###### Abstract  
Enhanced hard magnetic properties were achieved in M-type hexaferrite by optimizing the substitution levels of Mn, Al, and Si for Fe, and Ca for Sr within SrFe\({}_{12}\)O\({}_{19}\). The addition of Al-Si-Mn effectively controlled crystallite growth, resulting in an increased coercivity (H\({}_{\rm C}\)), while causing a decrease in the remanent magnetization (4\(\pi\)M\({}_{\rm s}\)). A higher Ca content exhibited a trend of increasing the sintered density but decreasing the 4\(\pi\)M\({}_{\rm s}\) and H\({}_{\rm C}\). The optimized composition, considering both the 4\(\pi\)M\({}_{\rm s}\) and H\({}_{\rm C}\), was determined to be Sr\({}_{\rm{6}}\)Ca\({}_{0.2}\)Fe\({}_{10.2}\)Mn\({}_{0.1}\)Al\({}_{0.2}\)Si\({}_{0.1}\)O\({}_{19-.4}\), with a sintered density of 4.84 g/cm\({}^{3}\), 4\(\pi\)M\({}_{\rm s}\) = 2.22 kG, and H\({}_{\rm C}\) = 5.10 kOe. This result demonstrates the achievement of isotropic magnets with controlled crystal growth and densification without additional sintering additives. This development is promising, as this enhancement could be achieved without the use of cobalt, an expensive but essential ingredient in high-performance permanent magnets. M-type hexaferrites; cation substitution; coercivity; saturation magnetization; permanent magnet +
Footnote †: journal: Applied Sciences  
level increases [26], in contrast to the substitution with La\({}^{3+}\)-Co\({}^{2+}\). Therefore, research has extensively focused on the combinations of various substituting elements to enhance magnetic characteristics. Despite numerous studies, manufacturing high-performance ferrite magnets has remained challenging, and more effective results than the substitution of La\({}^{3+}\)-Co\({}^{2+}\) have not been achieved. Since the cost of Co is significantly higher than that of other elements, developing cation substitution compositions that reduce or completely eliminate the need for Co is of paramount importance. Recent advances in the field of hard magnetic materials have shown significant improvements in hexaferrite nanomagnets prepared using sol-gel-based methods [12; 27; 28]. These studies have demonstrated the attainment of a substantial H\({}_{\text{C}}\) exceeding 6 kOe, primarily due to the nanocrystallization of hexaferrite grains. It is well-established that the coercivity of a single grain (\(h_{\text{C}}\)) increases as its size decreases, reaching the upper limit defined by the critical grain diameter for a single domain (\(d_{cri}\)). This phenomenon exhibits a reciprocal dependence on the grain size (\(d\)), expressed by the following equation [29]:  
\[h_{\text{C}}=d_{cri}/d^{1.08} \tag{1}\]  
However, when considering the practical application of sintered magnets, a method capable of mass production through solid-state reaction processes becomes imperative, as opposed to chemical synthesis methods like those of sol-gels. Even when the magnetic properties of M-hexaferrite, such as the M\({}_{\text{S}}\) and MCA, are improved through cation substitution during the calcination powder stage, these properties often deteriorate again due to the influence of sintering additives during the sintering process. Therefore, it is crucial to develop cation substitution compositions while considering the impact of sintering additives. Commonly used sintering additives, such as SiO\({}_{2}\), play a significant role in controlling crystalline grain growth. However, during high-temperature sintering, Si can infiltrate the M-hexaferrite lattice, leading to a tendency to reduce magnetic properties like M\({}_{\text{S}}\)[13; 22]. Additionally, sintering additives like CaO and CaCO\({}_{3}\) promote grain growth and densification during sintering and can also affect the magnetic properties of M-hexaferrites when substituting for Sr or Fe sites [7; 16; 21; 22; 23]. In this study, our objective was to develop sintered magnets with improved magnetic properties, all while avoiding the use of sintering additives.