# Development of Multi-Cation-Doped M-Type Hexaferrite Permanent Magnets
## 3 Results and Discussion  
### Crystalline Structure and Microstructure Analysis  
Figure 1a shows the powder XRD patterns of the SrFe\({}_{12-2x}\)Si\({}_{x}\)Mg\({}_{x}\)O\({}_{19}\) (\(x\) = 0.0, 0.05, 0.1, 0.2) samples sintered at 1230 \({}^{\circ}\)C. A secondary phase peak of Fe\({}_{2}\)O\({}_{3}\) is observed as the substitution level increases from \(x\) = 0.0 to \(x\) = 0.1, and it becomes noticeably larger at \(x\) = 0.2. The powder XRD patterns of the Sr\({}_{0.4}\)Ca\({}_{0.3}\)La\({}_{0.3}\)Fe\({}_{11.7-y}\)Co\({}_{0.2}\)Si\({}_{0.05}\)Mg\({}_{0.05}\)O\({}_{19}\) (\(y\) = 0.0, 1.0, 1.5, and 2.0) samples are shown in Figure 1b. Fe\({}_{2}\)O\({}_{3}\) peaks are found at \(y\) = 0, and they decrease significantly at \(y\) = 1.0; no Fe\({}_{2}\)O\({}_{3}\) peak is found at \(x\) \(\geq\) 1.5. The diffraction peaks  
for the M-type hexaferrites were indexed based on hexagonal magnetoplumbite crystal structures with space group \(P6_{3}\)/\(mmc\) [International Center for Diffraction Data (ICDD), Powder Diffraction File no. 00-33-1340]. As shown in Figure 1c, no secondary phase peaks were observed in the XRD patterns of the Sr\({}_{0.4}\)Ca\({}_{0.3}\)La\({}_{0.3}\)Fe\({}_{10.2}\)Co\({}_{0.2-z}\)Mn\({}_{z}\)Si\({}_{0.05}\)Mg\({}_{0.05}\)O\({}_{19}\) (\(z\) = 0, 0.05, 0.1, 0.2) samples. The samples without Fe\({}_{2}\)O\({}_{3}\) peaks are considered to have a single-phase M-phase. Figure 2 shows the magnetic hysteresis curves of the SrFe\({}_{12-2x}\)Si\({}_{x}\)Mg\({}_{x}\)O\({}_{19}\) (\(x\) = 0, 0.05, 0.1, 0.2) samples sintered at 1230 \({}^{\circ}\)C measured using VSM. The \(M_{\rm S}\) and \(H_{\rm C}\) values with  
respect to \(x\) are shown in Figure 2b. The sintered sample densities and the \(M_{\rm S}\) and \(H_{\rm C}\) values of the sintered samples are presented in Table 1. All the samples were sintered without any sintering additives, and thus the densities of the samples were much lower than the theoretical density of SrM (-5.1 g/cm\({}^{3}\)). Nevertheless, because \(M_{\rm S}\) was measured using VSM in units of emu/g, the densities of the samples did not affect the value of \(M_{\rm S}\). The \(M_{\rm S}\) value increased slightly at \(x\) = 0.05, whereas the \(H_{\rm C}\) value increased significantly. Then, the \(M_{\rm S}\) and \(H_{\rm C}\) values decreased as \(x\) increased to 0.2. Because \(H_{\rm C}\) increased without a decrease in the \(M_{\rm S}\) value at a Si-Mg substitution amount of \(x\) = 0.05, this value of \(x\) is considered to be a very effective substitution composition for a permanent magnet. The \(M_{\rm S}\) value is an intrinsic magnetic property that depends on cation substitution, and the possible mechanism of the \(M_{\rm S}\) increase may have been the preferred substitution of non-magnetic Si\({}^{4+}\) or Mg\({}^{2+}\) into the down-spin site of Fe\({}^{3+}\)[4; 5; 6]. The microstructures of the SrFe\({}_{12-2x}\)Si\({}_{x}\)Mg\({}_{x}\)O\({}_{19}\) (\(x\) = 0, 0.05, 0.1, 0.2) samples sintered at 1230 \({}^{\circ}\)C are presented in Figure 3a-d. The samples show fine microstructures at \(x\) = 0.05 and 0.1 compared to the \(x\) = 0 sample, and they are very porous from \(x\) = 0 to 0.1. The Sr\({}_{0.4}\)Ca\({}_{0.3}\)La\({}_{0.3}\)Fe\({}_{11.7-y}\)Co\({}_{0.2}\)Si\({}_{0.05}\)Mg\({}_{0.05}\)O\({}_{19}\) (\(y\) = 0, 1, 1.5, 2) samples sintered at 1230 \({}^{\circ}\)C showed a much denser microstructure with larger grains (Figure 3e-h). Similar results showing that grain growth and densification are effectively enhanced by doping with Ca [22] or LaCaCo [23; 24] have been previously reported. The sintering densities of the samples are presented in Table 2. When the Fe dependency \(y\) increased to 2.0 in the Sr\({}_{0.4}\)Ca\({}_{0.3}\)La\({}_{0.3}\)Fe\({}_{11.7-y}\)Co\({}_{0.2}\)Si\({}_{0.05}\)Mg\({}_{0.05}\)O\({}_{19}\) samples (Figure 3h), significant grain growth occurred. From the XRD patterns shown in Figure 1b, it was verified that Fe\({}_{2}\)O\({}_{3}\) was present at \(x\) = 0 and 0.1 but lost at \(x\) = 1.5.