The Understanding of Size‐Dependent Magnetic Loss Mechanisms Based on Surface Atoms Moment to Tune Electromagnetic Wave Response

ABSTRACT

Magnetic loss is a key mechanism in electromagnetic wave (EMW) absorption, but it is still a challenge to understand the relationships between the size effect and magnetic loss ability. Here, we synthesized Fe₃O₄@CeO₂ core‐shell composites to reveal the above relationship. Our synthesis started with the preparation of Fe₂O₃ nanocubes, followed by coating CeO₂ shell by hydrothermal technology. After undergoing H₂ reductive annealing, Fe₃O₄@CeO₂ core‐shell nanocubes were obtained with their magnetic core size fixed to 155 ± 10 nm, 305 ± 10 nm, 510 ± 15 nm, and 705 ± 15 nm, respectively, where CeO₂ shell can stabilize the magnetic cores against agglomeration and adjust the dielectric feature. Within 2–6 GHz, the smallest‐sized Fe₃O₄@CeO₂ represents the highest magnetic loss ability by the natural resonance for the largest number of surface atoms. Within 6–14 GHz, the exchange resonance from the Fe²⁺‐O‐Fe²⁺ super‐exchange interactions is suppressed by the increased oxygen vacancies and super‐exchange distances for the small‐sized particles. As a result, the largest‐sized Fe₃O₄@CeO₂ achieved an effective absorption bandwidth of 5.7 GHz (8.1–13.8 GHz) for the medium‐frequency application. Our work clarifies the key role of surface atom moment in magnetic loss, offering guidance for understanding the relationship among size‐mechanism‐performance.

The Fe₃O₄@CeO₂ core‐shell nanoparticles with controllable size have been synthesized to understand the relationships between the size effect and magnetic loss ability. With the increased size, the natural resonance is weakened for decreased surface moment, while the exchange resonance from the Fe²⁺‐O‐Fe²⁺ interactions is enhanced for the reduction of oxygen vacancies.

1. Introduction

The electromagnetic wave (EMW) is a kind of important radiant energy by oscillating electric and magnetic fields [1, 2, 3]. Especially, the EMW at 2–18 GHz is most common for their wide applications in electronic communications, radar detection, medical imaging, and so on [4, 5, 6, 7, 8]. The electromagnetic wave absorption (EMA) materials that can effectively transform incident EM energy into thermal energy, which can protect electronic devices from EM interference and achieve aircraft invisibility [9, 10, 11, 12, 13]. More importantly, EMA materials are very promising to provide the energy source for wearable devices by combining the thermoelectric materials, where the thermal energy converted from EM energy via EMA materials can be transformed into electric energy again by the thermoelectric materials [14, 15, 16].

Generally, EMA materials can attenuate EMW by magnetic loss, dielectric loss, and conductive loss [17, 18, 19, 20, 21, 22]. Among the above three mechanisms, the magnetic loss is a very key attenuation mechanism, which exhibits excellent absorption feature even at low frequency [23, 24, 25]. At 2–18 GHz, the magnetic loss mainly involves natural resonance, exchange resonance, and eddy‐current loss, which have been proven to respond to the EMW at 2–6 GHz, 6–14 GHz, and 14–18 GHz, respectively [26, 27, 28, 29, 30, 31].

The typical magnetic loss‐typed EMA materials should own a soft magnetic feature, containing the high saturation moment (M _s) and low coercivity [32, 33, 34]. The former mainly provides much magnetic moment to achieve resonance with EMW, and the latter can impede frequency dispersion effect to maintain a relatively high magnetic loss ability at high frequency [35, 36, 37, 38]. To date, the ferrites, magnetic metals or alloys based on Fe, Co, and Ni have been developed to achieve high magnetic loss [39, 40, 41, 42, 43, 44]. However, the relationship between the size of ferrimagnetic materials and magnetic loss ability is still unclear, which is very important to understand the EMW loss mechanisms and develop high‐performance EMA materials.

In this work, we selected the typical Fe₃O₄ as the model material to reveal the relationship between size and magnetic loss ability. We first synthesized Fe₂O₃ nanocubes with their particle size controlled at 155 ± 10 nm, 305 ± 10 nm, 510 ± 15 nm, and 705 ± 15 nm by hydrothermal synthesis route. These as‐synthesized Fe₂O₃ nanocubes were further coated with a CeO₂ shell to form Fe₂O₃@CeO₂ core‐shell structure, and then were converted into Fe₃O₄@CeO₂ after H₂ annealing treatment. During the H₂ reduction process, the CeO₂ shell can protect Fe₃O₄ core from agglomeration to maintain the monodispersed magnetic core. Furthermore, H₂ reduction can induce the coexistence of Ce³⁺ and Ce⁴⁺ in the CeO₂ shell, which enables electron transferring between them under EMW to adjust the dielectric feature and allows more EMW to enter the absorbers. As a result, the well‐monodispersed Fe₃O₄@CeO₂ were successfully obtained with magnetic cores size maintaining to 155 ± 10, 305 ± 10, 510 ± 15, and 705 ± 15 nm, corresponding to overall particle sizes of 185 ± 10, 350 ± 10, 565 ± 15, and 775 ± 15 nm, respectively. Under the same weight filling ratio, the smallest‐sized Fe₃O₄ nanoparticles own the most “surface magnetic moment”, contributing to the strongest natural resonance. Thus, in the range of 2–6 GHz, the size of Fe₃O₄@CeO₂ with high u″ values (magnetic loss ability) is in the order of 185 ± 10 nm > 350 ± 10 nm > 565 ± 15 nm > 775 ± 15 nm. Correspondingly, the smaller‐sized Fe₃O₄ nanoparticles also lead to more oxygen vacancy defects and larger atom distance induced by the large curvature, which weakens the exchange resonance among surface magnetic moments. As a consequence, the size of Fe₃O₄@CeO₂ with high u″ values was in the order of 775 ± 15 nm > 565 ± 15 nm > 350 ± 10 nm > 185 ± 10 nm in the range of 6–14 GHz. As for 14–18 GHz, there is little magnetic loss since the eddy loss plays a key role in this frequency range. Specifically, the 775 ± 15 nm sample achieved a minimum reflection loss of −49.4 dB, with an effective absorption bandwidth (EAB) of 8.12–13.78 GHz (5.7 GHz), covering nearly the entire X band, outperforming most Fe₃O₄‐based absorbers. This work reveals the key role of surface magnetic moment in the magnetic loss process, and provides an important reference for studying magnetic loss mechanisms and developing high‐performance EMA materials.

2. Results and Discussion

The synthetic procedure for Fe₃O₄@CeO₂ nanoparticles is illustrated schematically in Figure 1a. The α‐Fe₂O₃ nanocubes, which crystallize in a rhombohedral structure (R‐3c), have been obtained by reacting FeCl₃ and NaOH under hydrothermal conditions, as shown in X‐ray diffraction patterns (XRD, Figure S1) [45]. The size of Fe₂O₃ particles with cube‐like morphology can be adjusted by controlling NaOH amount and iron precursor, as shown in scanning electron microscopy images (SEM, Figure 1b–e). In detail, using 0.27 mol of FeCl₃ with 0.54 or 0.50 mol NaOH can yield 155 ± 10 or 305 ± 10 nm α‐Fe₂O₃ cubes, while 0.27 mol of FeCl₃·6H₂O reacts with 0.54 or 0.50 mol NaOH would produce 510 ± 15 or 705 ± 15 nm α‐Fe₂O₃ nanocubes, respectively. The cube morphology mainly originates from the anisotropic growth regulated by the selective adsorption of Cl⁻ ions on specific crystal faces. At high chloride concentrations, the growth rates of the {012}, {104}, and {110} faces become comparable, leading to the formation of cubic‐shaped particles.

FIGURE 1.

(a) The synthetic process of Fe₃O₄@CeO₂ nanoparticles. The SEM images of Fe₂O₃: (b) 155 ± 10 nm, (c) 305 ± 10 nm, (d) 510 ± 15 nm, (e) 705 ± 15 nm. (f) TEM image and (g) elemental mapping images of 350 ± 10 nm Fe₂O₃@CeO₂.

Furthermore, these as‐prepared Fe₂O₃ nanocubes were dispersed in Ce(NO₃)₃/ethanol/water mixed solution, followed by hydrothermal treatment to obtain corresponding Fe₂O₃@CeO₂ composites (Figure S2) [46]. Transmission electron microscopy (TEM) and elemental mapping images (Figure 1f–g) demonstrate that the Fe₂O₃@CeO₂ nanoparticles have retained the cubic morphology with 10–35 nm CeO₂ nanoparticles coated on the surface of Fe₂O₃ nanocubes. And the as‐synthesized Fe₂O₃@CeO₂ nanoparticles represent the overall particle sizes of approximately 185 ± 10 nm, 350 ± 10 nm, 565 ± 15 nm, and 775 ± 15 nm, respectively (Figure S3). For 185 ± 10 nm Fe₂O₃@CeO₂, the CeO₂ shell is unsound with partially exposed Fe₂O₃ (Figure S3a). With the increase of Fe₂O₃ size, the CeO₂ nanoparticles shell becomes dense (Figure S3b–d). The phenomenon can be attributed to two reasons. On the one hand, the small‐sized Fe₂O₃ nanoparticles represent a large specific surface area, and the amount of CeO₂ was not enough to cover the entire surface of Fe₂O₃ nanoparticles. On the other hand, the small‐sized Fe₂O₃ nanoparticles own a large curvature, which would yield strong stress to induce the CeO₂ shell cracking.

The above synthesized Fe₂O₃@CeO₂ nanoparticles were further reduced by 95% Ar + 5% H₂, which generated the corresponding Fe₃O₄@CeO₂ nanoparticles. The H₂ reduction only changed the phases of Fe₂O₃ without any effect on CeO₂, as shown in XRD patterns (Figure S4). And the morphology and size of Fe₃O₄@CeO₂ (Figure 2a–d) are the same as those of the corresponding Fe₂O₃@CeO₂ nanoparticles, which suggests the coated CeO₂ shells can protect Fe₃O₄ nanoparticles from agglomeration and growth during the H₂ annealing process. TEM image of the 350 ± 10 nm Fe₃O₄@CeO₂ nanoparticles clearly reveals the distinct core‐shell structure (Figure 2e). The selected‐area electron diffraction (SAED, Figure 2f) pattern displays the diffraction spots corresponding to the (511) crystal plane of Fe₃O₄ and the (111) crystal plane of CeO₂. The high‐resolution TEM (HRTEM, Figure 2g) image further reveals lattice spacings of 0.31 and 0.26 nm, which can be equivalent to the (111) crystal plane of CeO₂ and the (511) crystal plane of Fe₃O₄, respectively. Figure 2h,i presents the high‐angle annular dark‐field scanning TEM (HAADF‐STEM) and elemental mapping of Fe₃O₄@CeO₂, in which the spatial distributions of Fe, O, and Ce elements are clearly identified. It can be observed that the Fe element is predominantly concentrated in the central region, while the Ce element is uniformly distributed around the external shell, indicating that the CeO₂ shell is intactly coated on the surface of Fe₃O₄ nanocubes.

FIGURE 2.

The SEM images of Fe₃O₄@CeO₂: (a) 185 ± 10 nm, (b) 350 ± 10 nm, (c) 565 ± 15 nm, (d) 775 ± 15 nm. (e–i) The characterization of 350 ± 10 nm Fe₃O₄@CeO₂. (e) TEM image, (f) SAED pattern, (g) HRTEM image, (h) HAADF‐STEM image, (i) elemental mapping images.

To further elucidate the electronic states of Fe₃O₄@CeO₂ composites, X‐ray photoelectron spectroscopy (XPS) measurements have been conducted on as‐synthesized samples with different particle sizes. All samples represent the coexistence of Fe²⁺ and Fe³⁺ species accompanied by typical satellite peaks, as shown in the Fe 2p spectrum (Figure 3a), further confirming the successful formation of the Fe₃O₄ phase after reduction treatment. In addition, with the increase of Fe₃O₄ core size from 155 ± 10 to 705 ± 15 nm, the Fe²⁺‐related peaks gradually weaken, while the Fe³⁺ peaks correspondingly intensify, indicating a decreasing Fe²⁺/Fe³⁺ ratio with increasing particle size. This trend can be attributed to the fact that smaller Fe₃O₄ particles are more prone to surface oxygen loss during the H₂ annealing process, which facilitates the generation of a higher proportion of Fe²⁺ species at the particle surface. During the H₂ reduction process, the O atoms were removed by combining with H atoms to form H₂O. In fact, it is difficult to exactly control the amount of H₂. After all Fe₂O₃ nanoparticles were converted into Fe₃O₄, the O atoms on the surface of Fe₃O₄ nanoparticles are easily further removed since they are more active than the internal O atoms. As a result, there are many oxygen vacancy defects on the surface of Fe₃O₄ nanoparticles. Figure 3b presents the high‐resolution Ce 3d XPS spectra of Fe₃O₄@CeO₂ samples with different particle sizes. All samples exhibit characteristic Ce³⁺/Ce⁴⁺ features [47]. Furthermore, with increasing Fe₃O₄ core size from 155 ± 10 to 705 ± 15 nm, the relative area fraction of Ce³⁺‐related peaks gradually decreases (from 20.9% to 9.79%), accompanied by a corresponding increase in the Ce⁴⁺ peaks contribution, indicating a reduction of the Ce³⁺/Ce⁴⁺ ratio with increasing particle size. Meanwhile, the overall Ce 3d main peaks shift slightly toward higher binding energy, suggesting that there is electron transfer from CeO₂ shell to Fe₃O₄ core.

FIGURE 3.

The surface chemical state and magnetic properties of all Fe₃O₄@CeO₂. (a) Fe 2p high‐resolution XPS spectra, (b) Ce 3d high‐resolution XPS spectra, (c) EPR spectra of all Fe₃O₄@CeO₂, (d) Magnetic hysteresis loops at room temperature.

Figure 3c displays the electron paramagnetic resonance (EPR) spectra of Fe₃O₄@CeO₂. All samples exhibit a distinct resonance signal at g ≈ 2.003, which is attributed to unpaired electrons associated with oxygen vacancies. As the particle size increases from 185 ± 10 to 775 ± 15 nm, the EPR signal intensity gradually decreases, indicating a continuous reduction in oxygen vacancy concentration. Above data demonstrate that the size decrease of Fe₃O₄@CeO₂ nanoparticles can lead to the increase of oxygen vacancy defects on the surface of both Fe₃O₄ and CeO₂ nanoparticles.

The magnetic properties of Fe₃O₄@CeO₂ samples have been further characterized by vibrating sample magnetometry (VSM) at room temperature (Figure 3d). The saturation magnetization (M _s) values of 56.93, 58.91, 65.43, and 66.39 emu/g are obtained in 185 ± 10, 350 ± 10, 565 ± 15, and 775 ± 15 nm Fe₃O₄@CeO₂, respectively. These M _s values are far lower than Fe₃O₄ bulk (more than 80 emu/g). Besides the size effect, the decreased M _s is mainly attributed to the introduction of non‐magnetic CeO₂ shells. And the coercivity (H _c) also increases slightly from 187.86 to 253.56 Oe with the increase of particle size. The phenomenon can be attributed to the strong demagnetizing field induced by many oxygen vacancy defects on the surface of the small‐sized Fe₃O₄, which can weaken magnetocrystalline anisotropy and M _s [48]. These results also confirm that small‐sized particles possess more oxygen vacancy defects on the surface.

The EMW absorption performances of all Fe₃O₄@CeO₂ nanoparticles in the 2–18 GHz range have been systematically evaluated according to the transmission line theory, as shown in Figure 4. With the increase of particle size, the EAB (RL≤−10 dB) of Fe₃O₄@CeO₂ particles is gradually increasing. For the 185 ± 10 nm sample, the value of RL_min reaches −30.7 dB with an EAB of 4.2 GHz at 2.4 mm (Figure 4a,e). When the particle size increases to 350 ± 10 nm, the RL_min value is −42.2 dB (Figure 4b) with an EAB of 4.3 GHz at 2.5 mm (Figure 4f). Further increasing the particle size to 565 ± 15 nm leads to RL_min of −50.9 dB (Figure 4c) and EAB of 4.8 GHz at 2.3 mm (Figure 4g). When the size reaches 775 ± 15 nm, RL_min is −49.4 dB (Figure 4d), and the widest EAB of 5.7 GHz (8.1–13.8 GHz) is achieved at 2.3 mm (Figure 4h), almost covering the entire X‐band. These results demonstrate that particle size regulation effectively enables the synergistic optimization of impedance matching and energy dissipation. Figure 4i further summarizes the variations of RL_min and EAB for Fe₃O₄@CeO₂ particles with different sizes in both low‐frequency (2–8 GHz) and medium‐high‐frequency (8–18 GHz) regions. In the low‐frequency range, all samples represent an EAB around 2.5 GHz, suggesting a promising application in low‐frequency EM field. Furthermore, the EAB of 5.7 GHz for 775 ± 15 nm Fe₃O₄@CeO₂ particles indicates the high EMA feature in the medium‐high‐frequency range.

FIGURE 4.

The EMA performances for Fe₃O₄@CeO₂ samples. (a–d) The 3D plots of RL values vs. frequency at different thicknesses of Fe₃O₄@CeO₂: (a) 185 ± 10 nm, (b) 350 ± 10 nm, (c) 565 ± 15 nm, (d) 775 ± 15 nm. (e–h) The 2D contours of RL as functions of thickness and frequency of Fe₃O₄@CeO₂: (e) 185 ± 10 nm, (f) 350 ± 10 nm, (g) 565 ± 15 nm, (h) 775 ± 15 nm. (i) The collection of RL_min and EAB for all the Fe₃O₄@CeO₂ at both low and medium frequency.

The complex permittivity (ε′, ε″) and permeability (µ′, µ″) within the 2–18 GHz range for Fe₃O₄@CeO₂ with different particle sizes have been shown in Figure 5. The real parts of permittivity (ε′) and permeability (µ′) represent the energy‐storage capability, while the imaginary parts (ε″ and µ″) are associated with dielectric and magnetic loss abilities. As presented in Figure 5a,b, both ε′ and ε″ decrease overall with increasing particle size from 185 ± 10 nm to 775 ± 15 nm, indicating weaker dielectric polarization capability for larger particles. This phenomenon can be mainly attributed to the largest number of oxygen vacancies for 185 ± 10 nm Fe₃O₄@CeO₂ among all samples, which induces many Ce³⁺/Ce⁴⁺ ion pairs. Such ion pairs provide a large number of mobile electrons, thereby enhancing the electrical conductivity and substantially increasing ε′ and ε″ values. Meanwhile, the small‐sized Fe₃O₄@CeO₂ particles also provide more abundant interfacial and defect polarizations than large‐sized particles.

FIGURE 5.

The electromagnetic parameters and RCS values for all the Fe₃O₄@CeO₂ samples. (a) ε′‐f curves, (b) ε“‐f curves, (c) µ′‐f curves, (d) µ”‐f curves, (e) tan δ _µ , (f) tan δ _ε , and (g) α values. (h) 3D RCS plot of Fe₃O₄@CeO₂ (775 ± 15 nm). (i) RCS simulation curves for all the Fe₃O₄@CeO₂ and PEC at scanning angles of −90° to 90°.

Figure 5c,d displays the variation of µ′ and µ″ as a function of frequency. For all samples, µ′‐f curves exhibit similar values and variation trends, suggesting that the change of particle size has little effect on the magnetic storage capability. However, the size effect can deliver the magnetic loss ability (µ″). Within the 2–6 GHz range where natural resonance occurs, µ″ values are increasing with the decrease of particle sizes. This phenomenon can be attributed that the smaller size particles with higher specific surface own the more surface magnetic moment than the large particles. It demonstrates that the magnetic loss capacity caused by natural resonance is mainly dependent on the surface magnetic moment interaction with EMW, while those magnetic moments in the inner core play little role in magnetic loss since the inner magnetic moment is bonded by high lattice energy. Within the 6–14 GHz range, where exchange resonance occurs, the µ″ value variation trend is consistent with the particle size change trend. The 775 ± 15 nm Fe₃O₄@CeO₂ particles exhibit the highest µ″ value among samples. This change also originates from the surface magnetic moment. For Fe₃O₄, the exchange resonance is mainly induced by the super‐exchange interaction of Fe²⁺‐O‐Fe²⁺. On the surface of small‐sized Fe₃O₄ particles, there is a large number of oxygen vacancies, which disrupt the super‐exchange interaction of Fe²⁺‐O‐Fe²⁺, thus weakening the exchange resonance and decreasing the µ″ value. Furthermore, the small‐sized Fe₃O₄ particles represent large curvature with tensile stress among surface atoms, which would increase the exchange distance of Fe²⁺‐O‐Fe²⁺ and thus further weaken the exchange resonance interaction. It is worth noting that the thickness of the CeO₂ shell is different since all Fe₃O₄@CeO₂ use the same Fe/Ce ratio. In large‐sized Fe₃O₄@CeO₂ core‐shell nanoparticles, the shell of CeO₂ is relatively thin, and they will generate a small impact on the surface moment. In small‐sized Fe₃O₄@CeO₂ nanoparticles, the shell of CeO₂ is thicker than large‐size samples. The thick CeO₂ shell has a stronger effect on the surface moment than a thin shell because the EMW mainly interacts with the surface of absorbing materials. As a consequence, in fact, the size effect of Fe₃O₄@CeO₂ on magnetic loss ability would be further enhanced when excluding the influence of CeO₂ shell thickness. In other words, the small‐sized nanoparticles will have an obviously enhanced natural resonance interaction than large‐size samples. These data further confirm that the surface magnetic moment other than the total magnetic moment plays a dominant role in magnetic loss process.

The magnetic loss tangent (tan δ_µ = µ″/µ′) is employed to evaluate the magnetic energy dissipation ability of the absorbers. As shown in Figure 5e, tan δ_µ values are higher for smaller particles in the low‐frequency range, while larger particles exhibit higher values in the medium‐high‐frequency range, which is consistent with above µ″ value. Furthermore, tan δ_µ values across the 2–14 GHz range are greater than 0.3, which is much higher than the dielectric loss tangent (tan δ_ε, less than 0.1) in Figure 5f, indicating that magnetic loss dominates the EMW attenuation process in the Fe₃O₄@CeO₂ system.

To further identify the origin of magnetic loss, the eddy current loss coefficient (C ₀ = µ″(µ′)⁻² f ⁻¹) was calculated. A constant C ₀ indicates eddy current dominance, whereas a fluctuating C ₀‐f curves suggest the coexistence of resonance‐related mechanisms. As shown in Figure S5, the coefficient C ₀ exhibits pronounced fluctuations with frequency. At low frequency, the natural resonance plays a predominant role, while exchange resonance mainly contributes to the loss within medium frequency. Therefore, the change trend of C ₀ in the medium‐to‐high‐frequency region is consistent with the µ″ value. At high frequency where the eddy‐current effect is the main loss factor, C ₀ value is close to 0, suggesting the eddy‐current loss is suppressed. The attenuation constant α, plotted in Figure 5g, represents the ability of the absorber to dissipate incident EMW energy during propagation. All samples exhibit α values that first increase and then decrease with frequency, which explains the reason for the excellent absorption ability at medium frequency. And the variation trend of α values with particle size is consistent with the changes observed in µ″ and tan δ_µ. The impedance matching (|Z _in/Z ₀|) is generally employed to evaluate the extent to which incident electromagnetic waves can penetrate into the absorber (Figure S6). The results demonstrate that the 185 ± 10 nm sample exhibits a relatively narrow matching region in the 2–18 GHz range. As the particle size increases, the impedance matching region becomes significantly broad. The 775 ± 15 nm Fe₃O₄@CeO₂ exhibits an optimal impedance matching at medium frequency, which allows more EMW to enter the absorbers. Furthermore, the 775 ± 15 nm Fe₃O₄@CeO₂ also exhibits the largest attenuation constant (Figure 5g) within the medium frequency range. And thus, a broad EAB of 5.7 GHz in the range of medium frequency was obtained in the 775 ± 15 nm sample.

The radar cross‐section (RCS) simulations were performed using CST Studio Suite to evaluate the practical electromagnetic absorption potential of Fe₃O₄@CeO₂ composites. The simulated model consisted of a perfect electric conductor (PEC) substrate covered by a layer of Fe₃O₄@CeO₂ absorbers, with the incident plane wave propagated along the negative z‐axis. As shown in Figure S7a, the pure PEC substrate exhibits an intense and uniform 3D RCS scattering pattern, confirming its almost complete reflection of incident microwaves. When coated with Fe₃O₄@CeO₂ layers (Figure S7b–d), the scattering intensity was markedly reduced, suggesting effective dissipation of electromagnetic energy within the composites. Especially, 775 ± 15 nm Fe₃O₄@CeO₂ (Figure 5h) exhibits the weakest scattering signals among all samples, suggesting a superior EMW attenuation ability. Furthermore, Figure 5i presents the simulated 2D RCS curves for all Fe₃O₄@CeO₂ samples and the PEC substrate over scanning angles from −90° to 90°. These results indicate that the RCS values of all Fe₃O₄@CeO₂ composites are significantly lower than that of the PEC, and the RCS reduction at the incident angle of 0° exceeds 23 dB m² for all samples. In particular, the 185 ± 10 nm Fe₃O₄@CeO₂ sample exhibits the most remarkable performances, achieving an RCS reduction of up to 28.6 dB m² at 0°. Moreover, when the incident angle exceeds 7°, the RCS values of all samples remain below −17.2 dB m², further confirming their excellent scattering‐suppression capability over a broad incident‐angle range.

The EMW attenuation mechanisms were further summarized in Figure 6. In Fe₃O₄@CeO₂ system, the magnetic loss is the main EMW attenuation form, while the dielectric loss can optimize the impedance matching to achieve the broadband absorption. The Fe₃O₄@CeO₂ particles with 775 ± 15 nm have the largest EAB value among all samples, which mainly is attributed to the optimal impedance matching. In the magnetic loss mechanism, the surface moments play a key role since they are more easily to rotate than inner body moments.

FIGURE 6.

The magnetic loss mechanisms for Fe₃O₄@CeO₂ absorbers.

In the low‐frequency region of 2–6 GHz, the magnetic loss is predominantly governed by the natural resonance mechanism (Figure 6a). With decreasing particle size, the specific surface area increases significantly, markedly increasing the number of surface magnetic moments per unit mass that participate in resonance responses. Meanwhile, many oxygen vacancies in the smaller‐sized Fe₃O₄ can induce more Fe²⁺ ions (magnetic moment) than that of larger nanoparticles on the surface of magnetic particles, which also increases the number of surface moments. Consequently, the samples with smaller size (185 ± 10 and 350 ± 10 nm) exhibit stronger natural resonance in the low‐frequency region, as reflected by their higher µ″ values compared with large‐sized samples. In the medium‐frequency region of 6–14 GHz, magnetic loss remains mainly associated with the exchange resonance process (Figure 6b). Such exchange resonance mainly originates from the Fe²⁺‐O‐Fe²⁺ super‐exchange interaction on the surface of Fe₃O₄, whose effective response frequency is primarily distributed in the medium‐to‐high‐frequency range.

In this system, there are three factors that influence the exchange resonance interaction. On the one hand, the small‐sized Fe₃O₄ nanoparticles with many surface moments allow stronger exchange resonance than large‐size samples. On the other hand, these abundant oxygen vacancies on the surface of small‐sized samples would disrupt the Fe²⁺‐O‐Fe²⁺ super‐exchange pathways, weakening exchange resonance and significantly reducing their magnetic loss capability. Furthermore, the small‐sized samples own a large curvature, which can yield strong tensile stress among surface atoms and increase the exchange resonance distance, further weakening exchange resonance interaction. To sum up, the small size effect is unfavorable to exchange resonance, which can reduce the magnetic loss capability. With further increasing frequency, the dynamic response of magnetic moments becomes progressively constrained, and exchange resonance can no longer maintain effective coupling with the high‐frequency electromagnetic field, resulting in an overall decrease in µ″.

3. Conclusion

In summary, size‐controlled Fe₃O₄@CeO₂ core‐shell composites with Fe₃O₄ core sizes ranging from 155 ± 10 to 705 ± 15 nm have been successfully constructed to systematically elucidate the intrinsic relationship among particle size, magnetic loss mechanisms, and EMW absorption performances. By employing Fe₃O₄ as a model ferrimagnetic system and introducing a stabilizing CeO₂ shell, a reliable platform has been established to investigate size‐dependent magnetic loss ability. Our results demonstrate that the surface moments play a key role since they are more easily to rotate than inner body moments. In the low‐frequency region of 2–6 GHz, Fe₃O₄ with the smallest size exhibits the strongest magnetic loss ability in the form of natural resonance by providing the most surface atoms and inducing many Fe²⁺ ions (magnetic moment) on the surface. In the medium‐frequency region of 6–14 GHz, exchange resonance originated from the Fe²⁺‐O‐Fe²⁺ super‐exchange interaction on the surface of Fe₃O₄, is the leading loss mechanism. And the increase of oxygen vacancies and super‐exchange distances on the surface of small‐sized magnetic particles significantly weakens the exchange resonance, which overwhelms the positive effect from the increasing number of surface moments. As a result, the small‐sized magnetic nanoparticles are promising for low‐frequency applications, and the large‐sized Fe₃O₄@CeO₂ with a core size of 705 ± 15 nm exhibits superior EMW absorption performance at medium frequency, achieving a RL_min of −49.4 dB and a broadened EAB width of 5.7 GHz (8.1−13.8 GHz) at 2.3 mm matching thickness. These findings not only deepen the fundamental understanding of magnetic loss mechanisms in ferrimagnetic systems but also provide valuable guidance for the rational design of high‐performance EMW absorbing materials through precise size and surface engineering.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File: smll73879‐sup‐0001‐SuppMat.docx.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.