Preparation and Microwave Absorption Properties of C@Fe3O4 Magnetic Composite Microspheres

In this work, C@Fe3O4 magnetic microspheres were designed and prepared by a novel strategy, and the microwave absorption properties of the materials were investigated. Four kinds of monodisperse P(MAA/St) microspheres with different carboxyl content were synthesized via facile dispersion polymerization. The Fe3O4 nanoparticles were grown on the surface of P(MAA/St) to obtain P(MAA/St)@Fe3O4 microspheres. Using P(MAA/St)@Fe3O4 as the precursors, after vacuum carbonization, C@Fe3O4 were obtained. It was observed that the carboxyl content on the microspheres’ surface increased with the increasing of MAA, which made the magnetic content and maximum specific saturation magnetization of P(MAA/St)@Fe3O4 and C@Fe3O4 increase. The obtained four kinds of C@Fe3O4 microspheres had a particle size range of 4–6 μm. The microwave absorption properties indicated that the magnetic content made a difference to the microwave absorption properties of C@Fe3O4 magnetic microspheres. The microwave absorption properties of materials were determined by controlling dielectric loss, magnetic loss and impedance matching. C@Fe3O4 microspheres exhibited excellent microwave absorption properties. The maximum reflection loss could reach −45.6 dB at 12.8 GHz with 3 mm in thickness. The effective bandwidth was 5.9 GHz with RL < −10 dB. Therefore, C@Fe3O4 microspheres were lightweight and efficient microwave absorption materials.


Introduction
Electromagnetic waves have been widely used in various fields of civil and military applications, such as communications, catering, medical care, stealth, navigation, electromagnetic interference, etc. While bringing convenience to people's daily lives and providing security for national defense, the deterioration of the electromagnetic environment caused by electromagnetic leakage cannot be ignored. Microwave absorbers have been considered as the most effective way to solve the electromagnetic leakage problem [1][2][3][4][5][6][7]. Among all the microwave absorption materials developed currently, carbon materials [8,9], magnetic materials [10,11] and their composites [12,13] are mainly used for three mechanisms of absorption and loss microwaves by absorbing materials, resistive loss, dielectric loss and magnetic loss mechanisms, respectively.
Composite particles containing magnetic materials and carbon materials are highly efficient absorbing materials, which combine the characteristics and advantages of both materials. Magnetic carbon particles with various morphologies, particle size scales, pore properties, magnetic contents, and magnetic responsiveness were developed and used as absorbing agents [14][15][16][17][18]. There are various techniques to prepare magnetic carbon composite particles, such as (1) Preparation of magnetic

Preparation of P(MAA/St)@Fe 3 O 4 Magnetic Composite Microspheres
The following shows the process of Fe 3 O 4 particles growth on the P(MAA/St) microspheres surface by solvothermal method. Sodium citrate (0.25 g), sodium acetate (1.60 g), ferric chloride (1.00 g) and P(MAA/St) microspheres (0.7 g) were dispersed and dissolved in ethylene glycol (33 mL) by ultrasonic for 30 min. Then, the mixture was transferred to a Teflon-lined stainless steel reaction vessel and reacted at 200 • C for 10 h. After cooling to room temperature naturally, the products were washed 3 times with anhydrous ethanol and deionized water, respectively. After drying, the P(MAA/St)@Fe 3 O 4 magnetic composite microspheres were obtained.

Preparation of C@Fe 3 O 4 Magnetic Composite Microspheres
The as-prepared P(MAA/St)@Fe 3 O 4 magnetic composite microspheres were placed in a quartz crucible and calcined in a vacuum at 550 • C for 8 h with a heating rate of 5 • C/min. Then, the C@Fe 3 O 4 magnetic composite microspheres were obtained after cooling to room temperature with the furnace.

Characterization
The crystal structure of the samples was examined by X-ray diffraction (XRD) using the XRD-7000 diffractometer instrument (Shimadzu, Kyoto, Japan) (Cu target Kα radiation, diffraction beam graphite crystal monochromator, tube pressure 40 KV, tube flow 40 mA). The morphology of the materials was characterized by scanning electron microscopy (SEM) (AMERY-1000B, AMERY, AMERY, WI, USA. A vibrating-sample magnetometer (VSM, LakeShore7307, LakeShore, Columbus, OH, USA) was used to measure the magnetic properties. Heat resistance and magnetic contents of the materials were obtained by a thermal gravimetric analyzer (TGA) (HCT-1, METTLER, Zurich, Switzerland). The microwave absorption properties were evaluated using a vector network analyzer (VNA) (N5227, Agilent Technologies, Santa Clara, CA, USA).
The carboxyl contents were determined by acid-base titration. P(MAA/St) (30 mg) microspheres were added into the calibrated NaOH solution (50 mL). After magnetic stirring for 12 h, the filtrate was obtained using a microporous membrane. With methyl orange and methylene blue mixed solution as the indicator, the filtrate (15 mL) was titrated with calibrated hydrochloric acid solution three times. The surface carboxyl content of P(MAA/St) microspheres (mmoL·g −1 ) was calculated based on the equation: carboxyl group content = (N 1 V 1 − N 2 V 2 × 50/10)/W, where N 1 and V 1 were the concentration and volume of the standard sodium hydroxide solution. N 2 and V 2 were the concentrations of the standard hydrochloric acid solution and the volume consumed. W was the mass of the P(MAA/St) microspheres.

Morphology and Composition Analysis of the Synthesized P(MAA/St) Microspheres
Polymer microspheres have carboxyl functional groups, thus they induce the growth of Fe 3 O 4 on the compound surface. The content of the carboxyl functional groups is controlled by the proportion of MAA monomer in the copolymerization process. Therefore, the influence of St: MAA ratio on the morphology, the particle size distribution and the carboxyl content of P(MAA/St) microspheres were studied. P(MAA/St) microspheres with different St: MAA ratios were prepared. According to the SEM images ( Figure 1), all the four kinds of composites had a smooth surface and uniform particle sizes. The particle sizes of the microspheres were about 4-7 µm. When the amount of MAA is too large or too small, small P(MAA/St) microspheres appear in the product. This is because the MAA polymerization activity is higher than St. When a small amount of MAA is used in the system, the amount of copolymer of initial PMAA (polymethylacrylic acid) as the main component is less. This copolymer plays an important role in stabilizing primary nucleating particles. Meanwhile, the content of PMAA in the copolymer affects the solubility of initial P(MAA/St). Premature and homogeneous nucleation led to a wide particle size distribution. Therefore, we can see the small P(MAA/St) microspheres in Figure 1A. An overload of MAA content in the system severely caused a large difference in monomer components in the system before and after the polymerization.
particles. Meanwhile, the content of PMAA in the copolymer affects the solubility of initial P(MAA/St). Premature and homogeneous nucleation led to a wide particle size distribution. Therefore, we can see the small P(MAA/St) microspheres in Figure 1A. An overload of MAA content in the system severely caused a large difference in monomer components in the system before and after the polymerization.

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Materials 2019, 12, x FOR PEER REVIEW 4 of 14 The particle size distribution of P(MAA/St) microspheres with different St:MAA ratios were calculated and is shown in Figure 2. The particle size distribution of the microspheres all exhibit a monodisperse property. When the MAA content is 0.10 or 0.15 g, the particle size distribution of P(MAA/St) microspheres is the narrowest. The average particle sizes of P-1, P-2, P-3 and P-4 are 5.32, 6.01, 5.45 and 6.55 μm, respectively. The calculated particle size distribution of the microspheres agrees well with the results of SEM observations.  The particle size distribution of P(MAA/St) microspheres with different St:MAA ratios were calculated and is shown in Figure 2. The particle size distribution of the microspheres all exhibit a monodisperse property. When the MAA content is 0.10 or 0.15 g, the particle size distribution of P(MAA/St) microspheres is the narrowest. The average particle sizes of P-1, P-2, P-3 and P-4 are 5.32, 6.01, 5.45 and 6.55 µm, respectively. The calculated particle size distribution of the microspheres agrees well with the results of SEM observations. The particle size distribution of P(MAA/St) microspheres with different St:MAA ratios were calculated and is shown in Figure 2. The particle size distribution of the microspheres all exhibit a monodisperse property. When the MAA content is 0.10 or 0.15 g, the particle size distribution of P(MAA/St) microspheres is the narrowest. The average particle sizes of P-1, P-2, P-3 and P-4 are 5.32, 6.01, 5.45 and 6.55 μm, respectively. The calculated particle size distribution of the microspheres agrees well with the results of SEM observations. The COOH concentrations on the surface of the P(MAA/St) microspheres were determined by titration, which is shown in Table 2. As the amount of MAA increases, the content of carboxyl groups on the surface of the microspheres increases. The statistical method was used to calculate the surface area of microspheres and the surface density of carboxyl groups on the microspheres, The COOH concentrations on the surface of the P(MAA/St) microspheres were determined by titration, which is shown in Table 2. As the amount of MAA increases, the content of carboxyl groups on the surface of the microspheres increases. The statistical method was used to calculate the surface area of microspheres and the surface density of carboxyl groups on the microspheres, which are shown in Table 2.  increases from P1 to P4. Moreover, the area of the Fe3O4 particles covering the polymer microspheres also increases. However, the Fe3O4 particle cluster becomes smaller. According to the analysis, as the carboxyl content of the microspheres increases, the chelation of the polymer microspheres with the Fe3O4 particles is enhanced. Therefore, the growth amount of Fe3O4 particles increases. Meanwhile, strong chelation increases the growth sites of Fe3O4 particles. In the case of the same iron source, the Fe3O4 particle cluster becomes smaller. It can be seen that the thickness of Fe3O4 layers are different in the SEM images of P(MAA/St)@Fe3O4 magnetic composite microspheres. With the increasing of the carboxyl groups, the thickness of Fe3O4 layers decreases.

Characterization of the C@Fe3O4 Magnetic Composite Microsphere
The MP-1, MP-2, MP-3 and MP-4 were carbonized in a vacuum atmosphere. The obtained samples were named MC-1, MC-2, MC-3 and MC-4, respectively. SEM images are shown in Figure  5, and it can be seen that Fe3O4 particles on the surface of C@Fe3O4 magnetic composite microspheres are well maintained after the carbonization process. However, there are some changes in the morphology of the Fe3O4 nanoparticles and aggregates on the surface of the microspheres. For MP-3 and MP-4, Fe3O4 nanoparticles are attached to the surface of the polymer microspheres in a toroidal or flat sheet morphology ( Figure 3). The morphology of these aggregates changed significantly after carbonization. The Fe3O4 nanoparticle clusters on the surface of MC-3 and MC-4 microspheres have a higher degree of aggregation, as shown in Figure 5C and Figure 5D. Simultaneously, the amount of Fe3O4 on the surface of the microspheres is gradually increased from MC-1 to MC-4. The C@Fe3O4 magnetic composite microspheres basically maintain the morphology of P(MAA/St)/Fe3O4 microspheres. The particle size of the microspheres concentrated in 4-6 μm. The reason for the particle size reduction is volume shrinkage due to the loss of organic components during carbonization.  Due to the consistency of the four kinds of C@Fe3O4 magnetic composite microspheres in material composition and functional groups, we chose MC-4 composite microspheres as the analyzed objects for material composition characterization. XRD and FTIR analysis of the MC-4 composite microspheres were carried out to determine the composition of the composite microspheres after carbonization. The results were shown in Figure 6. It can be seen from the XRD spectrum of Figure 6A Figure  6B), there is no obvious adsorption peak of organic components, indicating that the polymers were completely carbonized. In addition, an obvious absorption peak was found and assigned to Fe-O bonding in MC-4 at 582 cm −1 . It was confirmed again that the inorganic component was iron oxide. The different C/Fe3O4 composite microspheres were characterized by TGA and VSM as shown in Figure 7. It can be seen from the TGA curve that the initial decomposition temperature of C/Fe3O4 is above 300 °C. According to the TGA results and calculations, the iron oxide contents of samples  Figure 6B), there is no obvious adsorption peak of organic components, indicating that the polymers were completely carbonized. In addition, an obvious absorption peak was found and assigned to Fe-O bonding in MC-4 at 582 cm −1 . It was confirmed again that the inorganic component was iron oxide. Due to the consistency of the four kinds of C@Fe3O4 magnetic composite microspheres in material composition and functional groups, we chose MC-4 composite microspheres as the analyzed objects for material composition characterization. XRD and FTIR analysis of the MC-4 composite microspheres were carried out to determine the composition of the composite microspheres after carbonization. The results were shown in Figure 6. It can be seen from the XRD spectrum of Figure 6A. MC-4 showed obvious crystal diffraction peaks in the range of 20-80°. The diffraction peaks agree well with spinel structure Fe3O4 (JCPDS 19-0629). XRD peaks at 30.14°, 35.28°, 43°, 56.76° and 62.62° is corresponding to the (220), (311), (400), (511) and (440) planes of Fe3O4, respectively. Thus, the inorganic component in MC-4 is Fe3O4. In the FTIR spectrum ( Figure  6B), there is no obvious adsorption peak of organic components, indicating that the polymers were completely carbonized. In addition, an obvious absorption peak was found and assigned to Fe-O bonding in MC-4 at 582 cm −1 . It was confirmed again that the inorganic component was iron oxide. The different C/Fe3O4 composite microspheres were characterized by TGA and VSM as shown in Figure 7. It can be seen from the TGA curve that the initial decomposition temperature of C/Fe3O4 is above 300 °C. According to the TGA results and calculations, the iron oxide contents of samples The different C/Fe 3 O 4 composite microspheres were characterized by TGA and VSM as shown in Figure 7. It can be seen from the TGA curve that the initial decomposition temperature of C/Fe 3 O 4 is above 300 • C. According to the TGA results and calculations, the iron oxide contents of samples from MC-1 to MC-4 were calculated to be 4.85%, 7.70%, 12.17% and 21.56%, respectively. According to the VSM curve, carbonization rarely influenced the superparamagnetic of the microsphere material. The maximum saturation magnetization values of MC-1, MC-2, MC-3 and MC-4 were 9.06, 10

Evaluation of Microwave Absorbing Properties of C@Fe3O4
This section will evaluate the microwave absorbing properties of the obtained C@Fe3O4. Electromagnetic parameters of the C@Fe3O4 microspheres were measured by the coaxial method with paraffin as the matrix. The results were shown in Figure 8A-D. The real parts of the complex permittivity (ε') and complex permeability (μ') represented the ability of the material to store electric and magnetic field energies, respectively. The imaginary parts of the complex permittivity (ε'') and complex permeability (μ'') represented the ability of the material to lose the energy of electric and magnetic fields, respectively [25,26]. As can be seen from Figure 8A,B, the complex permittivity increased gradually with the increase of the magnetic content of Fe3O4 on the surface of the carbon sphere. The increasing ε' indicated a greater ability to store electric fields and more polarization. The larger ε'' indicated a stronger dielectric loss. The imaginary parts of the complex permeability also indicated the same trend. In particular, μ'' turned to negative in the frequency range of 13-17 GHz, which indicated the existence of eddy current loss. This can be attributed to the eddy current, which produced a reverse magnetic field. It counteracted the intrinsic magnetic field, causing the magnetic permeability to become negative ( Figure 8D). The dielectric loss tangent (tan δe = ε''/ε') and the magnetic loss tangent (tan δ m = μ''/μ') were used to indicate the dielectric loss and the magnetic loss [27]. The relationship curves of the dielectric loss and magnetic loss versus frequency were shown in Figure 8E. It was seen that the dielectric loss was significantly larger than the magnetic loss. This indicated that the dielectric loss was dominant. The two curves were symmetrically up and down, demonstrating the complementarity between dielectric loss and magnetic loss. Moreover, the dielectric loss and magnetic loss both increased with the increase of Fe3O4 loading. The reason was described as that the magnetic properties of the composite absorbing materials increased with the increase of Fe3O4 loading. Therefore, the magnetic loss performance was further improved. At the same time, the interface between the carbon spheres and the Fe3O4 particles also increased. This resulted in more interfacial polarization and improved the dielectric loss capability. The comprehensive absorbing properties of the absorbing materials were also affected by the impedance matching characteristics. The impedance matching curves of C@Fe3O4 magnetic composite microspheres with different magnetic contents were shown in Figure 8F. It was clear to see that the characteristic impedance ( = / / ) of the material decreased continuously with the increase of Fe3O4 particle loading. The outcomes illustrated that the impedance matching had reduced. This will have a negative impact on the overall absorbing properties of C@Fe3O4 magnetic composite microspheres.

Evaluation of Microwave Absorbing Properties of C@Fe 3 O 4
This section will evaluate the microwave absorbing properties of the obtained C@Fe 3 O 4 . Electromagnetic parameters of the C@Fe 3 O 4 microspheres were measured by the coaxial method with paraffin as the matrix. The results were shown in Figure 8A-D. The real parts of the complex permittivity (ε ) and complex permeability (µ ) represented the ability of the material to store electric and magnetic field energies, respectively. The imaginary parts of the complex permittivity (ε") and complex permeability (µ") represented the ability of the material to lose the energy of electric and magnetic fields, respectively [25,26]. As can be seen from Figure 8A,B, the complex permittivity increased gradually with the increase of the magnetic content of Fe 3 O 4 on the surface of the carbon sphere. The increasing ε indicated a greater ability to store electric fields and more polarization. The larger ε" indicated a stronger dielectric loss. The imaginary parts of the complex permeability also indicated the same trend. In particular, µ" turned to negative in the frequency range of 13-17 GHz, which indicated the existence of eddy current loss. This can be attributed to the eddy current, which produced a reverse magnetic field. It counteracted the intrinsic magnetic field, causing the magnetic permeability to become negative ( Figure 8D). The dielectric loss tangent (tan δ e = ε"/ε ) and the magnetic loss tangent (tan δ m = µ"/µ ) were used to indicate the dielectric loss and the magnetic loss [27]. The relationship curves of the dielectric loss and magnetic loss versus frequency were shown in Figure 8E. It was seen that the dielectric loss was significantly larger than the magnetic loss. This indicated that the dielectric loss was dominant. The two curves were symmetrically up and down, demonstrating the complementarity between dielectric loss and magnetic loss. Moreover, the dielectric loss and magnetic loss both increased with the increase of Fe 3 O 4 loading. The reason was described as that the magnetic properties of the composite absorbing materials increased with the increase of Fe 3 O 4 loading. Therefore, the magnetic loss performance was further improved. At the same time, the interface between the carbon spheres and the Fe 3 O 4 particles also increased. This resulted in more interfacial polarization and improved the dielectric loss capability. The comprehensive absorbing properties of the absorbing materials were also affected by the impedance matching characteristics. The impedance matching curves of C@Fe 3 O 4 magnetic composite microspheres with different magnetic contents were shown in Figure 8F. It was clear to see that the characteristic impedance (Z im = µ 0 /ε 0 µ r /ε r ) of the material decreased continuously with the increase of Fe 3 O 4 particle loading. The outcomes illustrated that The electromagnetic wave absorption efficiency of the absorbing materials was expressed by the reflection loss (RL). According to the transmission line theory, the calculation formula was as follows [28]: The electromagnetic wave absorption efficiency of the absorbing materials was expressed by the reflection loss (RL). According to the transmission line theory, the calculation formula was as follows [28]: where µ r and ε r were the complex permeability and complex permittivity of the materials, f was the frequency of the electromagnetic wave, d was the thickness of the absorbing materials, and c was the velocity at which the electromagnetic wave propagated in the vacuum. Figure 9 gives the reflection loss curves of C@Fe 3 O 4 magnetic composite microspheres with different magnetic contents at different matching thicknesses. It can be seen that the reflection loss first increased and then decreased with the increase of magnetic contents. The order of the reflection loss was −12.1 dB, −30.1 dB, −45.6 dB and −32.6 dB. The corresponding matching frequencies were 15.9 GHz, 8.0 GHz, 12.8 GHz and 14.2 GHz, respectively. The matching thickness was 3.5 mm, 5.5 mm, 3 mm and 3 mm. In particular, MC-3 had the best absorbing properties. Its effective bandwidth with an absorption rate greater than 90% (RL < −10 dB) reached 5.9 GHz. The above results show that the absorbing properties of C@Fe 3 O 4 magnetic composite microspheres increased first and then decreased with the increase of magnetic contents. This is because the dielectric loss and magnetic loss of the C@Fe 3 O 4 both increased with the increase of the magnetic contents while the impedance matching decreased. Therefore, the ultimate electromagnetic wave loss capability was controlled by these two factors. The optimum magnetic content of the C@Fe 3 O 4 was 12.17%.
where μr and εr were the complex permeability and complex permittivity of the materials, f was the frequency of the electromagnetic wave, d was the thickness of the absorbing materials, and c was the velocity at which the electromagnetic wave propagated in the vacuum. Figure 9 gives the reflection loss curves of C@Fe3O4 magnetic composite microspheres with different magnetic contents at different matching thicknesses. It can be seen that the reflection loss first increased and then decreased with the increase of magnetic contents. The order of the reflection loss was −12.1 dB, −30.1 dB, −45.6 dB and −32.6 dB. The corresponding matching frequencies were 15.9 GHz, 8.0 GHz, 12.8 GHz and 14.2 GHz, respectively. The matching thickness was 3.5 mm, 5.5 mm, 3 mm and 3 mm. In particular, MC-3 had the best absorbing properties. Its effective bandwidth with an absorption rate greater than 90% (RL < −10 dB) reached 5.9 GHz. The above results show that the absorbing properties of C@Fe3O4 magnetic composite microspheres increased first and then decreased with the increase of magnetic contents. This is because the dielectric loss and magnetic loss of the C@Fe3O4 both increased with the increase of the magnetic contents while the impedance matching decreased. Therefore, the ultimate electromagnetic wave loss capability was controlled by these two factors. The optimum magnetic content of the C@Fe3O4 was 12.17%. In order to further reveal the electromagnetic wave loss mechanism of C@Fe3O4, the electromagnetic parameters of MC-3 were analyzed in depth. The reason was its excellent microwave absorbing properties. The TEM image of MC-3 is shown in Figure 10. Inorganic   In order to further reveal the electromagnetic wave loss mechanism of C@Fe 3 O 4 , the electromagnetic parameters of MC-3 were analyzed in depth. The reason was its excellent microwave absorbing properties. The TEM image of MC-3 is shown in Figure 10. Inorganic nanoparticles were the materials with high mass thickness contrast. Their distribution was partially clustered. The space in the microspheres with low mass thickness contrast was carbon. nanoparticles were the materials with high mass thickness contrast. Their distribution was partially clustered. The space in the microspheres with low mass thickness contrast was carbon. According to Debye theory, the complex permittivity can derive the following relationship [29,30]: where εs is the static dielectric constant, ε∞ is the limit of the relative dielectric constant at high frequencies, and ε0 is a dielectric constant in vacuum. From this expression, it is known that the curve about ε' and ε'' is a semicircle, which is called the Cole-Cole semicircle. Each semicircle corresponded to a Debye relaxation process [3]. A plot of ε'' versus ε' is presented in Figure 11A. A clear Cole-Cole semicircle can be seen from the figure. This confirmed the existence of the Debye relaxation process. The eddy current loss effect was judged by the equation . If the eddy current loss existed in the electromagnetic wave absorption process, C0 was always constant as the frequency changed [31,32]. The relationship between C0 and the frequency of C@Fe3O4 is shown in Figure 10B. The curve was approximately straight in the range of 6-9 GHz and 14-16 GHz. This further indicated the presence of eddy current losses in this frequency range. The natural resonance effect was described by the following formula [11]: , where μo was the vacuum permeability (4π × 10 −7 H/m), r was the gyromagnetic ratio, Hα was the anisotropic energy, K1 was the anisotropy coefficient, and Ms and Hc were the saturation magnetization and coercive force, respectively. It was inferred that the resonant frequency depended on the effective anisotropy field. The effective anisotropy field was related to the material coercivity value [33]. Combined with the hysteresis loop (the inset of Figure 7B), it can be seen that the C@Fe3O4 had a larger coercive force. The higher the coercivity is, the higher frequency resonance will be generated. This will improve the magnetic loss performance of the material effectively [34]. According to Debye theory, the complex permittivity can derive the following relationship [29,30]: where ε s is the static dielectric constant, ε ∞ is the limit of the relative dielectric constant at high frequencies, and ε 0 is a dielectric constant in vacuum. From this expression, it is known that the curve about ε and ε" is a semicircle, which is called the Cole-Cole semicircle. Each semicircle corresponded to a Debye relaxation process [3]. A plot of ε" versus ε is presented in Figure 11A. A clear Cole-Cole semicircle can be seen from the figure. This confirmed the existence of the Debye relaxation process. The eddy current loss effect was judged by the equation C 0 = µ (µ ) −2 f −1 = 2πµ 0 d 2 δ. If the eddy current loss existed in the electromagnetic wave absorption process, C 0 was always constant as the frequency changed [31,32]. The relationship between C 0 and the frequency of C@Fe 3 O 4 is shown in Figure 10B. The curve was approximately straight in the range of 6-9 GHz and 14-16 GHz. This further indicated the presence of eddy current losses in this frequency range. The natural resonance effect was described by the following formula [11]: where µ o was the vacuum permeability (4π × 10 −7 H/m), r was the gyromagnetic ratio, H α was the anisotropic energy, K 1 was the anisotropy coefficient, and M s and H c were the saturation magnetization and coercive force, respectively. It was inferred that the resonant frequency depended on the effective anisotropy field. The effective anisotropy field was related to the material coercivity value [33]. Combined with the hysteresis loop (the inset of Figure 7B), it can be seen that the C@Fe 3 O 4 had a larger coercive force. The higher the coercivity is, the higher frequency resonance will be generated. This will improve the magnetic loss performance of the material effectively [34].

Conclusions
In this study, C@Fe 3 O 4 magnetic microsphere absorbing materials with controllable Fe 3 O 4 contents were successfully prepared. The magnetic contents of the surface of C@Fe 3 O 4 were controlled by adjusting the carboxyl contents of the surface of the polymer precursor microspheres. The absorbing performance analysis showed that the magnetic contents had a significant effect on the absorbing properties of C@Fe 3 O 4 . With the increase of magnetic contents, the dielectric loss and magnetic loss increased, and the characteristic impedance decreased. Benefiting from the effective compounding of carbon and Fe 3 O 4 , C@Fe 3 O 4 had multiple loss mechanisms, including interfacial polarization, Debye relaxation, eddy current loss, and natural resonance. The C@Fe 3 O 4 magnetic microspheres exhibited excellent absorption properties. The maximum reflection loss at 12.8 GHz reached −45.6 dB when the matching thickness was 3 mm. Moreover, the effective bandwidth of RL < −10 dB was 5.9 GHz, which demonstrates that the C@Fe 3 O 4 magnetic microspheres are promising materials for microwave absorption applications.