Structural, Magnetic, and Electrical Properties of RE Doped Sr_0.82RE_0.18Fe_12-xAl_xO₁₉ (RE = Gd, Pr, Sm) Compound

Among the family of ferrites, M-type hexaferrites has many industrial applications ranging from simple magnets to microwave devices. Improvement in magnetic and dielectric properties of ferrites is of continuous interest. In this present work details study is done to observe the effect of co-doping of rare- earth (RE³⁺: Pr³⁺, Sm³⁺, and Gd³⁺) and aluminum in Sr_0.82RE_0.18Fe_12-xAl_xO₁₉ (x = 0.0, 0.5, 1.0, 1.5, 2.0). The adopted samples were synthesized via autocombustion technique. Detailed synthesis, structural, magnetic, and electrical measurements of samples were performed to understand structural-magnetic-elec trical property relationship. The Al³⁺ substitution for Fe³⁺ brings in a significant enhancement in coercivity but reduces magnetization due to the magnetic dilution effect. Additional coercivity enhancement was possible with RE³⁺ doping without affecting the magnetization of samples. Among all RE³⁺ doped samples, Pr³⁺ doped samples showed the highest Curie temperature, (T_c ~ 465 ℃ ), while Gd ³⁺ doped samples showed little variation in dielectric properties in GHz frequency range. This makes RE³⁺ doped samples as an ideal candidate for high-frequency microwave applications. Pr³⁺ with oblate charge distribution (negative Stevens constant) was observed to substitute well into the lattice consequently bringing in desired improvements in physical properties of Sr_0.82RE_0.18Fe_12-xAl_xO₁₉ ferrite.

• Sr-Ferrite
• Nanocomposite
• Magnetization
• Curie Temperature
• Coercivity
• Dielectric Constant

1. Introduction

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 (M_s) and coercivity (H_c), low manufacturing cost for industrial production and stability [1] [2] [3] . 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 [4] . 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 [5] . 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) [6] . 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⁺ [7] , Nd³⁺ [8] , Sm³⁺ [9] [10] , Gd³⁺ [11] , Fe³⁺ ions by magnetic ions such as Co²⁺ [12] [13] and Cr³⁺ [14] ions and non-magnetic ions such as Al³⁺ [15] , Zn³⁺ [16] , Ga³⁺ [17] and Cd³⁺ [18] [19] , and replacement of Sr²⁺/Fe³⁺ together with Pr-Zn [20] , La-Cu [21] , and La-Zn [22] . 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 [23] . 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) [24] , 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 [25] [26] . So, proper substitution of magnetic RE³⁺ for Sr²⁺ and Al³⁺ for Fe³⁺ brings enhancement in coercivity of Sr-Ferrites [15] [23] .

In the present work, we report the effect of co-doping RE³⁺-Al³⁺ on magnetic and dielectric properties of Sr_0.82RE_0.18Fe_12-xAl_xO₁₉ (x = 0.0, 0.5, 1.0, 1.5, 2.0) nanoparticles. The M-type Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 [15] .

2. Experimental

Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 Sr_0.82RE_0.18Fe_12−xAl₂O₁₉ hexaferrite powder.

Table 1

Details of the chemicals used for 1 g preparation of Sr 0.82 RE 0.18 Fe 12−x Al x O 19

	Weight (g)
Pr doped Samples	Sr(NO3)2	Pr (NO3)3∙6H2O	Fe(NO3)3∙9H2O	Al(NO3)3∙9H2O	Citric Acid
Sr0.82Pr0.18Fe12O19	0.16116	0.05684	4.5173	0.000	2.5454
Sr0.82Pr0.18Fe11.5Al0.5O19	0.16391	0.05761	4.3854	0.1772	2.5803
Sr0.82Pr0.18Fe11Al1O19	0.16618	0.05842	4.2558	0.3592	2.6162
Sr0.82Pr0.18Fe10.5Al1.5O19	0.16853	0.05924	4.1195	0.5465	2.6528
Sr0.82Pr0.18Fe10Al2O19	0.1706	0.05997	3.9716	0.7376	2.6856
Sm doped Samples	Sr(NO3)2	Sm(NO3)3∙6H2O	Fe(NO3)3∙9H2O	Al(NO3)3∙9H2O	Citric Acid
Sr0.82Sm0.18Fe12O19	0.1618	0.07461	4.5226	0.000	2.5484
Sr0.82Sm0.18Fe11.5Al0.5O19	0.1641	0.07565	4.3933	0.1774	2.5832
Sr0.82Sm0.18Fe11Al1O19	0.1663	0.07669	4.2605	0.3596	2.6189
Sr0.82Sm0.18Fe10.5Al1.5O19	0.1687	0.07777	4.1238	0.5471	2.6557
Sr0.82Sm0.18Fe10Al2O19	0.1712	0.07896	3.9874	0.7405	2.6963
Gd doped Samples	Sr(NO3)2	Gd(NO3)3∙6H2O	Fe(NO3)3∙9H2O	Al(NO3)3∙9H2O	Citric Acid
Sr0.82Gd0.18Fe12O19	0.1615	0.07562	4.5124	0.000	2.5427
Sr0.82Gd0.18Fe11.5Al0.5O19	0.1637	0.07655	4.3833	0.1769	2.5773
Sr0.82Gd0.18Fe11Al1O19	0.1659	0.07771	4.2506	0.3588	2.6129
Sr0.82Gd0.18Fe10.5Al1.5O19	0.1683	0.07879	4.1142	0.5457	2.6495
Sr0.82Gd0.18Fe10Al2O19	0.1707	0.07991	3.9739	0.7379	2.6872

The balanced chemical reaction during the process is given as:

0.82 Sr ( NO 3 ) 2 + 0.18 RE ( NO 3 ) 3 + ( 12 − x ) Fe ( NO 3 ) 3 + x Al ( NO 3 ) 3 + C 6 H 8 O 7 + NH 4 OH → Sr 0.82 RE 0.18 Fe 12 − x Al x O 19 + NH 4 NO 3 + CO 2 + H 2 O (1)

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 [25] is given by

ρ = ρ 0 exp ( E a K B T ) (2)

where E a is the activation energy and K B 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 Sr_0.82RE_0.18Fe_12-xAl_xO₁₉ 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 Sr_0.82RE_0.18Fe_12-xAl_xO₁₉. 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

TOPAS software to determine the lattice parameters “a”, “c” and the unit cell volume, “V” of Sr_0.82RE_0.18Fe_12-xAl_xO₁₉. Lattice parameters of Sr_0.8RE_0.18Fe_12-xAl_xO₁₉ 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 ų 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 Sr 0.82 RE 0.18 Fe 12−x Al x O 19

Samples	a (Å)	c (Å)	V (Å3)	Crystallite size (HWL) nm	Micro deformation (-ε)
Sr0.82Pr0.18Fe12O19	5.88563	23.0744	692.224	47.8	0.0049
Sr0.82Pr0.18Fe11.5Al0.5O19	5.86557	22.9962	685.183	45.7	0.0049
Sr0.82Pr0.18Fe11Al1O19	5.85534	22.9462	680.397	44.0	0.0051
Sr0.82Pr0.18Fe10.5Al1.5O19	5.84753	22.9147	678.562	42.9	0.005
Sr0.82Pr0.18Fe10Al2O19	5.83511	22.8703	674.699	40.8	0.0054
Sr0.82Sm0.18Fe12O19	5.87716	23.0498	689.493	49.4	0.0042
Sr0.82Sm0.18Fe11.5Al0.5O19	5.86394	22.9882	684.475	44.9	0.0052
Sr0.82Sm0.18Fe11Al1O19	5.85402	22.9404	678.345	42.7	0.005
Sr0.82Sm0.18Fe10.5Al1.5O19	5.84225	22.8972	676.823	41.7	0.005
Sr0.82Sm0.18Fe10Al2O19	5.83245	22.8635	673.558	40.1	0.0055
Sr0.82Gd0.18Fe12O19	5.87874	23.0475	688.891	46.3	0.0042
Sr0.82Gd0.18Fe11.5Al0.5O19	5.86246	22.9741	683.799	42.1	0.0052
Sr0.82Gd0.18Fe11Al1O19	5.84994	22.9343	676.984	40.5	0.0048
Sr0.82Gd0.18Fe10.5Al1.5O19	5.83809	22.8907	674.356	39.7	0.0057
Sr0.82Gd0.18Fe10Al2O19	5.83107	22.8607	673.157	38.6	0.0059

replacing Fe³⁺ (0.65 Å) [24] . 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 Sr_0.82RE_0.18Fe_12-xAl_xO₁₉. 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) [24] .

The average crystallite size and micro-deformation were determined by using Halder-Wagner-Langford’s (HWL) plot technique applied to the XRD data [26] . 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

( β * d * ) 2 = 1 T ( β * d * 2 ) + ( ε 2 ) 2 (3)

where β^* is given by β ∗ = β λ cos ( θ ) , λ the x-rays wavelength, and d^* is given as d ∗ = 2 λ sin ( θ ) . The plot of the Equation (3) is shown in Figures 3(a)-(c).

Crystallite size and micro-strain deformation measured from the plot is summarized in Table 2. The variation of the crystallite size of Sr_0.82Pr_0.18Fe_12-xAl_xO₁₉ 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 [27] .

The mean crystallite size of Sr_0.82RE_0.18Fe_12-xAl_x calculated using Halder-Wagner Langford’s (HWL) plot technique follows a decreasing trend with increasing Al³⁺ content. The measured mean crystallite size of Sr_0.82Pr_0.18Fe_12-xAl_xO₁₉ (47.8 to 40.8 nm), Sr_0.82Sm_0.18Fe_12-xAl_xO₁₉ (49.4 to 40.1 nm) and Sr_0.82Gd_0.18Fe_12-xAl_xO₁₉ (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 Sr_0.82Gd_0.18Fe_12-xAl_xO₁₉ 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 [28] [42] . It has been reported earlier by Lechiviller et al. [29] 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, α_J) 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 [30] .

FTIR spectra of Sr_0.82RE_0.18Fe_12-xAl_xO₁₉ is shown in Figure 5. From Figure 5,

the FTIR spectrum of Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 [31] [32] [33] . A very approximate bands were also observed in the SrZr_0.2Cd_0.2Fe_11.6O₁₉ [18] . 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 Sr_0.82RE_0.18Fe_12−xAl_xO₁₉. 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 [27] . 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 Sr_0.82RE_0.18Fe_12−xAl_xO₁₉. Even though Pr³⁺ doped Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 α_j (Pr³⁺) can fit well into Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 [34] . 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 [35] .

Figure 6 shows RT demagnetization curves Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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, M_s of Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 Sr_0.82RE_0.18Fe_12−xAl_xO₁₉. On an average

Table 3

Wave numbers for peak 1 and peak 2 of Sr 0.82 RE 0.18 Fe 12−x Al x O 19 obtained from FTIR measurements

Al3+ content,	Wave-number( cm−1)		Wave-number (cm−1)		Wave-number (cm−1)
x	for Pr3+-Al3+ samples		for Sm3+-Al3+-doped samples		for Gd3+-Al3+-doped samples
	Peak 1	Peak 2	Peak 1	Peak 2	Peak 1	Peak 2
0.0	447.40	609.40	447.40	609.4	447.40	609.40
0.5	455.12	617.11	455.12	617.11	445.12	617.11
1.0	462.83	624.82	455.12	617.11	455.12	617.11
1.5	462.83	624.82	455.12	624.82	462.83	624.82
2.0	470.55	632.54	462.83	624.82	462.83	624.82

Table 4

Resistivity (×10 7 Ω-cm) of Sr 0.82 RE 0.18 Fe 12−x Al x O 19 (RE 3+ = Pr 3+ , Sm 3+ , Gd 3+ , x = 0.0, 0.5, 1.0, 1.5, 2.0)

Composition	x = 0.0	x = 0.5	x = 1.0	x = 1.5	x = 2.0
Sr0.82Pr0.18Fe12−xAlxO19	0.1498	0.1828	0.1983	1.1940	1.286
Sr0.82Sm0.18Fe12−xAlxO19	0.1262	0.1521	0.7061	0.9106	1.145
Sr0.82Gd0.18Fe12−xAlxO19	1.0580	10.222	10.920	10.223	15.24

the saturation magnetization, M_s decreases linearly with Al³⁺ content at the rate of −15.8 emu/g per Al³⁺ substitution.

The M_s 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) [4] . 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 μ_B) from the sites having spin up direction, mainly 12k, which is responsible for the reduction in saturation magnetization and remanence of the synthesized materials [15] [36] [37] .

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 Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ samples_.

The variation of M_r/M_s of Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 [38] , 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 M_r/M_s values are very close to 0.5, which indicate the presence of monodomain particles in the sample.

The variation of coercivity of Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 SrFe_12−xAl_xO₁₉. The coercivity of SrFe₁₂O₁₉ is often associated to the magnetocrystalline anisotropy of trigonal pyramidal 2b site [15] [39] [40] . The higher concentration of Al³⁺ doping causes a decrease in a number of Fe³⁺ ions at 2b

sites, which in turn, changes magnetocrystalline anisotropy significantly [15] . In addition, Al³⁺ doping case distortion of 2b site, which alters the magnetocrystalline anisotropy of 2b site [41] . This collective change in anisotropy promotes an increase in coercivity.

Stoner-Wohlfarth relation [38] shows that H_c = K₁/M_s, where K₁ is magnetocrystalline anisotropy, and M_s is saturation magnetization. With Al³⁺ doping, saturation magnetization, M_s decreases thus coercivity, H_c increases. A decrease in saturation magnetization, M_s and changes in K₁, enhance the coercivity of Sr_0.82RE_0.18Fe_12-xAl_xO₁₉ 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 [4] ; 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 [23] . 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 Sr_0.82RE_0.18Fe_12-xAl_xO₁₉ samples.

The variation of Curie temperature, T_c, as a function of Al³⁺ content for Sr_0.82RE_0.18Fe_12-xAl_xO₁₉ is shown in Figure 10, and values are listed in Table 4. From Figure 10, it is observed that T_c is decreasing with Al³⁺ content. The T_c decreases at the rate of −58˚C per Al³⁺ content of all the samples. The Pr³⁺ substituted ferrite exhibits a maximum value of T_c ~ 465.21˚C for x = 0. The following factors affect the T_c; 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 T_c with RE³⁺-Al³⁺ substitution. The observed variation of T_c values among RE³⁺ substituted Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ results from subtle difference in exchange interaction ensuing from the variation in the lattice distortion upon inserting rare-earth ions of varying ionic radii.

Figures 11(a)-(c) shows the variation of electrical resistivity as function of temperature of Sr_0.82RE_0.18Fe_12-xAl_xO₁₉. 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 [42] [43] . 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 [17] , 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.

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 Sr 0.82 RE 0.18 Fe 12−x Al x O 19 (RE 3+ = Pr 3+ , Sm 3+ , Gd 3+ , x = 0.0, 0.5, 1.0, 1.5, 2.0)

Composition	x = 0	x = 0.5	x = 1	x = 1.5	x = 2
Sr0.82Pr0.18Fe12−xAlxO19	0.2319	0.254	0.2972	0.312	0.3623
Sr0.82Sm0.18Fe12−xAlxO19	0.2692	0.297	0.3271	0.342	0.3875
Sr0.82Gd0.18Fe12−xAlxO19	0.3633	0.4158	0.4283	0.436	0.4532

due to reduced grain size and increased grain boundaries. The activation energy was observed to increase with decreasing ionic radii of RE³⁺ [44] . 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 [45] .

The variation of dielectric constant and tangent loss (δ) of Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 Sr_0.82RE_0.18Fe_12-xAl_xO₁₉ 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 [46] associated with Koop’s phenomenological theory [47] . 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 [22] [48] . At low frequency, there is a large value of dielectric constant due to the grain boundary defects, interfacial dislocation, oxygen vacancies, etc. [49] . 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

polarization is governed by the available free charges on the grain boundaries and conductivity of the sample [50] . 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 [36] [43] . 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 [48] . The dielectric loss factor is minimum for Gd³⁺-Al³⁺ samples, which is attributed to the smallest radial size used among three sets of samples [51] .

4. Conclusion

The structural, magnetic, and electrical properties of Re³⁺-Al³⁺ substitution in Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ hexaferrite synthesized via auto-combustion were investigated. The room temperature magnetization was observed to decrease with increase in Al³⁺ substitution in Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ 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 Sr_0.82RE_0.18Fe_12−xAl_xO₁₉. 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 Sr_0.82Gd_0.18Fe_12−xAl_xO₁₉ as it also has the smallest grain size among all rare-earth substituted Sr_0.82RE_0.18Fe_12−xAl_xO₁₉. 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 α_j ~ −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 T_c value was observed to decrease with Al³⁺ substitution due to a reduction in super-exchange interactions. The DC electrical resistivity of Sr_0.82RE_0.18Fe_12−xAl_xO₁₉ was observed to decrease with increase in temperature. The activation energy was observed to be highest for Gd³⁺ doped Sr_0.82Gd_0.18Fe_12−xAl_xO₁₉, 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.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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