## 3 Results and Discussion

Table 1: Lattice parameters \(a\) and \(c\), ratio of \(c/a\), and lattice volume of the SrFe\({}_{12-2x}\)Zn\({}_{x}\)Ti\({}_{x}\)O\({}_{19}\), SrFe\({}_{12-2x}\)Mn\({}_{x}\)Ti\({}_{x}\)O\({}_{19}\) (\(x=0\), 0.5, 1.0, 1.5, 2.0), and SrFe\({}_{12-2x}\)Zn\({}_{x}\)Zr\({}_{x}\)O\({}_{19}\) (\(x=0\), 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.5, 2.0) samples calcined at 1250 \({}^{\circ}\)C.  
Figure 1: XRD patterns of (**a**) SrFe\({}_{12-2\chi}\)Zn\({}_{x}\)Ti\({}_{x}\)O\({}_{19}\) (\(x=0,0.5,1.0,1.5,2.0\)), (**b**) SrFe\({}_{12-2\chi}\)Mn\({}_{x}\)Ti\({}_{x}\)O\({}_{19}\) (\(x=0,0.5,1.0,1.5,2.0\)), and (**c**) SrFe\({}_{12-2\chi}\)Zn\({}_{x}\)Zr\({}_{x}\)O\({}_{19}\) (\(x=0,0.5,0.6,0.7,0.8,0.9,1.0,1.1\,1.5,2.0\)) samples. For Zn-Ti and Mn-Ti substitution (\(0\leq x\leq 2.0\)), shown in Figure 2a,b, \(a\), \(c\), and the cell volume increase gradually with increasing \(x\). Meanwhile, for the Zn-Zr substitution shown in Figure 2c, the increase in lattice parameters with \(x\) is much greater, but at \(x=1.0\) and above the cell parameter values are constant. Based on the lattice changes with substitution amount \(x\), the solubility limit for Zn-Ti and Mn-Ti is estimated to be above \(x=2.0\), and for Zn-Zr, it is estimated to be \(x=\) -1.0. The high-frequency permeability characteristics of the three groups of samples, SrFe\({}_{12-2x}\)Zn\({}_{x}\)Ti\({}_{x}\)O\({}_{19}\), SrFe\({}_{12-2x}\)Mn\({}_{x}\)Ti\({}_{x}\)O\({}_{19}\), and SrFe\({}_{12-2x}\)Zn\({}_{x}\)Zr\({}_{x}\)O\({}_{19}\), were evaluated. In the case of hexaferrites, utilization as an EM absorber in the GHz range requires a peak increase in \(\mu^{\prime\prime}\) in the corresponding frequency band, which can be caused by FMR phenomena. Figure 3a-f show the \(\mu^{\prime}\) and \(\mu^{\prime\prime}\) spectra of these samples. As can be seen in the \(\mu^{\prime}\) spectra, the samples have \(\mu^{\prime}\) values between 1.5 and 2.0, and \(\mu^{\prime}\) commonly decreases to close to 1.0 in the range of \(f<\) 1 GHz. This \(\mu^{\prime}\) spectral transition (\(f<\) 1 GHz) is associated with magnetic domain wall motion [21]. In addition, the transition of \(\mu^{\prime\prime}\) in the frequency range of \(f<\) 1 GHz corresponds to the magnetic loss associated with magnetic domain wall motion. Therefore, it is believed that domain wall motion cannot contribute to the permeability at frequencies higher than 1 GHz, and the peak increase of \(\mu^{\prime}>\) 1 and \(\mu^{\prime\prime}>\) 0 at \(f>\) 1 GHz is mostly caused by electron spin motions, that is, FMR [6,7]. It is known that non-substituted M-type Sr-hexaferrite, SrFe\({}_{12}\)O\({}_{19}\), has \(f_{FMR}\sim\)50 GHz. Thus, no \(\mu^{\prime\prime}\) peak is observed in the measured frequency range of \(f\leq\) 18 GHz. When Zn-Ti is substituted into SrM, \(f_{FMR}\) decreases with increasing \(x\). In Figure 3a,b sharp increases in the \(\mu^{\prime}\), \(\mu^{\prime\prime}\) peaks can be observed at the right edge. We can see that \(f_{FMR}\) is approximately 18 GHz for SrFe\({}_{12-2x}\)Zn\({}_{x}\)Ti\({}_{x}\)O\({}_{19}\) (\(x=2.0\)), and that it is above 18 GHz for samples with \(x<2.0\). For the case of Mn-Ti substitution (Figure 3c,d), no clear peaks of \(\mu^{\prime}\), \(\mu^{\prime\prime}\) spectra are absorbed at \(f>\) 1.0 GHz for all samples. Meanwhile, a clear FMR signal is absorbed by the Zn-Zr substituted samples, as shown in Figure 3e,f. In the vicinity of 10 GHz in the \(\mu^{\prime\prime}\) spectra, a peak from FMR is shown for \(x=1.0\), and the height gradually decreases as \(x\) reaches 2.0. For the sample with \(x=0.5\), there is no FMR peak at \(f>\)1 GHz because its \(f_{FMR}\) is greater than 18 GHz. Although the FMR peak is supposed to shift to a lower frequency upon increasing \(x\) to 1.5, and 2.0, its position is almost the same. This is because even for \(x\) higher than 1.0, no substitution of Zn-Zr can occur, as mentioned previously in Figure 2c.