The remarkable advancements in electronic technology have undoubtedly brought about a significant degree of convenience for human beings. However, it is important to acknowledge the concomitant problems that have arisen, including but not limited to electromagnetic interference and radiation pollution^[1-3]. In order to solve these critical issues, considerable efforts have been made to develop microwave absorption materials that exhibit a broad absorption bandwidth, a thin structure, a high degree of absorption, and a low weight^[4-6]. Based on the electromagnetic wave (EMW) loss mechanism, EMW absorption materials can be categorized into two main types: dielectric loss-type and magnetic loss-type materials^[7-10].Among many promising materials, ferrites, especially the spinel ferrites, exhibit excellent electromagnetic properties, including high saturation magnetization, high magnetic crystal anisotropy, high Curie temperature and reliable chemical stability^[11-13]. However, the ferrite-based absorbers usually present a high filling ratio and a heavy coating, which greatly limits their military and practical application^[13-15]. Fortunately, this issue can be efficiently addressed through the combination of ferrites and low-density materials with excellent dielectric properties^[16,17]. For example, Tang et al.^[18] reported the development of a zinc ferrite/multi-walled carbon nanotubes (MWCNTs) composite using a combined co-hydrothermal and sol-gel approach, with an optimal reflection loss (RL) of -40.65 dB achieved at 0.81 GHz. Zong et al.^[19] reported a maximum RL of -47.8 dB at 10.7 GHz for their reduced graphene oxide-Ni_0.5Zn_0.5Fe₂O₄ composite, which was produced via a simple approach. Zhou et al.^[20] fabricated carbon nanotube/Ni_0.5Zn_0.5Fe₂O₄ composite by a combined precipitation-hydrothermal method, exhibiting a strong RL value of -32.5 dB at 3.9 GHz.

Furthermore, another determinant for adjusting EMW absorption performance lies in the morphology and structural design of the materials themselves. Extensive research has confirmed that hollow structures not only alleviate the weight of ferrite-based coatings, but also enhance their electromagnetic performance^[21-23]. It is feasible to summarize the advantages of hollow ferrite structures as: (i) enhanced impedance matching, (ii) reduced the filling ratio to achieve material lightweighting, and (iii) reinforced interfacial polarization^[24]. For instance, Sui et al.^[25] fabricated hollow Fe₃O₄ particles by solvothermal method, which exhibited the effective absorption bandwidth (EAB) of 4.72 GHz at 2.49 mm. Moreover, the RL of -55.14 dB was attained at a matching thickness of 2.07 mm. Mandal et al.^[26] prepared NiFe₂O₄ nano-hollow spheres via a solvothermal process, which demonstrated an EAB of 2.82 GHz at a thickness of 2 mm and a strong RL of -59.2 dB at 11.7 GHz. Zhu et al.^[27] obtained hollow Fe/Fe₃O₄@porous carbon composites, exhibiting an EAB of 5.20 GHz and an RL of -50.05 dB.

Both the incorporation of ferrite with high dielectric materials such as nickel, zinc, and carbon, and the design of hollow structures demonstrate distinct advantages. Using these two methods in combination will maximize the microwave absorption properties of the obtained material. Thus, the Ni_0.5Zn_0.5Fe₂O₄/C hollow microspheres were prepared by self-sacrifice processing and annealing treatment. These hollow microspheres are further characterized, with their morphology, crystalline structure, and microwave electromagnetic performance being investigated as a function of annealing temperature. This Ni_0.5Zn_0.5Fe₂O₄/C hollow microsphere is a ternary composite material. Under the interfacial polarization effects between Ni-Zn ferrite, carbon, and nickel, the composite exhibits multiple loss mechanisms, delivering excellent impedance matching and absorptive properties while achieving the integration of various single-type materials. This work offers a novel strategy for preparing high-performance ferrite-based microwave absorbers.

XRD was employed to investigate the crystal structure of each sample, with the resulting patterns presented in Figure 1A. The cubic-structured Ni_0.5Zn_0.5Fe₂O₄ (JCPDS 08-0234) is identified by the diffraction peaks marked ★. The corresponding characteristic peaks at 18.3°, 30.0°, 35.4°, 37.0°, 43.0°, 53.3°, 56.8°, 62.4°, 70.8°, and 73.8° correspond to the (111), (220), (311), (222), (400), (422), (511), (440), (620), and (533) crystal planes, respectively^[28]. Meanwhile, the diffraction peaks marked ▼ are attributed to the face-centered cubic structure Ni (JCPDS 65-0308), with the characteristic peaks at 44.4°, 51.7°, and 76.2° being indexed to its (111), (200), and (220) planes, respectively^[29]. The XRD diffraction spectra of S1 shows the weak diffraction peaks, indicating poor crystallinity of Ni_0.5Zn_0.5Fe₂O₄. The broad diffraction peak at 10°-20° of S1 attributed to amorphous carbon^[30]. For sample S2, S3 and S4, the diffraction peaks of carbon gradually become weaker as annealing temperature increases, showing the content of carbon decreases. The characteristic peaks of the Ni_0.5Zn_0.5Fe₂O₄ become sharper, indicating the Ni_0.5Zn_0.5Fe₂O₄ is well crystallized. As the temperature increases, the diffraction peaks associated with metallic Ni grow progressively, indicating the development of higher crystallinity at elevated temperatures. During high-temperature annealing under the Ar atmosphere, metallic Ni results from the reduction of Ni²⁺ by carbon^[31].

Figure 1B shows the Raman spectra for all samples, spanning from 100 cm^-1 to 1,700 cm^-1. There are five major Raman active modes (A_1g + E_g+ 3T_2g), however, only 3 modes peaks are detected^[32]. The Raman peaks located at ~330, ~470, and ~690 cm^-1 assign to the E_g, T_2g, and A_1g modes, respectively^[33]. The splitting of the A_1g mode into the A_1g(1) and A_1g(2) branches arises from an alteration in structural symmetry, caused by the reordering of Ni²⁺,Zn²⁺ and Fe^3+[34]. In addition, two prominent bands are observed: one centering on ~1,327 cm^-1, attributed to sp³ defects; and the other at ~1,594 cm^-1, corresponding to the in-plane vibrations of sp² bonded carbon^[35]. For samples S3 and S4, the D and G bands are difficult to identify in Figure 1B, indicating a low carbon content, which is consistent with the XRD results. The measured D/G peak intensity ratios (I_D/I_G) for the four samples are 1.67 (S1), 1.09 (S2), 1.04 (S3), and 0.95 (S4). This ratio serves as a standard indicator for assessing the graphitization level of carbon materials. The notably high value for S1 (1.67) indicates a predominantly amorphous carbon structure with low graphitization^[36]. And the decline in the I_D/I_G ratio with increasing annealing temperature reflects an enhancement in the graphitization degree of the carbon components.

Figure 2A-D display the SEM morphology of all samples, which consist of numerous microspheres. The presence of fractured microspheres reveals their hollow structure. The average particle diameters were determined to be 1.058 ± 0.160, 0.972 ± 0.237, 0.689 ± 0.148, and 0.561 ± 0.142 μm for S1, S2, S3, and S4, respectively. These size distributions are illustrated in Figure 3. As the temperature rises, the hollow microspheres undergo volumetric contraction. This shrinkage is primarily due to the densification of adsorbed metal ions into oxides and the further carbonization of organic matter during heat treatment^[37].

The TEM, high-resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED) are investigated to understand the morphology of samples. TEM micrographs in Figure 2E-H show that these microspheres possess a hollow structure constructed from numerous nanoparticles. The HRTEM images Figure 2I-L reveal no discernible lattice fringes in sample S1, confirming its poor crystallinity. The observed lattice fringes in samples S2, S3, and S4 correspond to the (111) crystallographic plane of Ni_0.5Zn_0.5Fe₂O₄, with interplanar distances measured as 0.484, 0.485, and 0.486 nm, respectively. Additionally, a lattice fringe of 0.253 nm is observed in sample S3, which corresponds to the (311) plane of Ni_0.5Zn_0.5Fe₂O₄. As displayed in Figure 2M-P, the SAED pattern of S1 shows no obvious diffraction rings. And the SAED pattern of S2 exhibiting sharp and discrete rings can be matched with the (111), (220), (311) and (400) planes, which is consistent with the planes of Ni_0.5Zn_0.5Fe₂O₄. Moreover, the appearance of diffraction ring according with (111) plane of Ni can be observed in S3 and S4, further indicating the existence of metallic Ni.

Elemental mapping of samples S1-S4 [Figure 4] serves to examine the effect of annealing temperature on the composition distribution of Fe, Ni, Zn, O, and C. The red flaky areas belong to the substrate used in the TEM preparation process rather than the sample. As shown, the Zn, Fe, O, and C elements exhibit a homogeneous distribution on the microsphere surfaces. As the annealing temperature rises, the distribution of element C decreases, corresponding to a lower surface carbon content. In contrast, Ni tends to aggregate towards the particle surface, especially in sample S4. This illustrates the partial carbothermal reduction of Ni_0.5Zn_0.5Fe₂O₄ to metallic Ni by amorphous carbon.

The elemental composition and chemical states of samples S1-S4 are analyzed by XPS. Figure 5 shows Ni 2p_3/2 spectrum, the peaks at around 853.5, 855.0, and 856.6 eV are attributed to satellite peak of Ni⁰⁺, Ni²⁺ in the octahedral site [Ni²⁺(O_h)] and Ni²⁺ in the tetrahedral site [Ni²⁺(T_d)], respectively^[38]. Strikingly, a low-valence Ni⁰⁺ peak can be detected in S2, S3 and S4, confirming that Ni²⁺ in the Ni_0.5Zn_0.5Fe₂O₄ is partly reduced to metallic Ni^[39]. Meanwhile, the increased peak intensity of Ni⁰⁺ as temperature increasing indicates more Ni²⁺ is reduced to metallic Ni, a finding that corresponds to the XRD data. The C 1s XPS spectra [Figure 6] are fitted with three peaks at approximately 284.8, 288.8, and 286.0 eV, ascribed to C-C/C=C, C-O, and C=O functional groups, respectively^[40]. The C-C/C=C peak is the most intense, and its area decreases with increasing annealing temperature. This decrease reflects a progressive graphitization of the carbon components as the annealing temperature increases. As shown in the Figure 7, the Fe 2p XPS spectra exhibits characteristic satellite peaks. The peak at approximately 718.6 eV is associated with the Fe 2p_3/2 component, while the one at about 733.2 eV belongs to the Fe 2p_1/2 component. Each of the Fe 2p_3/2 and Fe 2p_1/2 bands was deconvoluted into two component peaks. For the Fe 2p_3/2 region, the peaks at 710.5 eV and 712.2 eV are attributed to Fe²⁺ and Fe³⁺ states, respectively. Similarly, the Fe 2p_1/2 peaks at 723.7 eV and 725.4 eV are assigned to Fe²⁺ and Fe^3+[41]. The Fe²⁺ area ratio of Fe element in XPS can be used to measure the variation trend of Fe²⁺ in ferrite with annealing temperature. The corresponding Fe²⁺ area ratios for the four samples (S1-S4) are 0.38, 0.51, 0.53, and 0.52. This increase mainly because when Ni²⁺ is reduced to metallic Ni, Fe³⁺ will replace the Ni²⁺ sites and become Fe²⁺.

The complex permittivity (ε_r = ε’ - jε”) and dielectric loss tangent of the samples are presented in Figure 8A-C, whereas their complex permeability (μ_r = μ’ - jμ”) and magnetic loss tangent are shown in Figure 8D-F. The energy storage capacity within a material is respectively represented by the real parts of its complex permittivity (ε’) for electric energy and permeability (μ’) for magnetic energy. Conversely, the dissipation of electric and magnetic energy is respectively reflected in the imaginary parts ε’’ and μ’’^[42]. Notably, for sample S1, both the permittivity and permeability are not only the lowest but also show minimal variation across the frequency range, pointing to a limited dielectric loss capability. A clear upward trend in both ε’ and ε’’ is observed for samples S2, S3, and S4. The reasons for this enhancement in complex permittivity are as follows: (1) During the formation of Ni_0.5Zn_0.5Fe₂O₄/C hollow microspheres at high temperature, the enhanced crystallization of carbon facilitates the generation of polar bonds and polarization charges, leading to the increase in electrical conductivity (δ)^[43]. As dictated by the classical free electron theory (ε” = δ ⁄ 2πε₀f), the value of ε’’ scales linearly with the electrical conductivity (δ)^[24]. (2) The appearance of metallic Ni can lead to the increase of complex permittivity^[44]. Therefore, as the annealing temperature rises and the metallic Ni content correspondingly increases, sample S4 achieves the largest dielectric imaginary part. This value is nearly double that observed in S2 and S3. In addition, as indicated by the preceding XRD results and Raman spectra, the graphitization degree of S2 has increased while the carbon content of S3 has decreased. Consequently, the ε’ and ε’’ values of S2 have risen, whereas the reduction in carbon content for S3 has led to a decrease in its ε’ and ε’’ values. Overall, the variation in permittivity results from the combined effects of metallic Ni content, carbon content, and carbon crystallinity/graphitization degree. As frequency increases, the μ’ values of samples S2-S4 exhibit a decrease within the 2-8 GHz band before gradually converging toward 1, while those of S1 remain around 1 with only minor fluctuations, as depicted in Figure 8D. The values of μ’’ decrease significantly during 2-14 GHz and basically stay 0 at 14-18 GHz for S2-S4. The decline in permeability is primarily governed by the Snoek limit, which posits that the product of permeability and cut-off frequency is approximately constant. This relationship is formally described by the following equation^[45]:

(1) $$ \left(\mu^{\prime}-1\right) f_{c}=\gamma M_{s} / 3 \pi $$

Here μ’ denotes the initial permeability, f_c represents the cut-off frequency, γ stands for the gyromagnetic ratio, and M_s signifies the saturation magnetization. As inferred from Equation (1), a higher permeability of the material corresponds to a lower cut-off frequency. Ni is a ferromagnetic material with a M_s higher than that of ferrite. Consequently, the incorporation of metallic Ni not only enhances the permeability of the sample but also elevates its cut-off frequency relative to ferrite. For this reason, while permeability decreases sharply in the high-frequency regime, the introduction of metallic Ni slightly shifts the cut-off frequency toward higher frequencies, which mitigates the rapid attenuation of permeability to a certain extent. This observation aligns with the results presented in Figure 8E.

To elucidate the microwave absorption mechanism, the dielectric (tanδ_ε = ε’’/ε’) and magnetic (tanδ_μ = μ’’/μ’) loss tangents of the samples were analyzed. As presented in Figure 8C, the tanδ_ε of S4 surpasses that of all other samples, indicating its strongest dielectric loss. Concurrently, the tanδ_ε for all samples exhibits fluctuations with increasing frequency. Regarding the characteristics of magnetic loss, as shown in Figure 8F, the S4 sample exhibits the highest tanδ_μ value among samples S1-S4. A direct comparison between tanδ_μ and tanδ_ε shows that within the 2-8 GHz range, tanδ_μ exceeds tanδ_ε, while from 8 GHz to 18 GHz, tanδ_ε is higher than tanδ_μ. This comparison indicates that magnetic loss dominates in the lower frequency band (2-8 GHz), whereas dielectric loss prevails in the higher frequency band (8-18 GHz).

In absorbing materials, the relaxation during polarization process is the primary source of dielectric loss. This process comprises multiple mechanisms: interfacial polarization, dipole orientation polarization, ionic polarization, and electron polarization^[27]. Since ion and electron polarization are effective within the 10³-10⁶ Hz range, their contribution is negligible at microwave frequencies. The multiple loss mechanisms operating at these higher frequencies are commonly analyzed using Debye theory. The following equation characterizes the behavior of the complex permittivity^[46]:

(2) $$ \left(\varepsilon^{\prime}-\varepsilon_{\infty}\right)^{2}+\left(\varepsilon^{\prime \prime}\right)^{2}=\left(\varepsilon_{s}-\varepsilon_{\infty}\right)^{2} $$

Here, ε_∞ and ε_s denote the relative permittivity and static permittivity, respectively. In generally, a Debye relaxation process is indicated by each semicircle observed in the Cole-Cole plot (ε’ - ε’’).

Figure 9A-D show the ε’ - ε’’ plots of samples S1, S2, S3 and S4, it is clear that Cole-Cole curves of S2, S3 and S4 consists of semicircles and straight tails. Such straight tails in S2, S3 and S4 are regarded as the evidence of the contribution of conduction loss, which is mainly brought out by the carbon^[47]. It is well established that interfacial polarization significantly contributes to EMW relaxation losses in composite materials, as supported by experimental and computational studies^[48]. EMW radiation exposure of the composite surface induces the formation of interfacial space charge regions and local electric fields, thereby giving rise to free charge accumulation^[24]. The free electron theory indicates that the emergence of relaxation peaks arises from the abnormal increase in local resistance. Furthermore, structural imperfections such as broken holes or cracks introduce edge effects, promoting the formation of additional dipoles^[49]. Therefore, it can be inferred that conductive loss and interfacial polarization loss predominantly govern EMW dissipation in this case.

To further quantify the relative contributions of conduction loss and polarization loss, Debye relaxation fitting was performed on all samples. According to Debye theory, the total dielectric loss can be expressed as the sum of the conduction loss (ε”_c) and the polarization loss (ε”_p)^[50]. Figure 10A and B display the frequency-dependent curves of ε”_c and ε”_p for the four samples over the 2-18 GHz range. The results indicate that both the conduction loss and polarization loss increase with rising annealing temperature. The enhancement in conduction loss is mainly attributed to the increase in metallic Ni content, which raises the electrical conductivity of the material. Additionally, as noted earlier, the carbon content of sample S3 is lower than that of S2, thus leading to a slight decrease in the conduction loss of S3. The growth in polarization loss primarily originates from the increased interfaces between metallic Ni and the ferrite, which strengthens the interfacial polarization effect.

Magnetic losses are mainly attributed to hysteresis and eddy current effects, along with the multiple resonance mechanisms (including exchange, domain wall, and natural resonance)^[51]. Given their predominant occurrence at lower frequencies (MHz), domain wall resonance loss and hysteresis loss are negligible in this context. The eddy current loss is given by^[52]:

(3) $$ C_{0}=\mu^{\prime \prime}\left(\mu^{\prime}\right)^{-2} f^{-1}=2 \pi \sigma d^{2} \mu_{0} $$

Here, σ and μ₀ are respectively the electrical conductivity and the vacuum permeability, while C₀ (ns) represents the eddy current coefficient. If the RL arises exclusively from eddy currents, then the C₀ values will exhibit no variation across the frequency spectrum. The C₀ values of all samples are presented in Figure 11A, the attenuation constant (α) is shown in Figure 11B, and the |Z_in/Z₀| values are displayed individually in Figure 11C-F. Notably, the C₀ values of the S2, S3, and S4 show minimal variation across the 14-18 GHz frequencies, suggesting that eddy current losses dominate the magnetic loss within this spectrum. Meanwhile, across the 2-14 GHz range, magnetic loss is significantly reduced and is primarily characterized by exchange and natural resonance effects.

For the quantitative evaluation and comparison of absorber performance, the RL is calculated using transmission line theory, with the relevant equations given below^[53]:

(4) $$ R L(d B)=20 log \left|\left(Z_{i n}-Z_{0}\right) /\left(Z_{i n}+Z_{0}\right)\right| $$

(5) $$ Z_{i n}=Z_{0} \sqrt{\mu_{r} / \varepsilon_{r}} tan \ h \left[j(2 \pi f d / c) \sqrt{\mu_{r} \varepsilon_{r}}\right] $$

Here, Z_in and Z₀ are the input impedance of the EMW absorbing materials and the impedance of free space, respectively; ε_r and μ_r represent the relative complex permittivity and permeability; c, f, and d correspond to the speed of light in the vacuum, the frequency of the EMW, and the absorber thickness.

In general, the RL value below -10 dB is defined as indicating effective EMW absorption, corresponding to an EMW absorption rate exceeding 90%. This is commonly used as the criterion for determining effective EMW absorption. Figure 12 depicts the RL curves for samples S1 through S4 across a thickness range of 1.5 mm to 6.0 mm. Possessing an excellent RL and a broad EAB (RL ≤ -10 dB), sample S3 emerged as the best performer in EMW absorption among the four samples tested. Sample S3 delivers the strongest RL of -35.79 dB at 12.00 GHz with a 2.5 mm thickness (EAB: 4.12 GHz), and the widest EAB of 5.29 GHz at 2.0 mm, where the RL is -34.14 dB. For S2, the maximum RL is -32.30 dB (EAB: 3.09 GHz) at 1.5 mm, and -18.66 dB (EAB: 3.66 GHz) at 2.0 mm. S1 and S4 display weak performance, with peak RLs of only -21.44 dB at 6.0 mm (EAB: 1.84 GHz at 5.5 mm) and -15.86 dB at 1.5 mm (EAB: 3.84 GHz).

The RL peaks exhibited a consistent shift to lower frequencies with greater thickness. This trend is attributed to the quarter-wavelength model^[54]:

(6) $$ t_{m}=\frac{n \lambda}{4}=n c /\left(4 f_{m} \sqrt{\left|\mu_{r}\right|\left|\varepsilon_{r}\right|}\right) \ (n=1,3,5 \cdots) $$

Here, t_m, f_m, λ, and c represent the matching thickness, matching frequency, wavelength, and the speed of light in vacuum, respectively. Figure 12 plots the tm against the dm for samples S1-S4 at the λ/4 and 3λ/4 wavelengths. The peak layer thickness for all samples matches well with the quarter wavelength, confirming that the quarter-wavelength cancellation model governs the microwave absorption mechanism.

The microwave absorption properties of materials are primarily determined by two key factors: impedance matching and electromagnetic attenuation. The impedance matching |Z_in/Z₀|, calculated using Equation (5) above, reflects the efficiency with which incident EMW enter the absorber and are subsequently converted into thermal energy^[55]. The |Z_in/Z₀| value close to 1 is a direct indicator of optimal impedance matching, thereby allowing a greater proportion of incident EMW to enter the material. In addition, good impedance matching enables the material to minimize the reflection of EMW at its surface. In Figure 11C-F, the |Z_in/Z₀| curves for S2 and S3 approach 1, indicating well-matched impedance. However, since the |Z_in/Z₀| values for S1 and S4 deviate from 1, the majority of the incident EMW undergoes reflection at the surface. Thus, S1 and S4 have poor absorption performance.

The α can be estimated by the following formula^[56]:

(7) $$ \alpha=\sqrt{2} \pi f / c \times \sqrt{\left(\mu^{\prime \prime} \varepsilon^{\prime \prime}-\mu^{\prime} \varepsilon^{\prime}\right)+\sqrt{\left(\mu^{\prime \prime} \varepsilon^{\prime \prime}-\mu^{\prime} \varepsilon^{\prime}\right)^{2}+\left(\mu^{\prime} \varepsilon^{\prime \prime}+\mu^{\prime \prime} \varepsilon^{\prime}\right)^{2}}} $$

As shown in Figure 11B, α values of all samples show an increasing tendency as frequency varies. The α values follow the sequence S4 > S2 > S3 > S1. This order aligns with that of the tangent dielectric loss, underscoring the crucial role of dielectric loss^[24]. The highest α value observed in S4 can be attributed to its higher ε’’ and μ’’ values. However, as the annealing temperature increases, the content of metallic Ni gradually increases, leading to an increase in material conductivity, enhanced surface reflection, and prevention of electromagnetic wave entry, resulting in deterioration of the impedance matching of S4. Therefore, based on the preceding impedance matching analysis, S3 is identified as the most promising absorbent candidate.

In addition, the Ni_0.5Zn_0.5Fe₂O₄/C/Ni microspheres, based on a hollow structure, can achieve excellent microwave absorption performance at low filling ratios, demonstrating the advantage of lightweight. Table 1 compares the filling ratios and microwave absorption performance of other ferrite-based materials.

The analysis shows that as the annealing temperature increases, the crystallinity of carbon in the samples is progressively enhanced, which in turn leads to improved electrical conductivity. Simultaneously, Ni elements progressively aggregate to form metallic particles. Consequently, when the annealing temperature reaches 800 °C, the content of metallic Ni reaches its peak, resulting in the highest dielectric loss for the S4 sample. However, this also compromises its impedance matching performance. In contrast, the S3 sample, benefiting from an optimal annealing temperature, achieves better control over carbonization degree and metallic Ni content. This results in a well-balanced dielectric loss capability and impedance matching performance, yielding a satisfactory attenuation constant. The mechanism of EMW loss in Ni_0.5Zn_0.5Fe₂O₄/C/Ni hollow microspheres primarily stems from the following factors. First, through the synergistic effect of controlling the metallic Ni content via annealing temperature and the hollow structure within the microspheres, Ni_0.5Zn_0.5Fe₂O₄/C/Ni hollow microspheres achieve excellent impedance matching. Second, the hollow architecture effectively reduces the sample weight, enabling the composite to achieve excellent microwave absorption at a low filling ratio, which is beneficial for lightweighting and broadens the application scope. Meanwhile, the hollow structure creates heterogeneous interfaces with air, thereby enhancing interfacial polarization. Structural defects such as fractured pores and cracks serve as additional dipole centers, giving rise to dipole polarization loss. Furthermore, conductive loss primarily attributed to carbon and natural resonance induced by the ferrite are also significant contributors. These characteristics collectively contribute to the realization of broadband absorption performance.

In summary, Ni_0.5Zn_0.5Fe₂O₄/C hollow microspheres were successfully fabricated through a simple two-stage method of hydrothermal and calcination. The study reveals that Ni_0.5Zn_0.5Fe₂O₄/C hollow microspheres annealed at 700 °C exhibit superior microwave absorption. The optimal performance includes an RL value of -35.79 dB at 2.5 mm, while with a thinner layer of 2.0 mm, it offers an EAB reaching 5.29 GHz. The excellent broadband absorption arises from the synergistic combination of interfacial polarization, dipole polarization, conduction loss, and natural resonance, facilitated by the hollow architecture, the graphitized carbon, and the formed metallic Ni. This research offers novel inspiration and perspectives for enhancing the performance of ferrite absorbers.