Enhanced Electromagnetic Wave Absorption in W-Type Ba-Hexaferrites: Role of Composition and Grain Growth

Abstract

W-type Ba-hexaferrite, BaZn_2−xCo_xFe₁₆O₂₇, 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_ani) decreased, reaching its minimum at x = 0.75, before rising again as x continued to increase up to 1.5. H_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 < −50 dB) and a wide absorption bandwidth where RL < −10 dB extended beyond 10 GHz (Δf_wb > 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 Δf_wb = 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.

1. Introduction

The development of electromagnetic (EM) wave absorbers has garnered significant attention due to increasing demand in sectors such as telecommunications, defense, and aerospace. Recent research has focused on incorporating various absorbing materials into polymeric insulators, including conductive carbon-based nanoparticles with layered or porous nanostructures [1,2,3,4], magnetic metal particles [5,6], and dielectric or magnetic ceramics [7,8,9]. For efficient EM wave absorption, materials must exhibit dielectric loss mechanisms driven by charge movement or magnetic loss mechanisms associated with domain wall or electron spin motion. The combination of dielectric loss and magnetic loss for EM wave absorption is an effective approach to enhancing absorption performance. Reports have shown excellent EM wave absorption properties in the broad frequency range using core–shell structures made of magnetic particles and dielectrics [9]. Alternatively, magnetic ceramics can be given dielectric loss characteristics by introducing electrical conductivity through cation substitution [10]. In such cases, iron in hexaferrite crystals can have mixed valences, such as Fe³⁺ and Fe²⁺, which can create mobile charges through electron hopping, thereby increasing dielectric loss. However, controlling both permittivity and permeability independently to optimize absorption characteristics remains challenging, as these properties are inherently linked.

Among the diverse EM wave absorption materials, W-type hexaferrites have emerged as a highly promising option. Their primary absorption mechanism, ferromagnetic resonance (FMR), enables them to absorb EM waves in the GHz to tens of GHz range [11,12]. A 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_C) of approximately 729 K [13,14,15]. The general chemical formula for W-type hexaferrite is AMe₂Fe₁₆O₂₇ (AMe₂W), 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° 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]:

$$f_{FMR}={\displaystyle \frac{\gamma {\mu }_0}{2\pi }}{H}_a$$

(1)

$$f_{FMR}={\displaystyle \frac{\gamma {\mu }_0}{2\pi }}{\left(H_{\theta }{H}_{\phi }\right)}^{1/2}$$

(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_θ and H_φ refer to the out-of-plane and in-plane anisotropy fields, respectively, for c-plane magnetic anisotropy. Additionally, γ is the gyromagnetic ratio constant, and μ₀ is the vacuum permeability. Typically, H_φ ranges from several tens to hundreds of Oe, which is significantly smaller than H_θ (~10⁴ Oe). Assuming that H_θ and H_φ are proportional, and introducing a constant α, Equation (2) can be approximated as follows:

$$f_{FMR}=\alpha H_{\theta }$$

(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]. Under conditions of impedance matching, these materials have demonstrated exceptional absorption properties. However, research on actively controlling the EM wave absorption frequency band by tuning the f_FMR remains limited, and reports of extraordinary broadband absorption characteristics are scarce.

In this study, the composition was designed by varying the substitution level (x) of Co in the base formula BaZn₂Fe₁₆O₂₇ (BaZn₂W), and the process conditions required to ensure a single-phase W-type hexaferrite were verified. The effects of x on the microstructure, magnetic properties, high-frequency dielectric and permeability characteristics, and EM wave absorption properties were investigated. Furthermore, the differences in characteristics between samples synthesized via the solid-state reaction method and the molten-salt method were examined for the same composition.

2. Materials and Methods

W-type hexaferrite powders with the chemical composition BaZn_2−xCo_xFe₁₆O₂₇ (x = 0.4, 0.5, 0.6, 0.75, 1.0, 1.25, 1.5) were synthesized using a conventional solid-state reaction method. Additionally, for compositions x = 0.75, 1.0, and 1.25, the molten-salt (M-S) method was employed to synthesize the powders. The precursor materials, BaCO₃ (99+%, Kojundo Chemical, Saitama, Japan), ZnO (99.9%, Kojundo Chemical), CoO (99%, Sigma-Aldrich, St. Louis, MO, USA), and Fe₂O₃ (99.9%, Kojundo Chemical), were weighed according to the cation composition ratio and ball-milled with ZnO₂ balls in deionized (DI) water. After the mixture was dried in an electric oven, it was placed in an alumina crucible and subjected to an initial calcination in air at 900 °C for 6 h. The calcined powder was then crushed and returned to the crucible for a second calcination at 1250 °C for 6 h, with the furnace left to cool naturally.

For the M-S process, the same procedures were followed, from powder weighing to the first calcination, as in the solid-state method. After the initial calcination, portions of the BaZn_2−xCo_xFe₁₆O₂₇ (x = 0.75, 1.0, 1.25) samples were separated, mixed with NaCl (99%, Alfa Aesar, Haverhill, MA, USA) powder at a 1:1 weight ratio, and subjected to a second calcination under the same conditions as the solid-state method. The calcined powders were then crushed to obtain W-type hexaferrite powders for each composition and synthesis method. The hexaferrite powders were mixed with solid epoxy resin (YD-014, Kuk-do Chemical, Seoul, Republic of Korea) at a 9:1 weight ratio and placed into a toroidal mold (inner diameter = 3.03 mm, outer diameter = 7.00 mm). The samples were shaped under a pressure of 0.2 tons and cured at 180 °C for 20 min. Post-processing ensured that the samples conformed to the desired dimensions of an inner diameter of 3.03 mm and an outer diameter of 7.00 mm.

Phase analysis was carried out using an X-ray diffractometer (XRD, D8 Advance, Bruker, Billerica, MA, USA) with Cu Kα radiation (λ = 0.154056 nm). Microstructural observations were performed using field emission scanning electron microscopy (FE-SEM, JSM-7610F, JEOL, Seoul, Republic of Korea). The magnetization curves of the powder samples were measured at room temperature using a vibrating sample magnetometer (VSM, LakeShore 7410, Westerville, OH, USA) within a magnetic field range of −25 kOe ≤ H ≤ 25 kOe, with the hexaferrite powders embedded in epoxy resin for the VSM measurements. The complex permittivity (ε′, ε″) and complex permeability (μ′, μ″) spectra were obtained across the frequency range of 0.1 to 18 GHz using a vector network analyzer (VNA, E50356A, Keysight, Santa Rosa, CA, USA) in conjunction with an airline kit (85052BR03) and software (N1500A) integrated into the VNA. The reflection loss (RL) of the composites was calculated based on the ε′, ε″, μ′, and μ″ spectra.

3. Results and Discussion

Figure 1a shows the XRD patterns of BaZn_2−xCo_xFe₁₆O₂₇ (BaZn_2−xCo_xW) samples synthesized via the conventional solid-state method (x = 0.4, 0.5, 0.6, 0.75, 1.0, 1.25, 1.5), while Figure 1b presents the XRD patterns of samples with x = 0.75, 1.0, and 1.25 synthesized using the molten-salt (M-S) method. The diffraction patterns of the samples were matched with the peak positions of BaW from the International Center for Diffraction Data (ICDD, 01-084-0927), and the corresponding Miller indices are labeled at the top of each diffraction pattern. All sample compositions were confirmed to have an almost single-phase W structure. Using the d_hkl values obtained from the 2θ positions of the (110), (1010), (116), and (1011) planes, the lattice constants a and c, along with the cell volume of the W-type hexaferrite phase, were calculated and are presented in

Table 1. Lattice parameters (a, c), cell volume (Vol.), saturation magnetization (M_S), and coercivity (H_C) values of the BaZn_2−xCo_xFe₁₆O₂₇ samples after the second calcination, with and without the application of the M-S method.

Composition	x	a (Å)	c (Å)	Vol. (Å3)	MS (emu/g)	HC (Oe)
BaZn2−xCoxW (non M-S)	0.4	5.913	32.97	998.3	77.08	86.98
	0.5	5.910	32.98	997.5	78.44	83.89
	0.6	5.910	32.96	997.1	78.77	67.01
	0.75	5.904	32.94	994.3	78.06	32.64
	1.00	5.903	32.90	993.5	80.34	38.42
	1.25	5.902	32.92	993.1	77.77	48.69
	1.50	5.902	32.91	992.8	75.64	58.56
BaZn2−xCoxW (M-S)	0.75	5.898	32.91	991.3	-	-
	1.00	5.987	32.91	991.2	-	-
	1.25	5.898	32.89	990.9	-	-

The error bar for M_S is ±0.2%, and for H_C is ±1%, of the original values. M-H for M-S samples were not measured. M-H measurements for M-S samples were not taken.

. It can be observed that as Co, which has a slightly smaller ionic radius, substitutes for Zn, the cell volume continuously decreases with increasing x.

Figure 2a–f presents BaZn_2−xCo_xW samples synthesized using the conventional solid-state method for x = 0.4, 0.5, 0.6, 0.75, 1.0, and 1.25. The images display plate-like crystallites after grinding, with sizes ranging from small fragments to approximately 10 μm. No significant variation in average crystallite size is observed with changes in the x value. Figure 2g–i shows samples with compositions x = 0.75, 1.0, and 1.25 produced using the M-S method. It is evident that secondary calcination caused substantial crystallite growth compared to those synthesized by the conventional solid-state method. Numerous large, flat, plate-like particles exceeding 10 μm are visible, with no clear trend of microstructural change as the x value increases.

In Figure 3, the particle size distribution of BaZn_2−xCo_xW powder samples is presented as a histogram derived from SEM micrographs. Owing to the grinding process following secondary calcination, the grain sizes exhibit an irregular morphology. Grain size was quantified using the average line intercept method, with the mean particle size indicated in each figure panel. 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 µm. Conversely, for powders synthesized via the M-S method, as shown in Figure 3g–i, the average particle size is approximately 14 µm, indicating substantially larger grains compared to those obtained via the conventional solid-state method. In the case of the M-S method, grain size measurements were conducted using lower-magnification images than those presented in Figure 2.

Figure 4 presents the M-H curves of BaZn_2−xCo_xW 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 ≤ H ≤ 200 Oe, while the upper right inset displays the magnetization curves for the range of 0 ≤ H ≤ 5000 Oe. In the lower right, the changes in saturation magnetization M_S and coercivity (H_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 ≤ H ≤ 5000 Oe, differences in magnetization ease are noticeable depending on x, which can be attributed to changes in magnetocrystalline anisotropy. The H_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 ε′, ε″, μ′, and μ″ for BaZn_2−xCo_xW–epoxy (10 wt%) composites synthesized via the conventional solid-state method, measured within the frequency range of 0.1 to 18 GHz. In the ε′ 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 ε″ spectra in Figure 5b display no clear trend relative to the x values, with values consistently below 1. These ε′ and ε″ 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 μ′ and μ″ spectra vary depending on the x values. In hexaferrite, the mechanism contributing to the μ′ value is related to the movement of magnetic domain walls (f < ~1 GHz) and the electron spins (f > ~1 GHz). The μ′ 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 μ′ value but decreases the fastest, while the sample with x = 0.4 shows the lowest value at 100 MHz but maintains μ′ > 1 up to the highest frequency. The μ″ spectra in Figure 5d generally increase with frequency, exhibit a peak, and then decrease. The frequency of the μ″ 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 μ″ 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. This change in the f_FMR is attributed to the relationship with magnetic anisotropy depending on the x values. In the region where x ≤ 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 ≥ 0.75, the f_FMR gradually increases with x, corresponding to c-plane anisotropy, following Equations (2) or (3). Previous studies have reported that the magnetic anisotropy of BaZn_2−xCo_xW has a minimum around x = 0.6 [24], while for Sr_0.75Ca_0.25Zn_2−xCo_xW, 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_C values in Figure 4. Additionally, the permeability behavior corresponding to changes in the x value can be explained well by Snoek’s limitation law [16].

Figure 5c,d illustrate how the μ′ and μ″ spectra vary depending on the x values. In hexaferrite, the mechanism contributing to the μ′ value is associated with the movement of magnetic domain walls (for f < ~1 GHz) and electron spins (for f > ~1 GHz). As shown in Figure 5c, the μ′ spectra generally decreases as the frequency increases. At 100 MHz, the sample with x = 0.75 exhibits the highest μ′ value, though it declines most rapidly, while the sample with x = 0.4 shows the lowest initial value at 100 MHz but maintains μ′ > 1 across the entire frequency range. The μ″ spectra in Figure 5d show a general increase with frequency, reaching a peak and then declining. The peak frequency of μ″, observed above 1 GHz, is considered the f_FMR for hexaferrites. The f_FMR, identified as the peak in the μ″ 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 ≤ 0.75, the f_FMR decreases as x increases, indicating that c-axis anisotropy dominates, following Equation (1). For x ≥ 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−xCo_xW [24] and around x = 1.0 for Sr_0.75Ca_0.25Zn_2−xCo_xW [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_C values, as shown in Figure 4. Additionally, the permeability behavior in relation to x can be explained by Snoek’s limitation law [16].

$$({\mu }_S\prime -1)·f_{\mathit{FMR}} \frac{2}{3}\gamma ·4\pi M_S$$

(4)

Here, μ_S′ refers to the static permeability, which represents the μ′ value maintained at low frequencies. γ 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 μ′ value remains stable up to higher frequencies, while the f_FMR frequency also rises. However, as the f_FMR increases, the μ_S′ value decreases. If the μ_S′ value is estimated from the μ′ value at 100 MHz in Figure 5c, it can be observed that the sample with x = 0.75, which exhibits the lowest f_FMR, also has the highest μ_S′ value. Furthermore, as the f_FMR increases with changes in the x value, the μ_S′ value declines accordingly. Given that the sample with x = 0.4 shows the lowest μ_S′ value, it is expected that it will have the highest f_FMR, even though FMR is not observed within the measurement range.

Figure 6a–d presents the ε′, ε″, μ′, and μ″ spectra for BaZn_2−xCo_xW–epoxy (10 wt%) composites (x = 0.75, 1.0, 1.25) synthesized via the M-S method. The ε′ and ε″ spectra show no significant differences compared to the corresponding spectra for the same compositions in Figure 5a,b. However, the μ′ and μ″ spectra display a noticeable shift towards lower frequencies compared to Figure 5c,d. The f_FMR values for each composition are listed in

Table 2. FMR frequency (f_FMR), frequency of RL_min (f_RLmin), minimum RL (RL_min) values, thickness of RL_min (d_RLmin), frequency range for RL < 10 dB (Δf_wb), and the thickness (d_wb) for the wide-band absorption in hexaferrite–epoxy (10 wt%) composites. The data are marked as N/A for the x = 0.4 sample because its f_FMR is outside the measured frequency range.

Composition	x	fFMR (GHz)	fRLmin (GHz)	RLmin (dB)	dRLmin (mm)	Δfwb (GHz)	dwb (mm)
BaZn2−xCoxW	0.4	N/A	N/A	N/A	N/A	N/A	N/A
	0.5	15.1	16.5	−30.9	1.75	>3.82 14.18–18(+)	1.75
	0.6	9.99	12.6	−65.7	2.22	>8.92 9.08–18(+)	2.24
	0.75	2.01	3.41	−50.3	5.23	9.58 3.59–13.17	3.37
	1.0	4.89	5.29	−57.8	3.41	12.52 5.12–17.64	2.33
	1.25	8.11	7.89	−69.0	2.57	>11.68 6.32–18(+)	2.37
	1.5	10.7	9.94	−56.2	2.25	>10.54 7.46–18(+)	2.35
BaZn2−xCoxW (M-S)	0.75	1.87	3.42	−46.1	4.99	9.77 4.32–14.09	2.92
	1.0	4.13	4.61	−46.5	4.01	11.09 4.36–15.45	2.81
	1.25	6.75	2.59	−47.7	2.59	12.37 5.48–17.85	2.42

. A comparison indicates that samples prepared using the M-S method exhibit lower f_FMR values than those synthesized by the conventional solid-state method. This discrepancy is attributed to the influence of the average grain size. In structures where magnetic particles are dispersed in a non-magnetic binder, smaller grain sizes lead to an increase in internal magnetic fields, causing the f_FMR to shift to higher values.

The RL of BaZn_2−xCo_xW–epoxy (10 wt%) composites, which characterizes EM wave absorption, can be calculated using the ε′, ε″, μ′, μ″ spectrum data in Figure 5 and Figure 6. The calculations are based on the following two Equations (5) and (6), derived from transmission line theory [25]:

$$\frac{Z_{in}}{Z_0}=\sqrt{\frac{{\mu }_r}{{\epsilon }_r}}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}(j\frac{2\pi fd}{c}\sqrt{{\mu }_r{\epsilon }_r})$$

(5)

$$\mathrm{R}\mathrm{L}\left(\mathrm{d}\mathrm{B}\right)=20\mathrm{l}\mathrm{o}\mathrm{g}\left|\frac{Z_{in}-Z_0}{Z_{in}+Z_0}\right|$$

(6)

In this context, Z_in represents the impedance of the incident material, while Z₀ denotes the impedance of free space. The complex permittivity ε_r is expressed as ε′ −jε″, and the complex permeability μ_r is expressed as μ′ −jμ″. The frequency of the incident EM wave is indicated by f, c represents the speed of light in a vacuum, and d is the thickness of the absorber. The RL values are calculated as a function of f and d over the range of 0 mm ≤ d ≤ 10 mm and are displayed as 2D maps in Figure 7a–j.

First, examining the RL map for the sample with the lowest f_FMR, x = 0.75 (Figure 7d), the maximum EM wave absorption, indicated by the minimum RL value (RL_min), occurs at f_RLmin = 3.4 GHz, with a thickness of, d_RLmin = 5.23 mm, and RL_min = −50.3 dB. The absorption region forms a diagonal pattern extending from the upper left to the lower right. As seen in Figure 7e–g, as the x value increases up to x = 1.5, the area of maximum absorption progressively shifts to higher frequencies and thinner thicknesses. All these samples demonstrate a broad EM wave absorption performance, with the shift in the strong absorption region corresponding to changes in f_FMR. For samples with x ≤ 0.6, significant changes are observed due to the sharp increase in c-axis magnetic anisotropy as x decreases from x = 0.75. This causes the absorption region to rapidly move towards higher frequencies and thinner thicknesses (around 2 mm or less). In the x = 0.6 sample (Figure 7c), the absorption region spans horizontally above approximately 10 GHz, and as the x value decreases further to x = 0.5 and 0.4, this region shifts towards even higher frequencies. For the x = 0.4 sample, no strong absorption is observed below a 2 mm thickness, as the f_FMR exceeds 18 GHz, pushing the strong absorption region beyond the 18 GHz range.

Meanwhile, Figure 7h–j show RL maps for x = 0.75, 1.0, and 1.25 samples synthesized using the M-S process. As the x value increases, the RL_min position shifts progressively to higher frequencies due to the rise in f_FMR. These RL maps can be compared with those of the conventionally synthesized samples shown just above (Figure 7d–f). Overall, the RL map patterns appear similar; however, the RL_min points are slightly shifted to the left, indicating lower frequencies. This shift occurs because the samples synthesized using the M-S process exhibit significantly larger grain sizes and lower f_FMR values. The RL_min and corresponding frequency (f_RLmin) values for these samples are presented in Table 2.

To elucidate the EM wave absorption mechanism, a simplified approach was applied to the x = 1.0 sample, which exhibited the broadest EM wave absorption performance across the measured frequency range. In Figure 7k, the reflection loss (RL) map was generated under the assumption of ε″ = 0 across the entire measured frequency range, while the remaining spectra (ε′, μ″, μ″) were kept unchanged. Similarly, in Figure 7l, the RL map was derived by assuming μ″ = 0, with the other spectra (ε′, ε″, μ′) held constant. A comparison with the original RL map in Figure 7e reveals that Figure 7k shows minimal alteration in the RL pattern, indicating only a shift in the absorption profile. In contrast, setting μ″ = 0 results in the complete disappearance of the primary absorption features in Figure 7l. These findings suggest that the EM wave absorption in the W-type hexaferrite composites studied here is predominantly influenced by μ″, which is closely associated with the FMR phenomenon.

Figure 8a–d presents the RL spectra for BaZn_2−xCo_xW powder–epoxy (10 wt%) composites of each composition at specific thicknesses, prepared by the conventional solid-state method and the M-S method. Figure 8a,c show the spectra at the RL_min point, where maximum absorption occurs, while Figure 8b,d depict the RL spectra at the thicknesses that provide the broadest frequency width (Δf_wb) satisfying RL < −10 dB. All samples demonstrated excellent EM wave absorption performance with RL_min ≤ −30 dB near the f_FMR. As shown in Figure 8a, the x = 1.25 sample exhibited outstanding absorption characteristics with RL_min = −69 dB at f =7.89 GHz, while Figure 8b indicates that the x = 1.0 sample showed the best broadband absorption properties, with Δf_wb = 12.52 GHz. Among the samples prepared using the M-S method in Figure 7d, the x = 1.25 sample demonstrated excellent broadband absorption characteristics, with Δf_wb = 12.37 GHz. For samples with x < 0.75 and x > 1.25, it was difficult to obtain precise Δf_wb values because their absorption bandwidth exceeded the measurement range over 18 GHz. Table 2 presents the Δf_wb and corresponding thicknesses (d_wb). Frequencies exceeding 18 GHz are indicated as 18(+) in the Table. The EM wave absorption properties observed in this study are compared with those of recently reported materials [26,27,28,29,30,31,32,33,34,35,36,37,38] in

Table 3. Electromagnetic wave absorption properties of various magnetic powder–polymer composite materials.

Materials	fFMR (GHz)	dRLmin (mm)	RLmin (dB)	fRLmin (GHz)	f-Range (RL < −10 dB)	Δf (GHz)	Ref. #
Ni-ZnFe2O4	1.45	5.6	−63	2.9	2.5–3.5	1.0	[26]
	1.45	3.1	−37	12.6	4.0–13.0	9.0	[26]
	-	3.7	−42	-	2.9–11.9	9.0	[27]
Mn-ZnFe2O4	-	4.3	−44	6.2	4.6–7.5	2.9	[28]
	-	7.6	−21	3.8	2.3–5.3	3.0	[28]
Co-Ti SrM	6.4	3.1	−42	6.4	5.1–9.1	4.0	[29]
	8.2	2.7	−40	8.5	6.7–13.3	6.6	[29]
	15.0	1.5	−30	13.5	11.8–18.0(+)	6.2+	[29]
Zn-Zr SrM	8.3	2.7	−45	8.8	7.5–14.7	7.2	[30]
	10.8	2.0	−39	11.8	10.2–18.0(+)	7.8+	[30]
Ni-Ti BaM	-	0.9	−52	29.5	34.8–44.9	10.1	[31]
SrZn2W	-	1.9	−66	11.3	9.7–13.4	3.7	[32]
Sr0.75Ca0.25Zn2−xCoxW	8.2	2.6	−38	7.6	7.1–18.0(+)	10.9	[12]
Sr3Co2Z	2.9	4.7	−51	3.1	2.2–7.8	8.7	[33]
Ba3−xLaxCo2Z	-	3.5	−47	3.5	3.7–13.7	10.0	[34]
(Ba0.7Bi0.2)4(Co1−xNix)2U	10.1	1.9	−39	11.0	-	6.3	[35]
	13.2	1.9	−44	11.3	-	8.6	[35]
Co2Y	-	3.0	−15	11.3	10.2–17.3	7.1	[36]
Carbon nanofiber	-	1.3	−22	17.5	9.8–18(+)	8.2+	[36]
Fe3O4@PANI	-	1.6	−56	17.3	12.6–18	5.4	[37]
FeSiAl	-	2.7	−21	-	9.0–14.2	5.2	[38]
BaZn0.75Co1.25W	8.1	2.6	−69	7.89	6.32–18(+)	11.7	this work
BaZn1.0Co1.0W	4.89	4.89	−58	5.29	5.12–17.64	12.5	this work

, focusing on the RL_min and Δf_wb values. The results of this study demonstrate superior absorption characteristics compared to other materials.

4. Summary

The W-type hexaferrite BaZn_2−xCo_xW (x = 0.5, 0.6, 0.75, 1.0, 1.25, 1.5) was synthesized via a solid-state method. For compositions of x = 0.75, 1.0, and 1.25, hexaferrite powders were additionally synthesized using the M-S method, and their EM wave absorption properties were compared with those of samples prepared by the conventional solid-state method. Magnetic powder prepared by the conventional solid-state method exhibited changes in M_S, H_C, and H_ani depending on the x value. H_ani was minimized at x = 0.75, and H_ani gradually increased as the x value increased or decreased from x = 0.75. BaZn_2−xCo_xW exhibited c-axis anisotropy for x ≤ 0.75 and c-plane anisotropy for x ≥ 0.75. This change in H_ani led to a shift in the f_FMR, which is the primary mechanism of EM wave absorption in BaZn_2−xCo_xW, actively controlling the absorption frequency range by varying x. The variations in the EM wave absorption regions depending on x and processing methods were presented on an RL map, derived from the high-frequency complex permittivity and permeability spectra, as a function of the frequency (0.1 ≤ f ≤ 18 GHz) and absorber thickness (0 ≤ d ≤ 10 mm). The x = 1.25 sample exhibited a maximum absorption of RL_min = −69 dB near f = 8 GHz with a thickness of d = 2.57 mm, and it achieved a maximum bandwidth for 90% energy absorption, Δf > 11.7 GHz, ranging from 6.3 GHz to beyond 18 GHz, with a thickness of d = 2.37 mm. When the same composition was fabricated using the M-S method and the epoxy composite, the FMR frequency slightly decreased, and the absorption bandwidth shifted to 5.48 GHz–17.85 GHz. The M-S process caused significant grain growth, shifting the permeability spectra towards lower frequencies, and the f_FMR also decreased slightly, resulting in a corresponding EM absorption band shift to a lower-frequency region. The BaZn_2−xCo_xW powder–epoxy (10 wt%) composites prepared by the solid-state method demonstrated outstanding EM wave absorption properties compared to other absorbing materials. Therefore, BaZn_2−xCo_xW is a highly promising material for broad-band absorbers in the C-Ku bands and even beyond, with tunable absorption frequency ranges depending on the Co substitution composition.