## 3 Results and Discussion
The frequency dependence of \(t_{m}\) (\(n=1,3\)) is calculated and plotted on the contour maps in Figure 3.0 It can be noticed that all the points of RL\({}_{\min}\) lie on the curves of \(t_{m}\) for sample B. Thus, it is demonstrated that the quarter-wavelength match principle is an effective tool that provides a crucial guide in the thickness design of absorbers. Figure 3.1 RL curves of paraffin samples containing 50 wt % Fe\({}_{3}\)O\({}_{4}\) (**a**) and sample A (**b**); RL curves of paraffin samples containing 30 wt % (**c**); 50 wt % (**d**) and 70 wt % (**e**) sample B, respectively. Figure 3.2 RL 2-D contour map representations in the frequency range of 2–18 GHz loaded with 50 wt % of sample B. Typically, the magnetic loss is implied by the imaginary part of permeability and mainly originates from hysteresis loss, domain wall displacement, natural resonance, and eddy current resonance. In general, hysteresis loss is mainly caused by the time lag of the magnetization vector behind the external EM-field vector and will always be negligible in a weak applied field, while domain wall resonance loss takes place in the MHz frequency range. The following equation is used to determine whether eddy currents contribute to the magnetic loss [33]:  
Figure 3.3  
If magnetic loss only stems from the eddy current, \(C_{0}\) should be equal to a constant value \(2\pi\mu_{0}d^{2}\sigma\) (\(d\) is the thickness of the MAMs, \(\sigma\) is the electrical conductivity, and \(\mu_{0}\) is the permeability in a vacuum) and would be independent of frequency; if not, the magnetic loss is ascribed to natural resonance. From Figure 8a, we find that the value of \(C_{0}\) varies with the frequency and presents a sharp declining tendency in the frequency range of 2-8 GHz. However, when the frequency is in the range of \(\sim\)8-12 GHz, the value of \(C_{0}\) closes to a constant. Based on this phenomenon, it can be concluded that magnetic loss results from the natural and exchange resonance and the eddy current effect. According to transmission line theory, EMW absorption properties can be expressed by the attenuation constant of \(\alpha\). The attenuation constants of sample B with 30, 50, and 70 wt % were calculated using the following expression [34; 35]:  
Figure 3.4  
where \(c\) is the velocity of light in a vacuum. Figure 8b shows the plot of the attenuation constant of \(\alpha\) versus frequency. It can be seen that the sample with 50 wt % filler loading has the largest value of \(\alpha\); thus, we supposed that the sample with 50 wt % filler loading possesses greater EMW attenuation and impedance matching than the other samples. Figure 9 shows the dielectric loss (tan\(\delta_{\varepsilon}=\varepsilon^{\prime\prime}/\varepsilon^{\prime}\)) and magnetic tangent loss (tan\(\delta_{\mu}=\mu^{\prime\prime}/\mu^{\prime}\)) of Fe\({}_{3}\)O\({}_{4}\)/ZnO and Fe\({}_{3}\)O\({}_{4}\) NPs, respectively. tan\(\delta_{\varepsilon}\) and tan\(\delta_{\mu}\) are two possible contributors for EMW absorption, and are commonly used to describe material loss capacity. Therefore, we calculated the tangent loss based on the data in Figure 3.5 Specifically, sample B has a higher tan\(\delta_{\varepsilon}\) value than the naked Fe\({}_{3}\)O\({}_{4}\) NPs, indicating that the ZnO shell obviously improves the dielectric properties of the composites. Additionally, Figure 7 clearly shows that the magnetic loss factor (tan\(\delta_{\mu}\)) is much higher than the dielectric loss factor (tan\(\delta_{\varepsilon}\)) in the low frequency range (\(\sim\)2-7 GHz), which indicates that magnetic loss plays a vital role in EMW absorption in this region. Meanwhile, in the high frequency range (\(\sim\)8-12 GHz), the value of tan\(\delta_{\varepsilon}\) is higher than tan\(\delta_{\mu}\), which indicates that dielectric loss is the main loss in this frequency region. Such a complementarity between dielectric loss and magnetic loss demonstrates the Fe\({}_{3}\)O\({}_{4}\)/ZnO composites to possess promising EMW absorption properties.