# Development of Multi-Cation-Doped M-Type Hexaferrite Permanent Magnets
## 3 Results and Discussion
### Magnetic Properties and Magnet Performances  
The demagnetization curves (4\(\pi\)\(M\) vs. \(H\)) of the sintered 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) and 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) hexaferrites are presented in Figure 4a-d, and the \(B_{\rm r}\) and \(H_{\rm C}\) values are presented in Table 2. The magnetization curves (4\(\pi\)\(M\)-\(H\)) were measured using a B-H loop tracer on the disk samples. In the B-H loop tracer measurement, the 4\(\pi\)\(M\) data were gathered in Gaussian units, unlike those obtained in emu/g units for the VSM measurements shown in Figure 2. The \(M\) (emu/g) values can be converted to 4\(\pi\)\(M\) (G) using the following equation:  
\[4\pi\rm{M}\left(G\right)=4\pi\rm{M}\left(emu/g\right)\times\rho, \tag{1}\]  
where \(\rho\) is the sintered sample density (g/cm\({}^{3}\)). The magnetic flux density \(B\) (G), magnetization (4\(\pi\)\(M\)), and applied magnetic field (\(H\)) in the cgs unit system have the following relations [25]:  
\[B\left(G\right)=4\pi\rm{M}\left(G\right)+H\left(Oe\right) \tag{2}\]The [G] and [Oe] units can be considered as the same physical quantity in the cgs unit system. Therefore, a sintering density close to the theoretical density is required for a permanent magnet to produce a high magnetic flux density. As shown in Figure 4a, the \(y=0\) sample exhibited a relatively low \(B_{\rm r}\) value of 2.37 kG owing to the presence of a non-magnetic second phase of Fe\({}_{2}\)O\({}_{3}\), which is shown in Figure 1b. The highest \(B_{\rm r}\) value of 2.69 kG was obtained for the \(y=1.5\) sample with no second phase. The \(H_{\rm C}\) values 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\({}_{19}\) samples increased from 3.78 to 3.91 kOe at \(y=1.0\), and it decreased with increasing \(y\). The sudden decrease in \(H_{\rm C}\) at \(y=2.0\) can be attributed to significant grain growth (Figure 3h). As mentioned above, the lack of Fe in the M-phase is believed to promote grain growth. Next, the magnetic properties were evaluated by substituting an amount of Co with Mn in a fixed composition of \(y=1.5\), in which a high \(B_{\rm r}\) value was obtained without a Fe\({}_{2}\)O\({}_{3}\) secondary phase. Figure 4b,c shows the 4\(\pi\)M-\(H\) curves of the Sr\({}_{0.4}\)Ca\({}_{0.3}\)La\({}_{0.3}\)Fe\({}_{10.2}\)Co\({}_{0.2-x}\)Mn\({}_{x}\) Si\({}_{0.05}\)Mg\({}_{0.05}\)O\({}_{19}\) (\(z=0\), 0.05, 0.1, 0.2) hexaferrites sintered at 1230 \({}^{\circ}\)C and 1210 \({}^{\circ}\)C, respectively. The \(\rho\), \(B_{\rm r}\), and \(H_{\rm C}\) values of the samples are presented in Table 2. In Figure 4b, the Mn-doped samples (\(z=0.05\), 0.1, 0.2) sintered at 1230 \({}^{\circ}\)C exhibit poor demagnetization curves, with significantly decreased \(B_{\rm r}\) and \(H_{\rm C}\) values. However, when these samples were sintered at 1210 \({}^{\circ}\)C, the \(B_{\rm r}\) and \(H_{\rm C}\) values of the Mn-doped samples were greatly enhanced. The \(z=1.0\) sample showed a significantly improved \(H_{\rm C}\) value of 4150 kOe and a relatively high \(B_{\rm r}\) value of 2.53 kG. Here, because the value of \(B_{\rm r}\) is proportional to the sintering density, there is room for improvement in \(B_{\rm r}\) when the sintering density is increased. To improve the sintering density, additional high-energy ball-milling was performed for 2, 4, and 6 h on a sample with a composition of \(z=1.0\) (Sr\({}_{0.4}\)Ca\({}_{0.3}\)La\({}_{0.3}\)Fe\({}_{10.2}\)Co\({}_{0.1}\)Mn\({}_{0.1}\)Si\({}_{0.05}\)Mg\({}_{0.05}\)O\({}_{19}\)) and the resulting 4\(\pi\)M-\(H\) curves were measured; the results are shown in Figure 4d. As the ball-milling time increased from 2 to 6 h,the sintering density and \(B_{\rm r}\) value increased.