## 3 Results and Discussion
In Table 2, the real (\(\epsilon^{\prime}\)) and imaginary (\(\epsilon^{\prime\prime}\)) parts of the permittivity at 1 GHz, the real part of the permeability (\(\upmu\)s\({}^{\prime}\)) in the steady region after the first transition (\(\sim\)3 GHz), and the frequencies of the maximum \(\upmu^{\prime\prime}\) values (\(f_{FMR}\)) are presented. In the \(\epsilon^{\prime}\) and \(\epsilon^{\prime\prime}\) spectra shown in Figure 6a,b, as the frequency increases, for all samples, \(\epsilon^{\prime}\) decreases and converges upon \(\sim\)7, and \(\epsilon^{\prime\prime}\) approaches zero. The real (\(\upmu\)) and imaginary (\(\upmu^{\prime\prime}\)) parts of the permeability spectra are shown in Figure 6c,d, the first transitions of \(\upmu\) and \(\upmu^{\prime\prime}\) are associated with magnetic domain wall motion (\(f<2\) GHz), and the peaks at higher frequencies (\(f>2\) GHz) are caused by FMR. In the \(\upmu^{\prime\prime}\) spectra (Figure 6d), a gradual \(\upmu^{\prime\prime}\) peak shift to the left is observed upon increasing \(x\) from 0.7 to 0.9, and a very small peak shift can be found between \(x=0.9\) and \(x=1.0\). The \(\upmu^{\prime\prime}\) peak frequency corresponds to \(f_{FMR}\) and is directly proportional to the magnetic anisotropy field (\(H_{a}\)), as expressed in Equation (1). The change in \(f_{FMR}\) is related to an intrinsic property change and can be caused by cation substitution. This is consistent with the change in H\({}_{\rm C}\) shown in Figure 5, as mentioned above. The \(\upmu^{\prime\prime}\) peak positions and H\({}_{\rm C}\) values of the samples with \(x=0.9\)-1.1 are very similar, because the solubility limit of Zn-Zr in the M-phase is approximately \(x=1.0\). The gradual increase in \(\upmu\)s\({}^{\prime}\) upon increasing \(x\) up to 0.9 can be explained by [PERSON]'s limit law [27], presented below:  
\[\left(\upmu\text{s}^{\prime}-1\right)\cdot f_{FMR}\ =\ \frac{2}{3}\gamma\cdot 4 \pi M_{S} \tag{3}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \(x\) & \(\upmu\text{M}_{\text{S}}\) & \(\mathbf{H}_{\text{C}}\) & \(\epsilon^{\prime}\) & \(\upmu\text{s}^{\prime}\) & \(f_{FMR}\) & \(\mathbf{RL}_{\text{min}}\) & \(f_{F\mathbf{RL}_{\text{min}}}\) \\  & (\(\mathbf{k}\)G) & (\(\mathbf{k}\)Oe) & (\(\mathbf{l}\) GHz) & (\(\mathbf{l}\) GHz) & (\(\mathbf{l}\) GHz) & (\(\mathbf{g}\) GHz) & (\(\mathbf{G}\)Hz) & (\(\mathbf{dB}\)) & (\(\mathbf{GHz}\)) \\ \hline
0.5 & 1.875 & 0.624 & 7.37 & 1.08 & 1.00 & - & - & - \\
0.6 & 1.810 & 0.466 & 7.32 & 0.82 & 1.02 & - & - & - \\
0.7 & 1.681 & 0.270 & 7.08 & 0.45 & 1.05 & 15.1 & \(-\)42.9 & 16.7 \\
0.8 & 1.607 & 0.225 & 7.34 & 0.51 & 1.12 & 10.8 & \(-\)38.6 & 11.8 \\
0.9 & 1.409 & 0.158 & 7.16 & 0.21 & 1.19 & 8.33 & \(-\)44.7 & 8.8 \\
1.0 & 1.295 & 0.155 & 6.85 & 0.20 & 1.17 & 7.89 & \(-\)49.7 & 8.6 \\
1.1 & 1.191 & 0.152 & 7.02 & 0.13 & 1.17 & 7.26 & \(-\)50.0 & 8.2 \\ \hline \end{tabular}
\end{table} 
Table 2: Saturation magnetization (4\(\upmu\)M\({}_{\text{S}}\)), coercivity (H\({}_{\text{C}}\)), real (\(\epsilon^{\prime}\)) and imaginary (\(\epsilon^{\prime\prime}\)) parts of permittivities at 1 GHz, real part of permeability (\(\upmu\)s\({}^{\prime}\)) at steady region (at 3 GHz), frequencies of maximum \(\upmu^{\prime\prime}\) values (\(f_{FMR}\)), minimum RLs (RL\({}_{\text{min}}\)), and frequencies of RL\({}_{\text{min}}\) (\(f_{FLRmin}\)) of SrFe\({}_{12-2\chi}\)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. Here, \(\gamma\) is a constant known as the gyromagnetic ratio, and \(M_{\rm s}\) is the saturation magnetization value. A decrease in static real permeability (us\({}^{\prime}\)) causes an increase in \(f_{FMR}\). This implies that changes in the high-frequency permeability property are governed by the intrinsic magnetic parameter of the magnetocrystalline anisotropy, which can be controlled by Zn-Zr substitution.