## 3 Results and Discussion
### Crystalline Structure and Microstructure Analysis
To maintain charge neutrality without producing Fe\({}^{2+}\), it is necessary to generate vacancies in the oxygen ion. Therefore, the effect of Co substitution on the lattice parameters \(a\) and \(c\) is considered insignificant. This is because the increase caused by Co\({}^{2+}\) substitution for Fe\({}^{3+}\) can be counteracted by the generation of oxygen ion vacancies. The initial increase in a and the monotonous decrease in \(c\) from \(x=0.0\) to \(x=0.1\) are well consistent with the previous report by [PERSON] et al. [17], although their values are somewhat different. However, in the \(x\) region of 0.1-0.3, unlike our samples, their lattice constant a values continuously increase with increasing \(x\) due to a gradual decrease in the Co/La molar ratio below 1.0. Figure 3a indicates that the presence of Fe\({}^{2+}\) at the \(2a\) site has a significant effect on the lattice parameter \(a\), while its effect on the lattice parameter \(c\) is negligible up to \(x=0.25\). Additionally, the upturn in the lattice parameter \(c\) at \(x=0.3\), deviating from its monotonous decrease up to \(x=0.25\), is attributable to a change in the occupancy of Co\({}^{2+}\) substituent at the \(2a\) site, affecting the formation of Fe\({}^{2+}\) and causing a shift in the oxygen vacancy positions. This peculiar behavior is also observed for the La-Co  
Figure 4: Crystallographic structure of (SrFe\({}_{12}\)O\({}_{19}\))\({}_{2}\). This figure was made using the TESTA program [32]. substituted SrM sample with \(x=0.4\), prepared using additives reported by [PERSON] et al. [22], although they never discussed the reason for its occurrence. In contrast to the variations in lattice parameters \(a\) and \(c\) with \(x\) shown in Figure 3a, [PERSON] et al. [23] reported different behaviors for La-Co co-substituted SrM powder synthesized by the sol-gel method and subsequently fired at 900 \({}^{\circ}\)C for 2 h in air. Their values for \(a\) and \(c\) slightly decreased from \(x=0.0\) to 0.1 and then gradually increased up to 0.2. Additionally, their values were much lower than ours, except for the composition of \(x=0.2\), which showed almost the same values. This discrepancy may be attributed to the significant difference in firing temperatures. However, additional experiments are necessary to confirm this. Figure 5 shows SEM micrographs and average grain sizes of Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) samples (\(0.0\leq x\leq 0.3\)). The grains have hexagonal plate shapes, and both the average plate width and thickness were measured on the micrographs. The average width and thickness values are approximately 2-4 \(\upmu\)m and 0.7-1.5 \(\upmu\)m, respectively. It is worth noting that the single domain size (\(d_{sd}\)) of SrM hexaferrite is approximately 940 nm [1]. Since most of the grains shown in Figure 5 are larger than \(d_{sd}\), they are likely composed of multi-domain structures. It appears that there is no significant difference in microstructure between the samples. From Figure 5g, it was observed that the morphological aspect ratios, defined as the average plate width over average plate thickness, sharply decrease from 3.80 to 2.45 as \(x\) increases from 0.0 to 0.10. The aspect ratio then increases to 3.66 for \(x=0.15\), and gradually decreases to 2.08 for \(x=0.30\). The aspect ratios versus \(x\) are not presented here. Figure 5: SEM micrographs of the Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) samples with (**a**) \(x=0.0\), (**b**) \(x=0.1\), (**c**) \(x=0.15\), (**d**) \(x=0.2\), (**e**) \(x=0.25\), (**f**) \(x=0.3\), and (**g**) average grain size (parallel and perpendicular to \(c\)-axis) of the samples.