## 3 Results and Discussion  
### Structure Identification  
In order to verify whether lanthanum successfully entered the crystal lattice of BaFe\({}_{12}\)O\({}_{19}\), replacing part of the barium, the powders' structure was identified by X-ray diffraction spectroscopy. Figure 1A shows the X-ray diffraction (XRD) spectrum of the as-prepared La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) powders, the discrete red lines corresponding to the standard diffraction pattern of BaFe\({}_{12}\)O\({}_{19}\) (PDF#84-0757). It can be seen from Figure 1A that all the diffraction peaks of the sample were in good agreement with the diffraction peaks of the standard card, and no oxides and other ferrite impurities were observed. The XRD data were systematically analyzed using Rietveld refinement, as shown in Figure 1B. Rietveld refinement could fit the XRD profiles well, with a weighted profile R-factor (\(R_{\mathrm{z}nt}\)) of 4.408% and a _GOF_ factor of 1.19 during the fit, which are at suitable standard levels. The lattice of La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) parameters (a) and (c) of 5.8783 and 23.076 A, respectively, showed some contraction compared to BaFe\({}_{12}\)O\({}_{19}\), and in the XRD diffraction pattern showed a shift in the diffraction peak to the right. This was due to the fact that the atomic radius of lanthanum is smaller than that of barium, so the substitution of lanthanum with barium led to a contraction of the lattice, which was reflected in the XRD pattern as a shift in the diffraction peak to the right. Therefore, it was certain that lanthanum had successfully replaced part of the barium and successfully made pure La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) powders in a single magnetoplumbite-5H phase. Figure 2 shows the morphology feature of the La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) ceramic specimen sintered at 1400 \({}^{\circ}\)C as measured by scanning electron microscopy (SEM). The results showed that most of the grains were long and flaky when sintered at 1400 \({}^{\circ}\)C. It can be seen from Figure 2 that most of the crystal grains of La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) were irregular hexagonal plate-like structures, after the substitution of lanthanum with barium, which led to the destruction of the hexagonal symmetry in the crystal lattice of BaFe\({}_{12}\)O\({}_{19}\). The [0001] orientation was parallel to the hexagonal edges of the grains. Since the grains were irregular plate-like structures, this indicated that the grains did not preferentially grow along the [0001] direction, but grew preferentially along the [0100] direction. The grain sizes in the SEM images were counted by Nano Measurer software. The average grain size of La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) was 8.44 \(\upmu\)m long, 6.50 \(\upmu\)m wide, and 4.04 \(\upmu\)m thick. The chemical composition of the sintered La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) ceramic samples was examined by Bruker scanning electron microscopy (SEM) and energy spectroscopy (EDS). The EDS spectra are shown in Figure 3, and it can be seen that all the elemental lines appear in the spectra. In addition, the atomic ratios are shown in the figure, which can be seen to be basically consistent with those of La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\). It can be further confirmed that La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) was successfully prepared. Figure 1: (**A**) Unprocessed XRD spectrum. (**B**) XRD spectra processed with Rietveld refinement. (a) XRD spectrum of La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) powders, which were sintered at 1400 \({}^{\circ}\)C for 3 h and subsequently annealed in an O\({}_{2}\) atmosphere at 800 \({}^{\circ}\)C for 15 h in 3 steps, and (b) standard XRD spectrum of the BaFe\({}_{12}\)O\({}_{19}\) (PDF#84-0757) in discrete red lines. It can be proved by previous studies that La\({}_{0.75}\)Ba\({}_{0.25}\)Fe\({}_{12}\)O\({}_{19}\) has been successfully prepared.