## 3 Results and Discussion
### EM Wave Absorption Properties
The abundant hetero-interfaces between C-Fe\({}_{3}\)O\({}_{4}\)/paraffin and C-Fe\({}_{3}\)O\({}_{4}\)/PVDF and the adsorbed functional groups can also induce strong interfacial polarization and multiple polarization relaxation [13]. The semicircles show several distortions which indicate that an additional loss mechanism (e.g., conduction loss) may be present, resulting in enhanced dielectric loss [33]. The magnetic loss is also an important loss mechanism for Fe\({}_{3}\)O\({}_{4}\)-based composites which should be explored. The magnetic loss \(\left(\tan\delta_{\mathrm{\mu}}\right)\) often originates from relaxation processes during magnetization, such as domain wall resonance, exchange resonance, natural resonance, hysteresis, and eddy current [7]. Hysteresis loss is mostly insignificant in a low magnetization field, whereas the domain wall resonance typically appear in the frequency range of 1-100 MHz, and therefore can be excluded in this case [34]. Analysis of the dependence of \(\mathrm{C_{o}}=\mu^{\prime\prime}\left(\mu^{\prime}\right)^{-2}\)f\({}^{-1}\) on frequency is often used to investigate magnetic loss from eddy current. Should the magnitude of \(\mathrm{C_{o}}\) remained constant with increase in frequency, eddy current loss can thus inferred as the dominant magnetic loss mechanism [35]. As shown in Figure 9, the \(\mathrm{C_{o}}\) values of all samples tend to decrease with an increase in applied frequency which indicates that attenuation of EM wave by magnetic loss mechanism does not  
Figure 8: The Cole-Cole plots of (**a**) M0, (**b**) M10, (**c**) M20 and (**d**) M40. result from eddy current resonance. These findings reveal that the magnetic loss comes from natural and exchange resonance. The magnitude of EM wave absorption represented by reflection loss (RL) of all samples were calculated from Equations (16)-(18) below based on the transmission line theory [25], using the FEM formulation. \[\mathrm{RL(dB)}=20\log_{10}\lvert\Gamma\rvert \tag{16}\]  
Figure 6:0  
Figure 6:1  
where \(Z_{\mathrm{in}},Z_{\mathrm{o}},\)\(\varepsilon_{\mathrm{r}},\)\(\mu_{\mathrm{r}},\)\(\mathrm{c},\)\(\mathrm{f},\)\(\mathrm{d}\), and \(\Gamma\) are the characteristic impedance of the absorptive material, impedance of free space, complex permittivity, complex permeability, the velocity of EM wave propagation in vacuum, microwave frequency, absorber thickness, and the reflection coefficient, respectively. Generally, RL value of \(-10\) dB or \(-20\) dB correspond to 90% or 99% EM wave absorption, respectively [36]. The range of frequency equivalent to this reflection loss (RL \(<-10\) dB) in a single absorber thickness can be regarded as the effective absorption bandwidth (EAB) [20]. The variation of the RL curves of all samples at layer thicknesses in the range 2.0-5.5 mm from 8.2-18 GHz is presented in Figure 6:2 The absorption coefficient of the samples strongly depends on the filler loadings. As presented in Figure 10a, sample M0 (i.e., ordinary C-Fe\({}_{3}\)O\({}_{4}\)) displayed poor absorption over the X-band frequency range and some EM wave absorption capacity at large thickness in the Ku-band frequency range. This finding confirms large density (\(\geq\)50 wt.%) and high thickness (\(\geq\)5.0 mm) as drawbacks of Fe\({}_{3}\)O\({}_{4}\). As such, composites formation with PVDF as a dielectric matrix was employed to regulate its EM parameters and optimize its MAP. Logically, the MAP of M10 (Figure 10b) is improved as compared with C-Fe\({}_{3}\)O\({}_{4}\). Within X-band, minimum RL value \(-48.6\) dB at a large absorber thickness of 5.5 mm was achieved at 11.7 GHz. At Ku-band, minimum RL of \(-46.1\) dB at 16.2 GHz was achieved at a reduced absorber thickness (4.0 mm), with an operating bandwidth of 2.4 GHz. The MAP improved significantly with M20 and M40 (Figure 10c,d) with the operating bandwidth spanning the whole X-band and Ku-band frequency range. Furthermore, with M40 the optimal thickness can effectively be reduced to 2.5 mm, with minimum RL of \(-47.3\) dB at 17.9 GHz.