Figure 3 shows the XRD patterns of BaFe_12−xAl_xO₁₉ (where x = 0.00, 0.02, 0.04, 0.06, and 0.08 Nano-hexaferrites). According to the image, all samples’ XRD pattern peaks matched space group P63/mmc and JCPD card No. 00 051-1879 [33]. The M-type HF peaks correspond to the hkl indexing of (110), (107), (114), (203), (205), (206), (217), (304), (220), and (219). These planes confirm the formation of the M-type hexagonal phase.

For M-type BHF with Al concentration (x) = 0.00 - 0.02, the M-type HF continues to be the predominant phase, but traces of the impurity phase start appearing with the increase in doping concentration. As the amount of dopant concentration increases from x = 0.04 - 0.08, the M-type phase remains as the predominant phase containing hematite [34]. As the dopant concentration increases, the intensity of the peaks of the hematite phase increases. This shows that the solubility of aluminium in the BHF phase is lower at 850˚C. This could be due to the smaller ionic radii of Al³⁺ ions as compared to Fe³⁺ ions. The solubility of Al³⁺ ions in Fe³⁺ could be improved by increasing calcination temperature and time [35][36].

Figure 3.X-Ray Diffraction Pattern for BaFe_12−xAl_xO₁₉ where x = 0.00, 0.02, 0.04, 0.06, and 0.08.

The values of the lattice parameters are given in Table 4. Figure 4 also shows the variation of structural parameters with dopant concentration. The formula below is used to compute the lattice constants [37]:

Table 4. Variation of lattice parameters, cell volume, crystallite size, strain, dislocation density, and density of Pure and Al-doped BHF.

where d_hkl is the interplanar spacing and h, k. l are the Miller indices of the planes. For the undoped sample, the values of “a” and “c” are 5.863 Å and 22.554 Å, respectively. The value of the lattice parameters decreases as the dopant concentration increases from x = 0.02 to x = 0.06, and then increases for x = 0.08. Identical patterns are also seen in the cell volume, which ranges from 649.61 ų to 671.40 ų. This shift is explained by the fact that the ionic radius of Al³⁺ (0.535 Å) is less than that of Fe³⁺ (0.645 Å) [38].

Grain size determination D (hkl) was done using Scherrer’s formula [39].

where the average crystallite size is denoted by D, the X-ray wavelength by λ, the full width at half maximum (FWHM) by β, and Bragg’s angle by θ. The value of crystallite size varies from 18.128 nm to 25.34 nm for pure and Al-doped BHF. The graphical variation of crystallite size with dopant concentration is shown in Figure 4. Table 4 shows the c/a ratio of pure and Al-doped BHF, which falls between 3.766 and 3.846. In comparison to the sample including an Al dopant, the c/a ratio for pure BHF is closer to 3.98. The limit of c/a = 3.98 for the M-type HF indicates that the samples have formed a distinct M-type phase [40].

The crystallinity of the material is determined by using its dislocation density. The value of dislocation density decreases as the crystallinity increases and vice versa [41]. Equation (3) is used to compute its value, which is given by:

where D is the crystallite size calculated using the Scherrer formula. Their values are shown in Table 4 lies in the range of 0.00172 - 0.0031.

Figure 4.Variation of (a): Lattice parameters (b) Cell volume and X-ray density (c) Crystallite size and Starin with Al-doping concentrationx = 0.00 - 0.08.

The formula [42] was used to determine the lattice strain (η) caused by doping.

The value of η lies in the range of 0.00107 to 0.11022. Its value is maximum for the undoped sample. Figure 4 shows the variation of η with dopant concentration. Analyzing the variation in the structural parameters is necessary to see the changes in magnetic and electromagnetic properties of the material.

FE-SEM micrographs of Al-doped BHF (BaFe_12−xAl_xO₁₉) are shown in Figure 5. Figures 5(a)-(c) corresponds to the micrographs and the lognormal distribution curve for x = 0.02, and Figures 5(d)-(f) for x = 0.08, respectively. The micrographs show the non-uniformity of the particle, where the micrographs predominantly display irregular, agglomerated particles.

Figure 5. FE-SEM graphs and average grain size distribution graph for BaFe_12-xAl_xO₁₉ (a)-(c) For x = 0.02 (d)-(f) For x = 0.08 respectively.

The SEM clearly shows the visible spaces by means of porosity between the grains, which hinder the passage of charge at the grain boundaries. This will affect the polarisation and alter electrical properties, like the manner in which porosity affects magnetic properties [43]. The grain size distribution was examined using ImageJ software. Figure 2(c), Figure 2(f) displays the distribution of grain size and histogram for composition x = 0.02 and x = 0.08. The average grain size is 290 nm at x = 0.02 and drops to 119 nm at x = 0.08. This decrease in grain size with increasing dopant concentration correlates well with the XRD-calculated variation in crystallite size.

The infrared spectra of aluminium-substituted BaAl_xFe_12−xO₁₉ with x = 0.00, 0.02, 0.04, 0.06, and 0.08 are obtained in the 2500 - 400 cm⁻¹ region. The absorption bands in the 1000 - 400 cm⁻¹ region suggest that ferrites or inorganic ions are forming in the crystal lattice [44].

Atoms in HF are arranged in three distinct locations: tetrahedral, octahedral, and trigonal bipyramidal. Figure 6 shows that for Al-doped BHF, the absorption bands are observed at 416 cm⁻¹, 568 cm⁻¹, 781 cm⁻¹, 1197 cm⁻¹, 1394 cm⁻¹, 1536 cm⁻¹, 1623 cm⁻¹, and 1702 cm⁻¹. A band centred around 418 cm⁻¹ represents the stretching vibrations of Fe³⁺-O²⁻ bonds at the octahedral sites inside the M-type HF. These are evidence of metal-oxygen and residual surface/precursor vibrations [45]. Two distinct absorption peaks between 540 - 580 cm⁻¹ in the spectra indicate the stretching vibrations associated with Fe³⁺-O²⁻ bonds confined at the tetrahedral locations [45]. The stretching vibrations of N-O are represented by the vibrational bands at 780 cm⁻¹ [46]. The bands in the range of 1050 - 1150 cm⁻¹ and 1350 - 1580 cm⁻¹ are caused by the C-O stretching vibration and the bending vibration of C-H, respectively. The bands in the ranges of 1620 - 1680 cm⁻¹ and 1700 - 1870 cm⁻¹, respectively, are caused by the stretching vibration of C=C and C=O [47].

Figure 6.FTIR Spectra for pure and Al-doped M-type BHF (BaFe_12−xAl_xO₁₉ for x = 0.00 - 0.08).

Using the VSM, the magnetic characteristics of pure and Al-doped BHF (BaFe_12−xAl_xO₁₉, where x = 0.00, 0.02, 0.04, 0.06, and 0.08) powdered material were investigated at RT (300 K) under an applied magnetic field of 10 kOe. Figure 7 shows the hysteresis loop obtained from the pure and Al-doped BHF samples. The usual behavior of all magnetic isotherms and the presence of a strong, observable hysteresis loop confirm the hard ferromagnetic behavior with a large H_c, which is also consistent with the previously reported hard ferromagnetic nature of HF [14][48]. Table 5 presents the obtained values of (magnetization at 10 kOe) M_s, M_r, and H_c for Al-doped BHF with different dopant concentrations, and Figure 8 illustrates their graphical change. Figure 8 shows that the magnetic property of doped BHF is significantly impacted by the Al³⁺ substitution. For pure BHF, the values of M_s, M_r, and H_c are 38.41 emu/g, 26.17 emu/g, and 3.04 kOe, respectively. With an increase in dopant concentration, the value of M_s and M_r. decreases from 34.41 emu/g and 22.83 emu/g for x = 0.02 to 25.73 emu/g, and 15.49 emu/g for x = 0.08.

Figure 7. M-H curve of BaFe_12−xAl_xO₁₉, where x = 0.00, 0.02, 0.04, 0.06 and 0.08 respectively.

Table 5. variation of M_R (emu/g), M_S (emu/g), H_c (kOe), and M_R/M_s of BaFe_12−xAl_xO₁₉, where x = 0.00, 0.02, 0.04, 0.06, and 0.08.

Figure 8. Variation of coercivity, saturation magnetization, and remanence with varying Al dopant concentration.

This magnetic attribute can be explained by the substitution of doped cations at different sites in the hexagonal structure of the ferrite. The magnetic moment in M-type HF is caused by the allocation of iron in five non-equivalent sublattices: 1 tetrahedral (4f₁), 1 trigonal bipyramidal (2b), and 3 octahedral (2a, 12k, and 4f₂) [14]. Of these 5 locations, the electron spins at 12k (6), 2a (1), and 2b (1) are ↑, while those at 4f₁ (2) and 4f₂ (2) are ↓. Uncompensated upward spins are the cause of the total magnetic moment, or 20 µ_B. According to the literature, Al³⁺ primarily replaces Fe³⁺ in the 2a and 12k octahedral sites, with a lower but considerable fraction entering the 4f₂ (octahedral) site, according to site occupancy refinements. The 4f₁ (tetrahedral) site has just a small percentage (<5%), whereas the 4e (trigonal bipyramidal) site has a greater substitution for x > 2 [49]. The reduction in M_s and M_r of the synthesised materials is caused by the nonmagnetic Al³⁺ replacing the Fe³⁺ ion (having magnetic moment = 5 µ_B) from the sites with spin upward orientation, primarily 12k [38]. The super-exchange interaction between Fe³⁺-O-Fe³⁺ also decreases when the diamagnetic Al³⁺ is substituted for Fe³⁺ ions [50][51]. From this decrease in exchange contact, a non-collinear spin arrangement is formed. This decrease in exchange contact also initiates the randomly oriented arrangement of spins with respect to the c-axis in the surface layer [38]. Now, the coupling of canted surface spins with the c-axis-aligned core spin can further diminish the net magnetisation of the material.

The coercivity, H_c, first decreases from 3.04 kOe for x = 0.00 to 1.79 kOe for x = 0.04 before sharply increasing to 4.84 kOe for x = 0.08. The behaviour is somewhat similar to the previous reported results on Al dope M-type ferrite [38]. The maximum increment of 59.21% is observed with just 0.66% substitution of Fe³⁺ with Al³⁺ ions. The size of the particle and magneto-crystalline anisotropy are the two possible reasons for the observed influence of H_c on Al doping. The BHF NPs used in this investigation have a mean particle size between 100 nm and 300 nm. Luo etal. claim that as the amount of Al doping grows, the NPs’ boundary of single domain (SD) increases and the grain size decreases [38]. The grains would thus exhibit SD behaviour. The creation of an SD impeded the domain-wall movement, which results in the rise of H_c. However, domain wall role in defining H_c is difficult since defects can pin and nucleate domain barriers [38]. Additionally, when Al³⁺ is added as a replacement for Fe³⁺, the H_c rises as predicted from H_c = α (2K/M_S) [52], where K is the magneto-crystalline anisotropy, and M_s is the magnetic saturation. This formula indicates that the H_c of the material increases as saturation magnetization decreases. This improvement in H_c behaviour is achieved with less than 0.7% Al substitution, demonstrating the effectiveness of aluminium doping in improving the hard magnetic properties of the material. This suggests that Al can serve as an efficient substitute to enhance coercivity, thereby optimizing magnetic performance for permanent magnet applications. Such a doping strategy offers a potential pathway towards developing a cost-effective, optimized ferrite-based material for high-performance applications, particularly in permanent magnetic technologies for electric vehicles.

a)Permittivityandpermeability

In complex permittivity, the real part ( ε ′ ) is the indicator of electric energy storage and the imaginary part ( ε ″ ) of electric loss. Both parts are frequency-dependent. Figure 9(a),Figure 9(b) represents the frequency-response of ε ′ and ε ″ for the prepared samples. Up to ~8 GHz, except x = 0.06, all samples exhibit almost constant ε ′ , indicating no space-charge and dipole polarisation lags. After 8 GHz ε ′ increase with frequency, this is more pronounced for the x = 0.06 sample observed after 6 GHz. This increase in ε ′ values with frequency may be attributed to resonance-type polarization dispersion instead of standard relaxation. Similar behaviour has been reported in the literature. G. Gultom etal. observed from 9.5 GHz to 10.5 GHz for Mg-Al doped and undoped barium FIG [53].

ε ′ is higher for the doped samples (the highest for x = 0.04) than undoped BHF. For ε ″ variation with frequency, all the samples show wavy curves that arise from the effects of polarisation, especially interfacial and dipole polarisation. The Debye model is utilised to investigate polarisation effects (discussed in the Cole-Cole section). Almost all the samples followed a similar ε ″ variation pattern as that of ε ′ . A discrepancy is seen for sample x = 0.06 after 8.5 GHz. Elevated values of ε ″ are related to greater Ohmic losses and AC conductivity (dielectric relaxation). The relation of ε ″ with electrical conductivity (σ) is well established (see Equation (5)) [54].

where f is the varying frequency range, ε₀ stands for the permittivity of the free space, and ε ″ is t imaginary value of complex permeability. Greater absorption requires a high value of ε ″ to get a better attenuation constant value [15]. The quantity and kind of ions present in the material show the relaxation behaviour and determine the dielectric loss of ferrite. The presence of ferric (Fe³⁺) and ferrous (Fe²⁺) in the ferrite also affects the ε ′ and ε ″ , due to enhanced conduction and electron hopping mechanisms [55]. Figure 9(c),Figure 9(d) shows the frequency-dependent real and imaginary parts of complex permeability ( μ ′ and μ ″ ). The range of values for the real part of permeability over a broad frequency range of 1 - 12 GHz for pure BHF is (1.21 - 1.33). At x = 0.00, the value of μ ′ is 1.33 at 1 GHz. The greatest value of 1.4 for μ ′ is found at 1 GHz for composition x = 0.04. On the other hand, the value of μ ″ remains close to zero over the frequency range of 1 - 12 GHz. The resonance peaks are also observed for the magnetic samples. The lowest value of imaginary permeability is observed for the composition of x = 0.06. G. Wang claims that hysteresis loss, ferromagnetic resonance loss, eddy current (EC) loss, and intergranular domain wall loss are the causes of magnetic energy dissipation in ferrite [56].

Figure 9. Frequency response of (a), (b): ε ′ and ε ″ of complex permittivity (c), (d): μ ′ and μ ″ of complex permeability for BaFe_12−xAl_xO₁₉, where x = 0.00, 0.02, 0.04, 0.06 and 0.08.

b)DielectricandMagneticLossTangents

The energy dissipation in the ferrite materials under electric and magnetic fields is indicated by the dielectric loss angle tangent ( tan δ ε = ε ″ / ε ′ ) and magnetic loss angle tangent ( tan δ µ = μ ″ / μ ′ ). Wave absorption is more advantageous when the tanδ value is higher [57]. Figure 10 shows the frequency-dependent behavior of dielectric and magnetic loss tangent (tanδ_ε and tanδ_µ) for pure and Al-doped BHF over the frequency range of 1 - 12 GHz. tanδ_ε and tanδ_µ behave similarly to the imaginary part of complex permittivity and permeability. tanδ_ε falls between 0.01 and 0.06 over the entire frequency range and dopant concentrations. The dopant concentrations x = 0.04 and x = 0.06 have maximum and minimum values of 0.06 and 0.01, respectively. Pure BHF exhibits the lowest tangent dielectric loss at the highest frequency of 12 GHz. Similarly, tanδ_µ also remains close to zero in the near range of 0.08 - 0.18. The maximum value is observed for the composition of 0.04, and the minimum is for the composition of 0.06, respectively.

Figure 10.Frequency response of (a) tanδ_ε and (b) tanδ_µ of pure and Al-doped BHF.

c)Cole-ColeGraphs

Figure 11 gives the pictorial representation of the Cole-Cole semicircular graphs for Al-doped BHF. Figure 11(a), Figure 11(b) represents the ε ″ vs ε ′ for x = 0.00, μ ″ vs μ ′ for x = 0.00; (c), (d) ε ″ vs ε ′ for x = 0.02, μ ″ vs μ ′ for x = 0.02; (e), (f) ε ″ vs ε ′ for x = 0.06, μ ″ vs μ ′ for x = 0.06 Al ions composition. Debye relaxation is frequently revealed by plotting (Cole-Cole plot). These arcs point to different dielectric relaxation mechanisms, most likely interfacial polarisation at the borders of the MNP [58]. The Debye model is utilized to investigate polarization effects.

where, ω is the angular frequency, τ is the relaxation period, ε s is static permittivity, and ε ∞ is high-frequency permittivity. Cole-Cole plots for undoped and x = 0.06 samples have multiple arcs attributed to various dielectric relaxation processes, likely interfacial polarization from the buildup of charge carriers when the material is exposed to an alternating electric field at the heterogeneous interfaces between various microstructural areas such as grains, grain borders, and defect sites (low calcination) [59][60]. At low GHz, conduction loss emerges in both samples, showing a tail indicating higher conductivity tiny Al addition (x ≈ 0.02) for the x = 0.02 sample seems to simplify the relaxation spectrum (around a single semicircle), either by anchoring specific defect states so that one relaxation predominates or by lowering inhomogeneity. Like the Cole-Cole semicircle of ε ″ vs ε ′ in dielectric absorbing materials, μ ″ vs μ ′ curve also has a similar Cole-Cole semicircle. Each similar Cole-Cole semicircle corresponds to a loss of resonance. The μ ′ vs μ ′ curves in Equation (4) are depicted based on Xing’s research to validate the explanation of μ ′ and μ¹ based on the natural resonance process [61].

where, B m is maximum induction, and H m is the maximum field. Figure 11(b), Figure 11(d), and f demonstrate that μ ″ vs. μ ′ frequently deviates from a perfect semicircle because of magnetisation damping [40]. Resonance and EC are the primary causes of magnetic loss in the 2 - 18 GHz range. Losses from ECs are represented via Equation (16) as:

Figure 11. Cole-Cole graphs of BaFe_12-xAl_xO₁₉ (a) ε ″ vs ε ′ forx= 0.00; (b) μ ″ vs μ ′ for x = 0.00; (c) ε ″ vs ε ′ for x = 0.02; (d) μ ″ vs μ ′ for x = 0.02; (e) ε ″ vs ε ′ for x = 0.06; (f) μ ″ vs μ ′ forx = 0.06.

In this equation, “d” stands for material thickness, μ₀ for free space permeability, and σ for electrical conductivity. The above equation suggests that the only cause of magnetic loss is EC loss, and that C₀ should be constant over the given frequency range. If the observed magnetic loss is solely due to EC loss, then the value of C₀ should not change as frequency rises. In this study, not all specimens meet the aforementioned criteria since the value of C₀ changes with frequency within the specified frequency range of 1 - 12 GHz (see Figure 12). Thus, resonance governs magnetic loss. Natural and exchange are the two major resonance losses in magnetic materials [61]. Natural resonance occurs if the material’s characteristic frequency meets the incoming EM wave’s cutoff, giving absorption [62].

Figure 12. EC loss C₀ (1/GHz) for Ba Al_xFe_12−xO₁₉ for x = 0.00 - 0.08.

d)Microwave(mW)absorptionproperties

Standard measuring techniques, such as direct evaluation of air-space reflection (S₁₁) or indirect evaluation of EM characteristics, are used to categorise absorbing materials. One of the most important needs for absorbers is to reduce mirror reflection while matching the impedance of the air at the absorption contact [63]. Additionally, the material must show notable insulating and magnetic losses in order to enhance EM wave absorption. Additionally, it is anticipated that these materials would be used across a broad frequency range. It is recommended that the absorbent materials be thin and light [64].

The MW absorption properties of a sample are represented by the RL. According to transmission line theory, the RL values have been calculated using the complex ε and µ at a certain thickness d and frequency f. The value of reflection loss can be calculated using Equations (13) and (14) given below [65].

where Z₀ represents the free space impedance (Ip), Z_in is the input Ip of the absorber, f gives frequency, d stands for thickness, μ_r and ε_r are the relative permeability and permittivity, and c is the speed of light in vacuum.

Figures 13(a)-(e) shows the MW absorption properties for Al-doped BHF, with varying frequency of 1 - 12 GHz. The MW absorption of EMWs at RL < −10 dB is thought suitable as it can vanish above 90% of the input EMW. For practical application, MW absorbers mostly aim for the EM absorption at RL < −20 dB, meaning that above 99% of the entering EMW is absorbed. The reflection loss performance is investigated by showing RL diagrams of two-dimensional Al-doped BHF nano-particles Ba Al_xFe_12−xO₁₉ at various thicknesses for composition x = 0.00, 0.02, 0.04, 0.06, and 0.08, respectively. The addition of a dopant has a significant impact on RL values, because it drops to a lower value of RL. As the frequency rises, the thickness range of the material expands.

Figure 13. RL value of Ba Al_xFe_12−xO₁₉ at various thicknesses for (a): x = 0.00 (b): for x = 0.02 (c) for x = 0.04 (d) for x = 0.06 (e) for x = 0.08.

For pure BHF, i.e., x = 0.00, there is no reflection loss observed in the frequency range of 1 - 12 GHz. For x = 0.02, the reflection loss value significantly declines to RL_min = −25.05 dB, for d_m = 5.8 mm at 11.7 GHz. The range of EBW_RL<−10dB = 0.3 increases with an increase in dopant amount. However, x = 0.02 also gives the effective values of RL_min < −20 dB for lower thickness. For d_m = 1.9 mm, RL_min = −24.00 dB, at the frequency of 11.9 GHz. The EBW_RL<−10dB for the same thickness is 0.2 GHz. It is evident from the data that the dopant concentration has a greater effect on the thickness at which the material exhibits the reduced reflection loss. The dopant concentration x = 0.02 could be considered as satisfactory, because it provides a drop in both the material’s thickness range and in reflection loss.

As the dopant concentration increases, i.e., for x = 0.04, RL_min = −11.51 dB and −11.76 dB, for d_m = 6.2 mm and 6.1 mm at 10.81 GHz and 11.1 GHz, respectively. The range of EBW_RL<−10dB = 0.58 and 0.67 GHz. This dopant amount has increased the value of the effective bandwidth by 0.3 GHz.

Further increase in the dopant amount would increase the matching thickness as shown in Figure 13(d), Figure 13(e). For x = 0.06, RL_min = −27.55 dB and −27.93 dB, for d_m = 7.3 mm and 7.9 mm at 10.9 GHz and 10.99 GHz, respectively. The range of EBW_RL<−10dB = 0.1 and 0.8 GHz, respectively. The value of RL_min decreases with further increase in dopant concentration, i.e., the lowest value of -12.00 dB is observed for composition x = 0.08 at the thickness of 8.6 mm.

e)Furtherdiscussion

Efficient MW attenuation must be considered to achieve highly effective MW absorption. The efficiency with which an absorber attenuates EM waves is demonstrated by the value of the attenuation constant (α). The value α increases with the strength of the EM attenuation ability [66][67]. Figure 14 displays the α curves of pure and Al-doped BHF NPs.

Figure 14.Attenuation constant for BaAl_xFe_12-xO₁₉, for x = 0.00 - 0.08.

For every dopant concentration, or x = 0.00 - 0.08, the value of α falls between 2 and 60. With a change in dopant concentration, α varies marginally up to 10 GHz, but beyond that, the fluctuation in α becomes more noticeable. Even while the sample with composition x = 0.02 exhibits resonance at 12 GHz, it attains the maximum value of 323.42. The sample at dopant concentrations x = 0.04 shows the maximum value of α.

The substitution of Al into BHF NP effectively modifies the EM parameters and significantly enhances the MW absorption characteristics. The composition x = 0.02 achieved a decline in RL_min with reduced thickness.