## 1 Introduction  
M-type (Ba, Sr)-hexaferrites are some of the most useful materials for permanent magnets [1]. Enhancing the magnetic and mechanical properties of these materials is economically important due to their widespread use across various global industries, such as consumer electronics and the electric automotive industry. Many studies have led to developments that have improved the intrinsic magnetic properties of Sr-hexaferrites, such as the saturation magnetization (\(M_{\rm s}\)) and crystalline anisotropy, by compositional design with elemental substitutions [2; 3; 4; 5; 6; 7]. Among these, La-, Ca-, and Co-substitution of the M-type Sr-hexaferrites (La-Ca-Co:SrM) is considered to be the most successful approach, leading to a significant enhancement in the crystalline anisotropy without reducing the \(M_{\rm s}\)[4; 8]. The resulting La-Ca-Co substituted M-type Sr-hexaferrites are thus high-grade ferrite magnets.  
The coercivity (\(H_{\rm c}\)) is dependent on the grain size of the La-Ca-Co:SrM permanent magnets [9; 10; 11]. Grain growth behavior involves the movement of interfaces, including grain boundary structures, by interface reactions. This behavior can be controlled by adding dopants to alter the diffusion of atoms into the materials [12; 13; 14], adjusting the sintering temperature [15], and changing the oxygen partial pressure [16; 17; 18]. Generally, it has been understood that dopants change the microstructure of ceramics by suppressing grain growth and increasing densification [19]. These additive elements can segregate at grain boundaries and form a secondary solid or liquid phase and suppress the migration of interfaces and grain boundaries by the solute drag and Zener effects [19; 20]. In the grain growth theory, grain growth behavior can be explained by the relationship between the critical driving force for grain growth (\(\Delta g_{c}\)) and the maximum driving force for grain growth (\(\Delta g_{max}\)) in the two-dimensional nucleation grain growth mechanism [20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. Phenomenologically, grain growth behavior is divided into normal grain growth (invariable distribution of relative growth sizes with sintering time) and abnormal grain growth (some large grains grow quickly) [17; 20; 22]. The grain growth type can be changed by the value of \(\Delta g_{c}\) relative to \(\Delta g_{max}\) during sintering [17; 18; 20; 22]. The abnormal grain growth behavior can be calculated and explained exactly by the two-dimensional nucleation grain growth mechanism [22]. To the best of our knowledge, while a number of studies have analyzed the grain growth in M-type hexaferrites [6; 23; 24; 25; 26; 27], no studies on La-Ca-Co:SrM grain growth have been reported. In the present study, the effects of SiO\({}_{2}\) additives on the grain growth in La-Ca-Co:SrM were investigated. There are many previous studies on Sr hexaferrites with addition of SiO\({}_{2}\)[12; 31; 32; 33; 34]. However, there has been no discussion of the position of Si elements regarding which Si element is in the lattice of grains or not.  
The purpose of this study is to provide experimental support for the predicted effect of adding SiO\({}_{2}\) and to determine the conditions that suppress the diffusion of Si into the crystalline lattice of the Sr\({}_{0.3}\)Ca\({}_{0.4}\)La\({}_{0.3}\)Fe\({}_{9.8}\)Co\({}_{0.2}\)O\({}_{19.8}\) (SCLFCO) system. The specific molar fraction of the elements in SCLFCO was selected concerning the previous works [3; 7; 8]. The selective diffusion of Si should be controlled in order to increase \(H_{c}\) without decreasing \(M_{s}\).