###### Abstract  
W-type Ba-hexaferrite, BaZn\({}_{2-x}\)Co\({}_{x}\)Fe\({}_{16}\)O\({}_{27}\), was synthesized via both conventional solid-state (\(x\) = 0.4, 0.5, 0.6, 0.75, 1.0, 1.25, 1.5) and molten-salt methods (\(x\) = 0.75, 1.0, 1.25). The structure, electromagnetic (EM) properties, and EM wave absorption characteristics were examined across a frequency range of 0.1-18 GHz, focusing on the influence of varying \(x\). As \(x\) increased from 0.4 to 0.75, the magnetic anisotropy field (\(H_{\mathrm{ani}}\)) decreased, reaching its minimum at \(x\) = 0.75, before rising again as \(x\) continued to increase up to 1.5. \(H_{\mathrm{ani}}\) was found to be proportional to the ferromagnetic resonance (_FMR_) frequency, allowing for the tuning of the EM wave absorption frequency range. W-type hexaferrite-epoxy composites (10 wt%) with \(x\) values between 0.6 and 1.5 exhibited outstanding wideband EM wave absorption, with a maximum absorption (\(RL_{min}\) \(\leftarrow\) 50 dB) and a wide absorption bandwidth where RL \(<\) \(-\)10 dB extended beyond 10 GHz (\(M_{\mathrm{fub}}\) > 10 GHz). The \(x\) = 1.25 sample with a thickness of 2.37 mm achieved \(RL_{min}\) = \(-\)69 dB at 7.8 GHz, while the \(x\) = 1.0 sample with a thickness of 2.33 mm delivered \(\Delta f_{\mathrm{sub}}\) = 12.5 GHz (5.1-17.6 GHz). Samples synthesized via the molten-salt method showed larger plate-like grain growth compared to those produced by the solid-state method, with permeability spectra shifting to lower frequencies, consequently lowering the EM wave absorption band. W-type hexaferrite; solid-state reaction; complex permeability; reflection loss; EM wave absorption +
Footnote †: journal: Applied sciences  
key advantage of these materials is the ability to actively tune the absorption frequency through cation substitution, which controls magnetic anisotropy. W-type hexaferrites boast high saturation magnetization (\(M_{S}\)) values, typically ranging from 72 to 88 emu/g, making them notable among the six types of hexaferrites (M, U, X, Y, W, and Z types). Additionally, they possess a high Curie temperature (T\({}_{\text{C}}\)) of approximately 729 K [13; 14; 15]. The general chemical formula for W-type hexaferrite is AMe\({}_{2}\)Fe\({}_{16}\)O\({}_{27}\) (AMe\({}_{2}\)W), where A represents Ba or Sr, and Me is a divalent metal such as Zn, Ni, or Co. This magnetic material is characterized by a hexagonal layered structure, composed of alternating S (spinel) and R (M-type hexaferrite) blocks. These form two molecular W units in a sequence of SSRSSR\({}^{*}\) (\({}^{*}\) denotes a 180\({}^{\circ}\) rotation of the block around the c-axis). Depending on its composition, W-type hexaferrite exhibits either c-axis or c-plane magnetic anisotropy, governed by the following two equations [16; 17; 18]:  
\[f_{FMR}=\frac{\gamma\mu_{0}}{2\pi}H_{a} \tag{1}\]  
\[f_{FMR}=\frac{\gamma\mu_{0}}{2\pi}\big{(}H_{\theta}H_{\varphi}\big{)}^{1/2} \tag{2}\]  
In these equations, \(f_{FMR}\) represents the ferromagnetic resonance (\(FMR\)) frequency, and \(H_{a}\) denotes the anisotropy field for c-axis magnetic anisotropy, while \(H_{\theta}\) and \(H_{\varphi}\) refer to the out-of-plane and in-plane anisotropy fields, respectively, for c-plane magnetic anisotropy. Additionally, \(\gamma\) is the gyromagnetic ratio constant, and \(\mu_{0}\) is the vacuum permeability. Typically, \(H_{\varphi}\) ranges from several tens to hundreds of Oe, which is significantly smaller than \(H_{\theta}\) (\(\sim\)10\({}^{4}\) Oe). Assuming that \(H_{\theta}\) and \(H_{\varphi}\) are proportional, and introducing a constant \(\alpha\), Equation (2) can be approximated as follows:  
\[f_{FMR}=\alpha H_{\theta} \tag{3}\]  
W-type hexaferrites are known for their ability to absorb EM waves in the GHz to tens of GHz range, attributed to their high magnetic anisotropy. Numerous studies have focused on modifying EM wave absorption characteristics by substituting various cations into the W-type hexaferrite structure or hybridizing it with other nanomaterials [11; 19; 20; 21; 22; 23].