In recent years，carbon-based absorbing materials such as carbon black，carbon nanotube，and graphene have gained significant attention due to their lightweight，dielectric dispersion，and loss characteristics. However，these pure carbon-based absorbers have some drawbacks，including single microwave loss mechanism，large thickness，and narrow bandwidth ^［1-4］. Fortunately，carbon-based magnetic metal composites have shown promise in overcoming these limitations by introducing a magnetic loss mechanism and enriching the regulatory mechanism，which alters the permittivity and permeability of the resulting composite materials ^［5-6］.

Metal-organic frameworks（MOFs）are commonly used as generic precursors for preparing carbon-based composites. During the pyrolysis process，ferromagnetic metal nanoparticles in MOFs grow in situ and become embedded in the carbon material，enabling the regulation of complex permittivity and permeability by adjusting the compositions and structures of MOF-derived materials ^［7-10］. Previous studies have successfully produced lightweight absorbent materials，such as 3-D honeycomb-like FeCo/C nanocomposites，porous Co/C composites，and hierarchically porous Co/C composites，with excellent microwave absorption performance^［11-13］. However，their practical application is still restricted by their narrow bandwidth and inadequate performance at low frequencies.

To address this issue，macrostructural design has been introduced to broaden the absorption bandwidth ^［14-18］. Recently，various carbon-based ADMMAs have been researched due to their own high dielectric loss and obvious dielectric dispersion，which is beneficial to broadband absorption ^［19-20］. Our group utilized a cylinder array structure design of all-dielectric metamaterial absorbers to broaden the absorption band. We achieved a less than -10 dB bandwidth from 6.1 to 18 GHz，with three absorption peaks，under a total thickness of 3.9 mm ^［21］. This method is expected to enhance the performance of carbon-based absorbing materials and broaden their absorption bandwidth.

In this work，we employed a simple and efficient one-step pyrolysis procedure to prepare MOF precursors based on a heat reaction of solvent at room temperature. C/Co composites with a rhombic dodecahedron shaped morphology were obtained by calcining the Co-based metal-organic frameworks at different temperatures. This environmentally friendly process is simpler compared to other methods that usually require high-temperature and high-pressure equipment. The effects of pyrolysis temperature，graphitization degree，and magnetic property were carefully investigated，and the resulting C/Co composites exhibited excellent absorbing performance. The minimum reflection achieved was -23.7 dB at 11.2 GHz with a thickness of 2.5 mm，and the bandwidth（RL≤-10dB）was 3.8 GHz. On this basis，we introduced all-dielectric metamaterial design to extend the bandwidth to 15 GHz，further improving the absorption performance.

Initially，5.284 g of 2-methylimidazole（C₄H₆N₂）and 1.164 g of cobaltous nitrate（Co（NO₃）₂·6H₂O）were dissolved in 200 mL of deionized water and stirred for 2 h at room temperature.（Above chemical reagents were all of analytical grades，purchased from National Chemical Reagent Ltd.，Shanghai，China）. The resulting solution was then transferred into a 300 mL beaker and left to settle for 12 h at 60 °C. The resulting purple precipitate was collected by centrifugation，washed three times with deionized water and ethanol，and dried under vacuum conditions at 60 °C for 12 h. Next，the as-prepared Co-MOFs were annealed in an Ar atmosphere at 500 °C，550 °C，and 600 °C for 2 hours，respectively，using a heating rate of 10 °C/min. The resulting samples were labeled as C/Co-500，C/Co-550，and C/Co-600，respectively. Finally，the C/Co-500，C/Co-550，and C/Co-600 were mixed with molten paraffin at a 35 wt% filling ratio for microwave measurements.

The morphologies and microstructures of the C/Co composites were examined using transmission electron microscopy（TEM，JEOL JEM-2100）and scanning electron microscopy（SEM，Hitachi S4800）equipped with energy-dispersive X-ray spectrometry（EDS）for elemental analysis. The chemical composition of the C/Co composites was analyzed using X-ray photoelectron spectroscopy（XPS）on a PHI 5000 Versa Probe. The Raman spectra of the samples were obtained using a Renishaw inVia 2000 Raman spectrometer. The magnetic properties of the composites were evaluated using a vibrating sample magnetometer（VSM）at room temperature. The electromagnetic parameters of the samples were measured using the coaxial-line method with a vector network analyzer（VNA，Agilent PNA N5244A）. Furthermore，the absorption properties of the C/Co metamaterial absorber under normal incidence were investigated through simulation using the electromagnetic simulation software CST Microwave Studio.

The morphology of the C/Co composites is depicted in Fig. 1. SEM images of C/Co-500，C/Co-550，and C/Co-600（Fig. 1a-c）reveal that the C/Co-500 sample does not form a rhombic dodecahedron，suggesting that the pyrolysis temperature at 500°C cannot facilitate the growth of C/Co particles，resulting in severe agglomeration of the composite. However，the C/Co-550 and C/Co-600 particles inherit the structure of the Co-MOF precursor，with radial sizes mostly in the range of 2~3μm. The EDS spectrum（Fig. 1d）shows that the C/Co-550 particles are composed of C，Co，and O elements. The corresponding HRTEM images of the C/Co-550 sample（Fig. 1e-g）show that the particles have clear lattice fringes with a distance of 0.21 nm，which can be attributed to the typical Co（111）crystal planes［9，22］. Additionally，a coating of amorphous carbon layers around metallic Co nanoparticles can be observed from Fig. 1g，which may provide good impedance matching characteristics for the C/Co composites［12］.

Furthermore，we discuss the chemical state and composition of the C/Co composites，as determined by X-ray photoelectron spectroscopy（XPS）. Fig. 2a shows the XPS survey scan，which confirms the presence of C，Co，N，and O elements in the C/Co composites. The O element may be derived from water molecules in the air. Fig. 2b presents the C1s peak for all three samples，which can be divided into three binding energies corresponding to C-C（C-C/C=C），C-N，and C-O bonds，respectively. Notably，the C-C peak at 284.8 eV indicates that the carbon atoms in the C/Co particles are in the form of a sp² conjugated carbon skeleton［23］，while the presence of C-N species suggests that nitrogen has been doped into the carbon skeleton，affecting the graphitization degree to some extent（Fig. 2e）. The N1s core survey spectrum（Fig. 2d）can be deconvoluted into three signals corresponding to pyridine N，pyrrole N，and graphitic N，respectively［24］. The creation of polar C-N bonds between C and N atoms may act as dipoles that respond to the polarization relaxation process under the electromagnetic field［25］. Additionally，N with extra valence electrons can serve as an electron donor and increase the conductivity of the carbon-based materials［26］.

The high-resolution Co 2p spectrum of the three Co/C samples shows slight but significant differences（Fig. 2c）. The fitted spectra can be deconvoluted into two dominant peaks located at about 780.9 and 796.4 eV，corresponding to Co 2p_3/2 and Co 2p_1/2，respectively，which further confirms the metallic state of Co nanoparticles. Moreover，two shakeup satellite peaks at about 786.2 eV and 803.1 eV assigned to Co in the high valence state（Co²⁺ or Co³⁺）are observed，indicating slight surface oxidation of Co nanoparticles. It is worth noting that the metallic Co can provide a magnetic response that improves the impedance matching characteristics and enhances the microwave absorption performance of the C/Co composites^{［13，27］}.

The annealing temperature has a direct influence on the graphitization degree of the carbon layer，which in turn governs the dielectric properties. The graphitization degree can be evaluated by calculating the integrated intensity ratio of D and G peaks（I_D/I_G），where a larger value of I_D/I_G indicates a higher degree of lattice defect and lower graphitization degree of the carbon component. As depicted in Fig. 2e，all the samples exhibit two prominent peaks at 1340 cm^-1 and 1580 cm^-1，corresponding to the D band and G band，respectively. The I_D/I_G values of C/Co-500，C/Co-550，and C/Co-600 are 0.92，0.90，and 0.89，respectively. The ratio decreases with annealing temperature，and the ratio of C/Co-550 is almost equal to C/Co-600. These findings suggest that the C/Co-550 and C/Co-600 have high graphitization degree，which is in favor of conduction loss^［28-29］.

The magnetic hysteresis loops of C/Co samples obtained at different pyrolysis temperatures are shown in Fig. 2（f）. Specifically，the saturation magnetization（Ms）values of samples C/Co-500，C/Co-550，and C/Co-600 are 18.2，70.4，and 26.7 emu·g^-1，respectively. Additionally，the coercivity（Hc）of C/Co-500，C/Co-550，and C/Co-600 is 139.3，134.1，and 141.2 Oe，respectively. All C/Co composites exhibit typical ferromagnetic hysteresis loops. Notably，the Ms values of C/Co-500 and C/Co-600 are significantly lower than that of C/Co-550，which could be attributed to the crystalline degree of metallic Co nanoparticles.

The storage and attenuation energy capacity of a material is represented by the real and imaginary parts of its complex permittivity（ε'，ε"）and complex permeability（μ'，μ"），respectively. Figure 3a illustrates the real and imaginary parts of the complex permittivity for C/Co-500，C/Co-550，and C/Co-600. The values of ε' for all three samples decrease with increasing frequency，with the ε' and ε" values of C/Co-500 being significantly lower than those of C/Co-550 and C/Co-600. This can be attributed to the lower graphitization degree of the carbon component and the incomplete reduction of the Co element in C/Co-500. In other words，the low pyrolysis temperature（500°C）cannot form a mosaic structure of C and Co. The dielectric response of C/Co composites is mainly influenced by the interface effect between the metal and carbon. The interaction between π and d orbitals of the metal and carbon leads to orbital hybridization，resulting in various physical properties. Additionally，conduction loss also contributes to the dielectric response. Furthermore，the interface polarization effect of the C/Co-500 sample is weaker than that of the other two samples due to the structural features of MOF-derived metal/carbon composites，resulting in the lowest values of ε' and ε". Although the initial real permittivity of C/Co-550 and C/Co-600 is similar，the C/Co-550 sample exhibits the most pronounced change in ε' with increasing frequency due to its moderate graphitization degree compared to the C/Co-600 sample，thus demonstrating better dispersion characteristics.

Fig. 3b shows that the μ' and μ" values of the three samples are very close and low in the whole frequency band. The C/Co-550 has the highest μ' and μ" values，consistent with the static magnetic parameters（Fig. 2a）. However，the maximum μ' and μ" values of C/Co-550 are only 1.08 and 0.10，respectively，indicating that the magnetic loss of C/Co composites contributes relatively little to the attenuation of electromagnetic waves. Fig. 3c and 3d reveal that the dielectric loss angle（tanδε）is much larger than the magnetic loss angle（tanδμ）. Based on the above analysis，it can be concluded that the dominant factor in the attenuation of electromagnetic waves in C/Co composites is dielectric loss.

Dielectric loss mechanisms are often described by the Cole-Cole model，where the semicircle in the Cole-Cole curve corresponds to polarization loss，while the linear part indicates conductivity loss. In Fig. 4a，the Cole-Cole curves of C/Co-500，C/Co-550，and C/Co-600 are plotted according to Eq.（1） and Eq.（2）^［29］：

Where εs is the static permittivity，ε∞is the permittivity at ultra-high limit frequency，and ω is the alternating electric field frequency，τ is the relaxation time. Multiple semicircles can be observed in the Cole-Cole curves of all three samples，indicating that the interfacial polarization effect plays an essential role in the dielectric loss of C/Co composites. Notably，the effect is most prominent in the C/Co-550 sample，owing to its higher dielectric loss capacity compared to C/Co-500 and C/Co-600.

The main sources of magnetic loss include domain wall resonance，natural resonance，and eddy current loss. However，in the C/Co composite，the Co nanoparticles are below the critical size for a single domain，which means there is no domain wall resonance. Moreover，the term C₀，as defined in Eq.（3），is commonly used to represent eddy current loss^［30］. When the magnetic loss is solely caused by eddy current loss，the C₀ value remains constant regardless of the frequency. From Fig. 4b，it is evident that as the frequency increases，the C₀ values tend to converge to a constant，indicating that magnetic loss primarily arises from the eddy current effect in the high-frequency range. Thus，at low frequencies，magnetic loss is dominated by natural resonance，while at high frequencies，it is primarily attributed to eddy current loss^［17］.

To evaluate the microwave absorption performance of a single-layer absorber，the reflection loss（RL）values can be calculated using transmission line theory. The equations used to calculate these values are shown in Eq.（4） and Eq.（5）：

where Z_in is the normalized input impedance，f is the frequency，and d is the layer thickness. Figures 5（a-c）display the RL values of three C/Co composites with different layer thicknesses across the 2∼18 GHz frequency range. Black lines indicate areas with RL values lower than ‐10 dB. The results reveal that the C/Co-500 sample has poor microwave absorption ability，as its RL value does not reach ‐10 dB within the tested frequency range. In contrast，the C/Co-550 and C/Co-600 samples exhibit excellent broadband absorbing performance in both C and X bands. Notably，Fig. 5（b-f）illustrates that C/Co-550 achieves a minimum RL of about ‐42.5 dB at 6.3 GHz and 4 mm thickness，while at 2.5 mm thickness，it shows an effective absorption bandwidth of 3.8 GHz with a minimum RL value of ‐23.7 dB.

In the case of absorbing materials，the absorption peak can be explained by the λ/4 resonance model. The ideal matching thickness for the absorbing coating should be an odd mutiple of 1/4 wavelength，which can be calculated using the following formula^［17］：

where c is the light velocity in vacuum，fm is the peak frequency of absorbing materials. Fig. 5（b，d）shows the simulation results of the matching thickness（t_m）for the C/Co-550 sample under λ/4 conditions. According to Eq.（6），the matching thickness is inversely proportional to the frequency. If μ' and ε' are constants，the optimal matching thickness will decrease as the frequency increases. However，this leads to a lack of change in the electrical thickness of the coating，resulting in a deterioration in the absorbing performance. Conversely，if the value of μ' or ε' decreases with increasing frequency while maintaining the coating thickness at λ⁄4，it becomes possible to achieve an ideal matching condition. This demonstrates that frequency dispersion of the material can significantly enhance the absorbing performance.

The C/Co-550 sample exhibits good absorbing performance and bandwidth，but it has some limitations such as the thick matching thickness，the narrow absorbing bandwidth，and strong dependency on λ/4 resonance to acquire absorption peaks. To address these issues，a periodic unit structure of C/Co-550 metamaterial absorber is proposed，which can introduce multiple response mechanisms to enhance the absorbing performance. The designed periodic unit structure is shown in Fig. 6a-c，with a periodic boundary condition used in both x and y directions and an open boundary applied in the z direction. The geometric parameters are determined as h=3.8 mm，h₁=0.8 mm，l=11 mm，and p=14 mm. The simulated RL curve for the metamaterial absorber with a 35wt% C/Co-550 filling concentration is plotted in Fig. 6d-e，which shows that the absorption bandwidth（RL≤-10dB）reaches up to 15.0 GHz（7.0~22.0 GHz），covering the whole X，Ku band and most of C band，and there are three absorption peaks appear near 8.6 GHz（f₁），11.4 GHz（f₂）and 19.5 GHz（f₃），respectively. In contrast，the absorption bandwidth of the single layer C/Co 550 coating with the same thickness is only 1.7 GHz（4.8-6.5 GHz）. Clearly，the periodic metamaterial structure greatly broadens the absorption bandwidth，which is 8.8 times more than the single-layer C/Co-550 coating at the same thickness. Moreover，the areal density of the C/Co-550 plate-block metamaterial with a thickness of 4.6mm is only 3.8 kg·m^-2，lower than that of the single C/Co-550 coating（5.38 kg·m^-2）. Thus，the periodic unit structure of the metamaterial absorber has great advantages in terms of absorption bandwidth and areal density compared with the single-layer coating.

Fig. 7 depicts the distribution of magnetic field density，electric field density，and power loss density at three absorption peaks（f_1-3），revealing the absorption mechanisms of the C/Co-550 metamaterial absorber. At the f₁ peak，as displayed in Fig. 7a-c，the magnetic field density mainly resides at the bottom of the periodic element，while the electric field density is distributed at the top of the element and the gap between the elements. The phase difference close to π/2 indicates the formation of standing waves inside the element. By comparing the distribution of power loss density（Fig. 7c）and the RL curve of the single-layer C/Co-550 coating in Fig. 6d，the absorption at 8.6 GHz is confirmed to be mainly caused by the λ/4 resonance inside the structural unit.

Regarding the mechanism of the peak（f₂），Fig. 7d-f illustrates that the magnetic field density is distributed in the gap of periodic units and the bottom of the groove，while Fig. 7e shows the electric field density to be distributed at the edge of the cavity between the adjacent units. The power loss density mainly occurs on both sides of the unit，especially at the top corner，indicating that the absorption peak at 11.4 GHz is due to the edge diffraction effect and the resonance occurring between the periodic structure units^［31］.

Fig. 7（g，h）reveals that the electric and magnetic fields at 19.5 GHz have two concentration regions within the unit. Fig. 7i displays the power loss density at the top and bottom plates of the periodic structure，which is close to the λ/4 and 3λ/4 interference region，indicating that the absorption peak（f₃）is caused by multiple λ/4 resonance. Considering the EM parameters shown in Fig. 4a，b，the dielectric loss of C/Co-550 is significantly higher than the magnetic loss at such a high frequency，and the position of the power loss density is similar to the area of the electric field density. Overall，the C/Co-550 sample demonstrates excellent loss capability for the periodic structure units，while the metamaterial absorber also enhances the microwave absorption performance and broadens the absorption bandwidth ^{［32，33］}.

In conclusion，we have successfully prepared MOF-derived C/Co composites with a rhombic dodecahedron shaped structure using a simple and cost-effective one-step procedure. The C/Co composite absorbents exhibited excellent dielectric dispersion properties at a filling concentration of 35wt%. With a thickness of 2.5 mm，the minimum reflection reached -23.7 dB at 11.2 GHz，and the bandwidth（RL≤-10 dB）covered 3.8 GHz. Moreover，by combining traditional absorbing materials with all-dielectric metamaterial design，we achieved a remarkable absorption bandwidth（RL≤-10 dB）of 15.0 GHz at 4.8 mm，thanks to the periodic structures employed. These findings have significant implications for the development and optimization of super broadband microwave absorbers. Our work provides valuable insights and serves as a reference for future research in this field.