## 1 Introduction  
Ferrite cores are a vital inductive component in motors for computer, communication and consumer Electronics (3C) products, so they are an important raw material for the industry. Traditional production methods use \(\mathrm{MnO_{2}}\), ZnO and \(\mathrm{Fe_{2}O_{3}}\) as raw materials, and a solid-state reaction is initiated. When the raw materials are mixed, sintered and ground, a powder is produced. This powder is granulated, formed and placed in a nitrogen furnace for sintering, before it is made into an iron core. If waste batteries are used as the raw material, this cost is reduced and the process is environmentally friendly. Dry batteries can only be used once and are then discarded, which is a waste of a resource and material and pollutes the environment because the batteries contain Hg. In this study, waste batteries are used as the raw material and co-precipitation is used to prepare Zn-Mn series ferrite. The magnetic properties, the particulate diameter and the magnetic flux density of both types of ferrite core are studied. The manufacture of ferrite involves forming and sintering an inorganic material (which does not contain carbon-hydrogen compounds) using a process that is the same as that for the production of ceramics. Ferrites are the earliest forms of fine ceramic [1,2]. Ferrite structures are classified into three main categories [3,4]: (1) spinel structure, such as the Zn-Mn series and the Ni-Zn series, which exhibits ferromagnetism and good permeability (i\({}_{\mathrm{i}}\)), magnetic flux density (B\({}_{\mathrm{s}}\)) and loss characteristics; (2) garnet structure, such as yttrium iron oxide, which exhibits anti-ferromagnetism and is mainly used in microwave communication and laser optics applications; and (3) hexagonal structure, such as ferrites of the Ba series and Sr series, which exhibits permanent magnetism and is also called hard ferrite. The preparation methods for ferrite include: (1) the solid-state reaction method,for which metallic oxide powder is used as the raw material and the raw materials are mixed, sintered and ground to produce ferrite powder [5; 6; 7]; (2) the co-precipitation method, for which metallic ion salt is used as the raw material and dissolved, mixed, neutralized by adding alkali, oxidized by aeration, rinsed with water, and baked and ground to produce ferrite powder [8; 9; 10], and then after high-temperature sintering, ferrite powder is produced; (3) the sol-gel process, for which metallic ion salt is used as the raw material and citric acid is added, whereupon the mixture is agitated and finally undergoes vacuum rotary evaporation to produce a viscous liquid [11; 12; 13; 14]; and (4) the hydrothermal method, which uses a pressurized solution at a temperature that is greater than the normal boiling point of water or the solvent in an autoclave. Because of the high temperature and high pressure, the solubility, the diffusion coefficient and the reactivity of the solute are significantly increased and the reaction is easier to initiate [15; 16; 17]. In 2017, [PERSON] reported precise control the Fe\({}^{2+}\) concentration, pH, temperature and aeration rate to synthesise, with size of 10-300 nm, cube-like and sphere-like crystalline Fe\({}_{3}\)O\({}_{4}\) nanoparticles [18]. In a primary battery, the positive electrode of a Zn-Mn dry battery is MnO\({}_{2}\), and the negative electrode is Zn. The electrolyte between the positive and negative electrodes is ZnCl\({}_{2}\) or NH\({}_{4}\)Cl. In an alkaline Mn battery, the positive electrode is also MnO\({}_{2}\) and the negative electrode is Zn, but the electrolyte between the positive and negative electrodes is KOH. The only difference between these two batteries is the electrolyte that is used. Therefore, waste batteries can be used as a raw material to produce of Zn-Mn ferrite. The recovery of Mn from Zn-Mn and Zn-C battery waste has been the subject of studies [19; 20; 21; 22].