## 3 Results and Discussion
This change in the \(f_{FMR}\) is attributed to the relationship with magnetic anisotropy depending on the \(x\) values. In the region where \(x\leq 0.75\), the \(f_{FMR}\) decreases with \(x\), \(c\)-axis anisotropy is working, and the \(f_{FMR}\) follows Equation (1). In the region where \(x\geq 0.75\), the \(f_{FMR}\) gradu  
ally increases with \(x\), corresponding to c-plane anisotropy, following Equations (2) or (3). Previous studies have reported that the magnetic anisotropy of BaZn\({}_{2-x}\)Co\({}_{x}\)W has a minimum around \(x=0.6\)[24], while for Sr\({}_{0.75}\)Ca\({}_{0.25}\)Zn\({}_{2-x}\)Co\({}_{x}\)W, the minimum occurs around \(x=1.0\)[12]. At this point, as \(x\) increases, the anisotropy transitions from c-axis to c-plane anisotropy. In this study, this transition is observed to occur at \(x=0.75\). This variation in magnetocrystalline anisotropy is also reflected in the changes in H\({}_{\rm C}\) values in Figure 4. Additionally, the permeability behavior corresponding to changes in the \(x\) value can be explained well by [PERSON]'s limitation law [16]. Figure 5c,d illustrate how the \(\upmu^{\prime}\) and \(\upmu^{\prime\prime}\) spectra vary depending on the \(x\) values. In hexaferrite, the mechanism contributing to the \(\upmu^{\prime}\) value is associated with the movement of magnetic domain walls (for \(f<\sim\)1 GHz) and electron spins (for \(f>\sim\)1 GHz). As shown in Figure 5c, the \(\upmu^{\prime}\) spectra generally decreases as the frequency increases. At 100 MHz, the sample with \(x=0.75\) exhibits the highest \(\upmu^{\prime}\) value, though it declines most rapidly, while the sample with \(x=0.4\) shows the lowest initial value at 100 MHz but maintains \(\upmu^{\prime}>1\) across the entire frequency range. The \(\upmu^{\prime\prime}\) spectra in Figure 5d show a general increase with frequency, reaching a peak and then declining. The peak frequency of \(\upmu^{\prime\prime}\), observed above 1 GHz, is considered the \(f_{FMR}\) for hexaferrites. The \(f_{FMR}\), identified as the peak in the \(\upmu^{\prime\prime}\) spectra, is plotted as a function of \(x\) in Figure 5e. The \(f_{FMR}\) reaches a minimum of 2.01 GHz at \(x=0.75\) and increases as \(x\) either decreases or increases beyond this value. For \(x=0.4\), the \(f_{FMR}\) is estimated as exceeding the measurement limit of 18 GHz. This variation in \(f_{FMR}\) is attributed to changes in magnetic anisotropy with respect to \(x\). When \(x\leq 0.75\), the \(f_{FMR}\) decreases as \(x\) increases, indicating that c-axis anisotropy dominates, following Equation (1). For \(x\geq 0.75\), the \(f_{FMR}\) increases with \(x\), corresponding to c-plane anisotropy and following Equations (2) or (3). Previous studies have reported a minimum magnetic anisotropy around \(x=0.6\) for BaZn\({}_{2-x}\)Co\({}_{x}\)W [24] and around \(x=1.0\) for Sr\({}_{0.75}\)Ca\({}_{0.25}\)Zn\({}_{2-x}\)Co\({}_{x}\)W [12]. This suggests that the transition from c-axis to c-plane anisotropy occurs as \(x\) increases. In this study, the transition is observed at \(x=0.75\). This variation in magnetocrystalline anisotropy is also reflected in the changes in \(H_{\rm C}\) values, as shown in Figure 4. Additionally, the permeability behavior in relation to \(x\) can be explained by [PERSON]'s limitation law [16]. \[(\mu_{S}\prime-1)\cdot f_{FMR}\ \frac{2}{3}\gamma\cdot 4\pi M_{S} \tag{4}\]  
Here, \(\mu_{S}\prime\) refers to the static permeability, which represents the \(\upmu^{\prime}\) value maintained at low frequencies. \(\gamma\) is a constant known as the gyromagnetic ratio, and \(M_{S}\) is the saturation magnetization. According to Equations (1)-(4), as the magnetic anisotropy increases, the \(\upmu^{\prime}\) value remains stable up to higher frequencies, while the \(f_{FMR}\) frequency also rises. However, as the \(f_{FMR}\) increases, the \(\mu_{S}\prime\) value decreases.