## 3 Results and Discussion
It can be observed that a thin layer of ZnO is growing on the edge of Fe\({}_{3}\)O\({}_{4}\) NP at a thickness of \(\sim\)15 nm. Figure 4f also presents the diffraction profile generated by the inserted SAED pattern and confirms the structure of ZnO and Fe\({}_{3}\)O\({}_{4}\). The SEM and TEM results clearly indicate that the nanocomposites possess a core-shell type structure, and that the inner Fe\({}_{3}\)O\({}_{4}\) NPs cores are successfully wrapped with the uniformed ZnO shells. In order to explore the microwave absorption properties of Fe\({}_{3}\)O\({}_{4}\)/ZnO nanocomposites, the relative complex permeability (\(\mu_{\rm r}=\mu^{\prime}-\rm j\mu^{\prime\prime}\)) and relative permittivity (\(\epsilon_{\rm r}=\)\(\varepsilon^{\prime}-\rm j\varepsilon^{\prime\prime}\)) were measured by a vector network analyzer in the frequency range of 2-18 GHz. The measured samples were prepared by uniformly mixing with paraffin (in mass fractions of 30%, 50%, and 70%) at 85 \({}^{\circ}\)C, pressed into toroidal-shaped samples. According to transmission line theory, EM properties can be evaluated based on the relative complex permeability (\(\mu_{\rm r}=\mu^{\prime}-\rm j\mu^{\prime\prime}\)) and relative permittivity (\(\epsilon_{\rm r}=\)\(\varepsilon^{\prime}-\rm j\varepsilon^{\prime\prime}\)). \(\mu^{\prime}\) and \(\varepsilon^{\prime}\) represent the ability to store EM energy, whereas \(\mu^{\prime\prime}\) and \(\varepsilon^{\prime\prime}\) represent the inner dissipation of EM energy, which originates from the relaxation and resonance mechanisms. The relative complex permittivity (\(\varepsilon^{\prime}\), \(\varepsilon^{\prime\prime}\)) and relative complex permeability (\(\mu^{\prime}\), \(\mu^{\prime\prime}\)) of Fe\({}_{3}\)O\({}_{4}\), sample A and sample B measured in the frequency range of 2-18 GHz are plotted in Figure 5a-d. From Figure 5a,b, it can be found that \(\varepsilon^{\prime}\) of Fe\({}_{3}\)O\({}_{4}\) is in the range of 4.67-5.03, and \(\varepsilon^{\prime\prime}\) of Fe\({}_{3}\)O\({}_{4}\) is in the range of 0.40-1.02. After being composited with ZnO, the values of \(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\) show a sharp growth. As for sample A, the values of \(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\) are in the range of 7.12-8.94 and 0.70-1.67, respectively. Meanwhile, the values of \(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\) raise to the range of 9.62-16.60 and 1.17-10.23, respectively, after the Fe\({}_{3}\)O\({}_{4}\) NPs were coated with the ZnO shell (sample B). The values of \(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\) for sample B fluctuate more and exhibit great change in the main measuring frequency region. As shown in Figure 5a, the \(\varepsilon^{\prime}\) of sample B presents a declining trend with increasing frequency, while the trend of \(\varepsilon^{\prime\prime}\) is the contrary, and some peaks appear in the high frequency region. The curves of \(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\) indicate that the ZnO shell can greatly improve the dielectric properties of the material. Figure 5c,d shows the relative complex permeability of the three materials. As for Fe\({}_{3}\)O\({}_{4}\) NPs, the value of \(\mu^{\prime}\) drops sharply from 1.27 in the frequency range of 2-6  GHz, and then shows a fluctuating trend versus the changing frequency, and the Fe\({}_{3}\)O\({}_{4}\)/ZnO (sample A and B) composites display a similar variation trend throughout the entire measured frequency range. This phenomenon may result from the eddy current effect. Compared to the value of \(\mu^{\prime}\), differences in  
Figure 4: The SEM images of Fe\({}_{3}\)O\({}_{4}\) (**a**); sample A (**b**); and sample B (**c**); TEM image (**d**); HRTEM image (**e**) of sample A and SAED pattern (**f**) of sample B, respectively. the \(\mu\)\" values of Fe\({}_{3}\)O\({}_{4}\) and Fe\({}_{3}\)O\({}_{4}\)/ZnO composites are distinguished at low frequency.