## 3 Results and Discussion
### The Influence of Different Cu and Ni Contents on Magnetic Properties  
Along with the change in the size and direction of the externally applied magnetic field, the magnetization state of the material started to deflect; after de-magnetization, the magnetic domain can return to its origin. The B, H slope caused by such a reversible boundary movement is called the initial permeability. When the magnetic field continues to increase and changes into an irreversible state, magnetization finally will reach saturation; at this moment, even if the externally applied magnetic field is enhanced, the magnetization strength cannot be increased. After magnetization reaches saturation, if the externally applied magnetic field is removed, some magnetic domains will remain the same with remanent magnetization (Br). If at this moment, a reverse magnetic field is added, then magnetization will, at coercive force (Hc), be reduced to zero. If the reversed externally applied magnetic field is continuously increased, the material will reach a saturated magnetization state that is the reverse of the original magnetization direction. When the externally applied magnetic field has cycled once from the positive direction to the negative direction, a hysteresis curve will be generated [21]. Figure 3a showsthe hysteresis curve for [Cu\({}_{x}\)Zn\({}_{1-x}\)] Fe\({}_{2}\)O\({}_{4}\) at different compositions and proportions. From the figure, it can be seen that saturated magnetization was 15.30 M(emu/g) for the composition and proportion of Cu\({}_{0.5}\) Zn\({}_{0.5}\)Fe\({}_{2}\)O\({}_{4}\). As the Cu content increased, saturated magnetization also increased. When the Cu content reached Cu\({}_{0.7}\)Zn\({}_{0.3}\)Fe\({}_{2}\)O\({}_{4}\), the saturated magnetization also reached a peak of 24.89 M(emu/g), and the crystal phase was the strongest too; later on, as the Cu content increased, the saturated magnetization decreased accordingly. When the Cu content reached the composition of Cu\({}_{1}\)Fe\({}_{2}\)O\({}_{4}\), the saturated magnetization was the lowest, only 1.20 M(emu/g), and its crystal phase was also the weakest. Concerning the Ni-Zn system, Figure 3b shows that Ni\({}_{0.5}\)Zn\({}_{0.5}\)Fe\({}_{2}\)O\({}_{4}\) ferrite had the optimal magnetization, which was 50.29 M(emu/g), and its crystal phase was the strongest. Ni\({}_{0.3}\)Zn\({}_{0.7}\)Fe\({}_{2}\)O\({}_{4}\) ferrite was the worst, at only about 1.86 M(emu/g), and its crystal phase was relatively weaker as well. Therefore, it is clear that the strength of the crystal phase can affect the magnetization of ferrite; however, the product with the worst crystal phase will not have the worst magnetization. Table 1 depicts the coercive force (Hc), saturated magnetization (Ms), and residual magnetization (Mr) of [Cu\({}_{x}\)Zn\({}_{1-x}\)]Fe\({}_{2}\)O\({}_{4}\) at different proportions. From the data, it can be seen that the magnetic characteristic and Hc values for different proportions did not exceed 200 Oe, and the Mr value (soft ferrite had lower remanent magnetization) approached zero. Therefore, we can be sure that we are dealing with soft ferrite. For the magnetic flux of [Cu\({}_{x}\)Zn\({}_{1-x}\)]Fe\({}_{2}\)O\({}_{4}\) at different compositions and proportions, from the formula, the units of magnetic flux (B) are gauss, and the table shows that the magnetic flux for Cu\({}_{0.5}\)Zn\({}_{0.5}\) was 186.12 gauss/g; as the Cu content increased, the magnetic flux increased accordingly. When the composition was Cu\({}_{0.7}\)Zn\({}_{0.3}\), it reached a peak of 306.39 gauss/g; later on, it dropped, since for Cu\({}_{1}\)Fe\({}_{2}\)O\({}_{4}\), the magnetic flux was only 15.47 gauss/g. In terms of coercive force (Hc), saturated magnetization (Ms), and remanent magnetization (Mr) for [Ni\({}_{x}\)Zn\({}_{1-x}\)]Fe\({}_{2}\)O\({}_{4}\) ferrite with different proportions, the experimental results show that the magnetic characteristic and Hc values did not exceed 200 Oe, and the Mr value approached zero.