absorption [Ref. R5]. Additionally, potential piezoelectric property of semiconductor ZnO can be harnessed to effectively regulate the interfacial electronic structure and polarization behaviors [Ref. R6, 7] by inducing tunable strain at the Fe C/ZnO magnetoelectric interface.\nOn the other hand, owing to the thermodynamic instability of ZnO under low oxygen partial pressure and elevated temperature [Ref. R7], an appropriate high-temperature thermal treatment can trigger the generation and outward migration of highly mobile zinc species in the composite system [Ref. R8]. Consequently, the distribution of ZnO can be effectively tailored by manipulating reaction parameters during this distinctive thermal diffusion process, enabling the targeted precise modulation of interfacial interaction in our fabricated Fe C/ZnO magnetoelectric heterostructure. These properties are pivotal for achieving enhanced and tailorable interfacial polarization response behaviors and electromagnetic absorption performance.\nReferences for Response 1: [R1] Dag, S., Wang, S., & Wang, L. W. Large surface dipole moments in ZnO nanorods. Nano Lett. 11, 2348-2352 (2011). [R2] Wu, W., Huang, X., Li, S., Jiang, P., & Toshikatsu, T. Novel three-dimensional zinc oxide superstructures for high dielectric constant polymer composites capable of withstanding high electric field. J. Phys. Chem. C, 116, 24887-24895 (2012). [R3] Lee, Jung-Hoon, et al. Atomic-scale origin of piezoelectricity in wurtzite ZnO. Phys. Chem. Chem. Phys. 17, 7857-7863 (2015). [R4] Wang, L. N., et al. Polarization mechanism of oxygen vacancy and its influence on dielectric properties in ZnO. Chinese Phys. Lett. 28, 027101 (2011). [R5] Yadav, R. S., & Kuřitka, I. Recent advances on outstanding microwave absorption and electromagnetic interference shielding nanocomposites of ZnO semiconductor. Adv. Colloid Interface Sci. 326, 103137 (2024). [R6] Shi, J. et al. Interface engineering by piezoelectric potential in ZnO-based photoelectrochemical anode. Nano Lett., 11, 5587-5593 (2011). [R7] Klingshirn, C. ZnO: material, physics and applications. ChemPhysChem 8, 782-803 (2007). [R8] Feng, X. et al. ZnOx overlayer confined on ZnCr2O4 spinel for direct syngas conversion to light olefins. Nat. Commun. 16, 3711 (2025).\nRevision in the manuscript: In certain dielectrics (e.g., piezoelectric, ferroelectric materials), residual static stress can trigger intrinsic electric polarization16, leading to energy band bending, barrier height modulation, and electron-hole compensation17. Zinc oxide (ZnO) exemplifies this class of functional dielectrics, exhibiting inherent piezoelectric and semiconductor properties18,19. Its pronounced high-temperature thermodynamic instability, which drives distinctive thermal diffusion behavior20, offers a practical pathway to leverage component rearrangement in designing interfacial interaction in the heterostructure systems. (Page 4 in revised manuscript)\n18. Wang, L. N., et al. Polarization Mechanism of Oxygen Vacancy and Its Influence on Dielectric Properties in ZnO. Chinese Phys. Lett. 28, 027101 (2011). 19. Yadav, R. S., & Kuřitka, I. Recent Advances on Outstanding Microwave Absorption and Electromagnetic Interference Shielding Nanocomposites of ZnO Semiconductor. Adv. Colloid Interface Sci. 326, 103137 (2024). 20. Feng, X. et al. ZnOx Overlayer Confined on ZnCr O Spinel for Direct Syngas Conversion to 2 4 Light Olefins. Nat. Commun. 16, 3711 (2025).\nQ2: In the DFT methodology, the DFT+U approach is generally required for Fe-containing systems, but the manuscript does not specify the Hubbard U parameter; this should be clarified.\nResponse 2: Thank you for this insightful comment. We fully agree on the necessity of the DFT+U approach for correctly describing the localized 3d electrons in our Fe C-involved system. In our calculations, we employed the PBE+U method, with an effective Hubbard U parameter of 4.0 eV applied to the Fe 3d orbitals. This choice of U = 4.0 eV is based on its established use in prior DFT studies on similar iron carbides [Ref. R1-2], where it has been shown to provide a balanced description of the electronic structure, magnetic properties, and stability. These details are also supplemented in the Supplementary Notes 2: Density function theory calculation.\nReferences for Response 2: [R1] Dessalle, A. et al. Modulating the Iron Microenvironment for a Cooperative Interplay Between Fe-N-C Single Atoms and Fe C Nanoclusters on the Oxygen Reduction Reaction. Small 21, 3 2409474. (2025). [R2] Chen, S. et al. Interaction between Iron and Graphene Nanocavity: Formation of Iron Membranes, Iron Clusters, or Iron Carbides. ACS Appl. Mater. Interfaces 9, 12100-12108 (2017).\nQ3: The authors should specify whether a high-spin or low-spin configuration and what kind of magnetic interactions were considered in the DFT simulations.\nResponse 3: We thank the reviewer for raising this important point regarding the magnetic configuration. In DFT simulation of the Fe C/ZnO heterostructure, the magnetic ground state of Fe C 3 3 was carefully considered. Based on established literature [Ref. R1], Fe C adopts a ferrimagnetic ordering 3 as its ground state, with local magnetic moments on Fe atoms approximately around 2.0 μB. Accordingly, in our fabricated models, the initial magnetic moments for each Fe atom were set to 2.0 μB, corresponding to a high-spin-like configuration consistent with its metallic character and previous studies [Ref. R1- 3]. ZnO was treated as non-magnetic initially. The calculations were performed using spin-polarized DFT+U (PBE+U) with an effective Hubbard U = 4.0 eV applied to the Fe 3d orbitals to better account for on-site electron correlations [Ref. R4]. Throughout the structural relaxation of the heterojunction, all atomic positions and the supercell were fully optimized while allowing the magnetic moments and ordering to relax freely. This approach ensures that our model not only starts from a physically justified magnetic state but also self-consistently converges to the lowest-energy magnetic configuration of the interface system.\nReferences for Response 3: [R1] Lv, Z. Q. et al. First-principles study on the mechanical, electronic and magnetic properties of Fe C. Comp. Mater. Sci. 44, 690-694 (2008). 3 [R2] Hatcher, N., Madsen, G. K., & Drautz, R. DFT-based tight-binding modeling of iron-carbon. Phys. Rev. B 86, 155115 (2012). [R3] Dobysheva, L. V. The alloyed cementite (Fe–Ni–Cr) C: Local environment, atomic magnetic 3 moments, and magnetization from DFT calculation. Physica B 690, 416279 (2024). [R4] Dessalle, A. et al. Modulating the Iron Microenvironment for a Cooperative Interplay Between Fe-N-C Single Atoms and Fe C Nanoclusters on the Oxygen Reduction Reaction. Small 21, 3 2409474. (2025).\nRevision in the manuscript: Supplementary Notes 2: Density function theory calculation. Spin-polarized calculations were conducted for all scenarios, and a Hubbard-like U parameter (4.0) was introduced to address strong correlation effects at Fe atoms11, and the initial magnetic moments for each Fe atom were set to 2.0 μB12. (Page 6 in revised Supplementary Materials)\n11. Dessalle, A. et al. Modulating the Iron Microenvironment for a Cooperative Interplay Between Fe-N-C Single Atoms and Fe C Nanoclusters on the Oxygen Reduction Reaction. Small 21, 3 2409474. (2025). 12. Lv, Z. Q. et al. First-principles study on the mechanical, electronic and magnetic properties of Fe C. Comp. Mater. Sci. 44, 690-694 (2008). 3\nQ4: The choice of (211) and (101) crystal planes for Fe₃C and ZnO, respectively, in the DFT models should be justified.\nResponse 4: We wish to clarify that the choice of (211) and (101) crystal planes for Fe C and ZnO, 3 respectively, is mainly based on a combined rationale of experimental observation by the spherical aberration-corrected HAADF-STEM and HRTEM (Fig. 1 and Supplementary Fig. 3) and theoretical relevance to our study. For Fe C, the (211) surface is one of the most prominently exposed and stable 3 facets observed experimentally in most Fe C-involved heterojunction systems [Ref. R1], and its atomic 3 configuration, which exposes both Fe and C sites, makes it an optimal model for investigating the atomic-level interfacial electronic interactions [Ref. R2-3]. For ZnO, the (101) surface is one of the most thermodynamically stable and commonly exposed facets under realistic conditions [Ref. R4]. It is characterized by alternating rows of Zn and O atoms, and is widely adopted in DFT studies because of its representative surface structure and electronic reactivity [Ref. R5-6], which is also suitable for investigating the variation of interfacial electrons distribution under the evolution of magnetoelectric interface state in our study. Therefore, these crystal planes were selected to provide a physically meaningful and relevant foundation to reliably model the heterointerface for revealing the involved atomic-level interfacial interactions.\nFigure 1 f Aberration-corrected atomic resolution STEM images of ZnO/Fe3C magnetoelectric interface. g iDPC-STEM images of each component, the inset shows the crystalline models of ZnO (top) and Fe C (bottom). 3\nSupplementary Fig. 3 HRTEM images of a Carbon confined Fe C/ZnO heterointerface (in ZFC-2), b 3 carbon encapsulated Fe C and separated ZnO. 3\nReferences for Response 4: [R1] Yang, X. et al. Constructing oxygen vacancies via engineering heterostructured Fe C/Fe O 3 3 4 catalysts for electrochemical ammonia synthesis. Angew. Chem. Int. Edit. 62, e202304797 (2023). [R2] Chang, J. et al. A Fe Single Atom Seed-Mediated Strategy Toward Fe C/Fe-N-C Catalysts with 3 Outstanding Bifunctional ORR/OER Activities. Adv. Sci. 10, 2301656 (2023). [R3] Das, S. et al. Harnessing the Trade-Off between CoFe/Fe C Interfacial Junction with 3 Unparalleled Potential Gap of 0.58 V for Reversible Oxygen Electrocatalysis: Application toward Liquid and Solid-State Zn-Air Batteries. Adv. Funct. Mater. 34, 2407078 (2024). [R4] Meyer, B., Rabaa, H., & Marx, D. Water adsorption on ZnO (1010): from single molecules to partially dissociated monolayers. Phys. Chem. Chem. Phys. 8, 1513-1520 (2006). [R5] Sun, M. et al. Electronic asymmetry of lattice oxygen sites in ZnO promotes the photocatalytic oxidative coupling of methane. Nat. Commun. 15, 9900 (2024). [R6] Wang, P., et al. Photocatalytic ethylene production by oxidative dehydrogenation of ethane with dioxygen on ZnO-supported PdZn intermetallic nanoparticles. Nat. Commun. 15, 789 (2024).\nRevision in the manuscript: The geometric structure of Fe C, ZnO and carbon were referred to the previous literature13. Based 3 on the HRTEM experimental characterizations, the (211) and (101) crystal faces were selected for Fe C 3 and ZnO layer, respectively. The (211) facet of Fe C is a prominently exposed and stable surface14. Its 3 atomic configuration exposes both Fe and C sites, thus making it the optimal model for studying interfacial electronic interactions at the atomic level. The (101) surface of ZnO is a thermodynamically stable and commonly exposed facet15. Featuring alternating rows of Zn and O atoms, it exhibits a representative structure and electronic reactivity, making it a suitable model for study. (Page 6 in revised Supplementary Materials)\n14. Chang, J. et al. A Fe Single Atom Seed-Mediated Strategy Toward Fe C/Fe-N-C Catalysts with 3 Outstanding Bifunctional ORR/OER Activities. Adv. Sci. 10, 2301656 (2023). 15. Sun, M. et al. Electronic asymmetry of lattice oxygen sites in ZnO promotes the photocatalytic oxidative coupling of methane. Nat. Commun. 15, 9900 (2024).\nQ5: In the XPS analysis, O 1s and C 1s spectra should be included alongside Fe and Zn, and the Fe 2p spectrum should be deconvoluted to show multiple splitting.\nResponse: We wish to clarify that Fig. 1c illustrates the in-situ Ar-etching XPS analysis (XPS depth profiles) for identifying the distribution of Fe C and ZnO in the carbon framework of ZFC-3 by 3 detecting signal intensity variation of the characteristic Fe and Zn elements along the etching depth. As shown in Fig. 1c, the signal and intensity of the Fe 2p were enhanced with the increased etching depth, which could be attributed to the removal of the uppermost effused ZnO layer and the covered carbon shells, thereby enabling the exposure of more underlying Fe C. The in-situ Ar-etched Fe 2p spectrum 3 at a depth of ~400 nm provided the optimum signal-to-noise ratio; thus, the spectrum was deconvoluted to identify the multiplet splitting peaks. The characteristic peaks at 707.2, 720.3, 709.6, 724.1, 711.8, and 726.4 eV were assigned to Fe0 2p , Fe0 2p , Fe2+ 2p , Fe2+ 2p , Fe3+ 2p , and Fe3+ 2p , 3/2 1/2 3/2 1/2 3/2 1/2 respectively, revealing the typical chemical states of the Fe C nanoparticles [Ref. R1]. The trend of an 3 enhanced Fe0 peak signal and a weakened Zn 2p signal with increasing etching depth clearly verifies the outward diffusion of ZnO. Additionally, according to your suggestion, the corresponding in-situ Ar-etching XPS spectra of nonmetal elements (O 1s and C 1s) are also supplemented in Supplementary Fig. 7. It could be detected that the characteristic signal of Zn-O peak [Ref. R2] in O 1s spectra was gradually weakened while the C-C/C=C peak [Ref. R3] in C 1s was enhanced with the increased etching depth, further confirming the occurrence of ZnO outward diffusion induced by the increased Zn species content.\nReferences for Response 5: [R1] Zhuang, L. et al. Enhancing aerobic oxidation of C-H bonds through efficient catalysis of iron MOF-derived Fe C nanoparticles embedded in porous carbon catalysts. Appl. Surf. Sci. 645, 3 158883 (2024). [R2] Al-Gaashani, R., Radiman, S., Daud, A. R., Tabet, N., & Al-Douri, Y. XPS and optical studies of different morphologies of ZnO nanostructures prepared by microwave methods. Ceram. Int., 39, 2283-2292 (2013). [R3] Akhavan, O. Graphene nanomesh by ZnO nanorod photocatalysts. ACS Nano, 4, 4174-4180 (2010).\nRevised in the manuscript: Fig. 1c XPS depth profiles identifying the distribution of ZnO and Fe C through the intensity variation 3 of characteristic Fe 2p and Zn 2p signals.\nSupplementary Fig. 7 XPS depth profiles of O 1s and C 1s in the ZFC-3. The Ar etching removed the uppermost effused ZnO layer and the covered carbon shells, as shown by the attenuated Zn-O peak in O 1s and the vanished C-O peak (from surface-adsorbed oxygen) in C 1s with the etch depth.\nQ6: The Fe 2p XPS (Fig. 1c) and Raman (Supplementary Fig. 4b) spectra exhibit a relatively low signal-to-noise ratio; improved data quality is recommended.\nResponse 6: We would like to clarify that the relatively low signal-to-noise ratio of the Fe 2p XPS spectra at Ar-etching depths below ~100 nm (Fig. 1c) is due to the operating principle of XPS and the intrinsic material properties of ZFC-3. Since XPS primarily detects electrons from the outermost surface (several nanometers in depth) [Ref. R1], and given that the Fe C nanoparticles in ZFC-3 are encapsulated 3 within a carbon framework with the outer surfaces further covered by diffused ZnO layers (Supplementary Fig. 2b and Fig. 3), the Fe 2p signals appear weak while the Zn 2p signals remain strong in the pristine ZFC-3 specimen. Owing to the gradual removal of surficial ZnO layers and carbon substrate by in-situ Ar etching, numerous Fe C nanoparticles were exposure, resulting in a gradually 3 strengthened Fe 2p signal with increasing signal-to-noise ratio as etching depth prolonged [Ref. R2], whereas the Zn 2p signal shows the opposite trend. These in-situ XPS depth profile analyses intuitively reflect the distribution of Fe C and ZnO, providing further evidence for the outward diffusion process 3 of ZnO.\nAdditionally, according to your suggestion, the Raman spectra are retested. As shown in the revised Supplementary Fig. 4b, the peak intensity ratio between D band and G band (I /I ) gradually increase D G with the higher ZnO content, suggesting a rise in defects such as nanovoids within the carbon skeleton [Ref. R3]. And this structural modification could also facilitate the effusion of ZnO from the carbon framework.\nReferences for Response 6: [R1] Li, D. et al. XPS depth profiling of functional materials: applications of ion beam etching techniques. Mater. Chem. Front. 8, 715-731 (2024). [R2] Kim, J. et al. Quasi-graphitic carbon shell-induced Cu confinement promotes electrocatalytic CO2 reduction toward C2+ products. Nat. Commun. 12, 3756 (2021). [R3] Liang, M. et al. A reverse-defect-engineering strategy toward high edge-nitrogen-doped nanotube-like carbon for high‐capacity and stable sodium ion capture. Adv. Funct. Mater. 32, 2209741 (2022).\nSupplementary Fig. 2b SEM images of ZFC-3 sample, the inset shows cross-section of the specimen after Focus ions beam manipulation, all scale bars are 2 μm. The detected wrinkled surface layers with a thickness about 270 nm were the effused ZnO, while the Fe C nanoparticles were mainly anchored in 3 the inner carbon frameworks. This distribution of Fe C and ZnO in ZFC-3 was also well evident by the 3 HRTEM results (Supplementary Fig. 3b-c), where Fe C nanoparticle was encapsulated by the carbon 3 layers while the wrinkled surface region illustrated obvious ZnO lattice structure.\nSupplementary Fig. 3b HRTEM images of b carbon encapsulated Fe C and separated ZnO, c Outside 3 effused ZnO layers.\nRevision in the manuscript: Supplementary Fig. 4b Raman Spectra of as-fabricated ZFC-x system. Characteristic peaks of D band and G band located at 1351 cm-1 and 1594 cm-1 were recognized as the defective and graphited structures of carbon skeleton, respectively. The increasing peak intensity ratio (I /I ) with the higher ZnO content D G suggested the increased structural distortion or defects in carbon substrates, which could facilitate the effusion of ZnO from the carbon framework.\nQ7: Supplementary Figures 10 and 12 can be merged for conciseness.\nResponse 7: According to your suggestions, we have merged the original Supplementary Figures 10 and 12 to the present Supplementary Fig. 13.\nSupplementary Fig. 13 Profiles of a real and b imaginary part of complex permittivity, c conduction loss ( ) and d polarization loss ( ) along the frequency. ′′ ′′ 𝜀𝑐 𝜀𝑝\nQ8: The Cole–Cole plots should be fitted using an appropriate equivalent circuit model to substantiate relaxation behavior.\nResponse 8: According to the reviewer’s valuable suggestion, the Cole-Cole plots of ZFC-x samples (Fig. 3c) were fitted with appropriate equivalent circuit models. In the frequency region corresponding to the strongest dielectric relaxation peaks detected in the tan plots (Fig. 3b), conduction loss and polarization loss jointly contributed to the overall dielectric lo 𝛿 ss𝜀 ability (Supplementary Fig. 13c-d). Thus, the equivalent circuit model comprises three parallel branches (Response Fig. 1): a high-frequency capacitance (C ) branch representing the instantaneous polarizations and providing the ∞ baseline dielectric value for all relaxation processes, a leakage resistance (R ) branch accounting for leak the ohmic loss due to electronic conductivity, and a relaxation branch formed by a series combination of a resistor (R ) and a capacitor (C ) to model the dielectric polarization loss [Ref. R1-3]. The R is 1 1 leak dominated by the intrinsic electronic conductivity of sample, thus, the increased R well accounted leak for the weakened conduction loss ability of the ZFC-x samples (from ZFC-1 to ZFC-2 and ZFC-3). In addition, the combination of resistor and capacitor governs the relaxation time (τ) and its corresponding characteristic frequency (ƒ), which are associated with the polarization responsiveness and the location r of the strongest dielectric loss peak, respectively. The gradually shortened τ from ZFC-3 to ZFC-1 and ZFC-2 revealed the accelerated polarization relaxation response, while the shift of the ƒ towards the r higher frequency was in accord with the variation of strongest dielectric loss peaks observed in the tan plot, indicating the rationality of the fitted equivalent circuit models. 𝛿𝜀\nIn the relaxation branch, the R and C represent the energy dissipation rate and the charge storage 1 1 capacity, respectively, associated with a specific polarization process. In the interfacial polarization dominated ZFC heterostructures, the value of R and C could reflect the potential barriers for electron 1 1 to cross the interface and the amount of the transported electrons [Ref. R3-4]. As the interface strain was implemented and evolved to the tensile strain (from ZFC-3 to ZFC-1 and ZFC-2), the increased capacitance of the C suggested the accumulation and depletion of more electrons on the heterointerface, 1 while the decreased R suggested the reduced interfacial barriers. These enhancements were well 1 assigned to the boosted electron transfer from the interfacial coupling (Fig. 2e) and increased interfacial charge density differential (Fig. 3d), respectively, demonstrating that interfacial strain could effectively accelerate the relaxation kinetics by promoting the interfacial polarization.\nReferences for Response 8: [R1] Shi, X. L. et al. Nonlinear resonant and high dielectric loss behavior of CdS/α-Fe O 2 3 heterostructure nanocomposites. Appl. Phys. Lett. 93, (2008). [R2] Duan, Y., Liu, Y., Cui, Y., Ma, G., & Wang, T. Graphene to tune microwave absorption frequencies and enhance absorption properties of carbonyl iron/polyurethane coating. Pro. Org Coat. 125, 89-98 (2018). [R3] Kuang, D. et al. Large-scale synthesis and outstanding microwave absorption properties of carbon nanotubes coated by extremely small FeCo-C core-shell nanoparticles. Carbon, 153, 52- 61 (2019). [R4] Zhu, T. et al. Controllable synthesis of MOF-derived FexNi1− x@ C composites with dielectric– magnetic synergy toward optimized impedance matching and outstanding microwave absorption. J. Mater. Sci. 56, 592-606 (2021).\nResponse Fig. 1 Fitted equivalent circuit of models of the Cole-Cole plots over the frequency region corresponding to the strongest dielectric relaxation peaks, where the involved circuit elements C , R , ∞ leak R , C assigned to the infinite-frequency capacitance, Ohmic loss resistor, relaxation resistance and 1 1 capacitance, respectively. τ and ƒ were the relaxation time and characteristic relaxation frequency, r receptively.\nFigure 2 e Projected atomic electric field map of ZnO effusion reconstructed magnetoelectric interfaces.\nFigure 3 b Tangent values of dielectric loss. c Cole-Cole plots over the frequency region corresponding to the strongest dielectric relaxation peaks detected in the tan plots. d Reconstructed electronic hologram and corresponding 3D charge density distribution imag 𝛿 e𝜀s.\nQ9: Extracted parameters from Rietveld refinement should be provided to validate structural claims.\nResponse 9: According to your reasonable suggestion, XRD patterns and Rietveld refinement results of the as-fabricated ZFC-x system are supplemented and rechecked (Supplementary Fig. 5), the corresponding refinement parameters (including phase composition ratio, bond length/angle and cell volumes of each phase) are provided in the Supplementary Table 1. As shown in the XRD patterns and Rietveld refinement results, the phase of Fe C and ZnO are well identified in all ZFC-x samples, 3 and the relative weight ratio of ZnO present a gradual augmented trend from the ZFC-1 to ZFC-3, indicating the Zn species content driven phase conversion variation.\nSupplementary Fig. 5 Phase composition identification. XRD patterns of a ZFO@C and b ZFC-x system. Corresponding Rietveld refinement of c ZFC-1, d ZFC-2, e ZFC-3. The extracted parameters were summarized in Supplementary Table 1. The XRD results demonstrated the phase transformation of ZnFe O (ZFO) into Fe C and ZnO (ZFC-x), and a Zn species content induced phase composition 2 4 3 variation process, confirming the ZnO content driven outward gradient diffusion.\nSupplementary Table 1 Extracted parameters from Rietveld refinement\nSample Phase composition Bond length (Å) Bond angle (º) Volume\n(wt. %) a b c α β γ (Å3)\n1-CFZ Fe C (67.1%) 5.0972 6.7530 4.5330 90 90 90 156.032 3\nZnO (32.9%) 3.2581 3.2581 5.2134 90 90 120 47.928\n2-CFZ Fe C (44.3%) 5.0984 6.7553 4.5336 90 90 90 156.143 3\nZnO (55.7%) 3.2581 3.2581 5.2141 90 90 120 47.933\n3-CFZ Fe C (28.6%) 5.1067 6.7693 4.5417 90 90 90 157.00 3\nZnO (71.4%) 3.2648 3.2648 5.2249 90 90 120 48.229\nQ10: The synthesis relies on precise ZnO outward diffusion and strain balancing; therefore, the manuscript should discuss reproducibility across batches and potential challenges in scaling up the process for industrial production.\nResponse 10: Thanks for your valuable comments. We wish to clarify that the ZnO/Fe C 3 magnetoelectric heterostructure with controllable interfacial strain is fabricated by a scalable spray-pyrolysis method. And the gradient ZnO outward diffusion and corresponding interfacial strain are precisely controlled by a ZnO content guided dynamics process, as evident by the theoretical molecular dynamics simulation (Fig. 2a-c and Supplementary Note 1) and series of microstructure characterization (Fig. 2d-e and Supplementary Fig. 10). As suggested, we have supplemented three batches of three distinct ZFC-x samples and carried out a systematic microstructure characterization, including the HRTEM and corresponding GPA, on the interfacial strain state to further verify the reproducibility of ZnO outward diffusion-driven interfacial strain modulation. As shown in Supplementary Fig. 12a, three supplemented ZFC-1 batches present a remarkable compressive strain concentration on the contacted magnetoelectric interface, which are well consistent with the compression state in the manuscript-mentioned ZFC-1 interface (Fig. 2c). Similarly, both of the tensile state in ZFC-2 interface and the relieved state in ZFC-3 are further confirmed by the supplemented several heterointerface regions (Supplementary Fig. 12b-c), demonstrating that the reproducibility and representativity of the qualitative determination of these heterointerface states. Regarding the quantitative relation, although there are slight fluctuations in the average values of these interfacial strain (ε ), most ε values locate in an acceptable error range, xy xy and the whole averaged values of all measured ε are – (11.2 2.0) %, (13.7 3.2) %, and – (0.25 0.6) % in ZFC-1, ZFC-2, and ZFC-3, respectively. These repeatability verification results convincingly evidence the feasibility and effectivity ± ± ± of interfacial strain state regulation by controlling ZnO outward diffusion gradient.\nRegarding the potential for scalable production of ZFC-based magnetoelectric composites, we performed a scaled-up synthesis using an industrial spray-dryer (Response Fig. 2a), achieving kilogram-scale output of spray-dried ZFC precursor powders (Response Fig. 2b). To investigate the consistency and reproducibility of the mass-produced ZFC‑x magnetoelectric composites, we measured the corresponding electromagnetic parameters and compared them with those of bench-scale samples. As shown in Response Fig. 1c, the profiles of permittivity in the scaling up-produced ZFC-x samples nearly present the same frequency-dependency properties as that of the bench-scale ZFC-x, and the average values with a slight variance are also closed to that of the bench-scale ZFC-x samples. These scaling-up verification results further suggest that the fabrication process of ZFC-based magnetoelectric composites exhibit promising application potential for meeting the increasing demands of high-performance electromagnetic wave absorption materials.\nResponse Fig. 2 Industrial production of ZFC-based magnetoelectric composite EM absorbers. Digital photographs for a Industrial-level spray-drying production process, b Kilogram-scale production of spray-dried ZFC precursors and its derivate ZFC-based composites. c Comparison of real ( ) and imaginary ( ) part of permittivity between the bench-scale and the industrialized scaled-up ZFC-x samples. 𝜀′ 𝜀′′\nSupplementary Fig. 12 Characterizations of interfacial strain states. HRTEM images, GPA results, and corresponding statistic histograms of ε strain values in the selected interfacial regions of a ZFC- xy 1, b ZFC-2, and c ZFC-3 heterostructures from different batches. Scale bars of HRTEM in a, b and c are 1 nm and 2 nm, respectively. These supplemented GPA distribution and corresponding strain statistics present approximate results to that of the main text (Fig. 2c and Supplementary Fig. 10), qualitatively demonstrating the reproductivity for the deterministic fabrication of the ZFC interfacial strain via the precise control of gradient ZnO diffusion.\nQ11: Long-term stability under cyclic heating or humid conditions should be examined, as Fe₃C and carbon shells may degrade upon oxidation.\nResponse 11: We agree with the reviewer's comment regarding the potential degradation of the carbon shells under high-temperature air conditions, as indicated by the TG curves where the decomposition of ZFC‑x starts above approximately 300 °C (Supplementary Fig. 4a). We wish to clarify that carbon substrates also play significant role in modulating the magnetoelectric interface by supporting and controlling the rearrangement of involved nanoparticles in our work, and the carbon decomposition inevitably affected this strain modulation strategy. According to your suggestion, we have evaluated the long-term cyclic thermal stability of the optimal ZFC-2 sample at 200 °C and 300°C, corresponding to a temperature below and at its decomposition point, respectively. Similar to the previous TG curves, the cyclic TG results (Response Fig. 3a) showed the occurrence of weight loss under 300°C, which was mainly attributed to the carbon decomposition. Notably, the sample could maintain a superior thermal stability below this temperature threshold. Regarding the potential oxidation induced phase transformation, the involved phase composition and valence state variation of these samples after cyclic heating test were examined. As shown in XRD patterns (Response Fig. 3b), only slight intensity variations without detectable shifts of the Fe C characteristic peaks were recorded, and no signals of 3 iron oxides species were identified, indicating the phase stability. In addition, the deconvoluted Fe 2p spectra also illustrated the existence of Fe0 2p3/2 and Fe0 2p1/2 (Response Fig. 3c), further confirming the thermal stability of the involved Fe C nanoparticles. 3\nThe humidity stability was evaluated by characterizing the variations in phase composition and chemical state of the two aging ZFC-2 samples. These include one sample subjected to 600 days of natural aging in ambient air, and another stored for 60 days at 75% RH in a constant temperature and humidity chamber. As shown in the XRD results (Response Fig. 3b), neither the characteristic peaks of Fe C and ZnO nor any new peaks attributable to oxides or hydroxides exhibited detectable variations. 3 Similarly, the Fe 2p spectra also showed negligibly slight fluctuation of the involved Fe valence states (including Fe0 2p , Fe0 2p , Fe2+ 2p , Fe2+ 2p , Fe3+ 2p , and Fe3+ 2p ,) in the two specimens, 3/2 1/2 3/2 1/2 3/2 1/2 which demonstrated the superior long-term humidity stability of the as-fabricated magnetoelectric heterostructures. Additionally, we also investigate the EM properties variation of these mentioned-above specimens after long-term cyclic thermal or humidity test, employing the permittivity as the evaluation index because of its dominated role in the eventual absorption performance in this work. As shown in Response Fig. 3d, all specimens except the one treated at 300 °C exhibited similar permittivity profiles to that of the pristine ZFC-2, with fluctuations below only 8%. This result further verifies the critical role of the carbon substrates in protecting the magnetoelectric heterostructures and in modulating the electromagnetic properties.\nAlthough the ZFC-2 is hard to withstand very high temperatures due to the intrinsic limits of most carbon-based nanomaterial [Ref. R1], it is noteworthy that in practical applications, such carbon-based powder-type absorbers are commonly used as encapsulated functional fillers within substrates like resins, gels, rubber, cements and ceramics [Ref. R2-5]. And these outer encapsulations with better high-temperature resistance further safeguards the absorber powders from oxidation and degradation at elevated temperatures. Consequently, our as-fabricated magnetoelectric composite ZFC system with superior humidity resistance and qualified long-term thermal stability can satisfy majority of civilian application situations [Ref. R6], including EM protection against signals from common devices like WiFi routers and mobile phones, as well as microelectronic components such as central and graphics processing unit (CPU and GPU).\nReferences for Response 11: [R1] Sádovská, G. et al. The thermal stability of carbon materials in the air: Quantitative structural investigation of thermal stability of carbon materials in air. Carbon 206, 211-225 (2023). [R2] Huang, Y. et al. The microwave absorption properties of carbon-encapsulated nickel nanoparticles/silicone resin flexible absorbing material. J. Alloy. Compd. 682, 138-143 (2016). [R3] Chung, D. D. L. A review of microwave absorption and reflection by cement‐based materials, with emphasis on electromagnetic interference shielding and admixture effects. Adv. Funct. Mater. 34, 2408220 (2024). [R4] Li, X., Zhu, L., Su, Z., Li, X., Yu, W., & Zou, B. Design and properties of ceramic-based microwave absorbing composites with carbon fibres as absorber. Ceram. Int., 50, 6836-6844 (2024). [R5] Liu, Y. et al. Multi-interfacial heterostructure design of carbon fiber/silicone rubber-oriented composites for microwave absorption and thermal management. Adv. Funct. Mater. 34, 2411573 (2024). [R6] Zhao, Z. et al. Advancements in microwave absorption motivated by interdisciplinary research. Adv. Mater. 36, 2304182 (2024).\nResponse Fig. 3 Long-term stability assessments. a Cyclic TG results of ZFC-2 specimens under 300 and 200 °C. b XRD patterns and c Fe 2p XPS spectra of ZFC-2 specimens after aging 600 days in air, storage under 75% RH ambience for 60 days, and cyclic heating. d Real ( ) and imaginary ( ) part ′ ′′ of permittivity profiles along the frequency. 𝜀 𝜀\nQ12: While qualitative relationships between strain, dielectric loss, and absorption are established, quantitative correlations would greatly strengthen the mechanistic understanding.\nResponse 12: Thanks reviewer for the recognition on our established relationships between strain, dielectric loss, and absorption. We wish to clarify that the motivation of this work is to design functional magnetoelectric heterostructure with tunable strain state of interface by a facile strategy of manipulating the ZnO oriented diffusion gradient. Systematical structure characterizations based on advanced electronic microscopy technologies (such as aberration-corrected atomic resolution STEM, DPC and electron holograms) combine with multidimensional theoretical simulations reveal that the diffusion-driven interface strain evolution can effectively reconfigure the interfacial electric field coupling behaviors, which further tailors the polarization ability and the eventual optimization of electromagnetic absorption properties.\nAchieving quantitative correlations between interfacial strain and polarization, the present interfacial strain engineering driven by gradient oriented diffusion remains challenge. The difficulty stems not only from the inherent complexity of the magnetoelectric interface but also from the pronounced size effects and potential quantum responses in the composite nanomaterials system [Ref. R1,2]. Different from the monodispersed nanocrystal heterostructures with uniform size [Ref. R3,4], the sizes of our fabricated Fe C/ZnO magnetoelectric heterostructures mainly located in a controlled range of 3 10~60 nm (Supplementary Fig. 2c). The dominance of surface atoms in these relatively fine particles and the size-dependent electronic structure collectively give rise to a strain field that is highly sensitive to minuscule variations in morphology and composition, eventually resulting in a ranged fluctuation of interfacial strain values [Ref. R5-7]. Nevertheless, our proposed oriented diffusion strategy could qualitatively program the interfacial strain state, evolving from the initial compression to tension and terminal relaxation as the ZnO outward diffused to the outer. Remarkably, specimens from different batches also consistently exhibited the same interfacial strain state (such as compressive strain in ZFC-1, tensile strain in ZFC-2, and relieved strain in ZFC-3), as evident by the HRTEM images and corresponding GPA results (Supplementary Fig. 12), confirming the semi-quantitative controllability of magnetoelectric interfacial strain state regulation. Unlike previously reported magnetoelectric composite nanoparticles, which primarily focused on material fabrication with limited tunability, our strategy of semi-quantitative interfacial strain modulation offers an effective pathway to bridge strain-polarization coupling by programming the interfacial contact behavior between the dielectric and magnetic components. And we found that the interfacial strain state evolution effectively tailored the polarization relaxation time. Specifically, the relaxation time shortened as strain implemented due to faster electron transport and wider interfacial dipoles distribution mediated by enhanced interfacial coupling, thereby enhancing the polarization responsiveness and dielectric loss ability towards the incident EM wave (Fig. 2 and 3). Eventually, the magnetoelectric heterostructure composite with interfacial strain exhibited the enhanced broadband absorption performance (Fig. 4a). Therefore, such a constructed investigation network from microscale materials design to atomic scale mechanism deciphering and macroscale performance controllability has provided a significant guidance for developing advanced EM absorption materials.\nReferences for Response 12: [R1] Miao, Y., Zhao, Y., Zhang, S., Shi, R., & Zhang, T. Strain Engineering: A Boosting Strategy for Photocatalysis. Adv. Mater. 34, 2200868 (2022). [R2] Yang, X., Wang, Y., Tong, X., & Yang, N. Strain Engineering in Electrocatalysts: Fundamentals, Progress, and Perspectives. Adv. Energy Mater. 12, 2102261 (2022). [R3] He, T. et al. Mastering the surface strain of platinum catalysts for efficient electrocatalysis. Nature 598, 76-81 (2021). [R4] Park, J., Kim, H. K., Park, J., Kim, B., Baik, H., Baik, M. H., & Lee, K. Flattening bent Janus nanodiscs expands lattice parameters. Chem 9, 948-962 (2023). [R5] Emamy, H., Kumar, S. K., & Starr, F. W. Diminishing interfacial effects with decreasing nanoparticle size in polymer-nanoparticle composites. Phys. Rev. Lett. 121, 207801(2018). [R6] Jiang, Z. et al. Lattice strain and Schottky junction dual regulation boosts ultrafine ruthenium nanoparticles anchored on a N-modified carbon catalyst for H production. J. Am. Chem. Soc. 2 144, 19619-19626 (2022). [R7] Kang, Z. et al. Interface engineering for modulation of charge carrier behavior in ZnO photoelectrochemical water splitting. Advanced functional materials, 29(15), 1808032 (2019).\nSupplementary Fig. 2 SEM images and corresponding size distribution statistics of b as-fabricated ZFC-x microspheres. c STEM images and corresponding size distribution statistics of nanoparticles in ZFC-x samples.\nSupplementary Fig. 12 Characterizations of interfacial strain states. HRTEM images, GPA results, and corresponding statistic histograms of ε strain values in the selected interfacial regions of a ZFC- xy 1, b ZFC-2, and c ZFC-3 heterostructures from different batches. Scale bars of HRTEM in a, b and c are 1 nm and 2 nm, respectively. These supplemented GPA distribution and corresponding strain statistics present approximate results to that of the main text (Fig. 2c and Supplementary Fig. 10), qualitatively demonstrating the reproductivity for the deterministic fabrication of the ZFC interfacial strain via the precise control of gradient ZnO diffusion.\nQ13: A comparison table contrasting EAB, reflection loss, and filler loading with representative Fe-, Co-, and Ni-based hybrid absorbers would help contextualize the performance gains.\nResponse 13: According to your valuable suggestion, we have compared the EAB, reflection loss and filler loading between ZFC system and recently reported representative Fe-, Co-, and Ni-based hybrid absorbers, and the results are shown in Supplementary Table 3. It can be observed that the tensile-strain enhanced ZFC-2 heterostructure exhibits a wider EAB and a stronger reflection loss at a relatively low filler loading, outperforming majority of reported Fe-, Co-, and Ni-based hybrid absorbers. This performance comparison further demonstrates that effective interface strain regulation is conducive for improving the electromagnetic absorption properties of magnetoelectric composites.\nRevision in the manuscript: The Fe C/ZnO heterostructure within tensile strain exhibited a broad EABmax of 7.38 GHz at a 3 thickness of 2.2 mm, covering entire Ku-band (from 12 to 18 GHz, the primary application band for radar stealth), outperforming majority of reported EM absorption materials (Fig. 4b and Supplementary Table 3, 4). (Page 10 in revised manuscript)\nSupplementary Table 3 Electromagnetic absorption performance comparisons among typical Fe-, Co-, Ni-based hybrid absorbers.\nType Absorbers EAB (GHz) RL (-dB) Filling wt% Ref.\ndesab-iN\netisopmoC\nNi/MXene/Carbon 5.15 41.55 20 27\nCCMC/ZnO@Ni 4.90 64.00 40 28\nNi/NiO@PCN 2.11 42.54 20 29\nNi/NiS/NiS @C 4.25 44.60 40 30\n2\ndesab-oC\netisopmoC\nMxene/Co@C 4.10 61.42 20 31\nCeO /C/Co@NCNTs 6.80 47.70 35 32\nCo/MnO/C 5.60 51.83 60 34\netisopmoC\ndesab-eF\nFe/Fe C@C 6.00 64.40 45 35\n7 8 2 3\nFeSiAl@ZnFe O @ZnO 3.28 72.40 50 37\n2 4\nCIP@ZnO-350 7.09 55.35 70 38\nFe C/ZnO@C-2 7.38 52.60 40 This work\nResponse 14: According to your valuable suggestion, we have revised the introduction and supplied the discussion of potential applicability of large-scale EM protection materials in industry and architecture.\nRevision in the manuscript: EM absorption materials provide an effective solution to this issue by harvesting the EM wave and dissipating it into thermal energy. This fundamental energy-dissipation mechanism endows them with EM protection capability as functional fillers, enabling versatile applications that span from micro-nano high-precision electronics (such as on-chip components and integrated RF modules)5 to large-scale architectural infrastructures6, 7 (such as hospitals, laboratories, and transportation hubs) for industrial interference suppression and environmental shielding. (Page 3 in revised manuscript)\n5. Zhao, Z. et al. Advancements in Microwave Absorption Motivated by Interdisciplinary Research. Adv. Mater. 36, 2304182 (2024). 6. Wang, X., Li, Q., Lai, H., Peng, Y., Hou, C., & Xu, S. A Bionic Grooving All‐Cementitious‐ Dielectric Metastructure with Unprecedented Wide‐Angle Broadband Electromagnetic Wave Absorption Properties. Adv. Funct. Mater. 2425949 (2025). 7. Lei, D. et al. A state-of-the-art on Electromagnetic and Mechanical Properties of Electromagnetic Waves Absorbing Cementitious Composites. Cement Concrete Comp., 157, 105889 (2025).\nReviewer #2 (Remarks to the Author):\nIn the manuscript \"Oriented Atomic Diffusion Tailors Strain-Polarization Coupling for Broadband Electromagnetic Absorption,\" the authors explore interfacial strain engineering to enhance the electronic properties of electromagnetic materials. They created a carbon-confined Fe C/ZnO 3 magnetoelectric heterointerface, where varying Zn precursor content influences the effusion of ZnO through the interface, leading to carbon-encapsulated yolk-shell nanostructures. The strain transition from compressive to tensile alters interfacial atomic electric fields, shifting from enhanced to decoupled coupling. This strain effect modifies the electronic structures, improving polarization relaxation and electron transport. The resulting heterostructure exhibited impressive electromagnetic absorption properties, with a broad effective absorption bandwidth of 7.38 GHz and an over 95% radiation attenuation efficiency from 2 to 18 GHz. This work significantly expands the design framework for advanced electromagnetic functional materials. The authors have thoroughly studied their samples and provided both theoretical simulation and application-based evidence to support their claims. However, there are a few questions to consider before publication.\nGeneral Response: We thank the reviewer for their careful reading of our manuscript and for noting that our work significantly expands the design framework for advanced electromagnetic functional materials.\nQ1: With the increase of ZnO diffusion, a variation in carbon shell thickness from ~635 nm to ~860 nm to ~270 nm is observed in the ZFC-x samples. Please explain why this large variation is observed.\nResponse 1: We wish to clarify that the measured thickness of ~270 nm corresponds to the effused ZnO layers on the ZFC-3 sample (the inset of Supplementary Fig. 2b), which is well confirmed by the HRTEM results of the ZnO lattice on the outer wrinkled surface (Supplementary Fig. 3c). The overall carbon framework evolves from a hollow structure with a carbon shell in ZFC-1 and ZFC-2 to a solid structure coated with ZnO layers in ZFC-3 as the ZnO diffusion gradient increased till the eventual effusion (Supplementary Fig. 2b). This carbon structure evolution from hollow to solid spheres can be attributed to the interplay between the Kirkendall effect and precursor concentration. At lower metal salt concentrations (ZFC-1), the outward diffusion of metal species during annealing surpasses the inward diffusion, leading to vacancy accumulation and the formation of a hollow cavity (Kirkendall effect) [Ref. R1-2]. Due to the low concentration, the outward diffusion of metal species lacks sufficient driving force to breach the outer carbon layer, resulting in their confinement within the carbon matrixes (ZFC-1). As the ZnO concentration increases, the increased metal flux and concomitant carbon redistribution widen the metal/carbon interfacial region [Ref. R3], making the carbon shell appear thicker, as evident by the increased carbon shell thickness from ~635 nm to ~860 nm. The outward diffusion, promoted by the higher ZnO concentration, manifests as distinct bulges on the surface of the ZFC-2 microspheres. Ultimately, as the concentration increased to cause effusion of ZnO (ZFC-3), the excessive metal species fill the interior nanovoids (Supplementary Fig. 2c), suppressing the Kirkendall effect and leading to the formation of a densely solid composite architecture. Meanwhile, the higher concentration increases the nucleation site density, which promotes the coalescence of outwardly effused ZnO nuclei into continuous wrinkled layers rather than discrete bulges.\nReferences for Response 1: [R1] Bin, D.S. et al. Manipulating particle chemistry for hollow carbon-based nanospheres: synthesis strategies, mechanistic insights, and electrochemical applications. Acc. Chem. Res., 54, 221-231 (2020). [R2] Wang, L. et al. Orientation growth modulated magnetic-carbon microspheres toward broadband electromagnetic wave absorption. Carbon, 172, 516-528 (2021). [R3] Fan, H. J. et al. Influence of surface diffusion on the formation of hollow nanostructures induced by the Kirkendall effect: the basic concept. Nano Lett., 7, 993-997 (2007).\nSupplementary Fig. 2 SEM images and corresponding size distribution statistics of b as-fabricated ZFC-x microspheres. c STEM images and corresponding size distribution statistics of nanoparticles in ZFC-x samples. The scale bars in b and c are 5 μm, 2 μm, and 100 nm, respectively. After a subsequent heat treatment of spray-dried precursors, the sizes of as-fabricated ZFC-x microspheres reduced owing to the pyrolysis of carbon-based matrixes. The contraction of the hollow structure caused an increase in carbon shell thickness from ~635 nm to ~860 nm and its eventual transformation into a solid structure. The effused ZnO formed wrinkled surface layers with a thickness of ~270 nm and packaged on the outside of the solid structure. Numerous nanovoids surrounded the nano heterostructures were detected owing to the consumption of carbon matrix during the carbothermal, forming yolk-shell-like structures. These voids were gradually filled by ZnO till the completion of outwards effusion of ZnO.\nSupplementary Fig. 3 HRTEM images of a Carbon confined Fe C/ZnO heterointerface, b carbon 3 encapsulated Fe C and separated ZnO, c Outside 3 effused ZnO layers. The breakdown of Fe C/ZnO 3 3 heterointerface was evidenced by component separation, with carbon layers identified within the interfacial region between the separated components. ZnO characteristic crystal facets were identified in the surface wrinkled layer, confirming the outward diffusion.\nQ2: The x-axis in Fig. 3f represents discrete ZnO samples; however, the graph displays a continuous 2D plot. Please clarify how this graph is created.\nResponse 2: Thanks for your reasonable correction. We wish to clarify that Fig. 3f is intended to demonstrate how the ratio of polarization loss ( ) to conduction loss ( ) varies across a continuous ′′ ′′ frequency range in three fabricated ZFC-x samp𝜀l𝑝es. This visualization h𝜀e𝑐lps to intuitively differentiate the relative contributions of the two dielectric loss mechanisms in the tested frequency range. As you pointed that the x-axis in Fig. 3f represents discrete ZFC-x samples, we agree that the original continuous 2D plot might cause misinterpretation. Accordingly, we have revised Fig. 3f into a split heatmap format to properly present the variation of the ratio across the measured frequency ′′ ′′ range for each sample. 𝜀𝑝/𝜀𝑐\nRevision in the manuscript: Figure 3f The frequency dependence of ratio in ZFC-x. ′′ ′′ 𝜀𝑝/𝜀𝑐\nQ3: The authors state in lines 339-340 that they tested the electron conductivity (σ) of the samples using a four-probe measurement. Based on this conductivity (σ), they categorized the dielectric loss (ε′′) into conduction loss (ε ′′) and polarization relaxation (ε ′′). However, they did not provide any details or data regarding this measurement.\nResponse 3: Thanks for the reviewers’ kind reminding. To distinguish the contributions of polarization and conduction loss, we measured the electrical conductivity of ZFC-based samples with the same paraffin filler ratio as used in the electromagnetic parameter measurements. We have supplemented the details of the related four-probe electrical conductivity measurements in the ‘Supplementary Methods: Electromagnetic parameters test and performance calculation’ section.\nRevision in the manuscript: Supplementary Methods: Electromagnetic parameters test and performance calculation. In the non-ideal Debye relaxation model, the contribution of conduction loss and polarization loss can be quantitatively fitted by the following formula: (4) ′ 𝜀𝑠+𝜀∞ 2 ′′ 2 𝜀𝑠−𝜀∞ 2 (𝜀 − 2 ) + (𝜀 ) = ( 2 ) (5) ′′ ′′ ′′ 𝜎 2𝜋𝑓𝜏 𝜀 = 𝜀𝑐 +𝜀𝑝 = 2𝜋𝑓𝜀0 + (𝜀𝑠 −𝜀∞)1+(2𝜋𝑓) 2 𝜏 2 where the and refers to the contribution of conduction loss and polarization loss, respectively; ′′ ′′ is the te𝜀s𝑝ted elec𝜀t𝑐ronic conductivity using a four-probe tester. For the σ measurement, the ZFC samples (40 wt%) were evenly immersed in molten paraffin and molded into a solid disk-shaped 𝜎 specimen (diameter: 7.0 mm, thickness: 2.5 mm). Then, the test specimen was placed on a four-probe tester using a linear four-point probe head with a probe spacing of 0.5 mm, and the probes are aligned along a diameter and meticulously centered on the sample. A constant current is applied through the outer pair of probes, while the resultant voltage drop is measured between the inner pair. The measured V/I ratio is then converted to electronic resistivity according to ASTM F84 standard4. The eventual σ is subsequently derived as the reciprocal of the corrected resistivity, which were listed in the Supplementary Table 2. (Page 3 in revised Supplementary Materials)\n4. Hu, B., et al. Non-Hermitian topological whispering gallery. Nature, 597, 655-659 (2021).\nSupplementary Table 2 Electron conductivity of tested ZFC-x based specimens.\nSamples Electronic conductivity (S/m)\nZFC-1 0.83\nZFC-2 0.48\nZFC-3 0.32\nQ4: The VNA typically provides S-parameters. What method is used for converting these S-parameter data into intrinsic sample parameters, such as permittivity and permeability?\nResponse 4: Thank you for this important question. We agree with the reviewer mentioned that the VNA fundamentally measures S-parameters. The complex permittivity and permeability values are derived from the calibrated S-parameters using a well-established inversion algorithm (Nicolson–Ross–Weir method [Ref. R1,2]) based on electromagnetic theory. The process is automated within the measurement system (VNA, Agilent N5230C, and its companion software, Keysight Material Measurement Suite), which may give the impression of \"direct measurement.\" The measurement of permittivity and permeability by VNA is detailed below:\nThe tested coaxial ring specimen was securely placed between the outer and inner conductors. Prior to measurements, a calibration procedure was carried out using an Agilent calibration kit (specifically, a Short-Open-Load-Thru calibration) to ensure the accuracy. The electromagnetic scattering parameters (S-parameters, S , where i, j = 1, 2) were measured over the frequency range of 2–18 GHz using the ij transmission/reflection coaxial line method with a network analyzer (Agilent Technologies, N5230C). The complex permittivity and permeability were subsequently derived from the measured S-parameters via the Nicolson–Ross–Weir method [Ref. R3,4]. According to your comments, we have also supplemented the mentioned descriptions into the section of ‘Supplementary Methods: Electromagnetic parameters test and performance calculation’.\nReferences for Response 4: [R1] Zhang, Y. et al. Electromagnetic interference shielding effectiveness of high entropy AlCoCrFeNi alloy powder laden composites. J. Alloy. Compd. 734, 220-228 (2018). [R2] Liu, Q. et al. Metal organic framework-derived Fe/carbon porous composite with low Fe content for lightweight and highly efficient electromagnetic wave absorber. Chem. Eng. J. 314, 320-327 (2017). [R3] Nicolson, A. M., & Ross, G. F. Measurement of the intrinsic properties of materials by time-domain techniques. IEEE T. Instrum. Meas. 19, 377-382 (2007). [R4] Weir, W B. Automatic measurement of complex dielectric constant and permeability at microwave frequencies. P. IEEE 62, 33-36 (2005).\nRevision in the manuscript: Supplementary Methods: Electromagnetic parameters test and performance calculation. The electromagnetic (EM) parameters of the tested samples were obtained using the coaxial line method on a vector network analyzer. Specifically, the ZFC-x composite microspheres (40 wt%) were evenly immersed in molten paraffin and molded into a coaxial ring (outer diameter: 7.0 mm, inner diameter: 3.0 mm). The tested coaxial ring specimen was securely placed between the outer and inner conductors. Prior to measurements, a calibration procedure was carried out using an Agilent calibration kit (specifically, a Short-Open-Load-Thru calibration) to ensure the accuracy. The electromagnetic scattering parameters (S-parameters) were measured over the frequency range of 2–18 GHz using the transmission/reflection coaxial line method with a network analyzer (Agilent Technologies, N5230C). The complex EM parameters including complex permittivity and permeability were subsequently derived from the measured S-parameters via the Nicolson–Ross–Weir method1, 2. (Page 2 in revised Supplementary Materials)\n1. Liu, Q. et al. Metal Organic Framework-derived Fe/carbon Porous Composite with Low Fe Content for Lightweight and Highly Efficient Electromagnetic Wave Absorber. Chem. Eng. J. 314, 320-327 (2017). 2. Weir, W B. Automatic Measurement of Complex Dielectric Constant and Permeability at Microwave Frequencies. P. IEEE 62, 33-36 (2005).\nQ5: Additionally, in the equations for input impedance and reflection (Equations 6 and 7 in the supplementary materials, lines 46 and 47), it appears that a constant term related to the free space impedance (Z ) is absent.\nResponse 5: Thanks for the reviewers’ kind correction. We have supplemented the absent space impedance (Z ) and rechecked the electromagnetic parameters calculation equations. The corrected 0 equations are presented in the revised version of ‘Supplementary Methods: Electromagnetic parameters test and performance calculation’ section.\nRevision in the manuscript: The EM wave absorption performance is evaluated by the reflection loss (RL), and the RL values were calculated according to transmission line theory using the measured EM parameters as follows: (6) 𝜇𝑟 2𝜋 𝑍𝑖𝑛 = 𝑍0 √𝜀𝑟 𝑡𝑎𝑛ℎ[𝑗( 𝑐 )𝑓𝑑√𝜇𝑟𝜀𝑟] (7) where 𝑅 𝐿(𝑑𝐵 i s = the 2 0 in 𝑙 p 𝑜 𝑢 𝑔 𝑡 | r ( 𝑍 𝑍0 ) / ( 𝑍 𝑍0 ) | , is the free space impedance whose value is 377.3 Ω; a 𝑍 𝑛𝑖𝑛d are the relative complex permittiv 𝑍 𝑖t0y and permeability ( ), ′ ′′ ′ ′′ resp 𝜀 e𝑟ctively; 𝜇 𝑟 is the velocity of light and equal to 3 × 108 m s−1; is 𝜀 t𝑟he = th 𝜀 ic − kn 𝑗 e 𝜀 ss , o 𝜇 f𝑟 th = e 𝜇 spe − ci 𝑗 m 𝜇 en, and is the frequency of electromagnetic wave. (Page 3 in revised Supplementary Materials) 𝑐 𝑑 𝑓\nQ6: The authors developed an electromagnetic (EM) metamaterial by combining a strain-mediated Fe C/ZnO heterostructure with resin, molding it into an 18 × 18 cm periodic metastructure to achieve 3 full-band absorption. However, the rationale behind selecting this specific metastructure and how its dimensions were determined remains unclear. A brief explanation of the reasoning behind this choice would be beneficial for the article.\nResponse 6: Thanks for the reviewers’ reasonable comments. We wish to clarify that the design of this periodic metastructure aims to broaden the EAB ranging from 10.62 to 18.00 GHz in original strain-mediated Fe C/ZnO heterostructure (ZFC-2) to the full-band frequency (2-18 GHz) absorption. 3 According to the equivalent medium theory, the periodic structure at subwavelength (for example, the wavelength at the frequency range of 2-18 GHz decreased from 15.0 to 1.67 cm) can produce uniform electromagnetic response [Ref. R1]. And the design principle of such a pyramid-like metastructure for broadband EM absorption lies in impedance gradient matching and spatial dispersion of resonant frequencies. The tapered geometry creates a transition in effective impedance from the tip (near free-space) to the base (near the substrate), which minimizes reflection at the air-material interface, allowing waves to enter efficiently. Simultaneously, different heights of the structure resonate at different frequencies, and these multiple resonances spatially overlap and merge, resulting in a continuous, ultra-wide absorption band [Ref. R2-4]. Different from the conventional solid pyramid structure, an internal perforation is set in the periodic unit (Supplementary Fig. 24), which can act as resonators for inducing additional localized resonances that synergize with the primary pyramid's gradient. This perforation can effectively broaden the absorption bandwidth, particularly extending performance toward lower frequencies. Meanwhile, strategic porosity significantly reduces the material's areal density while largely maintaining its external electromagnetic profile, achieving crucial weight savings for practical applications [Ref. R5-6]. Based on these considerations, an innovative metastructure is developed, as characterized by pyramid-shaped periodic units with a perforated architecture. Then, the involved dimensions for this proposed periodic metastructure were precisely optimized by a series of reflection loss (RL) simulations in the tested frequency region of 2-18 GHz using the EAB as the objective function. Eventually, the as-present ZFC-x based metamaterial with specific dimensions was deterministically fabricated, as evident by the geometry parameters varied 1D RL profiles Response Fig. 4. According to your suggestion, these descriptions of metamaterials design principle was supplemented in the revised ‘Supplementary Note 4: Electromagnetic simulation and metamaterials design’.\nReferences for Response 6: [R1] Zhang, T. et al. Polarization insensitive hierarchical metamaterial for broadband microwave absorption with multi-scale optimization and integrated design. Compos. Sci. Technol. 228, 109643 (2022). [R2] Ye, X., et al. Optimization design of 3D-printed pyramid structure for broadband electromagnetic wave absorption. J. Alloy. Compd. 963, 171258 (2023). [R3] Huang, Y. et al. Ultrathin flexible carbon fiber reinforced hierarchical metastructure for broadband microwave absorption with nano lossy composite and multiscale optimization. ACS Appl. Mater. Interface 10, 44731-44740 (2018). [R4] Chen, Z. et al. Bioinspired moth-eye multi-mechanism composite ultra-wideband microwave absorber based on the graphite powder. Carbon 201, 542-548 (2023). [R5] Ma, Y. et al. Resonant cavity structural design of carbon-based intrinsic metamaterial absorbers for broadening the effective absorption bandwidth. Chem. Eng. J., 500, 157508 (2024). [R6] Qu, Ning, et al. 2D/2D coupled MOF/Fe composite metamaterials enable robust ultra– broadband microwave absorption. Nat. Commun. 15 5642 (2024).\nSupplementary Fig. 24 Front/side and top view of the periodic unit in ZFC-based EM metamaterials. The marked geometric parameters are supplied in the Supplementary Table 5.\nResponse Fig. 4 Optimization of geometry dimensions in the ZFC-x based Metamaterials. Effect of varied geometric parameters a h , b h , c h , d h , e L , f L , g L , h L , i L , j L on the profiles of 2 3 4 5 2 3 4 5 6 7 RL values versus frequency.\nRevision in the manuscript: Supplementary Note 4: Electromagnetic simulation and metamaterials design. The design principle of such a pyramid-like metastructure for broadband EM absorption lied in impedance gradient matching and spatial dispersion of resonant frequencies. The tapered geometry created a transition in effective impedance from the tip (near free-space) to the base (near the substrate), which minimized reflection at the air-material interface, allowing waves to enter efficiently. Simultaneously, different heights of the structure resonated at different frequencies, and these multiple resonances spatially overlapped and merged, resulting in an ultra-wide absorption band24. Different from the conventional solid pyramid structure, an internal perforation was set in the periodic unit (Supplementary Fig. 24), which could act as resonators for inducing additional localized resonances that synergize with the primary pyramid's gradient. This effectively broadened the absorption bandwidth, particularly extending performance toward lower frequencies25. This strategic porosity significantly reduced the material's areal density while largely maintaining its external electromagnetic profile, achieving crucial weight savings for practical applications. And the involved dimensions for this proposed periodic metastructure were optimized by a series of reflection loss (RL) simulations in the tested frequency region of 2-18 GHz using the effective absorption bandwidth (EAB) as the objective function. Eventually, an innovative metastructure was developed, characterized by pyramid-shaped periodic units with a perforated architecture. (Page 9 in revised Supplementary Materials)\nQ7: There are also a few typing and grammatical errors in both the main article and the supplementary article. The annotated documents highlighting these errors are attached for consideration.\nResponse 7: Thanks for your careful reading and kind annotations. We have carefully corrected all formatting and writing issues in both the Manuscript and the Supplementary Information, and have thoroughly reviewed these files prior to resubmission. Once again, we are deeply grateful for your insightful comments, which have made a significant contribution to the revision of our paper.\nRevision in the manuscript: In certain dielectrics (e.g., piezoelectric, ferroelectric materials), residual static stress can residual static stress can trigger intrinsic electric polarization, …. (Page 4 in revised Manuscript)\nIn contrast, remarkable fluctuation characterized by the uneven arrangement of positive and negative charge, … (Page 9 in revised Manuscript)\nIn addition, the ZFC-x samples prepared at the Zn(NO ) ∙6H O amount of 1.0, 3.0, and 5.0 mmol 3 2 2 were denoted as ZFC-1, ZFC-2, and ZFC-3, respectively. (Page 13 in revised Manuscript)\nThe as-obtained ZFC/resin mixtures were poured into the 3D-printed inverted mold template and degassed for 60 min under the vacuum ambient… (Page 14 in revised Manuscript)\nX-ray absorption fine structure spectra were collected at the RapidXAFS… (Page 14 in revised Manuscript)\n(7) (Page 3 in revised Supplementary Materials)\n𝑅𝐿(𝑑𝐵) = 20 𝑙𝑜𝑔|(𝑍𝑖𝑛 −𝑍0)/(𝑍𝑖𝑛 +𝑍0)|\nThe 3D and planar-averaged charge density difference were calculated to assess the interaction processes. (Page 6 in revised Supplementary Materials)\nAfter a carbothermal reaction, the Fe and Zn species in ZFO@C were reduced and converted into Fe C and ZnO, respectively…. (Page 10 in revised Supplementary Materials) 3\nSupplementary Fig. 6 a XANES spectra at Zn k-edge, the inset is an enlarged peak of the selected region. (Page 15 in revised Supplementary Materials)\nSupplementary Fig. 18 The profiles of value along frequency at the thickness from 1.0 to 5.0 mm. The marked gray region corre | s 𝑍 p 𝑛 o𝑖n𝑛d / s 𝑍 t 𝑛 o0 t | he value of ranging from 0.8 to 1.2, indicating the qualifying impedance matching in samples. |𝑍 i 𝑛 n 𝑖r𝑛e / v 𝑍 is 𝑛 e0d | (Page 22 Supplementary Materials)\nReviewer #3 (Remarks to the Author):\nIn this paper, the authors propose a new method for designing yolk-shell composite nanoparticles with controllable interfacial strain between the two components. They demonstrate it by synthesizing ZnO/Fe C nanoparticles, where magnetoelectric interface forms through the outward diffusion of the 3 ZnO species from the Zn + Fe + O + C precursor mix. Further, they investigate the evolution of the microstructure and macroscopic properties of these nanoparticles with the change of Zn/Fe precursor ratio. With theoretical calculations (molecular dynamics) and experimental data, the authors show, that the strain at the interfaces changes from compressive to tensile and then to neutral (relaxed) with increasing Zn content, and that the interfaces with tensile strains can be efficiently used as a GHz radiation absorber. Overall, the article presents a very comprehensive and topical study with clear applications and therefore can be published in Nature Communications. However, several issues should be addressed before publication:\nGeneral Response: We thank the reviewer for their valuable suggestions and for noting that our article presents a very comprehensive and topical study with clear application and it can be published in Nature Communications.\nQ1: SEM images (supplementary Fig 2) show, that the size of the nanoparticles vary greatly, but I could not find any information about the average size or the size distribution for different ZFC powders. Fig 1b also features spherical particles of different size. Particle size is directly related to the magnetoelectric interface area to volume ratio, so it may skew the measured macroscopic parameters of the samples. I would like the authors to provide some statistical data on the ZFC powders morphological parameters and to comment on the relations between these parameters and the measured permittivity and GHz absorbing capabilities.\nResponse 1: Thanks for the reviewers’ reasonable considerations on the microsphere sizes distribution, we strongly agree with the reviewers’ point on the relation between microscale particle size and macroscopic parameters. To address the mentioned size variation in the original Supplementary Fig. 2a, we have resupplied the larger-horizon SEM images of the spray-drying prepared spherical precursors and their derivate ZFC-x products, and the size distribution statistics of spraying-dried precursors, ZFC-x microsphere and involved nanoparticles are also summarized in the revised Supplementary Fig.2.\nFirstly, we wish to clarify that the microspheres size fluctuation is mainly attributed to the intrinsic properties of spray-drying preparation technology, which firstly nebulize the precursor solution into numerous droplets with a certain size ranging and then evaporate the involved solvent by contacting with the input high-temperature flows, eventually obtaining the dried spherical powders with a normal size distribution [Ref. R1-3].\nIn this work, our motivation is modulating the magnetoelectric interface strain by controlling a ZnO content driven gradient outwards diffusion process, and the materials systems are prepared via spray-drying and post pyrolysis treatments. As shown in the Supplementary Fig. 2a, all spray-dried precursors possessed a spherical structure with a close average size of 2.55 0.05 um, demonstrating the slight effects of variate Zn source content on the size distribution. After the subsequent heat ± treatment of these precursors, the ZFC-x microspheres were yielded, and the corresponding spherical sizes were reduced owing to the pyrolysis of carbon-based matrixes in precursors. Even if the involved ZnO content were different, the overall size distributions of ZFC-x microspheres still maintained a close average values (Supplementary Fig. 2b), indicating that the morphology size might not be the dominated factor on the variation of permittivity and absorption performance in this work. As for the inside nanoparticles, potential particles aggregation might exist due to the inward contraction of carbon framework from the ZnO outward diffusion (the inset in Supplementary Fig. 2b), but majority of nanoparticles presented similar sizes with an average value slightly ranging from 23.10 nm to 25.02 nm, and 24.44 nm (Supplementary Fig. 2c). The similar and close size distributions in both of the overall microspheres and nanoparticles among the three as-fabricated ZFC-x samples revealed the slight effects of varied ZnO content on the size, further confirming that the size effect played limited roles in the variation of measured permittivity and absorption capability along the diffusion gradient.\nReference for Response 1: [R1] Carné-Sánchez, A., Imaz, I., Cano-Sarabia, M. & Maspoch, D. A spray-drying strategy for synthesis of nanoscale metal–organic frameworks and their assembly into hollow superstructures. Nat. Chem. 5(3), 203-211 (2013). [R2] Troyano, J., Camur, C., Garzon-Tovar, L., Carné-Sánchez, A., Imaz, I., & Maspoch, D. Spray-drying synthesis of MOFs, COFs, and related composites. Acc. Chem. Res. 53, 1206-1217(2020). [R3] Jiang, Z., Gao, Y., Pan, Z., Zhang, M., Guo, J., Zhang, J. & Gong, C. Pomegranate-like ATO/SiO microspheres for efficient microwave absorption in wide temperature spectrum. J. 2 Mater. Sci. Technol., 174, 195-203 (2024).\nSupplementary Fig. 2 SEM images and corresponding size distribution statistics of a spray-dried spherical precursor of ZFC-x, b as-fabricated ZFC-x microspheres. c STEM images and corresponding size distribution statistics of nanoparticles in ZFC-x samples. The scale bars in a, b and c are 5 um, 2um, and 100 nm, respectively. The spray-drying preparation method endowed the Zn source content-varied ZFC-x precursors with a spherical structure and a close averaged size of 2.55 0.05 um. After a subsequent heat treatment of these precursors, the sizes of as-fabricated ZFC-x microspheres reduced ± owing to the pyrolysis of carbon-based matrixes. The contraction of the hollow structure caused an increase in carbon shell thickness from ~635 nm to ~860 nm and its eventual transformation into a solid structure. The effused ZnO formed wrinkled surface layers with a thickness of ~270 nm and packaged on the outside of the solid structure. Numerous nanovoids surrounded the nano heterostructures were detected owing to the consumption of carbon matrix during the carbothermal, forming yolk-shell-like structures. These voids were gradually filled by ZnO till the completion of outwards effusion of ZnO.\nQ2: The comparison (Fig 4b and supplementary Table 1) with other microwave absorbing materials is lacking. For example, there are articles, reporting materials with better EAB at lower or similar thickness, such as FeCo-Ti C MXene (EAB 8.8 GHz at 1.6 mm thickness, 3 2 https://doi.org/10.1016/j.jmmm.2019.165639), ZF/rGO aerogels (EAB 8.4 GHz at 2.1 mm thickness, https://dx.doi.org/10.2139/ssrn.4414816) and SiO @FCIP+MWCNT (EAB 7.9 GHz at 1.9 mm 2 thickness, https://doi.org/10.1016/j.compositesa.2025.108719). While the parameters, obtained in the current manuscript are impressive, they cannot be called record-breaking. I would like the authors to expand the comparison with these and/or other reports to make it more balanced.\nResponse 2: According to the reviewers’ reasonable suggestions, we have expanded the EAB properties comparison by supplementing other reported high-performance absorbers including the reviewer listed examples to make the current performance presentation more balanced. The related comparison results are showed in Fig. 4b and Supplementary Table 4. It could be detected that the optimum sample tensile strain-modulated ZFC-2 in this work exhibited an impressive EAB performance at a relatively thin thickness, outperforming majority of reported EM absorbers.\nRevision in the manuscript: The Fe C/ZnO heterostructure within tensile strain exhibited a broad EAB of 7.38 GHz at a thin 3 max thickness, covering entire Ku-band (from 12 to 18 GHz, the primary application band for radar stealth39), outperforming majority of reported EM absorbers (Fig. 4b and Supplementary Table 3-4). (Page 11 in revised manuscript)\nFig. 4b EAB properties comparison among reported EM absorbers\nSupplementary Table 4 Comparison of EAB among reported EM wave absorption materials.\nlanoisnemid-woL\netisopmoC\nFeCo-Ti C MXene 1.60 8.80 70\n3 2\nZF/rGO aerogels 2.10 8.40 71\nSiO @FCIP/MWCNT 1.90 7.90 72\nTi C T MXene/Graphene 2.15 7.30 74\n3 2 x\nTiO /C@Co/NC@CNT 1.80 6.16 75\nnws\nQ3: Vertical axis break and change of scale in Figure 4b is misleading. I cannot find a good reason to make it this way. Please, remove the line break or explain why it is necessary.\nResponse 3: Thanks for the reviewers’ kind comments, we have removed the line break in the original Fig. 4b to avoid the unnecessary misleading, and the revised version of Fig. 4b is shown in the revised manuscript.\nRevision in the manuscript: Fig. 4b EAB properties comparison among reported EM absorbers\nQ4: Figures 4e and 4f show, that GHz radiation from a consumer grade WiFi router heats the shielding resin metastructure up to 45 oC in one minute. It is hard to believe, considering very low peak RF power density of 150 mW/m2 (Fig 4g). By my estimations even if the metastructure dissipates all of the RF radiation into the thermal energy, in one minute it could only heat up by less than 1 oC (or heat up a very thin < 1 mkm surface layer by 20 degrees). I would like the authors to clarify the thermal balance of this experiment.\nResponse 4: We thanks the reviewers’ specialized comments. We wish to clarify that the electromagnetic radiation signals from the civilian WiFi router are indeed effectively reduced after applying our as-fabricated ZFC-2 based metamaterials, as evident by the detection results of reduced RF signals (Fig. 4e and 4g). Regarding the thermal variation issue, we should acknowledge that the apparent significant heat variation under EM radiation was misinterpreted due to incomplete description of the experimental details in the original manuscript. We wish to supplement that the infrared thermal image variations are recorded by exposing the ZFC-2 based metamaterials under a solid-state microwave source with a fixed-frequency of 2.45 GHz and a power of 200W (WSPS-2450-200-CMFC, Chengdu Wattsine Electronic Technology Co., Ltd.) for 60s in a sealed box, as shown in Supplementary Fig. 25. The remarkable thermal increase detected on the ZFC-based metamaterial surface after radiating for 60s (Fig. 4f) confirms that the RF energy can be absorbed by the metamaterials and dissipated into the heat. Furthermore, we also supplement control experiments to underscore the critical role of synergy between the intrinsic electromagnetic properties of ZFC-2 composites and the metastructure in achieving the full-band absorption and efficient energy dissipation observed in ZFC metamaterials. (Supplementary Fig. 26 and Fig. 4).\nRevision in the manuscript: Positioned as a shield in front of the WiFi router, the metamaterial remarkably reduced the detected radio frequency (RF) signals to the qualified levels (Fig. 4e). And the pronounced surface temperature elevation of the ZFC-2 metamaterials after radiation under a solid-state microwave source confirms the involved dissipation process from absorbed EM energy to heat (Supplementary Fig. 25 and Fig. 4f). Time dependent radiation values variation revealed that over 95% reduction of RF signals could be continuously achieved by this magnetoelectric metamaterials (Fig. 4g). In contrast, both control samples (the all-resin metastructure and the ZFC-2/resin plate) failed to achieve effective EM attenuation (Supplementary Fig. 26), further demonstrating that the impressive EM protection arises from the synergistic contribution between the strain-mediated magnetoelectric absorbers and the tailored metastructure. (Page 12 in revised manuscript)\nSupplementary Methods: EM radiation detection and energy dissipation. The as-fabricated ZFC-based EM metamaterial was placed in front of a consumer-grade WiFi router (operating at ~5.2 GHz). The dynamic radiation signals were then measured for 60 seconds using an EM radiation detection recorder positioned 10 cm from the WiFi router. The relatively low intrinsic power density of civilian WiFi routers limited an obvious detection on the energy conversion from EM energy to heat in ZFC-based EM metamaterials within a short duration. To have a visualized observation of this EM energy dissipation process, the ZFC-based EM metamaterial was exposed under a higher-power a solid-state microwave source with a fixed-frequency of 2.45 GHz and a power of 200W (WSPS-2450-200-CMFC, Chengdu Wattsine Electronic Technology Co., Ltd.), as illustrated in Supplementary Fig. 25. The heat variation of the sample before and after the radiation for 60s was recorded by an infrared thermal imaging instrument. (Page 4 in revised Supplementary Materials)\nSupplementary Fig. 25 Test environment for detecting the electromagnetic energy dissipation. The as-fabricated ZFC-based metamaterial was exposed under a higher-power microwave source with a fixed-frequency of 2.45 GHz and a power of 200W, and the distance between the microwave source and the sample surface is set as 15 cm.\nSupplementary Fig. 26 Macroscale EM attenuation performances of parallel control groups. a Digital photo of the ZFC-2 composites filled resin film and the all-resin metamaterials under the arch method testing environment, and the scale bar is 5 cm. b Corresponding tested reflection loss values. c Photographs of EM signals detection with control group. d Digital photos of as-fabricated materials under the radiation of high-power microwave source, and corresponding infrared thermal images before and after EM radiation for 60s. No detectable EAB and only a narrow EAB at high-frequency were obtained in the all-resin metamaterials and ZFC-2 composites filled resin film, confirming that both of the intrinsic properties of ZFC-2 composites and the periodical metastructure jointly contributed to the full-band effective absorption of ZFC metamaterials. These comparison results of EM radiation protection demonstrated that the individual ZFC composite or metastructure could not satisfy effective EM energy dissipation, confirming the significance of constructing ZFC-based metamaterials.\nQ5: I could not find detailed information about the molecular dynamics simulation neither in the main text, nor in the supplementary notes. I would like the authors to provide a description of the initial state used in the simulations and how different ZnO concentrations were implemented.\nResponse 5: According to the reviewer's valuable comment, we have revised the molecular dynamics simulation protocol. Specifically, we optimized the gradient evolution in the diffusion models and refined the simulation steps to have a clearer understanding on the ZnO-concentration dominated outward diffusion process. Prior discussions demonstrated that the ZFC heterostructure composites is converted from the carbon nanocages confined ZFO hybrids via carbothermal reaction, resulting in the formation of nanoporous on the carbon substrate [Ref. R1], as evident by the HAADF-STEM results (Supplementary Fig. 2). Additionally, during the high-temperature carbothermal process, the metal species can catalyze the graphitization of the surrounding carbon matrixes [Ref. R2], as evidenced by HRTEM results that show the nanoparticles are closely encapsulated by graphitic carbon shells (Supplementary Fig. 3). Based on the primary experimental observation, the initial state of ZFC-x composite systems with different ZnO concentrations was modeled, and the description is below:\nThree ZFC-x systems with different ZnO content shared a common layered architecture. From the bottom to the top of the simulation box, the structure comprised a porous graphene layer, a layer of iron carbide molecules, a layer of zinc oxide molecules, two porous graphene layers, and a vacuum region. The relative pore offset between the two porous graphene layers was 0.1 nm. The three systems differed in the number of zinc oxide molecules, where the numbers of zinc oxide molecules in ZFC-1, 2, and 3 were 12, 24, and 36, respectively. Each system was first subjected to energy minimization, followed by simulations in the NVT ensemble at 873.15 K with a time step of 0.5 fs for a total duration of 10 ns. Temperature was controlled using the V-rescale thermostat. During the simulations, all components except the ZnO molecules were kept fixed to preserve the structural framework. Additionally, the MD simulation details (including the modeling of initial states and the simulation methods) and the corresponding analyses are supplemented into the revised Supplementary Note 1 and manuscript, respectively.\nReference for Response 5: [R1] Lv, H. et al. Staggered circular nanoporous graphene converts electromagnetic waves into electricity. Nat. Commun. 14, 1982 (2023). [R2] Hunter, R.D., Ramírez-Rico, J. and Schnepp, Z. Iron-catalyzed graphitization for the synthesis of nanostructured graphitic carbons. J. Mater. Chem. A, 10, 4489-4516 (2022).\nRevision in the Manuscript: To provide insights into the correlation between ZnO diffusion and magnetoelectric interface contact, molecular dynamics (MD) simulation (Supplementary Note 1) was employed to elucidate the ZnO content affected effusion process. The observations of recorded diffusion state indicated that at lower concentrations, ZnO was largely hindered from penetrating the carbon layers (Fig. 2a). Conversely, with a higher initial concentration, the confinement imposed by the carbon layers was progressively overwhelmed, leading a pronounced outward diffusion. Continuous increase of the number density of penetrated ZnO (Fig. 2b and Supplementary Fig. 9) and the mean-square displacement (MSD, Fig. 2b) with the augmented concentration further proved the controllability of the ZnO gradient effusion process. (Page 7 in revised manuscript)\nFig. 2 a ZnO content affected gradient outward effusion process resulted from molecular dynamics simulation. b Calculated number areal density of confined and penetrated ZnO and MSD variation along the time. c iDPC-STEM images of heterointerfaces and corresponding geometric phase analysis results.\nSupplementary Fig. 9 Number density distribution along the Z-axis coordinate in the MD simulated terminal state of the ZFC-x systems. The green-colored areas on the left and right sides of the carbon layers model represent the confined and penetrated ZnO, respectively. ZnO initially remains encapsulated within the carbon layers at low concentrations. As the content increases, gradual outward penetration of ZnO, overcoming the carbon layer's confinement. This simulation results further verified the concentration-dependent diffusional process.\nSupplementary Note 1 Molecular dynamics simulation. Molecular dynamics (MD) simulations were conducted for three ZFC-x systems sharing a common layered architecture. From the bottom to the top of the simulation box, the structure comprised a graphene layer, a layer of iron carbide molecules, a layer of zinc oxide molecules, two porous graphene layers, and a vacuum region. The relative pore offset between the two porous graphene layers was 0.1 nm. The three systems differed in the number of zinc oxide molecules, where the numbers of zinc oxide molecules in ZFC-1, 2, and 3 were 12, 24, and 36, respectively. Force field parameters were assigned as follows: iron carbide nanoparticles and zinc oxide molecules were described using the Universal Force Field (UFF)5, while all graphene layers were parameterized using the GAFF2 force field6. Topology parameter files were generated using the Sobtop program (Tian Lu, Sobtop, Version 1.0 (dev3.2), http://sobereva.com/soft/Sobtop, accessed on 31/12/2025). All MD simulations were performed using GROMACS 2019.67. Each system was first subjected to energy minimization, followed by simulations in the NVT ensemble at 873.15 K with a time step of 0.5 fs for a total duration of 10 ns. Temperature was controlled using the V-rescale thermostat. During the simulations, all components except the zinc oxide molecules were kept fixed to preserve the structural framework. Electrostatic interactions were treated using the PME method, while van der Waals interactions were modeled with a 12–6 Lennard–Jones potential using a cutoff distance of 1.2 nm, applying Lorentz–Berthelot combining rules for cross-interactions. Periodic boundary conditions were imposed in all directions. Molecular structures were visualized using VMD version 1.9.38. (Page 5 in revised Supplementary Materials)\nQ6: How the statistical data on Supplementary Fig. 8 were gathered? From the text it is not clear, if it is a strain distribution within a single heterointerface or a distribution of average strains of several interfaces? In my understanding, big part of the theoretical considerations in the manuscript rely on the results, presented in Supplementary Fig. 8, so I would like the authors to provide evidence, that these strain distributions are representative.\nResponse 6: We wish to clarify that the statistical data on original Supplementary Fig. 8 are gathered from the white dashed boxed region in the geometric phase analysis (GPA) results (Fig. 2c), which intuitively reflected the contact states of the as-built interfaces. And the related descriptions about the origin of the mentioned statistical data are supplemented in the revised footnotes of new Supplementary Fig. 10. Additionally, as suggested, we have also supplemented a series of HRTEM images and corresponding GPA results on the three distinct interfaces from different batches of ZFC-x samples to improve the representativity of the interfacial strain distribution regularity. As shown in Supplementary Fig. 12a, all selected interfaces in ZFC-1 samples present a remarkable compressive strain concentration, which are well consistent with the compression state in the manuscript-mentioned ZFC-1 interface (Fig. 2c). Similarly, both of the tensile state in ZFC-2 interface and the relieved state in ZFC-3 are further confirmed by the supplemented several heterointerface regions (Supplementary Fig. 12b-c), demonstrating that the reproducibility and representativity of the qualitative determination of these heterointerface states. Regarding the quantitative relation, although there are slight fluctuations in the average values of these interfacial strain (ε ), most ε values locate in an acceptable error range, xy xy and the whole averaged values of all measured ε are – (11.2 2.0) %, (13.7 3.2) %, and – (0.25 0.6) % in ZFC-1, ZFC-2, and ZFC-3, respectively. Therefore, the mentioned statistical data in Supplementary ± ± ± Fig. 10 could well reflect the characteristic strain state in these ZFC-based interfaces.\nSupplementary Fig. 12 Characterizations of interfacial strain states. HRTEM images, GPA results, and corresponding statistic histograms of ε strain values in the selected interfacial regions of a ZFC- xy 1, b ZFC-2, and c ZFC-3 heterostructures from different batches. Scale bars of HRTEM in a, b and c are 1 nm and 2 nm, respectively. These supplemented GPA distribution and corresponding strain statistics present approximate results to that of the main text (Fig. 2c and Supplementary Fig. 10), qualitatively demonstrating the reproductivity for the deterministic fabrication of the ZFC interfacial strain via the precise control of gradient ZnO diffusion.\nReviewer #4 (Remarks to the Author):\nA magnetoelectric Fe C/ZnO composite and its heterointerface were analyzed in detail, showing the 3 redistribution of interfacial strain and polarization fields. It is shown that the polarization fields are strong when interfacial strain is large and that this causes high dielectric loss. The authors demonstrate the properties of the strained heterointerface in an EM absorption experiment, showing wideband absorption. The authors use a suite of advanced analysis tools to demonstrate the interfacial properties of the heterointerface but the basic theory and physical principles behind the wideband absorption is not immediately clear. While the results are nice, polarization control for EM absorption has already been extensively studied in all types of forms of 2D TMCs, nanoparticles, composites, defects, etc. In this context, the novelty of the work is not remarkably persuasive. The physical aspects how it can be differentiated from those of other works should be elucidated very clearly.\nGeneral Response: We thank the reviewer for their careful reading and noting that our results are nice. We agree with the reviewer's pointed the feasibility on regulating EM absorption via polarization control. However, majority of current researches merely remain superficial methodologies explorations, mainly relying on ambiguous phenomenological descriptions (such as simple components optimization, dimension and microstructure design, and uncontrollable defects introduction), lacking deep and novel insights into the correlation between microscale polarization regulation mechanism and macroscale EM absorption performance. A fundamental yet crucial limitation is the lack of high-precision, visualized identification for the sources of induced polarization within materials, coupled with the absence of a finely programmable strategy for their precise modulation. This gap in mechanistic insight significantly hinders the development of advanced polarization loss-dominated EM absorbers.\nTo tackle these bottlenecks, our research aims to address it through several key innovations:\n(i) Deterministic fabrication of magnetoelectric heterostructure composite with adjustable interfacial strain state\nIn this work, we proposed an oriented diffusion strategy to construct atomic interfacial strain in magnetoelectric heterostructures. The interfacial strain states evolved from compression to tension and relaxation could be precisely programmed by manipulating the diffusion gradients, which was verified through theoretical simulation and experimental observation. This approach capitalized on the intrinsic thermodynamic properties of dielectric component ZnO itself, distinct from the additional composition and structural modifications, or external fields assistance required in conventional strain engineering.\n(ii) Atomic-level visualization on the strain-reconstructed interfacial coupling and electronic structure variation\nAdvanced electron microscopy characterization and analysis techniques (including DPC, iDPC, electronic hologram) were utilized to visualize variations in interfacial electronic properties under different strain states. Our observations unveiled a strain-induced atomic-level electric field coupling on the magnetoelectric heterointerface, along with a notable enhancement of this coupling upon the application of tensile strain. The interfacial coupling, verified by DFT calculations, increased atomic-scale orbital overlaps and reduced the work function, which accelerated carriers migration across the interface and enhanced the interfacial built-in electric field.\n(iii) Decipherment of the correlation between interfacial strain-polarization coupling mechanism and broadband EM absorption\nSystematic analysis of dielectric properties and theoretical calculation demonstrated that strain-induced interfacial electronic coupling effectively modified the polarization kinetics by shortening relaxation time and broadening the distribution, thereby enhancing the dielectric loss capability. This mechanism, distinct from reported strategies that rely solely on lengthening relaxation time, highlighted the role of strain-polarization coupling. Eventually, the broadened dielectric loss combined with optimized impedance matching jointly endowed the magnetoelectric heterostructures with a broadband EM absorption performance.\n(iv) Practicability demonstration of strain-engineered magnetoelectric metamaterials with excellent EM protection\nLeveraging the synergy between the strain-broadened interfacial loss mechanism and the metastructure design, the optimized tensile-strain-engineered magnetoelectric metamaterial achieved remarkable full-band (2~18 GHz) electromagnetic wave absorption and attenuated incident radiation by over 95%. These results demonstrated its promising potential for application in civilian EM protection, and provided significant guidance for developing advanced composite material systems with wideband EM absorption.\nIn addition, we have addressed the reviewer’s comments, especially, deepened the physical mechanism analysis for clearer understanding of the strain-polarization coupling correlation. The point-to-point responses are detailed as below:\nQ1: Please add classic references that link interfacial polarization to EM wave absorption.\nResponse 1: According to your suggestion, some classic references that bridge the relation between interfacial polarization and EM wave absorption are added in the revised manuscript. For example: Dong et al. [Ref. R1] unveiled that the accumulation and depletion of free space charge occurred on the interface of adjacent dielectrics under the altered electrical field, generating interfacial polarization for EM wave absorption. Zhang et al. [Ref. R2] revealed the significance of interfacial polarization in the core/shell structure composite nanoparticles for improving EM wave absorption performance. Cao et al. [Ref. R3] found that the interfacial polarization built by the nanocrystals and substrate could excite hopping charges for enhancing dielectric properties and microwave absorption. Ji et al. [Ref. R4] systematically summarized the feasibility and significance of designing heterointerface for enhancing interfacial polarization and EM absorption.\nReferences for Response 1: [R1] Lu, B. et al. Microwave absorption properties of the core/shell-type iron and nickel nanoparticles. J. Magn. Magn. Mater. 320, 1106-1111 (2008). [R2] Liu, Q., Zhang, D. & Fan, T. Electromagnetic wave absorption properties of porous carbon/Co nanocomposites. Appl. Phys. Lett. 93 (2008). [R3] Yang, H. et al. Enhanced dielectric properties and excellent microwave absorption of SiC powders driven with NiO nanorings. Adv. Opt. Mater. 2, 214-219 (2014). [R4] Liang, L. et al. Heterointerface Engineering in Electromagnetic Absorbers: New Insights and Opportunities. Adv. Mater. 34, 2106195 (2022).\nRevision in the manuscript: 11. Liu, Q., Zhang, D. & Fan, T. Electromagnetic wave absorption properties of porous carbon/Co nanocomposites. Appl. Phys. Lett. 93 (2008). 12. Yang, H. et al. Enhanced dielectric properties and excellent microwave absorption of SiC powders driven with NiO nanorings. Adv. Opt. Mater. 2, 214-219 (2014). 13. Liang, L. et al. Heterointerface Engineering in Electromagnetic Absorbers: New Insights and Opportunities. Adv. Mater. 34, 2106195 (2022). 32. Lu, B. et al. Microwave absorption properties of the core/shell-type iron and nickel nanoparticles. J. Magn. Magn. Mater. 320, 1106-1111 (2008).\nQ2: Pg. 6 Clarify which ZnO crystal plane is being analyzed. In one place it says (101). In another it says (111).\nResponse 2: Thanks for your careful reading and kind reminder. We wish to clarify that there is a typing errors in the 131 line of Pg. 6, the mentioned (111) crystal plane has been corrected to (101). Additionally, we have also carefully rechecked and revised the potential format and typing errors in the previous version of manuscript.\nRevision in the manuscript: Detection of Fig. 1g presented a strong quantitative agreement between the crystalline structure and STEM results, accurately verifying the formation of magnetoelectric heterointerface between Fe C 3 (211) and ZnO (101). (Page 6 in revised manuscript)\nQ3: In Figures, it is hard to tell without labels which figure refers to ZFC1, 2 and 3. (Figure 1b, 2a, 2c, etc)\nResponse 3: According to your valuable suggestions, we have added the corresponding labels into the mentioned Figures to have a more intuitionistic identification on the ZFC-x evolution.\nRevision in the manuscript: Fig. 1b TEM images and HAADF-STEM elements mapping of the ZnO effusion affected ZnO/Fe C 3 (ZFC-x) heterostructures.\nFigure 2 Effect of ZnO gradient diffusion on interface properties. a ZnO content affected gradient outward effusion process resulted from molecular dynamics simulation. b Calculated number areal density of confined and penetrated ZnO and MSD variation along the time. c iDPC-STEM images of heterointerfaces and corresponding geometric phase analysis (GPA) results. d Statistical histograms of strain values illustrating the variability of interfacial stress. e Projected atomic electric field map of ZnO effusion reconstructed magnetoelectric interface. f Effect of interfacial strain on the vector field distribution of the selected region in e, the color bar corresponds to the vector magnitude. All scale bars in c and e are 500 pm.\nQ4: It’s hard to understand the plot in Figure 3a. The text says that this is a dispersion curve, but there is no spectral data. What do the range of values refer to?\nResponse 4: We wish to clarify that the plot in Figure 3a show the relative variation range of permittivity values, which can reflect the frequency-dispersion property of EM absorbers in the tested 2-18 GHz band. For example, a large variation in permittivity across the 2-18 GHz band typically indicates the sensitive response characteristics towards the electric field of EM wave, such as dipole and interfacial polarization relaxation process [Ref. R1]. This behavior is directly linked to strong dielectric loss capability and pronounced frequency dispersion properties of EM absorbers [Ref. R1-3]. Conversely, a minimal change in permittivity suggests the absence or deficiency of such responsiveness within this frequency range, corresponding to weak dispersion and low loss. In addition, the profiles of frequency-depended permittivity variation were also shown in the Supplementary Fig. 13, assisting to further demonstrate the existence of polarization process. Once polarization relaxation occurs, it can affect both ε’ and ε’’ values in a frequency region, and thus two typically phenomena can be observed, that is, sharply decreased ε’ value due to the frequency dispersive effect, and dielectric resonance peak in ε’’ [Ref. R4]. To have a clearer understanding, we have revised the analysis description of Fig. 3a in the text.\nFig. 3a Complex permittivity of ZFC-x magnetoelectric heterostructures.\nSupplementary Fig. 13 Profiles of a real part (ε’) and b imaginary part (ε’) of permittivity in the ZFC-x system.\nReferences for Response 4: [R1] Tao, J. et al. Phenolic multiple kinetics-dynamics and discrete crystallization thermodynamics in amorphous carbon nanostructures for electromagnetic wave absorption. Nat. Commun. 15, 10337 (2024). [R2] Yao, K. et al. High-entropy perovskite oxides: Morphotropic phase boundary interfacial engineering for next-generation communications. Sci. Adv. 11, eaea0362 (2025). [R3] Ren, B. et al. Broadband electromagnetic absorption up to 1473 K enabled by dielectric frequency-dispersion engineering in ceramic composites. Nat. Commun. (2025). [R4] Lv, H., Yang, Z., Pan, H., & Wu, R. Electromagnetic absorption materials: Current progress and new frontiers. Prog. Mater. Sci. 127, 100946 (2022).\nRevision in manuscript: Dielectric dispersion, manifested in frequency-dependent permittivity, fundamentally originated from the dynamic dielectric loss of absorbers to an external alternating electric field31. The variation of permittivity revealed that the interfacial strain enhanced dielectric dispersion properties, as verified by a steeper decline in permittivity with increasing frequency (Supplemented Fig. 13a-b) and a broader variation range across the 2–18 GHz band (Fig. 3a). (Page 8 in revised manuscript)\nQ5: Pg. 8 “The dielectric dispersions arise from an electronic reconfiguration triggered by atomic-level stress regulated interfacial potential difference”. This is a general statement and can apply to any variation in the dielectric dispersion. Can the authors be more specific?\nResponse 5: We wish to clarify that the dielectric dispersions phenomenon typically presents as the frequency-dependence of permittivity in electromagnetic materials, which is originated from the varied responsiveness of the involved conduction and polarization loss mechanism towards different frequency [Ref. R1-2]. The conduction loss generally diminishes with increasing frequency, following a typical σ/ω dependence (Supplementary Fig. 13c), which is generated by the directional migration of carriers under the alternated electric field and exists in all materials with electronic conductivity [Ref. R3]. Polarization loss, especially the dominated interfacial polarization in the magnetoelectric composite system, mainly originates from the delayed reorientation or charge redistribution on the heterointerface under alternating electric field due to finite relaxation times [Ref. R3-4], leading to variations in both the real and imaginary parts of the complex permittivity across frequencies (Supplementary Fig. 13a-b). Additionally, polarization relaxation losses peak near their characteristic relaxation frequencies could be identified by the tangent of dielectric loss (Fig. 3b) and a nonlinear fitting of the modified Debye relaxation [Ref. R5] (Supplementary Fig. 13d).\nPrevious reports mainly ascribe the interfacial polarization dominated dielectric dispersion to the simple combination of components with different electronegativity [Ref. R3], and lacks deep deciphering on the interfacial strain-regulated interfacial polarization mechanism. In this work, we not only fabricated interfacial strain-controllable magnetoelectric heterointerfaces by relocating dielectric ZnO on the interface, but also leveraged advanced characterization technologies to have a more visualized understanding on the correlation between the interfacial polarization and strain from atomic-dimension. Therefore, the as-presented evolution of dielectric dispersions characteristics in the ZFC composite system primarily stemmed from the strain-reconfigured interfacial electrons arrangement (Fig. 2e-f), rather merely from the intrinsic interfacial potential difference between the dielectric and magnetic component across the interface. This interfacial electronic reconfiguration could be also verified by the subsequent theoretical calculation of projected density of state (PDOS), where more pronounced orbits overlaps were identified in the ZFC-1 and ZFC-2 (Fig. 3g), further confirming the strain-regulated interfacial properties. According to your valuable suggestion, we have revised the description about the ‘dielectric dispersions property’ in the main text.\nReferences for Response 8: [R1] Deng, L. & Han, M. Microwave absorbing performances of multiwalled carbon nanotube composites with negative permeability. Appl. Phys. Lett. 91 (2007). [R2] Zhang K. et al. All-Dielectric Ultra-broadband microwave absorbing aerogel with optimized dielectric dispersion via dielectric relaxation time regulation. Adv. Mater. 2506386 (2025). [R3] Lv, H., Yang, Z., Pan, H., & Wu, R. Electromagnetic absorption materials: Current progress and new frontiers. Prog. Mater. Sci. 127, 100946 (2022). [R4] Liang, L. et al. Heterointerface engineering in electromagnetic absorbers: new insights and opportunities. Adv. Mater. 34, 2106195 (2022). [R5] Tao, J. et al. Ion-exchange strategy for metal-organic frameworks-derived composites with tunable hollow porous and microwave absorption. Small Methods, 6, 2200429 (2022).\nSupplementary Fig. 13 Profiles of a real part (ε’) and b imaginary part (ε’) of permittivity and c divided conduction loss ( ) and d polarization loss ( ) in the ZFC-x system. ′′ ′′ 𝜀𝑐 𝜀𝑝\nFigure 3 b Tangent values of dielectric loss. g Projected density of states (PDOS) of ZnO-diffusion reconstructed interfaces.\nRevision in manuscript: Dielectric dispersion, manifested in frequency-dependent permittivity, fundamentally originated from the dynamic dielectric loss of absorbers to an external alternating electric field31. The variation of permittivity revealed that the interfacial strain enhanced dielectric dispersion properties, as verified by a steeper decline in permittivity with increasing frequency (Supplemented Fig. 13a-b) and a broader variation range across the 2–18 GHz band (Fig. 3a). This enhancement was mainly due to the strain-induced reconstruction of the local electronic structure via interfacial coupling (Fig. 2e-f), which accelerated realignment of interfacial potentials across the interface in response to the altering electric field, thereby improving polarization responsiveness32. The enhanced polarization relaxation could be characterized by the decreased real permittivity (ε′) and a more intense dielectric resonance peak in the imaginary part (ε″) for the strain-involved specimen (Supplemented Fig. 13a-b). According to the non-ideal Debye relaxation model33, the , referred to the dielectric loss ability, was divided into ′′ conduction loss ( ) and polarization relaxation ( ) based on the tested electronic conductivity 𝜀 ′′ ′′ (Supplemented Ta𝜀𝑐ble 2 and Supplemented Fig. 13c𝜀-𝑝d). (Page 8 in revised manuscript)\n31. Tao, J. et al. Phenolic multiple kinetics-dynamics and discrete crystallization thermodynamics in amorphous carbon nanostructures for electromagnetic wave absorption. Nat. Commun. 15, 10337 (2024). 32. Lu, B. et al. Microwave absorption properties of the core/shell-type iron and nickel nanoparticles. J. Magn. Magn. Mater. 320, 1106-1111 (2008). 33. Lv, H., Yang, Z., Pan, H. & Wu, R. Electromagnetic Absorption Materials: Current Progress and New Frontiers. Prog. Mater. Sci. 127, 100946 (2022).\nQ6: Pg. 8, In the loss tangent plot, the authors describe a polarization relaxation peak. Specify its location. Can its origin be clarified using the analysis before (eg. Why does it occur at the specified frequency. What is the physical reason?)\nResponse 6: Thanks for your valuable comments. We wish to clarify that the resonance peaks in the tested loss tangent plots are also identified in the plots of polarization loss (Supplementary Fig. 13d) using a nonlinear fitting of the modified Debye relaxation (Equation R1-5) [Ref. R1], confirming the assignment of polarization relaxation peak.\n(R1) ′ 𝜀𝑠−𝜀∞ 𝜀 = 𝜀∞ +1+(2𝜋𝑓) 2 𝜏 2 (R2) ′′ 2𝜋𝑓𝜏(𝜀𝑠−𝜀∞) 2 2 𝜀 = 1+(2𝜋𝑓) 𝜏 (R3) ′′ 𝜀 2𝜋𝑓𝜏(𝜀𝑠−𝜀∞) 𝑡𝑎𝑛𝛿𝜀 = 𝜀 ′ = 𝜀𝑠+𝜀∞(2𝜋𝑓) 2 𝜏 2 (R4) ′ 𝜀∞+𝜀𝑠 2 2 𝜀𝑠−𝜀∞ 2 (𝜀 − 2 ) +(𝜀′′) = ( 2 ) (R5) ′′ ′′ ′′ 𝜔𝜏 𝜎 where and 𝜀 is= th𝜀e 𝑝 o+p ti𝜀c 𝑐 al= an(d𝜀 𝑠 s−tat𝜀ic ∞ )di1e+l𝜔ec 2 t𝜏r 2 ic+ c𝜀o0n𝜔stant, respectively; , , and represents the rela 𝜀 x𝜀ation t 𝑠 im 𝜏 e, angular frequency, and electrical conductivity, respe 𝜏 ctiv 𝜔 ely. Ph 𝜎 ysically, the occurrence of polarization relaxation peaks is ascribed to that the driving frequency of the external electric field (ω) matches the intrinsic response rate (1/τ) of a specific polarization mechanism within the material. And the frequency can be determined using Equation (R6) as follows [Ref. R2]: (R6) 1 where is the freq𝑓u 𝑚 en=cy 2c𝜋o𝜏rresponding to the maximum value of the polarization peak, τ is the polariza 𝑓 t𝑚ion relaxation time. Therefore, the specific location of polarization relaxation peak is the intrinsic properties of dielectrics, which could be characterized by the loss tangent plots. Typically, in most heterostructure-dominated composite system, the polarization relaxation is originated from the interfacial polarization. The characteristic τ is mainly dominated by the interfacial potential difference and intrinsic permittivity of the involved components across the interface [Ref. R3,4], which further contributed to the specific frequency location of the resonance peak as detected in the tangent loss plots. Our previous analysis of strain-affected electric field redistribution has revealed the pronounced electrons coupling on the strain-involved magnetoelectric interfaces (Fig. 2e-f). This coupled interface created efficient carriers transports pathway for accelerating the migration of charge carriers owing to the more sufficient overlap of electron orbits, effectively shortening the τ [Ref. R5-6].\nIn addition, interfacial strain-induced reconfiguration of electrons also augmented the interfacial potential differences and enhanced the built-in electric field, as evident by the hologram results of these interfaces (Fig. 3d). This enhancement consequently lowers the average activation energy required for the directional migration or redistribution of these carriers under alternating electric field [Ref. R7], further promoting the induction of interfacial polarization. Meanwhile, density function theory (DFT) calculation results showed a lowered work function in the strain-involved interface (Fig. 3h), suggesting a decrease in the energy required to excite electrons from within the material for participation in polarization processes [Ref. R3, 7]. For interfacial polarization, this decrease in energy corresponds to a reduced average activation energy required for interfacial charge accumulation or reorientation of interfacial dipoles [Ref. R8]. According to the Arrhenius formula (equation R7), the reduction in Ea leads to an exponential shortening of τ [Ref. R8-10].\n(R7) 𝐸𝑎 where Ea is the activa𝜏ti(o𝑇n) e=ne𝜏rg 0 y e axnpd ( 𝑅𝑇) is a prefactor. As the interfacial strain state evolved from the relieved in ZFC-3 to the compressive 𝜏 i0n ZFC-1 and the tensile in ZFC-2, the gradually decreased ɸ implies the shortened τ (Fig. 3h), which also accounted for the polarization resonance peaks shifted towards the higher frequency in the loss tangent plots (Fig. 3b).\nIn summary, these mentioned characterization results and theoretical analysis clearly and qualitatively demonstrated the involved physical mechanism for the interfacial strain-resulted polarization resonance peak variations. Specifically, the interfacial strain regulated the interfacial electron’s structure and induced interfacial electric field coupling, effectively reducing the activation energy and accelerating the interfacial electrons transport, resulting in the shortened polarization relaxation time. This mechanism eventually exhibits as the polarization relaxation peaks in tangent loss plot in the ZFC-3 to ZFC-1 and ZFC-2 shifted towards the higher frequency owing to the gradual enhancement from the implemented interfacial compressed to tensile strain. Additionally, the related discussion on the shifts of polarization resonance peaks were also supplemented in the revised manuscript.\nReferences for Response 6: [R1] Liu, J. et al. Morphology-size synergy strategy of SiC@C nanoparticles towards lightweight and efficient microwave absorption. Chem. Eng. J. 433, 134484 (2022). [R2] Zhang K. et al. All-Dielectric Ultra-broadband microwave absorbing aerogel with optimized dielectric dispersion via dielectric relaxation time regulation. Adv. Mater. 2506386 (2025). [R3] Lv, H., Yang, Z., Pan, H., & Wu, R. Electromagnetic Absorption Materials: Current Progress and New Frontiers. Prog. Mater. Sci. 127, 100946 (2022). [R4] Li, M. et al. Ti C T /MoS self-rolling rod-based foam boosts interfacial polarization for 3 2 x 2 electromagnetic wave absorption. Adv. Sci. 9, 2201118 (2022). [R5] Lv, X. et al. Engineering orbital hybridization in advanced electrocatalysts for energy conversion:Fundamentals, Modulations, and Perspectives. Adv. Energy Mater. 2501129 (2025). [R6] Liu, Ying, et al. Local enhancement of polarization at PbTiO /BiFeO interfaces mediated by 3 3 charge transfer.\" Nano Lett. 17 3619-3628 (2017). [R7] Hui, S., Zhou, X., Zhang, L., & Wu, H. Constructing multiphase-induced interfacial polarization to surpass defect-induced polarization in multielement sulfide absorbers. Adv. Sci. 11, 2307649 (2024). [R8] Islam, R., Papathanassiou, A. N., Chan-Yu-King, R. & Roussel, F. On the sign of the relaxation activation energy for interfacial polarization in reduced graphene oxide–based nano-composites. Appl. Phys. Lett. 109 (2016). [R9] Cao, M. S., Song, W. L., Hou, Z. L., Wen, B., & Yuan, J. The effects of temperature and frequency on the dielectric properties, electromagnetic interference shielding and microwave-absorption of short carbon fiber/silica composites. Carbon 48, 788-796 (2010). [R10] Viehland, D., Jang, S. J., Cross, L. E., & Wuttig, M. Freezing of the polarization fluctuations in lead magnesium niobate relaxors. J. Appl. Phys. 68, 2916-2921 (1990).\nSupplementary Fig. 13 Profiles of d divided polarization loss ( ) in the ZFC-x system. ′′ 𝜀𝑝\nFigure 2 c iDPC-STEM images of heterointerfaces and corresponding geometric phase analysis (GPA) results. e Projected atomic electric field map of ZnO effusion reconstructed magnetoelectric interface. f Effect of interfacial strain on the vector field distribution of the selected region in e, the color bar corresponds to the vector magnitude. All scale bars in c and e are 500 pm.\nFigure 3 b Tangent values of dielectric loss. d Reconstructed electronic hologram and corresponding 3D charge density distribution images. h Calculated Φ values and charge distribution differences of ZnO diffusion reconstructed magnetoelectric heterostructure.\nRevision in the manuscript: According to the non-ideal Debye relaxation model33, the , referred to the dielectric loss ability, ′′ was divided into conduction loss ( ) and polarization relaxation ( ) based on the tested electronic 𝜀 ′′ ′′ conductivity (Supplemented Table𝜀 2𝑐 and Supplemented Fig. 13c-d)𝜀.𝑝 Multiple polarization peaks were identified in the strain-involved ZFC heterostructures, and both of the peak intensity and width were increased as the interfacial state evolved from the relieved to compressive and tensile. This enhancement was also confirmed by the loss tangent of complex permittivity (tan = ), where the increased ′′ ′ tan indicated the strain-improved dielectric loss ability (Fig. 3b). 𝛿 I𝜀n ad 𝜀 di ⁄ ti 𝜀 on, the interfacial strain affe 𝛿 c𝜀ted polarization relaxation variation were analyzed by Cole-Cole plots. As the interfacial strain evolved from a relieved state to compressive and tensile states, the maximum relaxation peak shifted to higher frequencies (Fig. 3b), along with a broadened peak width (Fig. 3c). Theoretically, polarization relaxation peaks occurred when the frequency of the external electric field coincides with the intrinsic response rate (the reciprocal of the relaxation time) of the polarization mechanism within the absorbers34,35. Thus, this trend of a shortened relaxation time with a widened distribution, demonstrating a sensitive yet broadband dielectric loss capability in the strain-involved magnetoelectric heterostructure. (Page 9 in revised manuscript)\n33. Lv, H., Yang, Z., Pan, H. & Wu, R. Electromagnetic Absorption Materials: Current Progress and New Frontiers. Prog. Mater. Sci. 127, 100946 (2022). 34. Zhang K. et al. All-Dielectric Ultra-broadband Microwave Absorbing Aerogel with Optimized Dielectric Dispersion via Dielectric Relaxation Time Regulation. Adv. Mater. 2506386 (2025). 35. Puzenko, A., Ishai, P. B., & Feldman, Y. Cole-Cole Broadening in Dielectric Relaxation and Strange Kinetics. Phys. Rev. Lett. 105, 037601 (2010).\nQ7: Pg.9 ‘The polarization enhancement, becoming more remarkable as the frequency moved to the higher band’. This sentence is hard to understand.\nResponse 7: Thanks for your correction. We wish to clarify that this original sentence is used to describe the effect of interfacial strain on frequency-dependence of the divided polarization loss ( ) and the ′′ 𝜀𝑝 relative ratio between and (Fig. 3f and Supplementary Fig. 13c-d). According to your ′′ ′′ suggestion, the original 𝜀s𝑝entence 𝜀h𝑐as been revised to have a clearer understanding on the frequency-dependence of polarization loss.\nRevision in the manuscript: Additionally, the / value could reflect the contribution of polarization loss within the tested ′′ ′′ frequency range. A 𝜀𝑝s s 𝜀 h𝑐own in Fig. 3f, the values of / ratio rise with increasing frequency, ′′ ′′ indicating that polarization loss played a more domina𝜀n𝑝t 𝜀ro𝑐le at higher frequencies. Notably, this frequency dependent enhancement was most significant in the ZFC-2 specimen with interfacial tensile strain, highlighting the controllability of polarization loss through strain engineering. (Page 10 in revised manuscript)\nFig. 3 f The frequency dependence of ratio in ZFC-x. ′′ ′′ 𝜀𝑝/𝜀𝑐\nSupplementary Fig. 13 Profiles of divided c conduction ( ) and d polarization loss ( ) in the ZFC- ′′ ′′ x system. 𝜀𝑐 𝜀𝑝\nQ8: If the goal is to show the properties of the composite in the EM absorption demonstration, it would be more convincing to perform the experiment on a film instead of a metasurface. Otherwise, it is hard to tell if the performance enhancement and wide-band absorption properties is due to the metasurface or the intrinsic properties of the composite. The relative contributions of the two effects are not explained in the current form.\nResponse 8: We wish to clarify that the tensile-strain enhanced magnetoelectric heterostructures (ZFC-2) exhibit an impressive EM absorption performance with an effective absorption bandwidth of 7.38 GHz, covering the tested high-frequency region from 10.62 GHz to 18.00 GHz. To meet the demand for ultrabroadband effective absorption, especially in the low-frequency regime relevant to sub‑6 GHz 5G devices, we designed a metastructure for ZFC‑2 composites to enhance its effective absorption performance towards lower frequency (Fig. 4d) by leveraging the periodic structure-endowed additional diffraction resonances.\nAdditionally, according to your suggestion, we also supplied two parallel control groups, which are the ZFC-2 filled resin film and the all-resin metastructure without the filling of functional materials (Supplementary Fig. 26a), respectively, to further elucidate the synergistic effect between the metastructure and the intrinsic properties of ZFC-2 absorbers toward the eventual full-band absorption performance. The arch-method tested RL values show that the single metastructure without the ZFC-2 filling cannot achieve effective absorption while the ZFC-2 filled resin film without metastructure only exhibit narrow effective absorption at the high-frequency band (Supplementary Fig. 26b). In the aspect of practical application, although ZFC-2 fill resin can reduce the EM radiation signals at a certain content, the efficiency is still unsatisfying (Supplementary Fig. 26c). In addition, we also investigate the EM energy attenuation performance by exposing the samples in a high-power microwave radiation source (2.45 GHz, 100W). As shown in Fig. 4f and Supplementary Fig. 26d, only ZFC-2 filled film and metamaterials exhibited remark heat variation after 60s microwave radiation. Based on these mentioned analyses, we can confirm that ZFC-2 magnetoelectric heterostructure dominate the EM energy loss while the metastructure design expand its effective absorption bandwidth in the lower frequency region, which jointly contributes the final full-band (2-18 GHz) absorption performance. The related contents have been also supplied in the revised version of main text and Supplementary Materials.\nRevision in the manuscript: In contrast, both control samples (the all-resin metastructure and the ZFC-2/resin plate) failed to achieve effective EM attenuation (Supplementary Fig. 26), further demonstrating that the impressive EM protection arises from the synergistic contribution between the strain-mediated magnetoelectric absorbers and the tailored metastructure (Page 12 in revised manuscript)\nSupplementary Fig. 26 Macroscale EM attenuation performances of parallel control groups. a Digital photo of the ZFC-2 composites filled resin film and the all-resin metamaterials under the arch method testing environment, and the scale bar is 5 cm. b Corresponding tested reflection loss values. c Photographs of EM signals detection with control group. d Digital photos of as-fabricated materials under the radiation of high-power microwave source, and corresponding infrared thermal images before and after EM source radiation for 60s. No detectable EAB and only a narrow EAB at high-frequency were obtained in the all-resin metamaterials and ZFC-2 composites filled resin film, respectively. confirming that both of the intrinsic properties of ZFC-2 composites and the periodical metastructure jointly contributed to the full-band effective absorption of ZFC metamaterials. These comparison results of EM radiation protection demonstrated that the individual ZFC composite or metastructure could not satisfy effective EM energy dissipation, confirming the significance of constructing ZFC-based metamaterials.\nQ9. Please clarify the physical principles that link the unique interface strain engineering to wide-band absorption.\nResponse 9: Thanks for your specialized comments. We wish to clarify that the enhanced EM wave absorption, reflected in the broadened effective absorption bandwidth (EAB, Fig. 4a), is governed by a multiscale physical mechanism, where interfacial strain induced microscopic changes propagate stepwise to define the eventual macroscopic performance. The following points details this causal chain with deepened physical insight:\ni) Interfacial strain reconstructed the distribution of interfacial charges and potential state\nThe implemented atomic-level interfacial strain (compressive and tensile strain) is not only a mere mechanical state, but also directly modifies the local crystal field and atomic interaction at the Fe C/ZnO 3 magnetoelectric heterointerface (Fig. 2c). Interfacial strain manipulates the formed interfacial bond and regulates orbital overlap, which alters the local density of states (evident by the DFT calculated projected density of states, Fig. 3g) and shifts the atomic alignment at the interface (observed from the iDPC results in Fig. 2c). This atomic-scale reconstruction induced the rearrangement of interfacial electron, reflected in the interfacial electric field coupling in the strain-involved magnetoelectric interface (Fig. 2e, f). Thus, these coupled atomic interfaces could provide more efficient carriers transports pathway for accelerating the migration of charge carriers owing to more sufficient overlap of electron orbits by interfacial coupling [Ref. R1]. In addition, interfacial strain also triggered the increased interfacial potential differences and the reduced work function (Φ), as evident by hologram-measured (Fig. 3d) and DFT-calculated charge density distribution (Fig. 3h), respectively. Such variation signifies a stronger built-in electric field (BIEF), which originates from the strain-amplified charge transfer dipole at the interface [Ref. R1-3]. This step defines the primary electrical boundary condition for subsequent polarization relaxation process.\nFigure 2 c iDPC-STEM images of heterointerfaces and corresponding geometric phase analysis (GPA) results. e Projected atomic electric field map of ZnO effusion reconstructed magnetoelectric interface. f Effect of interfacial strain on the vector field distribution of the selected region in e, the color bar corresponds to the vector magnitude. All scale bars in c and e are 500 pm.\nFigure 3 d Reconstructed electronic hologram and corresponding 3D charge density distribution images. g Projected density of states (PDOS) of ZnO-diffusion reconstructed interfaces. h Calculated Φ values and charge distribution differences of ZnO diffusion reconstructed magnetoelectric heterostructure.\nii) Strain-optimized interfacial state broadened dielectric loss by modifying relaxation time\nThe strain-enhanced BIEF could actively rearrange the energy landscape for charge carriers involved in polarization [Ref. R1], which effectively lowers the potential barrier (or average activation energy, Ea) for accumulatio or depletion of charges at the heterointerface [Ref. R4-5]. According to the Arrhenius formula ( ), the reduction in activation energy for polarization fluctuation (Ea) 𝐸𝑎 leads to an expone𝜏nt=ial𝜏 0 d eecxrpea (s𝑅e𝑇 )in the characteristic relaxation time (τ) [Ref. R6], which means the accelerated polarization response. Based on the relaxation relation ( , is the frequency 1 assigned to the maximum resonance peak) [Ref. R7, 8], the shortened τ wa𝜏s =al s2o𝜋 c𝑓𝑚onf𝑓ir 𝑚 med by the shift of the relaxation peak towards higher-frequency in the tangent dielectric loss plots (Fig. 3b). Crucially, interfacial strain did not create a single, unique τ but introduces nanoscale heterogenous strain distribution (Fig. 2c-d and Supplementary Fig. 12) for inducing multiple polarization responses, as reflected by numerous resonance peaks in and (Supplementary 13b, d), further resulting a ′′ ′′ broadened distribution of relaxation time [Re 𝜀 f. R9,10]. T𝜀h𝑝e wide distribution of relaxation time could be reflected as a slower decay of the imaginary part of permittivity [Ref. R11-13] (Supplementary Fig. 13b), as well as the wider resonance peak and more pronounced asymmetric Cole-Cole type dispersion observed in the strain-involved ZFC specimen (Fig. 3b, c). Meanwhile, the differential charge density distribution reveals pronounced yet heterogeneous charge accumulation and depletion at the coupled magnetoelectric interfaces (Fig. 3h), giving rise to robust interfacial dipoles with a non-uniform spatial distribution [Ref. R14-15]. This result further verified the wide distribution of interfacial polarization, also accounting for the broadened relaxation time. Therefore, the combined effect of a shorter τ and a broader τ distribution jointly contributed to a wide and elevated loss plateau in the tested frequency, which is essential for broadband dissipation.\nSupplementary Fig. 13 b Profiles of imaginary part ( ) of permittivity, and divided polarization loss ′′ ( ). 𝜀 ′′ 𝜀𝑝\nFig. 3 b Tangent values of dielectric loss. c Cole-Cole plots over the frequency region corresponding to the strongest dielectric relaxation peaks.\niii) Optimized impedance matching and the assistance of multiple loss mechanism in the oriented diffusion tailored magnetoelectric heterostructure system.\nOur previous analyses have demonstrated the interfacial strain endowed broadband dielectric loss ability, while this enhancement must be accompanied by satisfying impedance matching to achieve the eventual broadband absorption. Good impedance matching is a prerequisite for incident EM waves to penetrate into the absorption material [Ref. R16]. Distinct from conventional strain modulation based on an external mechanical manipulation, our work proposed an oriented diffusion strategy to precisely tailor the interfacial strain in a magnetoelectric heterostructure composite system. The gradient diffusion of dielectric component ZnO not only constructed the evolution of interfacial strain but also reconfigured the distribution of components and the microscale architectures such as the formed hollow and porous structure (Supplementary Fig. 2b, c), which could optimize the impedance matching of the overall composite material [Ref. R17] (Supplementary Fig. 18). And these micrometer-scaled hollow structures could trigger inside multiple scattering mechanism for dissipating the incident EM wave [Ref. R18]. In addition, the existence of magnetic component Fe C induced the magnetic loss mechanism such 3 as magnetic resonances and eddy current loss in the magnetoelectric heterostructures (Supplementary Note 3), which was also affected by the diffusion process owing to the rearrangement of component and structure (Supplementary Fig. 20, 21). Thus, the participation of magnetic loss mechanism could not be negligible, which also contributed to the as-presented EM absorption performance of the ZFC-based magnetoelectric heterostructure system.\nIn summary, our proposed distinct interfacial strain modulation strategy driven by the gradient oriented diffusion of dielectric component precisely tailored atomic-level strain states on the magnetoelectric heterointerfaces and regulated the microscale architectures of the overall composite system. The implemented interfacial strain constructed interfacial coupling for accelerating electron transports and enlarged interfacial potential difference for boosting polarization activation, leading to a widely distributed and shortened relaxation times and further a broadened dielectric loss capability. While the diffusion-induced component and structure reconfiguration provided satisfying impedance matching and additional magnetic loss and inner scattering attenuation mechanism. Eventually, the synergistic interaction of these multiple physical microscale mechanisms contributed the impressive macroscale wideband EM absorption performance of the magnetoelectric heterostructure.\nReferences for Response 9: [R1] Lv, X. et al. Engineering orbital hybridization in advanced electrocatalysts for energy conversion: Fundamentals, Modulations, and Perspectives. Adv. Energy Mater. 2501129 (2025). [R2] De Sanctis, A., Amit, I., Hepplestone, S. P., Craciun, M. F., & Russo, S. Strain-engineered inverse charge-funnelling in layered semiconductors. Nat. Commun. 9, 1652 (2018). [R3] Lv, B. et al. Probing permanent dipole moments and removing exciton fine structures in single perovskite nanocrystals by an electric field. Phys. Rev. Lett. 126, 197403 (2021). [R4] Li, H., Hao, X., Gong, H., Jin, Z., & Zhao, T. Efficient hydrogen production at a rationally designed MoSe @ Co O p-n heterojunction. J. Colloid Interf. Sci. 586, 84-94 (2021). 2 3 4 [R5] Baber, N., Scheffler, H., Ostmann, A., Wolf, T., & Bimberg, D. Field effect on electron emission from the deep Ti donor level in InP. Phys.l Rev. B 45, 4043 (1992). [R6] Viehland, D., Jang, S. J., Cross, L. E., & Wuttig, M. Freezing of the polarization fluctuations in lead magnesium niobate relaxors. J. Appl. Phys. 68, 2916-2921 (1990). [R7] Singh, K. P., & Gupta, P. N. Study of dielectric relaxation in polymer electrolytes. Eur. Polym. J. 34, 1023-1029 (1998). [R8] Zhang K. et al. All-Dielectric Ultra-broadband microwave absorbing aerogel with optimized dielectric dispersion via dielectric relaxation time regulation. Adv. Mater. 2506386 (2025). [R9] Jonscher, A. K. A new understanding of the dielectric relaxation of solids. J. Mater. Sci. 16, 2037-2060 (1981). [R10] Cole, R. H. On the analysis of dielectric relaxation measurements. J. Chem. Phys. 23, 493-499 (1955). [R11] Puzenko, A., Ishai, P.B. and Feldman, Y., Cole-Cole broadening in dielectric relaxation and strange kinetics. Physical Review Letters, 105(3), p.037601 (2010) [R12] Compan, V., Diaz-Calleja, R., Diaz-Boils, J., & Escorihuela, J. Distribution of Relaxation Times: Debye Length Distribution vs Electrode Polarization by a Cole-Cole Relaxation Model. J. Electrochem. Soc. 169, 013506 (2022). [R13] Kelley, D.F., Destan, T.J. & Luebbers, R.J. Debye function expansions of complex permittivity using a hybrid particle swarm-least squares optimization approach. IEEE T. Antenn. Propag. 55,1999-2005 (2007) [R14] Giovannetti, G.A.K.P.A., Khomyakov, P.A., Brocks, G., Karpan, V.V., van den Brink, J. and Kelly, P.J. Doping graphene with metal contacts. Phys. Rev. Lett. 101, 026803 (2008). [R15] Tung, R. T. Electron transport at metal-semiconductor interfaces: General theory. Phys. Rev. B 45, 13509 (1992). [R16] Hou, Z. L., Gao, X., Zhang, J. & Wang, G. A perspective on impedance matching and resonance absorption mechanism for electromagnetic wave absorbing. Carbon 222, 118935 (2024). [R17] Cheng, J. B., Shi, H. G., Cao, M., Wang, T., Zhao, H. B., & Wang, Y. Z. Porous carbon materials for microwave absorption. Mater. Adv. 1, 2631-2645 (2020). [R18] Deng, Z. et al. Lightweight Fe@C hollow microspheres with tunable cavity for broadband microwave absorption. Compos. Part B-Eng. 177, 107346 (2019).\nSupplementary Fig. 2 b SEM images of as-fabricated ZFC-x microspheres, and the inset shows inside architecture. c STEM images of the ZFC-x inner.\nSupplementary Fig. 18 The profiles of value along frequency at the thickness from 1.0 to 5.0 mm. The marked gray region corre | s 𝑍 p 𝑛 o𝑖n𝑛d / s 𝑍 t 𝑛 o0 t | he value of ranging from 0.8 to 1.2, indicating the qualifying impedance matching in samples. |𝑍𝑛𝑖𝑛/𝑍𝑛0|\nSupplementary Fig. 20 a Off-axis electron hologram images and b related reconstructed stray magnetic fluxes distribution of ZFC-x microsphere surface. All scale bars are 200 nm.\nSupplementary Fig. 21 Simulated magnetic fluxes of the surface with a bulges and b wrinkles. c Cross-section of magnetic moment distribution in ZFC with bulged (up) and wrinkled surface (bottom).\nRevision in the manuscript: To deeply decipher the regulation mechanism of the polarization loss, the reconfigured electronic structures in the ZnO gradient diffusion controlled ZFC-based heterointerfaces were further theoretically analyzed by density functional theory (Supplementary Note 2). The projected density of state (PDOS) analysis revealed a gradient diffusion-induced reconstruction of interfacial electronic structures (Fig. 3g) and BIEF, consistent with the observation from the DPC and electron holography. As tensile strain was formed on the ZFC heterointerface, more pronounced orbits overlaps were detected, assigning to the enhanced interfacial coupling interaction, thereby boosting electron transports of the external electric field across the interface. As the interfacial strain state evolved from the relieved to compressive and tensile, the reduced work function (Φ) suggested the lowered energy barriers for charge migration (Fig. 3h and Supplementary Fig. 14), which improved the electron mobility and activity36. This improvement facilitated the supply of polarizable charges, thereby promoting the response of interfacial dipoles to external alternating electric fields. In additional, the differential charge density distribution revealed pronounced and inhomogeneous charge accumulation and depletion at these coupled magnetoelectric interfaces (Supplementary Fig. 15), forming multiple localized space-charge regions. This result indicated the generation of robust interfacial dipole layers with a wide distribution37, which could account for broadening the distribution of polarization relaxation. Thus, these combined experimental results and theoretical analyses revealed a tunable strain-polarization coupling mechanism. The tailored interfacial strain evolution, induced by oriented diffusion, effectively orchestrated a reconfiguration of interfacial electronic properties via constructing interfacial coupling. This process created intense and wide-ranging polarization responsiveness, thereby significantly enhancing the dielectric loss performance in response to the external EM wave. (Page 10 in revised manuscript)\n34. Zhang K. et al. All-Dielectric Ultra-broadband Microwave Absorbing Aerogel with Optimized Dielectric Dispersion via Dielectric Relaxation Time Regulation. Adv. Mater. 2506386 (2025). 36. Zhang, S. et al. New prospects in Built‐in Electric Fields for Electromagnetic Wave Absorption: from Fundamentals to Interdisciplinary Applications. Adv. Funct. Mater. e13762 (2025). 37. Tung, R. T. Electron Transport at Metal-Semiconductor Interfaces: General Theory. Phys. Rev. B 45, 13509 (1992)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed satisfactorily all of my comments and therefore, the revised manuscript can be published.", "reviewer_2": "The manuscript titled \"Oriented Diffusion Tailors Interfacial Strain-Polarisation Coupling for Broadband Electromagnetic Absorption\" has been thoroughly revised in response to the feedback received. The authors have carefully addressed all questions and concerns raised during the initial review. Their comprehensive responses demonstrate a strong commitment to improving the quality of their work.\n\nThe revisions have significantly enhanced the manuscript, providing clearer arguments, better organisation, and a more in-depth exploration of key concepts. The authors have shown commendable dedication to incorporating the provided suggestions.\n\nOverall, the revised manuscript meets the publication standards of Nature Communications and is recommended for acceptance. The improvements made contribute valuable insights to the field.", "reviewer_3": "The authors have answered all my questions satisfactorily and have made appropriate changes to the manuscript. I have no further concerns and recommend acceptance.", "reviewer_4": "The authors have made the necessary clarifications."}, "author_response": "Response Letters\nReviewer #1:\nThe manuscript titled “Oriented atomic diffusion tailors strain–polarization coupling for broadband\nelectromagnetic absorption” presents a technically robust strategy to modulate interfacial strain for\nachieving broadband electromagnetic (EM) wave absorption. The authors construct ZnO/Fe₃C@C\nmicrospheres (ZFC–x) featuring gradient tensile–compressive strain fields induced by controlled\noutward ZnO diffusion during annealing. The study effectively integrates advanced characterization\ntechniques such as aberration-corrected STEM"}]

Decision letter