Functional Magnetic Composites Based on Hexaferrites: Correlation of the Composition, Magnetic and High-Frequency Properties

The paper describes preparation features of functional composites based on ferrites, such as “Ba(Fe1−xGax)12O19/epoxy,” and the results of studying their systems; namely, the correlation between structure, magnetic properties and electromagnetic absorption characteristics. We demonstrated the strong mutual influence of the chemical compositions of magnetic fillers (Ba(Fe1−xGax)12O19 0.01 < x < 0.1 solid solutions), and the main magnetic (coercivity, magnetization, anisotropy field and the first anisotropy constant) and microwave (resonant frequency and amplitude) characteristics of functional composites with 30 wt.% of hexaferrite. The paper presents a correlation between the chemical compositions of composites and amplitude–frequency characteristics. Increase of Ga-content from x = 0 to 0.1 in Ba(Fe1−xGax)12O19/epoxy composites leads to increase of the resonant frequency from 51 to 54 GHz and absorption amplitude from −1.5 to −10.5 dB/mm. The ability to control the electromagnetic properties in these types of composites opens great prospects for their practical applications due to high absorption efficiency, and lower cost in comparison with pure ceramics oxides.


Introduction
One of the major tasks in creating modern mobile communication devices is the development of new materials which can work in a wide (up to 100 GHz) frequency range in switches, circulators, phase shifters, transceivers, antennas and effective electromagnetic radiation (EMR) absorbers, which improve the electromagnetic compatibilities of devices [1][2][3][4][5]. M-type hexagonal ferrites are one of the most prospective electromagnetic materials for application in the centimeter and millimeter wave The crystal structures of Ba(Fe 1−x Ga x ) 12 O 19 filler powders and the samples of CMs were investigated by X-ray diffraction, which was carried out using a DRON-4-07 X-ray diffractometer (Bourevestnik, St. Petersburg, Russia) with Co K α filtered radiation (λ = 1.7902 A) at room temperature.
Keysight PNA N5227A vector network analyzer (Keysight Technologies, Inc. Santa Rosa, CA, USA) was used to determine the electromagnetic parameters of the composites in the frequency range of 1-67 GHz by the transmission line method. Full, two-port calibration was initially performed on the test setup to remove errors due to the directivity, source match, load match, isolation and frequency response of each of the forward and reverse measurements. The coaxial measuring cell ( Figure 1) had the inner conductor diameter of 0.8 cm and the outer conductor diameter of 1.85 cm (thickness of the samples was fixed at 1 cm). The tested samples were shaped into a form of a hollow cylinder, which tightly fit into the coaxial measuring cell. The measured reflection coefficient (S 11 ) and transmission coefficient (S 21 ) of each composite was converted into material shielding efficiency (SE T ), reflection coefficient (SE R ) and coefficient of absorption (SE A ) according to the equations: Nanomaterials 2019, 9,  Keysight PNA N5227A vector network analyzer (Keysight Technologies, Inc. Headquarters, Santa Rosa, CA, USA) was used to determine the electromagnetic parameters of the composites in the frequency range of 1-67 GHz by the transmission line method. Full, two-port calibration was initially performed on the test setup to remove errors due to the directivity, source match, load match, isolation and frequency response of each of the forward and reverse measurements. The coaxial measuring cell (Figure 1) had the inner conductor diameter of 0.8 cm and the outer conductor diameter of 1.85 cm (thickness of the samples was fixed at 1 cm). The tested samples were shaped into a form of a hollow cylinder, which tightly fit into the coaxial measuring cell. The measured reflection coefficient (S11) and transmission coefficient (S21) of each composite was converted into material shielding efficiency (SET), reflection coefficient (SER) and coefficient of absorption (SEA) according to the equations: The magnetic properties (field dependencies of the magnetization) were determined using a universal cryogenic high-field measuring system (Liquid Helium Free High Field Measuring System (B14T) by Cryogenic Ltd., London, UK) at the temperature of 300 K in external magnetic fields up to 5 T (field magnetization curve). The size of each sample for magnetic measurements was 5.2 × 2.6 × 2.6 mm 3 . Figure 2 shows the XRD X-ray diffraction patterns of initial Ba(Fe1−xGax)12O19 (0 ≤ x ≤ 0.1) powders measured at the room temperature. The calculated positions of reflections for BaFe12O19 (having a hexagonal lattice P63/mmc with parameters a = 5.887 Å, b = 5.887 Å and c = 23.2 Å and the positions of reflections for iron oxides Fe2O3 and Fe3O4 are also marked in the graphs. X-ray diffraction data analysis shows that the barium hexaferrite phase, the unit cell of which is a hexagon and belongs to the space group P63/mmc, prevails in the investigated powders. These data are in accordance with the results obtained previously for similar compounds [15,31,32].

Structural Characteristics
As for the unsubstituted sample of barium hexaferrite (x = 0), it is visible from the XRD pattern (  The magnetic properties (field dependencies of the magnetization) were determined using a universal cryogenic high-field measuring system (Liquid Helium Free High Field Measuring System (B14T) by Cryogenic Ltd., London, UK) at the temperature of 300 K in external magnetic fields up to 5 T (field magnetization curve). The size of each sample for magnetic measurements was 5.2 × 2.6 × 2.6 mm 3 . Figure 2 shows the XRD X-ray diffraction patterns of initial Ba(Fe 1−x Ga x ) 12 O 19 (0 ≤ x ≤ 0.1) powders measured at the room temperature. The calculated positions of reflections for BaFe 12 O 19 (having a hexagonal lattice P6 3 /mmc with parameters a = 5.887 Å, b = 5.887 Å and c = 23.2 Å and the positions of reflections for iron oxides Fe 2 O 3 and Fe 3 O 4 are also marked in the graphs. X-ray diffraction data analysis shows that the barium hexaferrite phase, the unit cell of which is a hexagon and belongs to the space group P6 3 /mmc, prevails in the investigated powders. These data are in accordance with the results obtained previously for similar compounds [15,31,32].

Structural Characteristics
As for the unsubstituted sample of barium hexaferrite (x = 0), it is visible from the XRD pattern ( Figure 2)  Some fairly intense reflections do not correspond to the data calculated for barium hexaferrite. One of the most intense reflections of that sample was observed at 2θ = 38.40° (between (107) and (114) BaFe12O19 reflections). It is the closest angle to the position calculated for (112) reflection of Fe2O3, but szs strongly biased in comparison with it. Intense reflection is also observed at 2θ = 43.440, which does not coincide with the available data calculated for BaFe12O19. Perhaps the reflection at 43.44° is a (222) reflection for Fe3O4, but this is doubtful, since the most intense line for Fe3O4 should be (311) at 2θ = 41.46°, and this was not observed for our sample. The reflection with the position of 2θ = 67.59° can be identified as (511) for Fe3O4, but its intensity is also lower than the expected tabulated values. Therefore, both Fe3O4 and Fe2O3 phases in the studied sample, if any, were estimated to have a small amount. 20 Table 1). In addition, the intensities of (112) and (222) reflections were significantly reduced in Ga-substituted hexaferrites. The unidentified reflection at 2θ = 38.40° of unsubstituted BaFe12O19 (between (107) and (114) BaFe12O19 reflections) was not observed for all Gasubstituted samples.
XRD data analysis of the hexaferrite powders showed that the relative intensities of (107) and (114) reflections, which correspond to the inclined c-axis orientation, are higher than other peaks. These results indicate that the materials we investigated have a polycrystalline structure with a random grains orientation.
The average crystallite size in Ba(Fe1−xGax)12O19 (0 ≤ x ≤ 0.1) was determined using the wellknown Scherrer formula from the line broadening of the diffraction profile of the strongest peaks of (107) and (114) planes:  Table 1). In addition, the intensities of (112) and (222) reflections were significantly reduced in Ga-substituted hexaferrites. The unidentified reflection at 2θ = 38.40 • of unsubstituted BaFe 12 O 19 (between (107) and (114) BaFe 12 O 19 reflections) was not observed for all Ga-substituted samples.
XRD data analysis of the hexaferrite powders showed that the relative intensities of (107) and (114) reflections, which correspond to the inclined c-axis orientation, are higher than other peaks. These results indicate that the materials we investigated have a polycrystalline structure with a random grains orientation.
The average crystallite size in Ba(Fe 1−x Ga x ) 12 O 19 (0 ≤ x ≤ 0.1) was determined using the well-known Scherrer formula from the line broadening of the diffraction profile of the strongest peaks of (107) and (114) planes: where D is the average crystallite size, k = 0.9-Scherrer constant for spheres, λ is the radiation wavelength (λ Co = 1.790263 Å), h 1/2 = Full width at half maximum-FWHM (in radians) and θ is the position of the reflection (in radians). The average size of the crystallites in the Ba(Fe 1−x Ga x ) 12 O 19 (0 ≤ x ≤ 0.1) powders (using the FWHM of (107) and (114) reflection) was calculated by Equation (4). The values are presented in Table 2. The average crystallite size of Ba(Fe 1−x Ga x ) 12 O 19 (0 ≤ x ≤ 0.1) was estimated to be about 33-37 nm and it depended on the content x of Ga in Ba(Fe 1−x Ga x ) 12 Table 2). Therefore, the Ba(Fe 1−x Ga x ) 12 O 19 (0 ≤ x ≤ 0.1) crystallites were single-domain which correlates well with data for BaM are 460 nm [33]. At average crystal size 10 nm, substituted M-type hexaferrites were in superparamagnetic state [34]. The XRD pattern of 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 (x = 0.1)/epoxy composite is shown in Figure 3. The pattern shows sharp peaks corresponding to the main reflection of Ba(Fe 1−x Ga x ) 12 O 19 (x = 0.1) which means that this composite contained crystalline barium hexaferrite. The preponderance of crystalline peaks of BaM was attributed to its encapsulation by epoxy resin. The relative intensity of 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composite is weakened compared to pure BaM powder. Again, using the above Scherrer formula with the line broadening of the diffraction profile of the strongest peaks of the planes (107)    The change in grain size is more significant for samples with low Ga concentration. The crystallites combine and form an entire ceramic. A certain dispersion of particle sizes was characteristic for all samples. This is in good agreement with our previous data: the grain size variation interval was between 0.223 and 1.279 μm for x = 0.01, and 52.4% of the crystallites were from     The change in grain size is more significant for samples with low Ga concentration. The crystallites combine and form an entire ceramic. A certain dispersion of particle sizes was characteristic for all samples. This is in good agreement with our previous data: the grain size variation interval was between 0.223 and 1.279 μm for x = 0.01, and 52.4% of the crystallites were from The change in grain size is more significant for samples with low Ga concentration. The crystallites combine and form an entire ceramic. A certain dispersion of particle sizes was characteristic for all samples. This is in good agreement with our previous data: the grain size variation interval was between 0.223 and 1.279 µm for x = 0.01, and 52.4% of the crystallites were from 0.740 µm to 0.860 µm. Grains with sizes smaller than 0.170 µm or larger than 1.400 µm were not detected. The precise value of the average crystallite size of D ≈ 0.873 µm for x = 0.01 was obtained from quantitative stereological analysis. The average crystallite size increased to ≈ 950 nm with an increase in the substitution coefficient to x = 0.1 [14]. 0.740 μm to 0.860 μm. Grains with sizes smaller than 0.170 μm or larger than 1.400 μm were not detected. The precise value of the average crystallite size of 〈D〉 ≈ 0.873 μm for x = 0.01 was obtained from quantitative stereological analysis. The average crystallite size increased to ≈950 nm with an increase in the substitution coefficient to x = 0.1 [14].

Magnetic Properties
We discussed in [15,32] the magnetic parameters of substituted with diamagnetic ions polycrystalline samples of Ba(Fe1-xGax)12O19 (0 ≤ x ≤ 0.1). Here, we present the magnetic properties of epoxy-based composites, namely, 30 wt.% Ba(Fe1-xGax)12O19/epoxy (0 ≤ x ≤ 0.1) with random distribution of the filler. Typical M-H field magnetization curves of the composites at room temperature are shown in Figure 6. The values of saturation magnetization (MS), residual magnetization (Mr), saturation magnetic field (Hsat) and coercivity (HC) are given in Table 3. Dependencies were measured for two orientations of each sample relative to the direction of the magnetic field H (where S is the designation of the sample orientation).

Magnetic Properties
We discussed in [15,32] the magnetic parameters of substituted with diamagnetic ions polycrystalline samples of Ba(Fe 1−x Ga x ) 12 O 19 (0 ≤ x ≤ 0.1). Here, we present the magnetic properties of epoxy-based composites, namely, 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy (0 ≤ x ≤ 0.1) with random distribution of the filler. Typical M-H field magnetization curves of the composites at room temperature are shown in Figure 6. The values of saturation magnetization (M S ), residual magnetization (Mr), saturation magnetic field (H sat ) and coercivity (H C ) are given in Table 3. Dependencies were measured for two orientations of each sample relative to the direction of the magnetic field H (where S is the designation of the sample orientation).  The magnetization field dependence for 30 wt.% Ba(Fe1-xGax)12O19/epoxy composites shows clear hysteresis behavior. Such magnetization field dependence is a characteristic for all investigated 30 wt.% Ba(Fe1-xGax)12O19/epoxy composites as a consequence of magnetic response of the Ba(Fe1-xGax)12O19 component. It is assumed that the total magnetization of the composite is formed only due to Ba(Fe1-xGax)12O19 filler, as epoxy is non-magnetic. As can be seen from the data in Figure 6 and Table 3, the coercive force HC increases monotonically from 0.060 to 0.166 T with an increase of Ga content in the filler while the saturation magnetization MS decreases with Ga content increase (    12 O 19 filler, as epoxy is non-magnetic. As can be seen from the data in Figure 6 and Table 3, the coercive force H C increases monotonically from 0.060 to 0.166 T with an increase of Ga content in the filler while the saturation magnetization M S decreases with Ga content increase (Figure 7). Nevertheless, an insignificant maximum of M S was observed for 30 wt.% Ba(Fe 1−x Ga x ) 12  As shown in [35], the specific saturation magnetization Mrfc of rubber-ferrite composites was found to be linearly dependent on the mass fraction of ferrite and obeys the following general relation: where MS and Wf are the saturation magnetization and weight fraction of the filler, respectively. As seen in Figure 7, the saturation magnetization MS (x) decreases with increasing Ga content x in the filler for both materials investigated, but the value of MS is higher for Ba(Fe1-xGax)12O19/epoxy (0 ≤ x ≤ 0.1) composites. As it was shown in our previous paper [15], such behavior of the specific saturation magnetization for the Ba(Fe1-xGax)12O19 (0 ≤ x ≤ 0.1) polycrystalline samples indicates a decrease in the maximum magnetic energy with an increase in the concentration of Ga 3+ cations and the absence of abrupt anomalies. It means a decrease in deviations from the linear dependence of magnetic energy with increasing substitution ratio, which testifies to the hypothesis of a statistical distribution of Ga 3+ cations between different nonequivalent crystallographic positions in the M-type barium hexaferrite structure. The polymer coating on magnetic particles obviously affects the contributions of the surface anisotropy, shape anisotropy and interface anisotropy to the total anisotropy [36,37]. The magnetic parameters of Ba(Fe1-xGax)12O19/epoxy composites are higher than the corresponding parameters of pure Ba(Fe1-xGax)12O19 (0 ≤ x ≤ 0.1) polycrystalline samples, while the shape of MS (x) dependencies remains unchanged. Figure 7 shows that coercivity HC of Ba(Fe1-xGax)12O19 polycrystals with low content of Ga (x = 0.01) notably decreases from 2.1 kOe to 0.6 kOe when they are embedded into the polymer matrix of the composite. A monotonic increase in HC is observed with increasing content of Ga in Ba(Fe1-xGax)12O19/epoxy composites.
The magnetization-field dependence for 30 wt.% Ba(Fe1-xGax)12O19/epoxy composites is relatively small, which may be due to the prevalence of domain rotation in the high-field region. The relationship between M and H in this region is called the "law of approach to saturation" and is As shown in [35], the specific saturation magnetization M rfc of rubber-ferrite composites was found to be linearly dependent on the mass fraction of ferrite and obeys the following general relation: where M S and W f are the saturation magnetization and weight fraction of the filler, respectively. As seen in Figure 7, the saturation magnetization M S (x) decreases with increasing Ga content x in the filler for both materials investigated, but the value of M S is higher for Ba(Fe 1−x Ga x ) 12 O 19 /epoxy (0 ≤ x ≤ 0.1) composites. As it was shown in our previous paper [15], such behavior of the specific saturation magnetization for the Ba(Fe 1−x Ga x ) 12 O 19 (0 ≤ x ≤ 0.1) polycrystalline samples indicates a decrease in the maximum magnetic energy with an increase in the concentration of Ga 3+ cations and the absence of abrupt anomalies. It means a decrease in deviations from the linear dependence of magnetic energy with increasing substitution ratio, which testifies to the hypothesis of a statistical distribution of Ga 3+ cations between different nonequivalent crystallographic positions in the M-type barium hexaferrite structure. The polymer coating on magnetic particles obviously affects the contributions of the surface anisotropy, shape anisotropy and interface anisotropy to the total anisotropy [36,37]. The magnetic parameters of Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites are higher than the corresponding parameters of pure Ba(Fe 1−x Ga x ) 12 O 19 (0 ≤ x ≤ 0.1) polycrystalline samples, while the shape of M S (x) dependencies remains unchanged. Figure 7 shows that coercivity H C of Ba(Fe 1−x Ga x ) 12 O 19 polycrystals with low content of Ga (x = 0.01) notably decreases from 2.1 kOe to 0.6 kOe when they are embedded into the polymer matrix of the composite. A monotonic increase in H C is observed with increasing content of Ga in Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites.
The magnetization-field dependence for 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites is relatively small, which may be due to the prevalence of domain rotation in the high-field region. The relationship between M and H in this region is called the "law of approach to saturation" and is usually written as [38]: where M S is the saturation magnetization of the domains. The term ΘH represents the field-induced increase in the saturation magnetization of the domains, or forced magnetization; this term is usually small at temperatures well below the Curie point and may often be neglected. Constant A is generally interpreted as a result of inclusions and/or microstress, and B is due to magnetocrystalline anisotropy. The magnetization data in a field range of about 3 kOe were plotted against 1/H 2 in [17], and straight lines were obtained, indicating that both A and ΘH are negligible in the aforementioned magnetic field range. Saturation magnetization values for the samples were obtained from the intersections of the straight lines. The slopes of the lines were used to determine the anisotropy field H a from the relationships [17]: The first anisotropy constant was evaluated using the relation [38]: The anisotropy field H a and anisotropy constant K 1 of 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites (0 ≤ x ≤ 0.1) were calculated using Equations (7) and (8), and the results are presented in Figure 8. where MS is the saturation magnetization of the domains. The term ΘH represents the field-induced increase in the saturation magnetization of the domains, or forced magnetization; this term is usually small at temperatures well below the Curie point and may often be neglected. Constant A is generally interpreted as a result of inclusions and/or microstress, and B is due to magnetocrystalline anisotropy. The magnetization data in a field range of about 3 kOe were plotted against 1/H 2 in [17], and straight lines were obtained, indicating that both A and ΘH are negligible in the aforementioned magnetic field range. Saturation magnetization values for the samples were obtained from the intersections of the straight lines. The slopes of the lines were used to determine the anisotropy field Ha from the relationships [17]: The first anisotropy constant was evaluated using the relation [38]: The anisotropy field Ha and anisotropy constant K1 of 30 wt.% Ba(Fe1-xGax)12O19/epoxy composites (0 ≤ x ≤ 0.1) were calculated using Equations (7) and (8), and the results are presented in Figure 8.

Microwave Properties
Transmittance spectra of 30 wt.% Ba(Fe1-xGax)12O19/epoxy composites (0 ≤ x ≤ 0.1) were recorded in millimeter wave range and are shown in Figure 9a. As seen in Figure 9a, the values of shielding efficiency (SET) are quite small up to frequencies of 40-45 GHz.

Microwave Properties
Transmittance spectra of 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites (0 ≤ x ≤ 0.1) were recorded in millimeter wave range and are shown in Figure 9a. As seen in Figure 9a, the values of shielding efficiency (SE T ) are quite small up to frequencies of 40-45 GHz.
It is known [39] that the value of total material shielding efficiency SE T is equal to the sum of the absorption coefficient SE A , reflection coefficient SE R and correction factor SE I , which takes into account multiple reflections in thin high-conductive shields or in shields with a small absorption coefficient: SE I is negligible in cases when SE A exceeds 10 dB. As seen in Figure 9a,b the main contribution to the total material shielding efficiency SET of 30 wt.% Ba(Fe1-xGax)12O19/epoxy composites (0 ≤ x ≤ 0.1) was the absorption of electromagnetic waves in the materials. The most intensive EMR absorption was observed in 40-50 GHz frequency range for all the above-mentioned composite samples. The NFMR in barium hexaferrite powders provides high EMR absorption in the indicated frequency range. The transmission value at the global minimum of microwave transmission spectrum determines the resonant transmission Ares. The frequency in the global minimum of microwave transmission spectrum determines the resonant transmission frequency fres. The global minimum width, measured at Ares/2, i.e., half of the resonant transmission value, determines the width of the absorption band Wres-the bandwidth. One can see in Figure 9a,b that all three above-mentioned quantities are sensitive to the substitution ratio x. The NFMR frequency fres was measured at the half of the bandwidth Wres/2 and the results are presented in Figure 10. It was assumed that the determined frequency was associated with fres in Ba(Fe1-xGax)12O19 ferrite filler. fres in unsubstituted BaFe12O19 is near 50 GHz and can be calculated as [17]: if the demagnetizing effects are neglected.
Here γ is the gyromagnetic ratio. Using the above-stated experimental results on the anisotropy field and saturation magnetization, the NFMR frequency fres for 30 wt.% Ba(Fe1-xGax)12O19/epoxy composites (0 ≤ x ≤ 0.1) was evaluated and the values are also presented in Figure 10. As seen in Figure 10, fres values determined from DC magnetization measurements are in a rather good agreement with fres values determined by microwave measurements.
As it was shown in our previous publications [31,32], the peak of absorption is shifted towards higher frequencies with increasing x in Ba(Fe1-xGax)12O19 (0 ≤ x ≤ 0.1) powders (see Figure 10). However, the concentration dependence of the resonant frequency for Ba(Fe1-xGax)12O19 (0 ≤ x ≤ 0.1) powders is non-monotonic and demonstrates the minimum at x = 0.05. As one can see, encapsulation of Ba(Fe1-xGax)12O19 particles in epoxy leads to the resonance frequency increase for 30 wt.% Ba(Fe1-xGax)12O19/epoxy composites in comparison with pure Ba(Fe1-xGax)12O19 (0 ≤ x ≤ 0.1) powders and it As seen in Figure 9a,b the main contribution to the total material shielding efficiency SE T of 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites (0 ≤ x ≤ 0.1) was the absorption of electromagnetic waves in the materials. The most intensive EMR absorption was observed in 40-50 GHz frequency range for all the above-mentioned composite samples. The NFMR in barium hexaferrite powders provides high EMR absorption in the indicated frequency range. The transmission value at the global minimum of microwave transmission spectrum determines the resonant transmission A res . The frequency in the global minimum of microwave transmission spectrum determines the resonant transmission frequency f res . The global minimum width, measured at A res /2, i.e., half of the resonant transmission value, determines the width of the absorption band W res -the bandwidth. One can see in Figure 9a,b that all three above-mentioned quantities are sensitive to the substitution ratio x. The NFMR frequency f res was measured at the half of the bandwidth W res /2 and the results are presented in Figure 10. It was assumed that the determined frequency was associated with f res in Ba(Fe 1−x Ga x ) 12 O 19 ferrite filler. f res in unsubstituted BaFe 12 O 19 is near 50 GHz and can be calculated as [17]: if the demagnetizing effects are neglected.
Here γ is the gyromagnetic ratio. Using the above-stated experimental results on the anisotropy field and saturation magnetization, the NFMR frequency f res for 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites (0 ≤ x ≤ 0.1) was evaluated and the values are also presented in Figure 10. As seen in Figure 10, f res values determined from DC magnetization measurements are in a rather good agreement with f res values determined by microwave measurements.
As it was shown in our previous publications [31,32], the peak of absorption is shifted towards higher frequencies with increasing x in Ba(Fe 1−x Ga x ) 12 O 19 (0 ≤ x ≤ 0.1) powders (see Figure 10). However, the concentration dependence of the resonant frequency for Ba(Fe 1−x Ga x ) 12  Higher fres values in 30 wt.% Ba(Fe1-xGax)12O19/epoxy composites (0.01 ≤ x ≤ 0.1) in comparison with fres in Ba(Fe1-xGax)12O19 (0 ≤ x ≤ 0.1) powders could be explained using the results of magnetic measurements.
As our previous research on BaFe12O19/epoxy polymer composite magnetic properties has shown [24], encapsulation of the magnetic powder in a polymer core leads to a change in chemical bonds on the surface of the particles. This causes a decrease in the saturation magnetization of these magnetic particles and affects the contributions of the surface anisotropy, the shape anisotropy and the interface anisotropy to the net anisotropy. So, polymer coating of fine particles and subsequent changes of their magnetic characteristics (in particular, a decrease in the saturation magnetization) in a polymer composite produces a shift of fres towards higher frequencies.
It is known that the magnitude of the absorption coefficient SEA is in direct proportion to the sample thickness t and can be expressed by the following equation [40]: where σT is total electrical conductivity which is composed of frequency dependent and independent components; μ is the permeability. So, in order to evaluate the influence of the Ga content in hexaferrite fillers on the absorption spectra of 30 wt.% Ba(Fe1-xGax)12O19/epoxy composites (0 ≤ x ≤ 0.1), the adjusted value of the absorption coefficient SEA/t was introduced, and the frequency dependencies of SEA/t are presented in Figure 11.
These data were used for Ares and Wres dependencies on the Ga content calculated for Ba(Fe1-xGax)12O19. These dependencies are presented in Figure 12.
As shown in Figures 11 and 12, Wres decreases monotonically with an increase in the substituent concentration of Ga 3+ . It is obvious that peculiar properties of Ba(Fe1-xGax)12O19 determined the frequency dependence of the EMR absorption process in the Ba(Fe1-xGax)12O19/epoxy composites. As our previous research on BaFe 12 O 19 /epoxy polymer composite magnetic properties has shown [24], encapsulation of the magnetic powder in a polymer core leads to a change in chemical bonds on the surface of the particles. This causes a decrease in the saturation magnetization of these magnetic particles and affects the contributions of the surface anisotropy, the shape anisotropy and the interface anisotropy to the net anisotropy. So, polymer coating of fine particles and subsequent changes of their magnetic characteristics (in particular, a decrease in the saturation magnetization) in a polymer composite produces a shift of f res towards higher frequencies.
It is known that the magnitude of the absorption coefficient SE A is in direct proportion to the sample thickness t and can be expressed by the following equation [40]: where σ T is total electrical conductivity which is composed of frequency dependent and independent components; µ is the permeability. So, in order to evaluate the influence of the Ga content in hexaferrite fillers on the absorption spectra of 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites (0 ≤ x ≤ 0.1), the adjusted value of the absorption coefficient SE A /t was introduced, and the frequency dependencies of SE A /t are presented in Figure 11. These data were used for A res and W res dependencies on the Ga content calculated for Ba(Fe 1−x Ga x ) 12 O 19 . These dependencies are presented in Figure 12.
As shown in Figures 11 and 12, W res decreases monotonically with an increase in the substituent concentration of Ga 3+ . It is obvious that peculiar properties of Ba(Fe 1−x Ga x ) 12    In polycrystalline ferrites, the total NFMR linewidth △H depends crucially on the superposition of intrinsic and extrinsic contributions [41]: where c is the intrinsic linewidth, △Ha is the crystalline anisotropy contribution and△Hp is the porosity induced line broadening contribution. Karim et al. in [42] speculated that barium hexaferrites have an intrinsic linewidth of 0.3-0.4 Oe/GHz. Parameter △Ha~0.7 Ha and relates to the  In polycrystalline ferrites, the total NFMR linewidth △H depends crucially on the superposition of intrinsic and extrinsic contributions [41]: where c is the intrinsic linewidth, △Ha is the crystalline anisotropy contribution and△Hp is the porosity induced line broadening contribution. Karim et al. in [42] speculated that barium hexaferrites have an intrinsic linewidth of 0.3-0.4 Oe/GHz. Parameter △Ha~0.7 Ha and relates to the crystalline anisotropy. Parameter △Hp1.5(4πMS)P accounts for porosity (P) induced linewidth In polycrystalline ferrites, the total NFMR linewidth H depends crucially on the superposition of intrinsic and extrinsic contributions [41]: where c is the intrinsic linewidth, H a is the crystalline anisotropy contribution and H p is the porosity induced line broadening contribution. Karim et al. in [42] speculated that barium hexaferrites have an intrinsic linewidth of 0.3-0.4 Oe/GHz. Parameter Ha~0.7 H a and relates to the crystalline anisotropy. Parameter Hp1.5(4πM S )P accounts for porosity (P) induced linewidth broadening contributions [43,44]. The main role in W res broadening in pure Ba(Fe 1−x Ga x ) 12 O 19 powders with different contents of Ga is played by static inhomogeneities, such as impurity cations, which lead to increases in the magnetocrystalline anisotropy; and W res values increase monotonically, increasing the substitution ratios. As the samples were obtained at the same time and using identical technology, they had identical morphologies in terms of their crystallites. However, it can be supposed that P does not appreciably differ in the samples with different x and the changes of P are negligible. A res and W res increases monotonically with an increase in x in the 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites. However, the values of ∆H were greater than those reported for BaFe 12−x Ga x O 19 , which can be explained by a random distribution of the anisotropy axes in the crystallites and by an increase of porosity and the random orientations of crystallites themselves [45][46][47][48][49]. This cause of A res variation from point to point within the material, in turn, broadening the resonance line.

Conclusions
Ga-substituted barium hexaferrite powders were synthesized via two-step solid state reactions and characterized by XRD and SEM methods. Calculations of the crystallite size of Ba(Fe 1−x Ga x ) 12 O 19 (0.01 ≤ x ≤ 0.1) grains using the Scherrer formula showed that the Ba(Fe 1−x Ga x ) 12 O 19 crystallites we investigated (not grains) are single domain, and the crystallite size remains unchanged in composites with Ba(Fe 1−x Ga x ) 12 O 19 filler. Encapsulation of Ga-substituted barium hexaferrite particles in the epoxy matrix allowed us to prepare microwave absorbing composites. The magnetization-field dependence measurements showed that coercive force H C of Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites increases monotonically from 0.060 to 0.166 T, while the saturation magnetization M S decreases with increasing Ga content in filler. The values of magnetic parameters of Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites were higher than that of pure Ba(Fe 1−x Ga x ) 12 O 19 polycrystalline samples, while the shape of M S (x) dependencies remained unchanged. Calculation of anisotropy field H a and anisotropy constant K 1 for 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites was carried out. Studies of Ba(Fe 1−x Ga x ) 12 O 19/ epoxy composites with different substitution ratio of gallium filler (0.01 ≤ x ≤ 0.1) showed a noticeable effect of Ga content on the microwave characteristics. The most intensive EMR absorption was observed in the 49-54 GHz frequency range for all composites tested, which was attributed to the effect of NFMR in Ba(Fe 1−x Ga x ) 12 O 19 hexaferrites. Higher resonance frequencies of 30 wt.% Ba(Fe 1−x Ga x ) 12 O 19 /epoxy composites (0.01 ≤ x ≤ 0.1) in comparison with resonance frequencies of Ba(Fe 1−x Ga x ) 12 O 19 (0.01 ≤ x ≤ 0.1) powders could be explained by a decrease in the saturation magnetization of the magnetic particles due to their encapsulation in the epoxy which affects the contributions of the surface anisotropy, the shape anisotropy and the interface anisotropy to the net anisotropy. The absorption band W res decreases monotonically with an increase in Ga concentration in the hexaferrite filler while the resonant amplitude A res increases.