## 3 Results and Discussion  
### Crystalline Structure and Microstructure Analysis  
Much effort has been devoted to identifying processing conditions that are suitable for the synthesis of the M-type single phase from samples with the nominal composition Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) (\(x\) = 0.3). To achieve this, we initially followed the conventional solid-state reaction in air. All precursors were mixed, ball-milled, and calcined at 1280 \({}^{\circ}\)C for 2 h. The as-calined powders were then ball-milled and peltetized before being sintered at 1300 \({}^{\circ}\)C for 2 h. Figure 1a (bottom) shows that obtaining the M-type single phase [SrM, JCPDS card 00-033-1340] was difficult due to the presence of second phases such as Fe\({}_{2}\)O\({}_{3}\) [JCPDS card 04-008-7623], CoFe\({}_{2}\)O\({}_{4}\) [JCPDS card 00-022-1086], and LaFeO\({}_{3}\) [JCPDS card 04-011-7994]. To address this issue, we modified our calcination process as described in the Experimental procedures. After the modified calcination process, the samples were sintered at 1230 \({}^{\circ}\)C for 2 h in air. This temperature and duration were found to be appropriate for obtaining the M-type single phase when using sintering additives of SiO\({}_{2}\) and CaCO\({}_{3}\), based on our independent experiments. However, as shown in Figure 1a (middle), it was not possible to obtain the M-type single phase. Instead, minor peaks of Fe\({}_{2}\)O\({}_{3}\), LaFeO\({}_{3}\), and CoFe\({}_{2}\)O\({}_{4}\) were always detectable. Subsequently, it was discovered that a sintering temperature of 1300 \({}^{\circ}\)C was necessary to prepare the M-type single phase without any second phase, as depicted in Figure 1a (top). Figure 1b shows the powder XRD patterns of Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) (0.0 \(\leq x\leq\) 0.4) samples sintered at 1300 \({}^{\circ}\)C for 2 h. It is evident that the M-type single phase is obtainable from all samples up to \(x\) = 0.3. The XRD pattern for the sample of \(x\) = 0.4 sintered at 1300 \({}^{\circ}\)C for 2 h is shown in Figure 1b. Fe\({}_{2}\)O\({}_{3}\), CoFe\({}_{2}\)O\({}_{4}\), and LaFeO\({}_{3}\) minor peaks are detectable. The inability to obtain the M-type single phase from the \(x\) = 0.4 sample may be due to a kinetic limit in our fabrication process rather than the solubility limit of La-Co. [PERSON] et al. [20] reported that the M-type single phase was obtainable from the \(x\) = 0.4 sample through a sol-gel process and subsequent firing at a relatively low temperature of 900 \({}^{\circ}\)C for 24 h in air [20]. The present results are significantly different from those previously reported by [PERSON] et al. [17], who prepared the samples by a solid-state reaction. According to their analysis of the contents of La and Co in La-Co co-substituted SrM samples sintered at 1300-1350 \({}^{\circ}\)C for 24 h in air, the molar ratio of Co/La is close to 1.0 for \(x\) = 0.1, but it gradually decreases with further increasing \(x\). Their powder XRD patterns for the samples synthesized in air (see Figure 1a in ref. [17]) were also examined. From the XRD pattern analysis of samples with \(x\) values of 0.1 and 0.2, it is evident that they consist solely of the M-type single phase. However, samples with \(x\) values of 0.3 and 0.5 contain second phases in addition to the M-type single phase. The XRD pattern of the sample with an \(x\) value of 0.2 shows that it is composed only of the M-type single phase. This suggests that the molar ratio of Co/La in this sample is at least close to 1.0. However, the analysis result (see Figure 3 in ref. [17]) indicates that it is significantly lower than 1.0, which may be difficult to comprehend. For instance, in the case of \(x\) = 0.3, the XRD pattern clearly shows the presence of a spinel phase (see Figure 1a in ref. [17]). Our XRD patterns in Figure 1b show only the M-type single phase, and no second phase was observed in their microstructure by SEM-EDS analyses.