M-types hexagonal ferrites like BaFe12O19 and SrFe12O19 with magnetoplumbite structure have been widely investigated and used as a permanent magnet because of their high magnetization (Ms) and coercivity (Hc), low manufacturing cost for industrial production and stability    . Crystal structure of this magnetoplumbite is characterized by close packing of oxygen and Sr ions with Fe atoms at the interstitial positions. The hexagonal Sr-Ferrite has 24 Fe3+ ions per unit cell which are distributed on five different crystallographic sites viz. three octahedral sites, 12k, 2a, and 4f2, one tetrahedral site, 4f1, and one trigonal bipyramidal site, 2b  . Among them, three sites 12k, 2a, and 2b have spin-up, while 4f1 and 4f2 have spin down. Because of the competing effect of these spins, the ferromagnetic coupling is favored with the superexchange between Fe-O-Fe. Therefore, the distance between Fe-O-Fe becomes smaller. This lattice distortion leads to the situation where the magnetic moments of the five Fe sublattices are not mutually parallel. The magnetic structure is a collinear ferrimagnet with a net moment per unit cell of the only 40 μB at 4.2K  . It is known that Fe ions at 2b site provide the largest positive contribution to magnetic moment than at 4f1, 4f2, 2a (relatively weak and positive moments), 12k sites (negative moments)  . Hence, the intrinsic magnetic properties of Sr-Ferrite can be enhanced by substitution for Fe ions in different sites with other suitable ions. The intrinsic magnetic properties of Sr-hexaferrite are found to be affected by the partial substitution for Sr or Fe sites, or both. The different group reported significant improvement on magnetic properties by doping for Sr or Fe sites or both.
A significant improvement in magnetic properties has been reported in SrFe12O19 hexaferrites by the substitution of Sr2+ by rare-earth (RE3+) ions such as by La3+  , Nd3+  , Sm3+   , Gd3+  , Fe3+ ions by magnetic ions such as Co2+   and Cr3+  ions and non-magnetic ions such as Al3+  , Zn3+  , Ga3+  and Cd3+   , and replacement of Sr2+/Fe3+ together with Pr-Zn  , La-Cu  , and La-Zn  . From this reported literature on hexaferrites, it is observed that the insertion of RE3+ into hexaferrite lattice inhibits grain growth, reduces grain size, and thus controls the coercive force for wide practical applications. Recently our group has reported substantial enhancement in coercivity 300% in SrFe8Al4O19 ferrite as compared to that of pure Sr-Ferrite  . The reported enhanced coercivity is attributed to the growth of monodomain particles. As ion size of the RE3+ element is smaller than Sr2+ (1.18 Å)  , Fe3+ would be closer in the O-Fe-O lattice and a stronger interaction might be anticipated, which would result in changed magnetic properties in RE3+ ions doped Sr-Ferrite particles. Overall low concentration of RE3+ substitution for Sr2+ ion has been found effective in improving magnetization of Sr-Ferrite   . So, proper substitution of magnetic RE3+ for Sr2+ and Al3+ for Fe3+ brings enhancement in coercivity of Sr-Ferrites   .
In the present work, we report the effect of co-doping RE3+-Al3+ on magnetic and dielectric properties of Sr0.82RE0.18Fe12-xAlxO19 (x = 0.0, 0.5, 1.0, 1.5, 2.0) nanoparticles. The M-type Sr0.82RE0.18Fe12−xAlxO19 ferrites were prepared via autocombustion method. The process has the advantages of using inexpensive precursors, and the powders obtained are nanosized and homogeneous as compared to ferrites prepared via traditional solid-state reaction, a process which often leaves secondary phases in the compound  .
Sr0.82RE0.18Fe12−xAlxO19 nanocomposite materials were prepared via a one-pot auto combustion method using nitrate salt. All the chemicals required for the synthesis were purchased from Sigma Aldrich. The stoichiometric weight of precursor used for the synthesis of Sr0.82RE0.18Fe12−xAlxO19 composites is listed in Table 1. A stoichiometric amount of RE(NO3)3∙6H2O, Sr(NO3)2, Fe(NO3)3∙9H2O, and Al(NO3)3∙9H2O were dissolved in a minimum amount of deionized water (100 ml for 0.1 mol of Fe3+) by stirring on a hotplate at 60˚C for 30 minutes. Citric acid was dissolved into the solutions to give a molar ratio of metal ions to citric acid of 1:1. NH4OH was added dropwise to the solution until the pH value ~6.5 maintained. Then the solution was heated on a hotplate at 300˚C until gel ignites with the formation of large amounts of gas, resulting in lightweight voluminous powder. The resulting “precursor” powder was calcined at 950˚C for 12 hours to obtain pure Sr0.82RE0.18Fe12−xAl2O19 hexaferrite powder.
Table 1. Details of the chemicals used for 1 g preparation of Sr0.82RE0.18Fe12−xAlxO19.
The balanced chemical reaction during the process is given as:
The crystal phases of the synthesized powders were determined by X-ray diffraction (XRD, Bruker D8 Advance, Germany) using Cu Kα (λ = 1.5406 Å) as the radiation source (40 kV, step size 0.02, scan rate 0.2 min/step, 20˚ ≤ 2θ ≤ 70˚). FTIR spectra were collected in transmission geometry on a disc-shaped sample prepared by mixing KBr 95 Wt% with samples of 5 Wt%. Thermo Nicolet iS 10 was used to collect FTIR spectra. Room temperature magnetic parameters were obtained from demagnetization curves measured using SQUID (Quantum Design, Inc.) with the sweeping magnetic field ± 50 KOe. A 6 mm diameter and 2 mm thick disc were prepared by mixing the powder with PVA Wt% in 200 mg powder samples. The pressure of 5 MPa was applied on samples using a press die. Electric measurement, including resistivity, was performed on the disc-shaped samples in a temperature range up to 190˚C using two probe method (TPR-EXP, SVS Labs, CA, USA). The activation energy was measured using the Arrhenius equation  is given by
where is the activation energy and is the Boltzmann constant. The activation energy in the present case was obtained by fitting the DC resistivity data. Dielectric measurements were performed on the same sample in the low-frequency range from 10 kHz to 10 MHz using HP 4275A Multi-Frequency LCR Meter and high-frequency range from 200 MHz to 13,700 MHz using Field Fox Analyzer (N9915A).
3. Result and Discussion
The room temperature XRD pattern of Sr0.82RE0.18Fe12-xAlxO19 is shown in Figures 1(a)-(c). It is found from the diffraction pattern that samples are single-phase magnetoplumbite structure (ICCD 080-1198) with small additional secondary phase Fe2O3. The phase of the as-prepared ferrite corresponds to the hexagonal P63/mmc symmetry group. The inset of Figure 1 gives the expanded view of the diffracted peaks (107), (200) and (203) between 2θ = 34˚ - 38˚. The peaks are shifting towards higher 2θ values implying the contraction of the lattice with Al3+ substitution. Observed peak broadening with Al3+ content also indicate a decrease in crystallite size of the Sr0.82RE0.18Fe12-xAlxO19. Furthermore, the presence of secondary phase Fe2O3was observed to increase with the atomic weight of the rare-earth viz., Pr3+, Sm3+, Gd3+. Additional, secondary phases, such as Gd(FeO3), PrFe2O3, and SmFe2O3 were also observed. The secondary phase obtained in Pr3+ doped samples is found to be smaller as compared to Sm3+ and Gd3+ doped samples.
The XRD data of all three sets of the sample was fitted and analyzed using
Figure 1. XRD patterns of (a) Sr0.82Pr0.18Fe12-xAlxO19 (b) Sr0.82Sm0.18Fe12-xAlxO19 Sr0.82 (x = 0.0, 0.5, 1.0, 1.5, 2.0). XRD patterns of (c) Sr0.82Gd0.18Fe12-xAlxO19 (x = 0.0, 0.5, 1.0, 1.5, 2.0).
TOPAS software to determine the lattice parameters “a”, “c” and the unit cell volume, “V” of Sr0.82RE0.18Fe12-xAlxO19. Lattice parameters of Sr0.8RE0.18Fe12-xAlxO19 are listed in Table 2 and plotted as a function of RE3+ and Al3+ content in Figures 2(a)-(c). It is observed from Figures 2(a)-(c) that “a” and “c” and “V” decrease at a rate of −0.0238 Å, −0.0979 Å and −8.33 Å3 per Al3+ content, respectively with increasing Al3+ substitution. The decrease in lattice parameters “a” and “c,” and the unit cell volume, “V,” is due to smaller radii of Al3+ (0.535 Å)
Table 2. Lattice parameters “a”, “c” and “V” and crystallite size of Sr0.82RE0.18Fe12−xAlxO19.
Figure 2. Lattice parameter as (a) “a” and (b) “c” (c) volume “V” of Sr0.82RE0.18Fe12-xAlxO19 as a function of Al3+ content (RE3+ = Pr3+, Sm3+, Gd3+, x = 0.0, 0.5, 1.0, 1.5, 2.0).
replacing Fe3+ (0.65 Å)  . It is evident from Table 2 that overall Pr3+-Al3+ substituted samples display higher lattice parameter values as compared to other RE3+ (Sm3+, Gd3+) doped Sr0.82RE0.18Fe12-xAlxO19. The higher lattice parameter value of Pr3+ doped sample results from its bigger ionic radii (1.13 Å) as compared to the radii of Sm3+ (1.098 Å) and Gd3+ (1.078 Å) upon replacing Sr2+ (1.38 Å)  .
The average crystallite size and micro-deformation were determined by using Halder-Wagner-Langford’s (HWL) plot technique applied to the XRD data  . According to HWL, the relationship between FWHM of x-ray diffraction peaks, “β”, with the mean crystallize size, “T”, and the micro-deformation of a grain, “ε”, is given
where β* is given by , λ the x-rays wavelength, and d* is given as . The plot of the Equation (3) is shown in Figures 3(a)-(c).
Figure 3. Halder-Wagner-Langford”s (HWL) plot of (a) Sr0.82Pr0.18Fe12−xAlxO19, (b) Sr0.82Pr0.18Fe12−xAlxO19, and (c) Sr0.82Gd0.18Fe12−x AlxO19 (x = 0.0, 0.5, 1.0, 1.5, 2.0).
Crystallite size and micro-strain deformation measured from the plot is summarized in Table 2. The variation of the crystallite size of Sr0.82Pr0.18Fe12-xAlxO19 as a function of Al3+ content is shown in Figure 4. The decrease in the crystallite size is because RE3+-Al3+ substitution inhibits the grain growth as they enter into grain boundaries and accelerate the formation of secondary phases. The observed secondary phases cause the grain refinement accompanied by reduced strain  .
The mean crystallite size of Sr0.82RE0.18Fe12-xAlx calculated using Halder-Wagner Langford’s (HWL) plot technique follows a decreasing trend with increasing Al3+ content. The measured mean crystallite size of Sr0.82Pr0.18Fe12-xAlxO19 (47.8 to 40.8 nm), Sr0.82Sm0.18Fe12-xAlxO19 (49.4 to 40.1 nm) and Sr0.82Gd0.18Fe12-xAlxO19 (46.3 to 38.6 nm) for x = 0.0 to x = 2.0. It has been observed that the value of crystallite size is highest for Pr3+ and lowest for Gd3+ doped samples in agreement with their ionic radii i.e. Pr3+ (1.13 Å) > Sm3+ (1.098 Å) > Gd3+ (1.078 Å).
Overall observed strain in Gd3+ doped Sr0.82Gd0.18Fe12-xAlxO19 is higher than other RE3+ (Pr3+, Sm3+) doped samples. The higher value of strain in Gd3+ (with spherical 4f charge distribution) doped samples is due to its smaller radii, which may result in the secondary phases as confirmed via XRD   . It has been reported earlier by Lechiviller et al.  that Pr3+, with oblate 4f charge distribution, is easily accommodated in SrFe12O19 unit cell. Thus, our results confirm the fact that the 4f charge symmetry of rare-earth controls the accommodation of RE3+ in SrFe12O19 unit cell. Sm3+ (positive Stevens constant, αJ) and Gd3+ (zero Stevens constant) are thus not as desired as Pr3+ (negative Stevens constant), as the later produces minimum lattice distortion and secondary phases  .
Figure 4. Variation of mean crystallite size of Sr0.82RE0.18Fe12−xAlxO19 as a function of Al3+ content (RE3+ = Pr3+, Sm3+, Gd3+, x = 0.0, 0.5, 1.0, 1.5, 2.0).
Figure 5. FTIR spectra of (a) Sr0.82Pr0.18Fe12−xAlxO19, (b) Sr0.82Sm0.18Fe12−xAlxO19, and (c) Sr0.82Gd0.18Fe12−xAlxO19.
the FTIR spectrum of Sr0.82RE0.18Fe12−xAlxO19 exhibit two high-frequency bands in the range between 900 cm−1 to 400 cm−1. The frequency absorption bands at 609.4 cm−1, and 447.4 cm−1 corresponds to tetrahedral and octahedral M-O stretching vibration of the pure Sr-ferrite, respectively. These absorption bands correspond to the typical absorption of SrFe12O19    . A very approximate bands were also observed in the SrZr0.2Cd0.2Fe11.6O19  . The shifting of absorption bands towards higher frequency has been observed with increasing Al3+ content. This shift in the wavenumber is due to higher energy absorption accompanied by a change in bond-length. Table 3 shows the wavenumber of the corresponding absorption peaks of Sr0.82RE0.18Fe12−xAlxO19. As the wavenumber shift is inversely proportional to the atomic mass, substitution for heavier Fe3+ by lighter Al3+ will thus lead to an increase in wavenumbers  . This shift in wavenumber to the higher values with increasing Al3+ content could also result from the decrease in bond length between Fe3+-O2− in the B-sites with the lattice contraction. The higher wavenumber shift is observed in Pr3+ doped samples as compared to other RE3+ (Sm3+, Gd3+) doping in Sr0.82RE0.18Fe12−xAlxO19. Even though Pr3+ doped Sr0.82RE0.18Fe12−xAlxO19 has a higher lattice volume, the shift in wavenumber to high values suggest tight bonding with near neighbor O2−. This again indicates that RE3+ with negative αj (Pr3+) can fit well into Sr0.82RE0.18Fe12−xAlxO19 unit cell. Also, Pr3+ is lighter than Sm3+ and Gd3+, thus Pr3+-Al3+ display slightly greater shift in wavenumber than Sm3+-Al3+ and Gd3+-Al3+ doped samples  . The vibrations bands are broadened by the substitution of RE3+ ions shown in Figures 5(a)-(c) is due to the decrease in particle size with doping ions  .
Figure 6 shows RT demagnetization curves Sr0.82RE0.18Fe12−xAlxO19 obtained using SQUID. The magnetic parameters saturation magnetization, remanence, and coercivity were extracted from the demagnetization curves and are listed in Table 4. The demagnetization curves show the characteristic behavior of hard ferrites with high coercivity. The saturation magnetization, Ms of Sr0.82RE0.18Fe12−xAlxO19 as a function of Al3+ content, is plotted in Figure 7. The magnetic properties of the substituted ferrite in comparison to pure SrFe12O19 has been changed significantly upon RE3+ and Al3+ substitution in Sr0.82RE0.18Fe12−xAlxO19. On an average
Table 3. Wave numbers for peak 1 and peak 2 of Sr0.82RE0.18Fe12−xAlxO19 obtained from FTIR measurements.
Figure 6. Room temperature demagnetization curves of (a) Sr0.82Pr0.18Fe12−xAlxO19 (b) Sr0.82Sm0.18Fe12−xAlxO19 (c) Sr0.82Gd0.18Fe12−xAlxO19.
Figure 7. Variation of saturation magnetization, Ms, of Sr0.82RE0.18Fe12−xAlxO19 as a function of Al3+ content (RE3+ = Pr3+, Sm3+, Gd3+, x = 0.0, 0.5, 1.0, 1.5, 2.0).
Table 4. Resistivity (×107 Ω-cm) of Sr0.82RE0.18Fe12−xAlxO19 (RE3+ = Pr3+, Sm3+, Gd3+, x = 0.0, 0.5, 1.0, 1.5, 2.0).
the saturation magnetization, Ms decreases linearly with Al3+ content at the rate of −15.8 emu/g per Al3+ substitution.
The Ms value is maximum for Pr3+-Al3+ doped ferrite (62.24 emu/g) and minimum for Gd3+ doped ferrite (56.88 emu/g) for (x = 0). This variation of magnetic properties can be explained based on the site occupancy of the substituted ions. The magnetic moment in M-type hexaferrite is due to the distribution of iron on five non-equivalent sublattices of which three are octahedral (2a, 12k, and 4f2), one tetrahedral (4f1) and one trigonal bipyramidal (2b)  . The sites 12k, 2a, and 2b have upward spins, and 4f1 and 4f2 have a downward spin of electrons. The non-magnetic Al3+ ion replaces Fe3+ ion (5 μB) from the sites having spin up direction, mainly 12k, which is responsible for the reduction in saturation magnetization and remanence of the synthesized materials    .
The decrease in magnetization is also attributed to the lattice contraction with the substitution of RE3+ and Al3+, which changes the bond angle of Fe3+-O2−-Fe3+ and alters the strength of the super-exchange interaction. To maintain the charge neutrality, the substitution of Sr2+ with RE3+ also changes some Fe3+ to Fe2+ and thus further reduces the net magnetic moment per unit volume, causing the decrease in magnetization. The magnetization also decreases due to the increased amount of paramagnetic secondary phases in heavier RE3+ doped Sr0.82RE0.18Fe12−xAlxO19 samples.
The variation of Mr/Ms of Sr0.82RE0.18Fe12−xAlxO19 as a function of Al3+ content is plotted in Figure 8. Most of the samples exhibit the squareness ratio of approximately 0.5. This ratio measures the squareness of the hysteresis loop. According to Stoner-Wohlfarth relation  , a squareness ratio of 0.5 or more indicates that the particles are single magnetic domain while with values much lower than 0.5 indicate the formation of the multidomain structure in the material. The observed Mr/Ms values are very close to 0.5, which indicate the presence of monodomain particles in the sample.
The variation of coercivity of Sr0.82RE0.18Fe12−xAlxO19 as a function of Al3+ content is shown in Figure 9. The coercivity of samples increases linearly with increasing value of Al3+ content. It is observed that the coercivity of the RE3+-Al3+ doped samples is significantly higher than that of coercivity of only Al3+ doped SrFe12−xAlxO19. The coercivity of SrFe12O19 is often associated to the magnetocrystalline anisotropy of trigonal pyramidal 2b site    . The higher concentration of Al3+ doping causes a decrease in a number of Fe3+ ions at 2b
Figure 8. Variation of Mr/Msof Sr0.82RE0.18Fe12−xAlxO19 as a function of Al3+ content (RE3+ = Pr3+, Sm3+, Gd3+, x = 0.0, 0.5, 1.0, 1.5, 2.0).
Figure 9. Variation of coercivity, Hc, of Sr0.82RE0.18Fe12−xAlxO19 as a function of Al3+ content (RE3+ = Pr3+, Sm3+, Gd3+, x = 0.0, 0.5, 1.0, 1.5, 2.0).
sites, which in turn, changes magnetocrystalline anisotropy significantly  . In addition, Al3+ doping case distortion of 2b site, which alters the magnetocrystalline anisotropy of 2b site  . This collective change in anisotropy promotes an increase in coercivity.
Stoner-Wohlfarth relation  shows that Hc = K1/Ms, where K1 is magnetocrystalline anisotropy, and Ms is saturation magnetization. With Al3+ doping, saturation magnetization, Ms decreases thus coercivity, Hc increases. A decrease in saturation magnetization, Ms and changes in K1, enhance the coercivity of Sr0.82RE0.18Fe12-xAlxO19 with Al3+ substitution. The grain size also affects the coercivity since the grain size of Al3+ doped sample is smaller the critical size 560 nm of SrFe12O19  ; the particles in the sample are single domain. In the absence of a domain wall, the energy required to flip the moment is high. Thus, the grain refinement additionally contributes to the coercivity  . Among doped samples, Gd3+-Al3+ doped samples show high coercivity, most likely due to its finer grain size (Table 2) as compared to other RE3+ (Pr3+, Sm3+)-Al3+ doped Sr0.82RE0.18Fe12-xAlxO19 samples.
The variation of Curie temperature, Tc, as a function of Al3+ content for Sr0.82RE0.18Fe12-xAlxO19 is shown in Figure 10, and values are listed in Table 4. From Figure 10, it is observed that Tc is decreasing with Al3+ content. The Tc decreases at the rate of −58˚C per Al3+ content of all the samples. The Pr3+ substituted ferrite exhibits a maximum value of Tc ~ 465.21˚C for x = 0. The following factors affect the Tc; 1) substitution of Al3+ for Fe3+ decreases the number and strength of the super-exchange interaction, Fe3+-O2−-Fe3+, 2) conversion of higher spin Fe3+ to lower spin Fe2+, to maintain charge neutrality, with RE3+ substitution also reduces the strength of super-exchange interaction, and 3) lattice contraction alters the bond length of Fe3+-O2−-Fe3+ from its optimum value. The above-combined factors lead to the reduction in Tc with RE3+-Al3+ substitution. The observed variation of Tc values among RE3+ substituted Sr0.82RE0.18Fe12−xAlxO19 results from subtle difference in exchange interaction ensuing from the variation in the lattice distortion upon inserting rare-earth ions of varying ionic radii.
Figure 10. Variation of Cure temperature, Tc, of Sr0.82RE0.18Fe12−xAlxO19 as a function of Al3+ content (RE3+ = Pr3+, Sm3+, Gd3+, x = 0.0, 0.5, 1.0, 1.5, 2.0).
Figures 11(a)-(c) shows the variation of electrical resistivity as function of temperature of Sr0.82RE0.18Fe12-xAlxO19. It is observed that electrical resistivity decreases with temperature exhibiting semiconducting behavior of samples. It is observed that the Al3+ doping increases electrical resistivity at room temperature. The highest electrical resistivity was observed for Gd3+-Al3+ samples (ρ ~ 15.2 × 107 ohm-cm) while the lowest for Pr3+-Al3+ sample (ρ ~ 1.28 × 107 ohm-cm) for x = 0.0. According to Verwey’s hopping model, the change in carrier mobility with temperature leads to conduction current by hopping electron between Fe3+ ↔ Fe2+ at various sites   . The increasing resistivity with Al3+ content can be explained based on on-site occupancy, grain size, grain boundaries, etc. As Al3+ ion predominantly replaces Fe3+ ion at 12k octahedral sites, it decreases the number of hopping electrons  , leading to an increase in electrical resistivity. The number of Fe2+ and Fe3+ ions is greater in large grain due to which hoping of an electron is easy in the large grain than in smaller grains. Therefore, strontium ferrite with Gd3+-Al3+ doped shows higher resistivity.
Figure 11. Electrical resistivity as a function of temperature for (a). Sr82Pr0.18Fe12−xAlxO19 (b) Sr0.82Sm0.18Fe12−xAlxO19, and (c) Sr0.82Gd0.18Fe12−xAlxO19.
The activation energy was calculated using the Arrhenius equation by plotting ln(ρ) vs. 1000/T. The ln(ρ) vs. 1000/T plots are shown in Figures 12(a)-(c). The slope of these plots gives activation energy and are listed in Table 5. Figure 13 shows the plot of activation energy vs. RE3+-Al3+ content. The activation energy increases with Al3+ content in all set of the samples. The activation energy for Gd3+-Al3+ doped samples is higher than Sm3+-Al3+and Pr3+-Al3+ doped samples
Table 5. Activation energy (eV) of Sr0.82RE0.18Fe12−xAlxO19 (RE3+ = Pr3+, Sm3+, Gd3+, x = 0.0, 0.5, 1.0, 1.5, 2.0).
Figure 12. Plot of ln(ρ) as a function of 1000/T for Sr0.82RE0.18Fe12−xAlxO19 (RE3+ = Pr3+, Sm3+, Gd3+, x = 0.0, 0.5, 1.0, 1.5, 2.0).
Figure 13. Variation of activation energy of Sr0.82RE0.18Fe12−xAlxO19 as a function of Al3+ content (RE3+ = Pr3+, Sm3+, Gd3+, x = 0.0, 0.5, 1.0, 1.5, 2.0).
due to reduced grain size and increased grain boundaries. The activation energy was observed to increase with decreasing ionic radii of RE3+  . The increase in activation energy with increasing RE3+-Al3+ means that higher energy is required to eject the trapped electron and participate in the conduction mechanism. Also, higher activation energy and enhanced DC resistivity with RE3+ substitution are due to the formation of a small amount of additional phases REFeO2  .
The variation of dielectric constant and tangent loss (δ) of Sr0.82RE0.18Fe12−xAlxO19 was measured as a function of frequency at room temperature. The dielectric behavior of each sample was found different depending upon types of RE3+ and Al3+ content. RE3+-Al3+ dependence of dielectric constant as function of frequency for Sr0.82RE0.18Fe12-xAlxO19 in low (100 Hz - 10 MHz) and high (200 MHz - 13,700 MHz) frequency range shown in Figures 14-16. It is observed that dielectric constant decreases with the increase in frequency in the low-frequency range. However, in the high-frequency range, the dielectric constant initially decreases and becomes constant at above f ≈ 3.5 GHz.
The variation of dielectric constant at frequency shows the dispersion due to Maxwell-Wagner type interfacial polarization  associated with Koop’s phenomenological theory  . Based on these models, the dielectric structure of the ferrite consists of well-conducting grains, separated by highly resistive thin layer grain boundaries formed during the sintering process   . At low frequency, there is a large value of dielectric constant due to the grain boundary defects, interfacial dislocation, oxygen vacancies, etc.  . At low frequency, applied alternating voltage on the ferrite drops across the thin grain boundaries so that space charge polarization is set up across the grain boundaries. The space charge
Figure 14. (a) Dielectric Constant and (b) tangent loss of Sr0.82Pr0.18Fe12−xAlxO19 as a function of frequency in low and high frequency range.
Figure 15. (a) Dielectric Constant and (b) tangent loss of Sr0.82Sm0.18Fe12−xAlxO19 as a function of frequency in low and high frequency range.
Figure 16. (a) Dielectric Constant and (b) tangent loss of Sr0.82Gd0.18Fe12−xAlxO19 as a function of frequency in low and high frequency range.
polarization is governed by the available free charges on the grain boundaries and conductivity of the sample  . For high-frequency range, the dielectric constant decreases with increasing frequency of an external field and become frequency-independent due to the fact that electron hopping between Fe2+ and Fe3+ cannot follow the alternating field means that frequency of exchange electrons lags behind the frequency of the applied field   . The dielectric constant of all set of samples remains almost constant in GHz range, but a sudden drop at ~12.7 GHz is observed due to the fact that the frequency of hopping electron between Fe3+ and Fe2+ becomes equal to the frequency of the applied alternating field leading to the resonance absorption. The dielectric loss factor decreases with increasing frequency for all sets of samples. The origin of dielectric loss in ferries came from electron hopping in response to low frequency and charged dipole defects response to high frequency  . The dielectric loss factor is minimum for Gd3+-Al3+ samples, which is attributed to the smallest radial size used among three sets of samples  .
The structural, magnetic, and electrical properties of Re3+-Al3+ substitution in Sr0.82RE0.18Fe12−xAlxO19 hexaferrite synthesized via auto-combustion were investigated. The room temperature magnetization was observed to decrease with increase in Al3+ substitution in Sr0.82RE0.18Fe12−xAlxO19 due to the magnetic dilution effect, reduction in Fe3+-O2−-Fe3+ strength due to lattice contraction, reduction in a number of super-exchange interactions, and conversion of Fe3+ to Fe2+ with RE3+ substitution. The substitution of Al3+ for Fe3+ was observed to increase the coercivity of Sr0.82RE0.18Fe12−xAlxO19. The increase in coercivity is attributed to a reduction in grain size leading monodomain grains and change in magnetocrystalline anisotropy. A maximum value of 12.21 KOe coercivity was observed for Sr0.82Gd0.18Fe12−xAlxO19 as it also has the smallest grain size among all rare-earth substituted Sr0.82RE0.18Fe12−xAlxO19. Our study suggests that magnetic RE3+ enhances coercivity but have a detrimental effect on the saturation magnetization. The oblate charge distribution of Pr3+ ions with Stevens’s constant αj ~ −2.2 × 10−2 gets well fitted in the lattice sites, which brings the desired high coercivity. The variation of magnetic properties arises due to the change in magneto-crystalline anisotropy attributed to the site occupancy of RE3+ and Al3+ ions. The Tc value was observed to decrease with Al3+ substitution due to a reduction in super-exchange interactions. The DC electrical resistivity of Sr0.82RE0.18Fe12−xAlxO19 was observed to decrease with increase in temperature. The activation energy was observed to be highest for Gd3+ doped Sr0.82Gd0.18Fe12−xAlxO19, which is attributed to increased grain boundaries and reduced grain size. The dielectric constant and dielectric loss were observed to decrease with frequency. This behavior of dielectric constant was attributed to the lagging of hopping electrons behind the applied alternating field. Also, dielectric constant decreases with the Al3+ content due to a reduced number of Fe3+ ions. As the coercivity and resistivity can be increased without much affecting the magnetization, RE3+ substitution in the strontium ferrite is beneficial for microwave devices.