## 3 Results and Discussion
In addition, the decrease in \(\mu^{\prime\prime}\) peak height with an increase in \(x\) up to 2.0 is due to an increase in the volume fraction of the non-magnetic secondary phase (Figure 1c). Figure 4a-e show microstructures of the SrFe\({}_{12-2\mathrm{x}}\)Zn\({}_{x}\)Zr\({}_{x}\)O\({}_{19}\) (\(x\) = 0, 0.5, 1.0, 1.5, 2.0) samples calcined at 1250 \({}^{\circ}\)C. The average grain size (\(d_{g}\)) roughly decreased with increasing \(x\) (\(d_{g}\) = 1.0, 1.0, 0.82, 0.80, and 0.65 \(\upmu\)m for \(x\) = 0, 0.5, 1.0, 1.5, and 2.0, respectively). It is notable that samples with \(x\leq 1.0\) only have a single M-type phase. Second phases (ZnFe\({}_{2}\)O\({}_{4}\), SrZrO\({}_{3}\), and ZrO\({}_{2}\)) are formed and increase with increasing \(x\) for \(x\) > 1.0, as shown in Figure 1c. SEM-BSE (back scattered electron) images of the \(x\) = 1.0, 1.5, and 2.0 samples are shown in Figure 4f-h. In the \(x\) = 1.0 sample (Figure 4f), all grains show nearly equal contrast, but brighter grains begin to appear at \(x\) = 1.5 (Figure 4g), and brighter spots increase at \(x\) = 2.0 (Figure 4h). Considering the XRD analysis results (Figure 1c) and average atomic weights of the second phases, the bright spots in Figure 4g,h correspond with SrZrO\({}_{3}\). Figure 5 shows the magnetization curves for the SrFe\({}_{12-2\mathrm{x}}\)Zn\({}_{x}\)Zr\({}_{x}\)O\({}_{19}\)-epoxy composition (\(x\) = 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1) samples. Because the solubility limit of  
SrFe\({}_{12-2x}\)Zn\({}_{x}\)Zr\({}_{x}\)O\({}_{19}\) was found to be approximately \(x\) = 1.0, sample compositions with smaller intervals of \(x\) below \(x\) = 1.0 (\(x\) = 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1) were also studied. The saturation magnetization (4\(\pi\)M\({}_{\rm S}\)) and coercivity (H\({}_{\rm C}\)) values of these samples are presented in Table 2. The 4\(\pi\)M-H curves in the low magnetic field range are shown in the inset. The 4\(\pi\)M\({}_{\rm S}\) of the sintered samples are expected to be twice these values because the volume fraction of the nonmagnetic epoxy binder is \(\sim\)50%. The 4\(\pi\)M\({}_{\rm S}\) of the \(x\) = 0.5 sample is 1.875 kG, and it decreases with increasing \(x\). The reason for this is that non-magnetic ions of Zn\({}^{2+}\)-Zr\({}^{4+}\) are substituted for the magnetic Fe\({}^{3+}\) ions. It has also been reported that a small amount of Zn substitution (\(x\)\(\leq\) 0.3) into SrM could increase M\({}_{\rm S}\) due to a selective substitution of Fe in the down-spin state [22; 23]. It is notable that the substitution amount (\(x\)\(\geq\) 0.5) in this study is too high to expect such an enhancement of M\({}_{\rm S}\) in the SrM. H\({}_{\rm C}\) decreases noticeably for an increase in \(x\) from \(x\) = 0.5 to \(x\) = 0.7 but decreases slightly from \(x\) = 0.7 to \(x\) = 0.9 and remains roughly constant above \(x\) = 0.9. The H\({}_{\rm C}\) value depends on both the intrinsic and extrinsic characteristics of the magnetic materials. Grain size is a dominating factor influencing H\({}_{\rm C}\). It is well known that H\({}_{\rm C}\) decreases with increasing grain size of hexaferrites [24; 25; 26]. Considering that the average grain size of the \(x\) = 0.5 sample is larger than that of the sample with \(x\) = 1.0, the smaller H\({}_{\rm C}\) for a higher \(x\) is due to a strong intrinsic property change caused by the Zn-Zr substitution, which overcomes the disadvantageous extrinsic factor. The real and imaginary parts of the complex permittivity (\(\varepsilon^{\prime}\) and \(\varepsilon^{\prime\prime}\)) and permeability (\(\mu^{\prime}\) and \(\mu^{\prime\prime}\)) spectra of the SrFe\({}_{12-2x}\)Zn\({}_{x}\)Zr\({}_{x}\)O\({}_{19}\) (\(x\) = 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1) powder epoxy (10 wt%) composite samples are shown in Figure 6a-d.