1. INTRODUCTION

The absorption and shielding of electromagnetic (EM) waves have become critical issues across numerous industries, including electronics, communications, defense, aviation, and automotive sectors. The growing need to protect human health from the adverse effects of EM waves and to reduce electromagnetic interference (EMI) in signal processing has driven increased demand for effective shielding and absorption solutions. Consequently, there has been a surge in research focused on the development of advanced materials for EM wave shielding and absorption [¹-⁵]. While traditional EM wave shielding can be effectively achieved using highly conductive materials such as metal plates, which reflect EM waves, this approach introduces challenges related to secondary EMI from reflected waves, thereby limiting its overall effectiveness. This has shifted the focus towards the development of EM wave absorption materials, which have recently garnered significant research interest as a more comprehensive solution to the EM wave problem.

Effective absorption of EM waves necessitates the presence of both dielectric and magnetic loss mechanisms [³-⁴]. Dielectric losses typically arise from the oscillation of charges or electric dipoles within the absorber in response to the electric field, while magnetic losses are associated with magnetic dipoles or electron spin motions. The performance of an EM wave absorber is fundamentally governed by the material's complex permittivity (ε_r = ε' - jε") and complex permeability (μ_r = μ' - jμ") values[⁵]. To achieve efficient EM wave absorption, impedance matching must be met. This condition depends on the relative magnitudes of ε', ε", μ', and μ" at the specific frequency of the EM wave, as well as the thickness (d) of the absorber, to minimize reflection at the incident surface. Therefore, optimizing EM wave absorption requires a strategic balance, where the relative magnitudes of ε" and μ" (with ε", μ" > 0) are enhanced, while ε', ε", μ', and μ" are precisely tuned to maximize absorption performance. Recent studies have increasingly concentrated on controlling the composition of various materials within a single layer, manipulating micro-scale material structures, and enhancing absorption properties through the integration of nanocomposites [⁶-¹⁴]. However, these approaches often face limitations in independently tuning the high-frequency ε', ε", μ', and μ" properties within a single-layer material to effectively manage EM wave absorption characteristics.

Among the materials emerging as promising EM wave absorbers, hexaferrites have gained particular attention due to their magnetic absorption mechanisms. In frequency ranges above GHz, hexaferrites can absorb EM waves through ferromagnetic resonance (FMR). By adjusting the FMR frequency, the frequency range of EM wave absorption can be precisely controlled. Previous research [¹⁵-¹⁶] has demonstrated that substituting Co-Ti for Fe in the basic composition of M-type hexaferrite SrFe₁₂O₁₉ can significantly lower the FMR frequency from 50 GHz to several GHz, depending on the substitution level (x) in SrFe_12-2xCo_xTi_xO₁₉. Specifically, when x = 1.25, the FMR frequency is reduced to around 10 GHz, enabling over 90% EM wave absorption within the X-band (8-12 GHz) range.

In contrast, La_0.7Sr_0.3MnO₃, a manganese oxide with a perovskite structure, is being explored for its potential as an EM wave absorption and shielding material, largely due to its relatively high electrical conductivity. When incorporated into polymer matrices, La_0.7Sr_0.3MnO₃ can achieve high permittivity and significant dielectric loss. La_0.7Sr_0.3MnO₃ is notable for its ferromagnetic properties, driven by spontaneous spin alignment through the double exchange mechanism, where Mn ions transfer electrons via oxygen ions [¹⁷-¹⁸]. It also possesses the highest Curie temperature (TC) among manganese oxides. The electrical conductivity of LSMO, attributed to electron hopping between Mn³⁺ and Mn⁴⁺ ions, allows it to provide effective EM wave shielding and absorption through both magnetic and dielectric losses, as highlighted by recent studies [¹⁹-²¹].

In this study, the electromagnetic (EM) wave absorption characteristics of a bilayer structure comprising an SrFe_9.5Co_1.25Ti_1.25O₁₉-epoxy layer (SFCTO) and a La_0.7Sr_0.3MnO₃-epoxy layer (LSMO) were investigated using the High Frequency Simulation Software (HFSS) simulation tool. The SFCTO layer, which exhibits ferromagnetic resonance (FMR) around 10 GHz, primarily absorbs EM waves through magnetic losses [¹⁶], while the LSMO layer, with FMR characteristics around 1 GHz, possesses a high dielectric constant due to its electrical conductivity [²²]. High-frequency dielectric and magnetic permeability spectra of each individual layer were measured and utilized for reflection loss (RL) calculations. To validate the reliability of the simulation results, initial RL calculations from the HFSS simulations were compared with measured data for the unpatterned SFCTO/LSMO bilayer structure. Subsequently, various configurations were explored by applying an unpatterned continuous LSMO layer, a cross-shaped patterned LSMO layer, and a square island-patterned LSMO layer on top of the SFCTO layer. The RL spectra were derived by adjusting the thickness of each layer and the size of the patterns. This study aimed to investigate how structural variations—such as the thickness and patterning of the LSMO layer—affect EM wave absorption characteristics, with the goal of identifying optimal configurations for broadband absorption.

2. EXPERIMENTAL

The M-type hexaferrite SrFe_12-2xCo_xTi_xO₁₉ (x = 1.25) and perovskite manganese oxide La_0.7Sr_0.3MnO₃ powders were synthesized using the solid-state reaction and sol-gel methods, respectively. These powders were then mixed with epoxy (YD-014, Kukdo Chemical) and formed into toroidal shapes to produce the final composite samples. The detailed manufacturing method has been described in previous studies [¹⁶,²²]. Both powder compositions were confirmed to be single-phase by X-ray diffraction (XRD, D8 Advance, Bruker). The S11 parameters, complex permittivity (εʹ, εʺ) and permeability (μʹ, μʺ) of the toroidal composites were measured over the frequency range of 0.1 to 18 GHz using a network analyzer (Vector Network Analyzer, E50356A, Keysight) with an air-line kit (85052BR03). For the actual measurements of reflection loss (RL), the S11 parameters were also measured by attaching the toroidal samples to a Cuend socket, which represents the reflection loss (RL) in actual measurements. The complex permeability and permittivity spectra of SFCTO and LSMO were obtained through separate calibration of the S-parameter measurements using software (N1500A) provided by Keysight [²³].

Based on the measured spectra of εʹ, εʺ, μʹ, and μʺ for the toroidal SFCTO and LSMO composite samples, various bilayer structures were modeled, and the RL spectra were calculated using the 3D High Frequency Simulation Software (HFSS, Ansys). The modeling included three structures, as depicted in Figure 1: a structure consisting of SFCTO as the bottom layer and LSMO as the top layer without patterns (P_A); a structure with SFCTO as the bottom layer and LSMO with a cross pattern as the top layer (P_B); and a structure with SFCTO as the bottom layer and LSMO with a square island pattern as the top layer (P_C).

For each of these three structures, the thickness and pattern width of each layer were varied. The RL was calculated under the condition that EM waves are incident perpendicularly to the x-y plane (in the -z direction), with the unit structure shown in the figure being infinitely repeated in the x-y plane direction.

3. RESULTS AND DISCUSSION

Figure 2 (a)–(d) shows the complex permittivity and permeability spectra of the SFCTO and LSMO samples. Figure 2(a) and 2(c) indicate that LSMO exhibits significantly higher εʹ and εʺ values across the entire frequency range compared to SFCTO.

This is attributed to the high conductivity of LSMO particles, resulting in space charge polarization, which is typically observed in structures where conductive particles are dispersed in an insulating epoxy matrix. The μʹ and μʺ spectra, shown in Figure 2(b) and 2(d), also reveal considerable differences between LSMO and SFCTO. LSMO exhibits a high μʹ value in the low-frequency range, but this value decreases rapidly with increasing frequency. In the GHz range, SFCTO shows higher μʹ values. The μʺ spectra of LSMO peak around 1 GHz, showing higher values than SFCTO, but decreases to near zero at frequencies above 10 GHz. Conversely, the μʹ spectra of SFCTO remain relatively constant up to several GHz before undergoing a transition around 10 GHz, where the μʺ spectra also show a peak. This behavior is due to the higher crystalline magnetic anisotropy of SFCTO compared to LSMO.

The RL, which indicates EM wave absorption performance, was calculated using the εʹ, ε″, μʹ and μ″ spectra shown in Figs 2(a)–2(d). The RL values were computed over a frequency range and a thickness range of up to 10 mm, and the results are presented as 2D RL maps for SFCTO and LSMO in Figs 2(e) and 2(f). The RL was calculated using the following two equations based on transmission line theory[²⁴]:

Where Z_in is the impedance of the material, Z₀ is the impedance of free space, ε_r = εʹ - jε″ is the complex permittivity, μ_r = μʹ - jμ″ is the complex permeability, f is the frequency of the incident EM wave, c is the speed of light, and d is the thickness of the absorber. In the RL maps, as the RL value becomes more negative, the color changes from yellow to red, with regions where RL < -30 dB marked in black. Additionally, contour lines are drawn at every RL = -10 dB interval.

From the RL maps in Figs 2(e) and 2(f), it can be seen that for SFCTO, strong EM wave absorption occurs within the 7–14 GHz frequency range and at thicknesses between 2.5 and 3.0 mm. Notably, at a thickness of 2.7 mm, the RL reaches a minimum of -43 dB, demonstrating excellent absorption characteristics with a frequency bandwidth (Δf) of 6.06 GHz where RL < -10 dB is satisfied. Additionally, at a thickness of 2.4 mm, the frequency range satisfying RL < -10 dB is from 7.41 to 14.39 GHz, yielding a maximum Δf of 6.98 GHz. In contrast, for LSMO, localized absorption points are observed in the lower frequency region around 1 GHz and in the higher frequency region above 13 GHz. However, the overall absorption area is not as broad as that of SFCTO, which is attributed to the higher reflectivity of EM waves in LSMO due to its higher permittivity compared to SFCTO.

In Figs 3(a) and 3(b), the RL spectra for SFCTO (manufactured with a thickness of 1.50 mm) and LSMO (manufactured with a thickness of 1.56 mm) are plotted. RL spectra both the measured and the obtained from HFSS simulations are shown.

Additionally, Figs 3(c) and 3(d) show the RL spectra obtained by changing the stacking order of SFCTO (1.50 mm) and LSMO (1.56 mm) and plotting the results together with the HFSS simulation results. The measurements were conducted by attaching each sample to a Cu-end socket and connecting it to the 1-port of a VNA to obtain the S11 spectra. Overall, the experimental measurements and HFSS simulation results match well. An interesting observation is that the RL spectra significantly change depending on the stacking order of SFCTO and LSMO. LSMO shows EM wave absorption regions in the relatively low-frequency range below 2 GHz and in the high-frequency range around 14–16 GHz, whereas SFCTO exhibits absorption in the 7–14 GHz range. Due to its high dielectric constant, LSMO exhibits predominant surface reflection. When EM waves are incident on the LSMO surface, the material shows poor absorption characteristics over a wide range, except in regions where impedance matching occurs.

In subsequent research, simulations using the HFSS tool will be conducted to evaluate the EM wave absorption characteristics of a bilayer structure with SFCTO as the lower layer and LSMO as the upper layer, with EM waves incident perpendicularly onto the LSMO surface. The study will calculate the RL and investigate how varying the thickness of each layer, as well as modeling the LSMO layer with different patterns such as cross-shaped or square island patterns and altering the size of these patterns.

Figure 4(a) shows the RL spectra for an LSMO/SFCTO bilayer structure where the total thickness is fixed at 2.7 mm, and the thickness of the LSMO (t_LSMO) layer is increased by increments of 0.6 mm (i.e., SFCTO (2.7 - x) mm / LSMO (x) mm with x = 0, 0.6, 1.2, 1.8, 2.4 mm).

The optimal SFCTO thickness (t_SFCTO) for maximum absorption (RL_min = -42.9 dB) as observed in the single-layer SFCTO spectra is 2.70 mm (Fig 2(e)). As the thickness of the t_LSMO increases, the frequency at which RL_min occurs shifts towards lower frequencies, and the absolute value of RL_min decreases. Specifically, the RL_min frequency (f_RLmin) drops sharply from 8.53 GHz at x = 0 to 4.94 GHz at x = 0.6 mm, and then decreases gradually as x increases further. Figure 4(b) illustrates the changes in the RL spectra when t_SFCTO is fixed at 2.4 mm while the thickness of the t_LSMO is incrementally increased from 0.2 mm to 1.0 mm in steps of 0.2 mm. As t_LSMO increases, f_RLmin decreases from 6.66 GHz to 3.56 GHz, and the absolute value of RL_min increases, reaching a maximum of 43.2 dB at t_LSMO = 0.8 mm before decreasing again at t_LSMO = 1.0 mm. Figure 4(c) shows the RL spectra changes when the t_SFCTO is fixed at 2.7 mm and the t_LSMO is similarly increased from 0.2 mm to 1.0 mm. As t_LSMO increases, f_RLmin gradually decreases, and the absolute value of RL_min progressively increases, reaching 45.1 dB at t_LSMO = 1.0 mm. Figure 4(d) presents the RL spectra for a structure with the t_LSMO fixed at 0.5 mm and the t_SFCTO increased from 1.5 mm to 3.0 mm in steps of 0.3 mm. The RL_min value of -50 dB is observed at t_SFCTO = 1.8 mm. The EM wave absorption properties of the LSMO/SFCTO bilayer, including RL_min, f_RLmin, the frequency range satisfying RL < -10 dB, and the Δf values, as presented in Figs 4(a-d), are summarized in Table 1.

The result indicates that the frequency range at which maximum absorption occurs can be adjusted by varying the thickness of each layer in the LSMO/SFCTO bilayer. However, in terms of the frequency bandwidth (Δf) where RL < -10 dB is satisfied, the single-layer SFCTO (2.4 mm) achieves a Δf = 6.98 GHz. No broader absorption bandwidth could be found in the LSMO/SFCTO bilayer structure. This is likely due to the strong overall surface reflection characteristics of LSMO resulting from its high permittivity. Nonetheless, as indicated in previous research [²³], the EM wave shielding properties of the LSMO (1.5 mm) layer are superior to those of the SFCTO single layer. When measuring shielding effectiveness (SE) using VNA 2-port S12 or S21 measurements, the 1.5 mm thick LSMO layer met the criteria of SE < -10 dB in the 4.8-13.6 GHz range. Therefore, the LSMO/SFCTO bilayer structure is advantageous in scenarios where both shielding and absorption properties are required.

Next, the EM wave absorption characteristics of the second structure (P_B) in Figure 1, which features a cross-shaped patterned LSMO layer on top of the SFCTO layer, were analyzed. The goal was to find the conditions that provide superior EM wave absorption by varying the thickness of each layer and the width of the LSMO pattern (w_LSMO). Figure 5(a) and 5(b) display the RL spectra obtained as the w_LSMO value is increased from 0.1 mm to 1.0 mm in increments of 0.1 mm, with the t_LSMO fixed at 0.2 mm and the t_SFCTO fixed at 2.4 mm.

The area ratio of LSMO covering the SFCTO surface (A_LSMO/A_SFCTO) increases from 2% to 19.0% as w_LSMO increases. Despite the changes in w_LSMO, the RL_min values show little variation, ranging between -22 dB and -28.5 dB, while the frequency at which RL_min occurs (f_RLmin) generally decreases slightly. The absorption bandwidth (Δf) tends to increase gradually with increasing w_LSMO, reaching a maximum at w_LSMO = 0.5 mm, and then decreases slowly beyond that point.

Figure 5(c) and 5(d) show the RL spectra when w_LSMO is fixed at 0.5 mm, and the total thickness of the SFCTO and LSMO layers (t_Total) is set at 2.4 mm and 3.0 mm, respectively. The t_LSMO and t_SFCTO layers were varied by increasing/decreasing each by 0.6 mm, starting from t_LSMO = 0 mm and t_SFCTO = 2.4 mm for Figure 5(c) and from t_LSMO = 0 mm and t_SFCTO = 3.0 mm for Figure 5(d). The resulting values of RL_min, f_RLmin, the Δf values obtained from the RL spectra are summarized in Table 2.

It was observed that significant changes in RL spectra occur when the thickness of each layer is varied. The most favorable absorption characteristics were achieved with t_LSMO = 1.2 mm and t_SFCTO = 1.8 mm, yielding RL_min = -41.4 dB and Δf = 7.16 GHz. It is noticeable that in the non-patterned LSMO structure (P_A), it was challenging to achieve broad absorption characteristics with even a slight increase in LSMO thickness (e.g., t_LSMO = 0.2 mm). However, when the LSMO layer was formed into a cross-shaped pattern, broad absorption exceeding Δf > 7 GHz became achievable under specific conditions.

Lastly, in the Figure 6(a-i), the RL spectra were obtained by varying the side length of the square LSMO pattern (l_LSMO), the distance between the patterns (d), and t_LSMO, t_SFCTO in the third structure (P_C) of Figure 1.

Figure 6 (a-i) can be categorized under the following conditions.

• Figs 6(a-c): l_LSMO = 0.5 mm, d = 1.5 mm

• Figs 6(d-f): l_LSMO = 1.0 mm, d = 1.0 mm

• Figs 6(g-i): l_LSMO = 1.5 mm, d = 0.5 mm

These configurations correspond to the LSMO pattern covering 6.25%, 25.0%, and 56.25% of the SFCTO surface, respectively. The total thickness of the LSMO/SFCTO structure was set to:

• Figs 6(a), 6(d), 6(g): t_Total = 2.4 mm

• Figs 6(b), 6(e), 6(h): t_Total = 2.7 mm

• Figs 6(c), 6(f), 6(i): t_Total = 3.0 mm

Since the maximum Δf of 6.98 GHz was obtained at t_SFCTO = 2.4 mm in the single SFCTO layer case, the thickness of SFCTO in each configuration was set to t_SFCTO = 1.8 mm, 2.1 mm, and 2.4 mm, with corresponding t_LSMO values adjusted accordingly. The RL spectra were then calculated and plotted.

The results, including RL_min, f_RLmin, the frequency range satisfying RL < -10 dB, and the Δf values, are summarized in Table 3.

In many cases, Δf values greater than 7 GHz were obtained. The most optimal broadband absorption characteristics were achieved in two conditions, both yielding Δf = 7.39 GHz:

1. t_LSMO = 0.9 mm, t_SFCTO = 2.1 mm, l_LSMO = 0.5 mm, d = 1.5 mm

2. t_LSMO = 0.9 mm, t_SFCTO = 1.8 mm, l_LSMO = 1.5 mm, d = 0.5 mm

These conditions represent the most favorable configurations for achieving wideband EM wave absorption in the square island patterned-LSMO/SFCTO bilayer structure.

4. CONCLUSION

In this study, we investigated the EM wave absorption properties of a two-layered structure composed of La_0.7Sr_0.3MnO₃-epoxy (LSMO) and SrFe_9.5Co_1.25Ti_1.25O₁₉-epoxy (SFCTO), which exhibit distinct high-frequency magnetic and dielectric properties, using HFSS simulations. La_0.7Sr_0.3MnO₃ and SrFe_9.5Co_1.25Ti_1.25O₁₉ powders were synthesized, respectively, as single phases and then combined with 10 wt% epoxy to obtain high-frequency permittivity and permeability data for the LSMO and SFCTO samples. First, we validated the reliability of the simulations by comparing the measured and simulated RL results for the LSMO/SFCTO bilayer structure without any patterning. Subsequently, RL spectra were obtained by varying the thickness of each layer and the size of the patterns in three different structures: the continuous LSMO/SFCTO structure, the cross-shaped patterned LSMO/SFCTO structure, and the square-patterned LSMO/SFCTO structure. In the continuous LSMO/SFCTO structure, the absorption frequency band could be easily adjusted by changing the thickness of each layer, but achieving broadband absorption was challenging due to the overall reflective characteristics of the high-dielectric LSMO layer. In the structure with cross-shaped LSMO patterns on the SFCTO layer, we identified conditions that allowed for broader bandwidth absorption compared to the single-layer SFCTO. In this structure, the EM wave absorption characteristics were more significantly influenced by the thickness of each layer than by the width of the patterns. The samples with square LSMO patterns aligned on the SFCTO layer exhibited the best EM wave absorption characteristics in terms of broadband frequency absorption. It was confirmed that broader EM wave absorption is achievable by partially covering the high-dielectric layer with patterns on a continuous hexaferrite sheet which has already good EM wave absorber. Exploring more diverse pattern structures and utilizing various magnetic and dielectric materials, which was not done in this study, could lead to even better EM wave absorption properties. The results of this study are expected to be widely applicable in various fields, including military aircraft, warships, and combat equipment where broadband electromagnetic wave absorption is required, as well as in autonomous vehicles and medical devices that demand electromagnetic interference shielding.