## 1 Introduction  
The origin of ferrite dates from very early in time, and it usually existed as Fe\({}_{3}\)O\({}_{4}\), as natural ferrite. Ferrite is an oxide of strong magnetic properties, with wide applications due to the booming development of electronic technology. Nowadays, it has become an indispensable material in the electronics industry. The production of ferrite was originally made through the calcination of an inorganic precursor material; therefore, its process was the same as that of ceramics and it belonged to the products of the ceramics industry. In its production, highly pure precursor materials were used, and the sintering environment and condition were controlled, as such, it is considered the earliest fine ceramic in history [1, 2]. Based on the structure, ferrite can be divided into three main categories [3]: spinel structure, garnet structure, and hexagonal structure. Methods for the preparation of ferrite can be roughly divided into: solid-state reaction [4, 5, 6], co-precipitation [7, 8, 9], sol-gel [10, 11, 12], and hydrothermal processes [13, 14, 15]. The ferrites in nanocrystalline form found applications in new fields, such as magnetically guided drug delivery, magnetic resonance imaging (MRI), catalysts, humidity and gas sensors, magnetic fluids, etc. [16, 17]. Presently, ferrite core has become an indispensable inductive component in 3C products. In this work, the pure material and the co-precipitation method were used to prepare Cu-Zn and Ni-Zn ferrite nano-powders and investigate their magnetic characteristics, particle diameters, and magnetic flux densities, etc. The co-precipitation method was used at different pH values (from 6 to 12) and different sintering temperatures (from 0 \({}^{\circ}\)C to 1200 \({}^{\circ}\)C) to synthesize [Cu\({}_{\mathrm{x}}\)Zn\({}_{\mathrm{1-x}}\)]Fe\({}_{\mathrm{2}}\)O\({}_{\mathrm{4}}\), [Ni\({}_{\mathrm{x}}\)Zn\({}_{\mathrm{1-x}}\)]Fe\({}_{\mathrm{2}}\)O\({}_{\mathrm{4}}\) ferrite powders. Then, the effect of the pH value on crystallinity and integrity was investigated, and the effect of sintering temperature on saturated magnetization (Ms), residual magnetization (Mr), coercive force (Hc), magnetic flux (B), and average particle diameter (D) was also studied. In 2008, [PERSON] used the solid-state reaction method to prepare ZnO-MnO\({}_{\mathrm{2}}\)-Fe\({}_{\mathrm{2}}\)O\({}_{\mathrm{3}}\); as the sintering temperature increased, the saturated magnetization also increased. Moreover, as the sintering temperature increased to 1150 \({}^{\circ}\)C, a maximum was reached, followed by a decline. When the temperature reached 1050 \({}^{\circ}\)C-1100 \({}^{\circ}\)C, the surface morphology was transformed from the original cluster into a chain shape, and when the sintering temperature reached 1150 \({}^{\circ}\)C-1200 \({}^{\circ}\)C, it was transformed into a laminating structure [4]. For the preparation of Ni-Cu-Zn ferrite nanoparticles using the chemical co-precipitation method and for the study of magnetic property after sintering, high purity Ni\({}_{\mathrm{2}}\)SO\({}_{\mathrm{4}}\), CuSO\({}_{\mathrm{4}}\), ZnSO\({}_{\mathrm{4}}\), and ferrous sulfate were used as precursor materials dissolved in water, with NaOH being used as the precipitation agent to form Ni\({}_{\mathrm{0}}\).39 Cu\({}_{\mathrm{0}}\).11 Zn\({}_{\mathrm{0}}\).5 Fe\({}_{\mathrm{2}}\)O\({}_{\mathrm{4}}\) with an obtained average particle diameter of about 30 nm. When Cu is added to ferrite, the density and magnetization can be increased. In 2011, [PERSON] et al. used strontium nitrate, nickel acetate, zinc acetate, ferric nitrate, and citric acid as precursor materials, and employed the sol-gel process to prepare ferrite nanofibers and SrFe\({}_{\mathrm{12}}\)O\({}_{\mathrm{19}}\)/Ni\({}_{\mathrm{0}}\).5 Zn\({}_{\mathrm{0}}\).5 Fe\({}_{\mathrm{2}}\)O\({}_{\mathrm{4}}\) nanocomposite ferrite. Single Ni\({}_{\mathrm{0}}\).5 Zn\({}_{\mathrm{0}}\).5 Fe\({}_{\mathrm{2}}\)O\({}_{\mathrm{4}}\) ultra fine fiber ferrite showed a particulate structure with a shiny surface morphology.