## 3 Results and Discussions
### The Effect of Different Mn and Zn Contents on the Magnetic Properties  
For a composition Mn\({}_{0.54}\)Zn\({}_{0.46}\)Fe\({}_{2}\)O\({}_{4}\), the saturated magnetization is about 0.01 M (emu/g) more than that for Mn\({}_{0.5}\)Zn\({}_{0.5}\)Fe\({}_{2}\)O\({}_{4}\), so the composition Mn\({}_{0.54}\)Zn\({}_{0.46}\)Fe\({}_{2}\)O\({}_{4}\) is used to determine the effect of sintering temperature on Mn-Zn ferrite. The hysteresis curves (pH of 9, 80 \({}^{\circ}\)C, air oxidation for 24 h) for ferrites with different compositions of Mn-Zn, Ni-Zn and Cu-Zn at the same pH value are shown. We show that the saturated magnetization for a [Mn\({}_{x}\)Zn\({}_{1-x}\)]Fe\({}_{2}\)O\({}_{4}\) system that is recycled from waste batteries is at a maximum. For ferrites of Mn-Zn, Ni-Zn and Cu-Zn, when the pH is 9, the results show that the value for the coercive force (Hc) does not exceed 200 Oersted (Oe) and the Mr value approaches zero (soft ferrite has a lower remanent magnetization), which demonstrates that the ferrites for all of the systems are soft ferrites, as shown in Figure 3.  
Figure 4 shows the effect of coercive force (Hc) on the saturated magnetization (Ms) and the remanent magnetization (Mr) for [Mn\({}_{0.54}\)Zn\({}_{0.46}\)]Fe\({}_{2}\)O\({}_{4}\) at different pH values. It is seen that the Hc value does not exceed 200 Oe and that the Mr value (soft ferrite has a lower remanent magnetization) approaches zero. This demonstrates that this series is soft ferrite. In terms of the effect of the pH value of the waste battery on the magnetic properties of Mn-Zn ferrite, it is seen that the saturated magnetization has the lowest value of 2.52 M (emu/g) for a pH value of 6, because metallic ions do not precipitate completely so a complete structure is not formed. The spinel structure at a pH value of 10 has a lower saturated magnetization. The peak value for the saturated magnetization is 62.85 M (emu/g), and the crystal phase is the most complete. The saturated magnetization decreases when the pH value is 11, because an increase in the pH value inhibits the precipitation of Zn ions. For a pH value of 12, the saturated magnetization is only 44.81 M (emu/g). The coercive force (Hc), the saturated magnetization  
Figure 3: The hysteresis curves for different compositions and proportions; [M\({}_{x}\)Zn\({}_{1-x}\)]Fe\({}_{2}\)O\({}_{4}\) (M = Mn, Zn, Cu). (Ms) and the remanent magnetization (Mr) for a composition of MnZnFe\({}_{2}\)O\({}_{4}\) at different pH values are shown in Table 1. The data shows that, for the different pH values, the magnetic properties and the value of Hc do not exceed 200 Oe. The value for Mr is also quite low, which demonstrates that this series is soft ferrite. The magnetic flux (B) for [Mn\({}_{0.54}\)Zn\({}_{0.46}\)]Fe\({}_{2}\)O\({}_{4}\) at different pH values is calculated in gauss. The magnetic flux at a pH of 6 is 102.95 gauss/g. An increase in the pH value produces a corresponding increase in magnetic flux. At a pH of 10, the peak value is 864.48 gauss/g. This value decreases to 637.78 gauss/g for a pH of 12. The magnetic flux (B) for [Mn\({}_{0.54}\)Zn\({}_{0.46}\)]Fe\({}_{2}\)O\({}_{4}\) increases from 102.95 (gauss/g) at a pH value of 6 to a peak value of 864.48 (gauss/g) at a pH value of 10. At pH values of greater than 10, the value begins to decrease because Zn ions do not precipitate completely. The pH was changed from 6 to 12, the particle size was changed from 31 to 59 nm, Ms was changed from 2.52 to 62.85 emu/g. The Mn-Zn ferrite nanoparticles' size and structure (cube-like NPs or sphere-like NPs) affects the NPs' magnetic properties. Smaller NPs have more defects, and a decrease of \(\mu\) and Ms properties. This is consistent with a previous study on the particle size and magnetic properties [18].