## 3 Results and Discussion
For samples synthesized by the conventional solid-state reaction method, as depicted in Figure 3a-f, there is no discernible trend in average grain size with respect to variations in \(x\), with an approximate mean particle size around 5 \(\upmu\)m. Conversely, for powders synthesized via the M-S method, as shown in Figure 3g-i, the av  
Figure 1: X-ray diffraction patterns of (**a**) BaZn\({}_{2-x}\)Co\({}_{x}\)Fe\({}_{16}\)O\({}_{27}\) powders for \(x\) = 0.4, 0.5, 0.6, 0.75, 1.0, 1.25, and 1.5, and (**b**) M-S-processed samples for \(x\) = 0.75, 1.0, and 1.25, all calcined at 1250 \({}^{\circ}\)C.  
Figure 4 presents the M-H curves of BaZn\({}_{2-x}\)Co\({}_{x}\)W powders synthesized using the solid-state reaction method (\(x\) = 0.4, 0.5, 0.6, 0.75, 1.0, 1.25, 1.5). The graph includes an inset in the upper left corner, showing the low magnetic field range of \(-200\leq\) H \(\leq\) 200 Oe, while the upper right inset displays the magnetization curves for the range of 0 \(\leq\) H \(\leq\) 5000 Oe. In the lower right, the changes in saturation magnetization \(M_{S}\) and coercivity (\(H_{\rm C}\)) as a function of \(x\) are plotted for clarity. The \(M_{S}\) value increases with the \(x\) value from 0.4 to 1.0, peaking at 80.3 emu/g at \(x\) = 1.0, and then decreases as \(x\) rises to 1.5. Examining the magnetization curves within the range of 0 \(\leq\) H \(\leq\) 5000 Oe, differences in magnetization ease are noticeable depending on \(x\), which can be attributed to changes in magnetocrystalline anisotropy. The \(H_{\rm C}\) value decreases as \(x\) increases from 0.4 to 0.75, reaching a minimum at \(x\) = 0.75, and then gradually rises as \(x\) increases to 1.5. Figure 5a-d presents the spectra of \(\epsilon^{\prime}\), \(\epsilon^{\prime\prime}\), \(\mu^{\prime}\), and \(\mu^{\prime\prime}\) for BaZn\({}_{2-x}\)Co\({}_{x}\)W-epoxy (10 wt%) composites synthesized via the conventional solid-state method, measured within the frequency range of 0.1 to 18 GHz. In the \(\epsilon^{\prime}\) spectra shown in Figure 5a, the values remain relatively stable, around 6 to 7, throughout the entire frequency range, with no significant trend observable across different \(x\) values. Similarly, the \(\epsilon^{\prime\prime}\) spectra in Figure 5b display no clear trend relative to the \(x\) values, with values consistently below 1. These \(\epsilon^{\prime}\) and \(\epsilon^{\prime\prime}\) characteristics, typical of ionic ceramic powder and highly insulating polymer composites, are not expected to have a significant impact on the EM wave absorption properties of the hexaferrite. The irregular peaks occurring above 10 GHz are due to measurement noise. This noise does not significantly impact EM wave absorption characteristics. Figure 5c,d show that the \(\upmu^{\prime}\) and \(\upmu^{\prime\prime}\) spectra vary depending on the \(x\) values. In hexaferrrite, the mechanism contributing to the \(\upmu^{\prime}\) value is related to the movement of magnetic domain walls (\(f<\) \(\sim\)1 GHz) and the electron spins (\(f>\) \(\sim\)1 GHz). The \(\upmu^{\prime}\) spectra in Figure 5c commonly exhibit a decreasing trend as the frequency increases. At 100 MHz, the sample with \(x=0.75\) shows the highest \(\upmu^{\prime}\) value but decreases the fastest, while the sample with \(x=0.4\) shows the lowest value at 100 MHz but maintains \(\upmu^{\prime}>1\) up to the highest frequency. The \(\upmu^{\prime\prime}\) spectra in Figure 5d generally increase with frequency, exhibit a peak, and then decrease. The frequency of the \(\upmu^{\prime\prime}\) peak observed above 1 GHz in hexaferrite can be considered the \(f_{FMR}\). In Figure 5d, the \(f_{FMR}\) is identified as the peak frequency of the \(\upmu^{\prime\prime}\) spectra, and it is plotted as a function of \(x\) in Figure 5e. The \(f_{FMR}\) shows a minimum of 2.01 GHz at \(x=0.75\), and it gradually increases as \(x\) either decreases or increases from \(x=0.75\). At \(x=0.4\), the \(f_{FMR}\) is presumed to be beyond the measurement range of 18 GHz.