## Introduction

The rapid development of modern electronic equipment and wireless devices has resulted in severe electromagnetic (EM) radiation pollution, which has implications in human health and the normal functioning of electronics. Thus, the design and exploration of effective EM wave absorption materials is of basic scientific importance1,2,3. EM waves consist of a time-varying electric and magnetic field, and EM wave absorption is achieved by the attenuation of EM wave energy through dielectric loss and magnetic loss as well as electromagnetic impedance match, which can minimize the reflection of the incident EM wave4. Therefore, dielectric loss and magnetic loss are the main factors determining absorption capability. The dielectric tangent loss (tan δε = ε″/ε′) is proportional to the dielectric loss, and it describes the dissipation of energy supplied by an external electric field as motion and heat5. Magnetic tangent loss (tan δμ = μ″/μ′) is known as magnetic loss factor or power factor; it is a measure of the energy loss inside a magnetic material due to the phase delay between the applied and induced magnetic fields.

Good impedance matching between the specimen and free space is necessary for enhancing EM wave absorption capability. The impedance matching coefficient |ZinZ0-1| can be expressed as6

$$|{Z}_{{\rm{in}}}/{Z}_{0}|={({\mu }_{r}/{\varepsilon }_{r})}^{1/2}\,\tanh \,[j(2\pi fd/c){({\mu }_{r}{\varepsilon }_{r})}^{1/2}]$$
(1)

And the reflection loss (RL) value is calculated according to the transmission line theory by Equation (2):

$${\rm{RL}}({\rm{dB}})=20\,\mathrm{log}\,|({Z}_{{\rm{in}}}-{Z}_{{\rm{0}}})/({Z}_{{\rm{in}}}+{Z}_{{\rm{0}}})|$$
(2)

Here, Z in is the input impedance of the absorber, Z0 is the characteristic impedance of free space (377 Ω)7. εr = ε′ − jε″ and μr = μ′ − jμ″ are, respectively, the complex permittivity and permeability of the absorber, c is the velocity of the EM wave in free space, f is the frequency of the EM wave, and d denotes the absorber thickness.

Carbon nanotubes (CNTs) offer the unique potential to be excellent EM wave absorbents. Besides their superior mechanical and thermal properties8, the carrier mobility and current carrying capacity of CNTs is up to 105 cm2 V−1 s−1 and 109 A cm−1, respectively9. Most of the research effort to date has focused on CNTs decorated with magnetic metal or metal oxide particles for enhancing magnetic attenuation. However, the anticipated improvement in EM wave absorption performance has often been hindered by the poor dispersion of CNTs and their impedance mismatch with free space10. CNT films, on the other hand, not only retain the high permittivity of individual CNTs in an isotropic network structure but also greatly facilitate the dispersion of CNTs in the matrix11. Furthermore, the dispersion of Fe3O4 nanoparticles on the surface of CNTs can effectively improve permeability and impedance matching12. Thus, the CNT film-Fe3O4 absorber provides a highly desirable combination to enhance dielectric and magnetic loss and impedance matching as well as facilitate ease in composites processing.

The other focus of this research is on graphene, which is well known for its excellent electronic, chemical and physical properties13,14,15. Graphene can support current densities greater than 108 A cm−216, its carrier mobility can exceed 15,000 cm2 V−1 s−1 even under ambient conditions17, and its real and imaginary parts of the theoretical permittivity exceed 104 at frequency less than 400 GHz18. Theoretical studies of large-scale graphene layers have shown strong EM wave absorption for normal incident wave. The maximum absorption reaches 50 percent at six layers of graphene and one-third of the incident EM energy is dissipated at a graphene-polymer interface19, 20. Although large-scale multilayer graphene/methyl methacrylate for EM wave absorption has been suggested theoretically and realized in numerical simulations18,19,20, large-scale graphene absorption has never been demonstrated experimentally. This is due to the fact that large-scale graphene suffers from statistical fluctuations in strength and toughness as well as impedance mismatch with free space due to the high permittivity and negligible permeability21. Consequently, almost all published work so far on graphene-related EM-absorbing materials has focused on graphene powder; little research has been devoted to the EM wave-absorbing performance of large-scale graphene. Moreover, in order to enhance impedance matching and absorption of both electric and magnetic fields in graphene, the improved decoration and blend of magnetic metal or metal oxide particles have become effective approaches for researchers. Some reports demonstrated that the combination of Fe3O422,23,24,25, TiO2 26 and NiFe2O4 27 magnetic nanoparticles with reduced graphene oxide powders improved the EM wave-absorbing property. However, the magnetic nanoparticles supported on graphene particles are generally aggregated, resulting in uneven distribution25. Therefore, the design and processing of high-performance EM-absorbing materials based on CNT and graphene remain a formidable challenge.

Here, a novel and simple approach was adopted to fabricate CNT film-Fe3O4 composites by the solvothermal method. The Fe3O4 nanoparticles on the surface of CNTs not only improved permeability but also enhanced impedance matching of the CNT film-Fe3O4-graphene composite. Then, the CNT film-Fe3O4 was used as a support substrate to prepare a large-scale graphene (LSG)-CNT film-Fe3O4 composite, which not only retained the dielectric performance of CNT and graphene but also avoided their aggregation.

## Results

To enhance the ability of EM wave absorption, highly conductive films (thickness: 2 μm; density: 807 mg cm−3) with randomly oriented CNTs coated by Fe3O4 nanoparticles were used as absorbing layers, the single chemical vapor deposition graphene were laid on the surface of CNT-Fe3O4 film as blocking layer (Supplementary Fig. S1), and the CNT film-Fe3O4 with epoxy resin (EPONTM Resin 862) was impedance matching layer. A schematic illustration of the fabrication process for constructing CNT film-Fe3O4-graphene-epoxy composites can be found as Supplementary Fig. S2.

The CNT film-Fe3O4 composites were processed using the solvothermal method. The morphology and diameters of the Fe3O4 particles prepared with different FeCl3 concentrations are shown in Fig. 1. For the CNT film-Fe3O4 composite prepared from 0.01 M FeCl3, Fe3O4 nanocrystals cover the CNT surface and form a few spherical particles with diameters ranging from 10–20 nm (Fig. 1a). The Fe3O4 particles of the as-prepared CNT film-Fe3O4 composite at FeCl3 concentrations of 0.02–0.10 M are spherical with a uniform diameter, aligned along the axial direction of the CNTs. It should be noted that with the increase of FeCl3 concentration from 0.02 to 0.10 M, the diameters of the Fe3O4 particles increase to a maximum value of 200 nm at 0.03 M and then decrease with a minimum value of 20–30 nm at 0.10 M (Fig. 1b–f). Such observations provide clear evidence of the direct relationship between Fe3O4 nanoparticle size and FeCl3 concentration. The growth of the Fe3O4 nanoparticles follows the two-stage growth model, in which nanocrystals nucleate first and then aggregate into larger particles on the CNT surface28.

Figure 1g is a TEM image of a CNT film-Fe3O4-0.04 M graphene composite. Crystal planes are identified in the selected-area electron diffraction pattern (Fig. 1h), which is consistent with the XRD pattern. Figure 2a shows the XRD patterns of the pure CNT film and CNT film-Fe3O4 composites prepared at various FeCl3 concentrations. The peak positions and relative intensities match well with the standard XRD data (JCPDS no. 19–0629), and the seven peaks at 18.17°, 30.07°, 35.48°, 43.01°, 53.42°, 57.04° and 62.55° are associated with the (111), (220), (311), (400), (422), (511) and (440) crystal planes of Fe3O4, respectively. No additional peaks belonging to other phases are observed, indicating the good crystallinity and high purity of the Fe3O4 nanoparticles. The energy dispersive spectroscopy (EDS) as shown in Fig. 1b reveals that the CNT film-Fe3O4–0.05 M composite is mainly composed of C, O, and Fe elements.

The average sizes of nanocrystals in the Fe3O4 nanoparticles are calculated for the strongest peak (311) by the Debye–Scherrer formula. The nanocrystal sizes from the data of Fig. 2 are 9.7, 14.5, 16.4, 18.7, 22.3 and 27.2 nm for CNT film-Fe3O4 composites prepared from 0.01, 0.02, 0.03, 0.04, 0.05 and 0.10 M FeCl3, respectively; this implies that the nanocrystal size increases significantly with increasing concentration of FeCl3. The saturation magnetization and relaxation values are directly related to the size of the nanocrystal size, and with the increase of Fe3O4 nanocrystal size, both the saturation magnetization and relaxation rate increase29.

The magnetic properties of the CNT film-Fe3O4 composites at room temperature are shown in Fig. 3. Significant hysteresis loops indicate the ferromagnetic behavior of CNT film-Fe3O4 composites (Fig. 3a). The saturation magnetization (Ms) and remnant magnetization (Mr) of the CNT film-Fe3O4-0.01 M and 0.02 M remain nearly the same as those of the CNT film. At FeCl3 concentrations higher than 0.02 M, the Ms and Mr values increase rapidly, as shown in Fig. 3b and c. The variation of coercivity (Hc) with FeCl3 concentration is shown in Fig. 3d. The values of μr and anisotropy energy, which are related to the values of Ms and Hc, affect the EM wave absorption capacities30.

Based on the above magnetic property data and morphology observations, CNT film-Fe3O4-0.05 M composites with various numbers of layers were fabricated. The values of tan δε and tan δμ, impedance matching coefficient |Zin/Z0| and reflection loss of composites consisting of one to seven CNT film-Fe3O4-0.05 M layers were deduced from the measured data of relative complex permittivity εr, permeability μr and thickness d. The effect of the number of layers on the composite EM wave-absorbing properties was studied. The results of Fig. 4a demonstrate that strong peaks of tan δε appear when the frequency is higher than 6 GHz. The locations of peaks shift toward lower frequencies with an increase in the number of layers of CNT film-Fe3O4 composite. The peak intensity varies with the number of layers and reaches a maximum value of 1.72 at four layers. Figure 4b depicts the variation of tan δμ of the CNT film-Fe3O4 composites with frequency and number of layers. Strong peaks of tan δμ can be seen in the frequency range of 10–17 GHz, and the peak location also shifts toward lower frequencies with increasing number of layers. The peak intensity of tan δμ decreases from a maximum value of 0.58 at one layer to a minimum value of 0.08 at four layers. It should be noted that the values of tan δμ become negative in some frequency ranges, indicating that the magnetic energy radiated out from the composites due to the high carrier mobility of CNTs7. Overall, the above results demonstrate the dependence of the dielectric and magnetic responses on the number of layers of CNT film-Fe3O4 composite. In addition, the values of tan δε are larger than those of tan δε for almost the entire frequency range, suggesting that dielectric loss plays a major role in the intrinsic EM wave absorption.

Results of |Zin/Z0| and RL calculated from the relative permittivity and permeability data are given in Fig. 4c and d, respectively. When |Zin/Z0| is close to unity, most of the EM waves can effectively enter the composite and then dissipate as heat. Figure 4c shows that when the number of layers is increased, the value of |Zin/Z0| of the CNT film-Fe3O4 composites increases and reaches a maximum value of 1.73 at six layers and then decreases to 0.80 at seven layers. Only the values of |Zin/Z0| of the CNT film-Fe3O4 composites with five and six layers are close to unity in the frequency range of 10–17 GHz. Figure 4d shows that for the CNT film-Fe3O4 composite with five layers, the minimum value of reflection loss is −19.3 dB, and the frequency bandwidth at −10 dB is 3.6 GHz. For the CNT film-Fe3O4 composite with six layers, the minimum value of reflection loss is −26.6 dB, and the frequency bandwidth at −10 dB is 2.9 GHz. However, although the CNT film-Fe3O4 composites with one, two, three, four and seven layers have higher dielectric loss, the frequency bandwidth at −10 dB and the magnitude of minimum reflection loss are far less than those of five- and six-layer composites.

Based on the results of CNT film-Fe3O4 composites with different layers, CNT film-Fe3O4 composites of six layers with different FeCl3 concentrations were prepared. As shown in Fig. 4e and f, the values of tan δε of the CNT film-Fe3O4 composites of 0.02–0.05 M are all less than that of the CNT film-Fe3O4–0.01 M composite, and the values of tan δμ are all higher than that of the CNT film-Fe3O4-0.01 M composite. It is interesting that tan δε of the CNT film-Fe3O4-0.10 M increases almost monotonically with frequency. The tan δμ value of the CNT film-Fe3O4-0.10 M is negative and shows a decreasing trend at frequencies higher than 8.5 GHz (Fig. 4f). Figure 4g shows that the |Zin/Z0| values of some composites are close to unity at frequencies higher than 11.7 GHz. The minimum values of reflection loss of the CNT film-Fe3O4-0.01, 0.04 and 0.05 M composites are -32.0 dB at 17.1 GHz, −43.6 dB at 15.7 GHz and −26.6 dB at 14.5 GHz, respectively, obviously shifting to lower frequency range with increase in FeCl3 concentrations (Fig. 4h). For the same composites, the bandwidths of the reflection loss at −10 dB are 3.1 GHz, 3.7 GHz and 2.9 GHz, respectively; their bandwidths of reflection loss at −20 dB are 1.2 GHz, 1.5 GHz and 0.3 GHz, respectively. Although the CNT film-Fe3O4-0.10 M composite has no strong RL peak, the bandwidth at −10 dB is 2.9 GHz.

On the basis of the results summarized above, CNT film-Fe3O4-LSG composites with six layers of CNT film-Fe3O4-0.04 M and various numbers of graphene layers have been processed and studied. Although the minimum reflection loss and thickness of the CNT film-Fe3O4 composite established from the above experiments are highly encouraging, the absorption bandwidth of 3.7 GHz is still relatively small. To further improve the EM wave-absorption performance, it is desirable to pursue a CNT film-Fe3O4-graphene composite in which the graphene layers are separated from one another by a thin layer of epoxy. Figure 5a and b show that tan δε increases and tan δμ decreases to negative values with an increasing number of graphene layers; the ranges of tan δε and tan δμ are, respectively, 0.2–1.6 and −0.4–0.1 for the frequencies of 3–18 GHz, indicating that the dielectric loss plays a major role in EM wave absorption.

In addition, EM wave attenuation in an absorber is a key factor for achieving EM wave absorption. The EM wave attenuation ability of an absorber can be characterized by the attenuation constant30

$${\rm{\alpha }}=\sqrt{2}\pi f{c}^{-1}\sqrt{({\rm{\varepsilon }}^{\prime\prime} {\rm{\mu }}^{\prime\prime} -{\rm{\varepsilon }}^{\prime} {\rm{\mu }}^{\prime} )+\sqrt{{({\rm{\varepsilon }}^{\prime\prime} {\rm{\mu }}^{\prime\prime} -{\rm{\varepsilon }}^{\prime} {\rm{\mu }}^{\prime} )}^{2}+{({\rm{\varepsilon }}^{\prime} {\rm{\mu }}^{\prime\prime} -{\rm{\varepsilon }}^{\prime\prime} {\rm{\mu }}^{\prime} )}^{2}}}$$
(3)

The results of Fig. 5c show that all samples exhibit a high attenuation constant (larger than 150) in the frequency range of 7–18 GHz. The values of α increased with an increasing number of graphene layers, and an obvious peak appears when the number of graphene layers is less than four. The locations of peaks shift toward higher frequencies as the number of graphene layers increases. Figure 5d shows the variations of impedance matching coefficient |Zin/Z0| with frequency. The |Zin/Z0| values of CNT film-Fe3O4–1L and 2L LSG composites are close to unity in the frequencies of 11–15 GHz, and the corresponding impedance matching bandwidth of frequency is enhanced by the large-scale graphene compared to that of the CNT film-Fe3O4-0.04 M composite without LSG. However, the |Zin/Z0| values decrease with the increase of graphene layers.

As shown in Fig. 5e, for the CNT film-Fe3O4-0.04 M-1L LSG composite, the reflection loss is below −10 dB at 12.0–16.7 GHz, and the minimum value is −44.7 dB at 13.9 GHz; the bandwidths of the reflection loss at −10 dB and −20 dB are 4.7 GHz and 2.2 GHz, respectively. Compared to the CNT film-Fe3O4-0.04 M composite without graphene, the bandwidths of the reflection loss at −10 dB and −20 dB increase by 27.0 percent and 46.7 percent, respectively; the minimum reflection loss increases by 2.5 percent, and the peak of the reflection loss shifts from 15.7 GHz to 13.9 GHz. For the case of two graphene layers, the reflection loss is below −10 dB at 10.9–13.5 GHz, and the minimum value is −44.6 dB at 11.9 GHz; the bandwidths of the reflection loss at −10 dB and −20 dB are 2.6 GHz and 1.6 GHz, respectively. However, with the further increase of graphene from three to six layers, the absorbing performance deteriorates sharply; the reflection loss has no bandwidth under −20 dB, and there is only a narrow bandwidth at −10 dB.

## Discussion

An important mechanism of dielectric loss, which arises from the polarization and its associated relaxation, can be evaluated by the Cole–Cole semicircle (ε″ versus ε′), and each semicircle is correlated with one Debye relaxation process7. The Cole–Cole semicircles of the composite samples are shown in Fig. 6a–e. For the CNT film-Fe3O4-1L LSG composite, one large Cole-Cole semicircle, which consists of many tiny semicircles, and three small semicircles can be identified in Fig. 6a. With an increasing number of graphene layers, the number of Cole−Cole semicircles increases (Fig. 6b–e), the large semicircle decreases in size, and the tiny semicircles increase in size. The presence of semicircles in the ε″ ~ ε′ relation provides the evidence that there are dual dielectric relaxation processes in the CNT film-Fe3O4-LSG composites and demonstrates that large-scale graphene improves the intensity of the Debye dipolar relaxation process31.

In the microwave frequency band, magnetic loss mainly comes from the eddy current effect, along with natural and exchange resonance6. The eddy current loss contribution to the imaginary part of permeability is related to the permeability of vacuum (μ0), thickness (d) and electrical conductivity (σ) of the composite as μ″ = 2πμ0(μ′)2σd2f/3. If the magnetic loss results from the eddy current effect, μ″(μ′)−2f−1 should be constant when the frequency varies. It is shown in Fig. 6f that the values of μ″(μ′)−2f−1 drastically fluctuate in the frequency range of 2.0–8.0 GHz. However, when f >8.0 GHz, the values of μ″(μ′)−2f−1 remain essentially constant. Thus, it can be concluded that the magnetic loss at 2.0–8.0 GHz is caused by natural resonance, and the other peaks at 8.0–18.0 GHz are ascribed to the eddy current effect.

A superb EM wave-absorbing material is expected to possess not only a high RL factor and broad absorption bandwidth, but also a fine thickness and, hence, light weight. The reflection loss, absorption bandwidth and thickness achieved in the composites of this work are shown in Fig. 7 and compared with those of previously reported graphene- and CNT-based EM wave-absorbing composites. Compared to other graphene particle or CNT-based absorbers, the absorption bandwidth achieved in this work is 0.6–161.1 percent higher than the others except for the CNT-CoFe2O4 and CNT-La(NO3)3 absorbers (Fig. 7a); the composite thickness of this work is reduced by 25–70 percent except for the CNT-Ni, -Ag and -La(NO3)3 absorbers at 0.9, 1 and 1.4 mm, respectively, and the GO-Fe3O4 absorber also at 1.5 mm. However, the maximum reflection loss of this work is 1.2–2.5 times the values of the above five absorbers CNT-Ni, -Ag -CoFe2O4 and -La(NO3)3, GO-Fe3O4 (Fig. 7b).

In summary, we have demonstrated that composites composed of large-scale graphene and CNT film-Fe3O4 substrate demonstrate superb EM wave-absorbing performance. Through optimization of the number of layers of CNT film-Fe3O4 composite and FeCl3 concentrations, the CNT film-Fe3O4-LSG-epoxy composites are processed using six layers of CNT film-Fe3O4 prepared from 0.04 M FeCl3. The CNT film-Fe3O4-1L LSG-epoxy composite has the highest wave-absorbing capability. Increasing the number of layers of graphene leads to an increase in wave attenuation ability but a decrease in impedance matching coefficient and a corresponding decrease in minimum reflection loss and absorbing bandwidth. Compared to the CNT film-Fe3O4-0.04 M composite without graphene, the minimum reflection loss and absorption bandwidth at −10 dB of the corresponding composite with one-layer graphene increase by 27.0 percent and 2.5 percent, respectively. This study provides a thorough explanation of nanocarbon-based electromagnetic wave-absorbing composites and opens up the opportunity to apply large-scale CNT and graphene films for EM wave absorption.

## Methods

### Sample preparation process

CNT film was fabricated by floating catalyst chemical vapor deposition (FCCVD) method32. Figure 8 shows the schematics of CNT film fabrication. In this process, the feedstock of ethanol containing 1.2 vol % ferrocene and 0.4 vol % thiophene, carried by Ar/H2, was injected at the rate of 20 mL/h into a reactor at high temperature (~1300 °C). Ethanol, ferrocene, and thiophene were used as carbon source, catalyst precursor, and promotor, respectively. CNTs were synthesized and entangled in the hot zone forming a stocking-like aerogel. The CNT aerogel was then blown out continuously from the reactor and collected layer-by-layer by a wheel rotating perpendicularly to the gas flow, which formed macroscopic CNT film (thickness: 2 μm; density: 807 mg/cm3) with randomly oriented CNTs33. This CNT film was further densified by spraying ethanol onto it to enhance its mechanical and physical properties.

The single-layer graphene films were synthesized on a Cu substrate using the CVD method. A Cu foil was annealed at 1000 °C for 1.5 h in a quartz tube with a 2 sccm H2 flow. Subsequently, a 20 sccm CH4 flow was introduced for graphene growth at 30 mTorr for 0.5 h. Then, the furnace was quickly cooled to room temperature under He flow, and the single-layer graphene on Cu foil was obtained34. The size of the graphen was 25 mm × 20 mm.

The CNT film-Fe3O4 composites were prepared in a solvothermal system by the reduction reaction between FeCl3 and ethylene glycol in the presence of CNT film. FeCl3·6H2O was dissolved into 50 mL ethylene glycol followed by the addition of 3.0 NaAc (protective agent) and 10 mL ethylene diamine (EDA) to form a homogeneous solution with magnetic stirring. The mixture was then transferred to a 100 mL Teflon-lined stainless steel autoclave, and 30 cm2 CNT film was completely immersed in the solution for solvothermal reaction at 200 °C for 10 h (Supplementary Fig. S3). After washed with deionized water five times and dried under vacuum at 70 °C for 20 min, the prepared production was cut uniformly into six pieces with dimensions 25 mm × 20 mm. The loading Fe3O4 prepared at FeCl3 concentrations of 0.01, 0.2, 0.3, 0.4, 0.5 and 0.10 M were 2, 4, 6, 6, 5 and 3 × 10−5 g/cm2, respectively. The Cu foil of the PMMA-graphene-copper foil was etched away by 0.2gml−1 FeCl3. After rinsing with deionized water, the floating PMMA/graphene film was scooped up by CNT film-Fe3O4 film. Then, the precoated PMMA was dissolved by acetone. Finally, the laminated graphene on CNT film-Fe3O4 substrate was obtained.

The individual CNT-Fe3O4-graphene films were first sprayed with a diluted epoxy solution prepared by mixing an epoxy base agent (EPONTM Resin 862), curing agent (DETDA) and ethyl acetate in the ratio of 10:1:100, followed by degassing in a vacuum oven for 30 min. Next, a CNT film-Fe3O4-graphene-epoxy composite was prepared by laminating the as fabricated films by spin coating Resin 862 and DETDA in the ratio of 10:1, followed by curing at 100 °C for 1 h. The thickness of one layer of CNT film-Fe3O4-epoxy composite was about 0.25 mm.

### Characterization

X-ray diffraction (XRD) patterns of the composites were measured on a Bruker D8 advance diffractometer using a Cu Kα source (λ = 0.154056 nm). Scanning electron microscopy (SEM) and transmission electron microscope (TEM) images were performed on the Auriga 60 and TEM Talos F200C, respectively. A magnetic study was performed by a vibrating sample magnetometer (VSM, Quantum Design, Versalab). The electromagnetic parameters of the samples were measured using a vector network analyzer (Agilent 8722ES) in the range of 1-18 GHz after a full two-port calibration (Supplementary Fig. S4S6). The composite was machined into a toroidal shaped sample with an outer diameter of 7.0 mm and inner diameter of 3.04 mm.

### Data Availability

All data generated or analysed during this study are included in this published article (and its Supplementary Information files).