# Development of Multi-Cation-Doped M-Type Hexaferrite Permanent Magnets
## 1 Introduction  
M-type hexaferrites, which have the basic formula (Ba,Sr)Fe\({}_{12}\)O\({}_{19}\) and were discovered in the early 1950s, have been utilized as permanent magnets owing to their excellent chemical stability and proper hard-magnetic properties, such as strong \(c\)-axis magnetic anisotropy and sufficient saturation magnetization (\(M_{\rm S}\)) [1; 2]. Ferrite magnets using the M-type hexaferrite phase account for the largest amount of permanent magnet usage worldwide, which makes enhancing magnet performance very important. Many studies have been conducted to enhance the magnetic properties of M-type hexaferrites, such as saturation magnetization (\(M_{\rm S}\)) and the uniaxial magnetocrystalline anisotropy constant (\(K_{\rm u}\)), by substituting various cations. It has been reported that the optimal substitution of La-Zn [3; 4], Mn-Zn [5], La-Ce-Zn [6], La-Mn-Zn [7], and Zn-Zr [8] into M-type hexaferrites increases the \(M_{\rm S}\) value. One possible reason for the increase in \(M_{\rm S}\) is that non-magnetic Zn\({}^{2+}\) ions selectively replace Fe\({}^{3+}\) ions with spin directions that are antiparallel to the net magnetization direction. It has also been reported that the substitution of Ce-Mn [9], Sm [10], Nd-Nb-Zn [11], Ga-Zn [12], Nb [13], Ce-Dy [14], Co-Al [15], Al [16], and Ho [17] enhances the \(K_{\rm u}\) value or coercivity (\(H_{\rm C}\)) of M-type hexaferrites. However, \(M_{\rm S}\) and \(K_{\rm u}\) do not improve simultaneously in all cases. Generally, in magnetic materials, an increase in \(M_{\rm S}\) causes a decrease in \(K_{\rm u}\), and an increase in \(K_{\rm u}\) causes a decrease in \(M_{\rm S}\). It is well-known that La-Ca-Co-substituted M-type hexaferrites exhibit significantly enhanced hard-magnetic properties because their magnetocrystalline anisotropy increases without scarifying the \(M_{\rm S}\) [18; 19; 20]. Therefore, La-Ca-Co-substituted Sr-hexaferrites (SrM) have been developed into high-grade ferrite magnet products. However, no meaningful progress has been made in the research and development of commercial ferrite magnets for more than 15 years. In addition, owing to the recent surge in the price of cobalt raw materials, the development of ferrite magnets with excellent performance without the use of cobalt is strongly required in the industry.  
The goal of this study was to determine the optimal composition for improving the hard-magnetic characteristics of multi-cation-substituted SrM. First, we sought to determine the optimal doping amount of Si-Mg in SrM. Normally, SiO\({}_{2}\) is used as a sintering additive to control grain growth. However, our previous studies [21] have shown that the Si can be applied as substitution elements by co-substituting Si\({}^{4+}\) and Mg\({}^{2+}\) at Fe\({}^{3+}\) sites in SrM. The co-substitution of a Si\({}^{4+}\)-Mg\({}^{2+}\) pair for two Fe\({}^{3+}\) ions in SrM satisfies charge neutrality. To further improve the characteristics, the La-Ca-Co substitution was combined with the optimal level of Si-Mg substitution while controlling the Fe content. Finally, we sought to determine the sintering conditions required for the replacement of Co with Mn to obtain excellent hard-magnetic properties. Based on the obtained optimal cation composition and sintering process conditions, anisotropic magnets were fabricated through magnetic-field molding and their performance as ferrite magnets was evaluated.