## 4 Conclusions  
In this study, M-hexaferrites (SrFe\({}_{12}\)O\({}_{19}\)) with Mn-Al-Si and Ca substitutions were fabricated by a solid-state reaction, and their crystalline structure, microstructure, and magnetic properties were evaluated. The goal was to optimize the cation substitution composition for permanent magnets by considering two key magnetic properties, 4\(\pi\)M\({}_{\rm r}\) and H\({}_{\rm C}\). It was also planned to achieve grain growth inhibition and densification through the compositional control of the initial raw materials without adding separate sintering additives. Initially, in the composition Sr\({}_{0.8}\)Ca\({}_{0.2}\)Fe\({}_{11-3x}\)Mn\({}_{x}\)Al\({}_{x}\)Si\({}_{x}\)O\({}_{19-\rm d}\), we obtained a significant improvement in the magnetic properties, with a well-controlled grain size at \(x=0.1\), that is, Sr\({}_{0.8}\)Ca\({}_{0.2}\)Fe\({}_{10.7}\)Mn\({}_{0.1}\)Al\({}_{0.1}\)Si\({}_{0.1}\)O\({}_{19-\rm d}\), resulting in an increased H\({}_{\rm C}\). From there, we increased the Mn and Al content step by step in the composition Sr\({}_{0.8}\)Ca\({}_{0.2}\)Fe\({}_{10.7-x-y}\)Mn\({}_{0.1+x}\)Al\({}_{0.1+y}\)Si\({}_{0.1}\)O\({}_{19-\rm d}\), and it was observed that the composition with \(x=0\) and \(y=0.1\) exhibited the best magnetic properties (4\(\pi\)M\({}_{\rm r}\) = 2.20 kG, H\({}_{\rm C}\) = 5.01 kOe). However, it was noted that Fe\({}_{2}\)O\({}_{3}\) existed in trace amounts as a secondary phase. In the next step, the Fe content was reduced, and the Sr to Ca ratio was adjusted in two compositions, Sr\({}_{0.7+x}\)Ca\({}_{0.3-x}\)Fe\({}_{10.2}\)Mn\({}_{0.1}\)Al\({}_{0.2}\)Si\({}_{0.1}\)O\({}_{19-\rm d}\) and Sr\({}_{0.7+x}\)Ca\({}_{0.3-x}\)Fe\({}_{9.7}\)Mn\({}_{0.1}\)Al\({}_{0.2}\)Si\({}_{0.1}\)O\({}_{19-\rm d}\) (\(z=0.05\), 0.1, 0.15, 0.2), resulting in the final optimized composition, Sr\({}_{0.8}\)Ca\({}_{0.2}\)Fe\({}_{10.2}\)Mn\({}_{0.1}\)Al\({}_{0.2}\)Si\({}_{0.1}\)O\({}_{19-\rm d}\). This sample exhibited a sintered density \(\rho=4.84\) g/cm\({}^{3}\), 4\(\pi\)M\({}_{\rm r}\) = 2.22 kG, and H\({}_{\rm C}\) = 5.10 kOe. This result is achieved in a completely isotropic magnet with no crystal orientation. Through the implementation of high-energy ball milling to obtain finer powders, which enhances the sintering density, and the application of a magnetic field pressing to align the c axis crystal orientation, there is potential to develop an anisotropic magnet with an M\({}_{\rm r}\)/M\({}_{\rm s}\) = 0.95 and \(\rho=5.0\) g/cm\({}^{3}\)[21; 22; 23]. Based on these assumptions, we anticipate that further process optimization will enable the same composition of anisotropic magnets to achieve 4\(\pi\)M\({}_{\rm r}\) = 4.40 kG, H\({}_{\rm C}\) = 4.8 kOe, and a maximum energy product (BH\({}_{\rm max}\)) of 4.65 M-G-Oe. Overall, these results are highly promising, particularly as they were achieved without the need for cobalt, a costly material typically essential for high-performance ferrite magnets.  
Conceptualization, Y.-M.K.; funding acquisition, Y.-M.K.; investigation, Y.-M.K.; methodology, J.-P.L. and E.-H.Y.; project administration, Y.-M.K.; software, J.-P.L. and E.-H.Y.; supervision, Y.-M.K.; writing--original draft, Y.-M.K. All authors have read and agreed to the published version of the manuscript. This research was supported by \"Regional Innovation Strategy (RIS)\" through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (MOE) (2021 RIS-001).  
Not applicable.  
Figure 5: Plot of 4\(\pi\)M\({}_{\rm r}\) and H\({}_{\rm C}\) of the sintered hexaferrite samples.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
**Acknowledgments:** The authors are also grateful to Union Materials Corp. in Pohang, South Korea, for the support with the raw materials for the magnet fabrication.  
**Conflicts of Interest:** The authors declare no conflict of interest.