Structural, Magnetic Properties and Electron Paramagnetic Resonance for BaFe_12-xHg_xO₁₉ Hexaferrite Nanoparticles Prepared by Co-Precipitation Method

Abstract

Barium hexaferrite nanoparticles are synthesized through co-precipitation technique at different annealing temperature. Series of BaFe_12-xHg_xO₁₉ nanoparticles, 0.00 ≤ x ≤ 0.30, are prepared under the best verified conditions (annealed at 1000°C) to investigate the effect of partial substitution of Hg²⁺ ions on the physical properties of BaFe₁₂O₁₉ nanoparticles. The hysteresis loops at room temperature show the behavior of hard ferromagnetic. The estimated values of saturation magnetization $M_s$, remnant magnetization $M_r$ and magnetic moment $m_B$ rise as Hg²⁺ ions content increases till x = 0.10, beyond which they reduce. A reverse trend is obtained for intrinsic coercivity Hi and coercivity Hc versus Hg²⁺ ions content. BaFe_12-xHg_xO₁₉ nanoparticles are investigated through the measurements of electron paramagnetic resonance (EPR). The calculated EPR parameters show an enhancement for BaFe_12-xHg_xO₁₉ nanoparticles up to x = 0.10. The obtained results reveal that samples under investigation can be suitable candidate for different industrial applications.

KEYWORDS:

• M-type hexagonal ferrites
• XRD
• TEM
• EPR
• Co-precipitation

1. Introduction

One type of magneto-plumbite group of oxides is M-type hexagonal ferrites with formula MFe₁₂O₁₉ (M = Ba, Sr). Specific attention for barium hexaferrite BaFe₁₂O₁₉ is always increasing as a result of its large saturation magnetization, strong uniaxial magnetic anisotropy, high Curie temperature, better coercivity, good chemical stability and perfect corrosion resistivity, as well as its low price for production [1]. Therefore, it plays an important role in the magnetic media as the production of permanent magnetic materials, microwave devices and magnetic recording media [2–5].

The structural and magnetic properties for BaFe₁₂O₁₉ can be achieved either by the substitution with different ions or by using different preparation techniques. The magnetic properties of barium hexaferrite can be enhanced by the partially ions substitution, especially at Fe³⁺ site either with di-, tri- or tetravalent ions [6,7]. The partial ions substitution at Fe³⁺ site leads to change the net magnetic moment per unit and tailor magnetic properties of BaFe₁₂O₁₉. The enhancement of the net magnetization for this magnetic material can be occurred when the substituted ions occupy spin down sites [8]. Many researchers [9–12] have been investigated the impact of using the suitable transition ions substation ratio at Fe site on coercivity, anisotropy and saturation magnetization for barium hexaferrite. A significant change in both magnetic and structural properties was obtained as a result of the influence of transition ions on the grains growth. On the other hand, the structural and lattice parameters, crystallite and grain sizes, as well as the dislocation density of hexaferrite samples were strongly affected by the composition and preparation conditions. Several techniques can be used for synthesizing hexaferrites such as micro-emulsion [13], sol–gel [14,15], combustion [16], co-precipitation [17], hydro-thermal [18], etc. The most efficient technique for preparing hexaferrites is co-precipitation technique due to its low cost, energy-efficient, easy method and short reaction time [19].

The aim of the present study is not only to obtain the optimum calcination temperature of the preparation of barium hexaferrite nanoparticles by the chemical co-precipitation method but also to study the effect of Hg²⁺ ions substitution on the structural and magnetic properties of it. In order to improve its properties to be a suitable candidate in for different industrial application.

2. Experimental techniques

2.1. Samples preparation

Barium hexaferrite nanoparticles, BaFe₁₂O₁₉ were synthesized by an efficient co-precipitation technique at different annealing temperature (700, 800, 900 and 1000°C) to obtain the optimum annealing temperature necessary for achieving pure phase of barium hexaferrite. The starting materials for this synthesis are barium chloride, (BaCl₂.2H₂O), ferric chloride (FeCl₃) and sodium hydroxide (NaOH). Stoichiometric amounts ratios of these chlorides were dissolved in distilled water, then mixed through magnetic stirrer at 60°C. An alkaline solution (NaOH) was put into the salt solution till pH was reached to 12.0. The resulting solution was heated at 90°C with continuous stirring for two hours. The precipitate was collected by magnet and washed with distilled water many times until the pH of the filtrate reached to 7.0 in order to remove unwanted impurities. Then, the precipitate was dried at 80°C. Finally, the dried powders were put into a ceramic crucible and annealed at different temperatures: 700°C (B-700), 800°C (B-800), 900°C (B-900) and 1000°C (B-1000) for four hours and followed by a slow cooled to room temperature. Nanoparticle samples were finally ground to fine nano powder.

In order to investigate the effect of partial substitution of Hg²⁺ ions on BaFe₁₂O₁₉ nanoparticles, a series of BaFe_12-xHg_xO₁₉ nanoparticle, x = 0.00, 0.05. 0.10, 0.20 and 0.30, were synthesized through the indicated co-precipitation technique under the best verified conditions (annealed at 1000°C).

2.2. Measurements

Phase identification of barium hexaferrite is carried out by X-ray powder diffractometer (Bruker D8 advance) with Cu-Kα radiation (λ = 1.54056 Å) in 2θ range 10–80°.

The lattice parameters $a$ and $c$ are determined using the following formula [20]: (1) $d_{hkl}={\left(\frac{4(h^2+hk+k^2}{3a^2}+\frac{l^2}{c^2}\right)}^{-1/2}$(1) where $d_{hkl}$ is the crystal face distance and ($hkl$) are the Miller indices.

The unit cell volume for barium hexaferrite can be estimated using the lattice parameters $a$ and $c$ from the following relation: (2) $V=\frac{\surd 3}{2}{a}^{2}c$(2) The theoretical (X-ray) density (${\rho }_x$) and bulk density (${\rho }_b$) of the prepared powders are determined by applying Eqs.3,4, respectively. (3) ${\rho }_x=\frac{Z{M}_{wt}}{N_{A}V}$(3) (4) ${\rho }_b=\frac{m}{\pi r^{2}h},$(4) where Z = 2 indicating 2 formula units, $M_{wt}$ is material molecular weight, m is the pellet mass, r is the pellet radius and h is the pellet thickness.

The percentage porosity ($P\mathrm{\%}$) of the samples is estimated in terms of both the theoretical and bulk densities of the samples as follows [21]: (5) $P\mathrm{\%}=\left(1-\frac{{\rho }_b}{{\rho }_x}\right)\times 100$(5) The average nanoparticle size is determined using Jeol transmission electron microscope JEM- 2100, carried out at 200 kV through dispersing the powders in diluted HCl on a copper grid. The elemental compositions of barium hexaferrites are studied by scanning electron microscopy (SEM/ EDS; JSM-7200F). Infrared absorption spectra of the samples are recorded in the range of 400–4000 cm⁻¹ using FTIR 8400S Shimadzu spectrophotometer. The magnetic properties of the prepared samples are studied by vibrating sample magnetometer VSM, Lakeshore 7410, at room temperature. EPR spectra are measured by EPR spectrometer, Bruker Elexsys 500, at room temperature.

3. Results and discussion

In order to study the effect of annealing temperature on phase formation, the percentage, the type of impurities formed and crystallite size were determined. XRD analysis was applied on the samples. Figure 1 shows XRD pattern of the barium hexaferrite, BaFe₁₂O₁₉, samples annealed at different temperatures 700°C (B-700), 800°C (B-800), 900°C (B-900) and 1000°C (B-1000). The estimated values of crystallite size and lattice parameters at different annealing temperature are listed in Table 1. Table 1 clarifies that with increasing temperature, the percentage of intermediate phase Fe₂O₃ decreases, while the percentage of barium hexaferrite increases until reached to single phase at annealing temperature 1000°C. The crystallite size increases with increasing annealing temperature as a result of the tendency of particles, where they are collected together and form large particles. The estimated value of lattice parameters for samples B-700, B-800 and B-900 are inconsistent with the reported values as a result of the presence of impurities beside the basic phase. On the other hand, the lattice parameters for sample B-1000 are consistent with published values [22,23].

Figure 1. XRD patterns of BaFe₁₂O₁₉ nanoparticles annealed at different temperatures.

Table 1. Barium hexaferrite and intermediate impurity phase percentages, lattice constants and average crystallite size for BaFe₁₂O₁₉ nanoparticles prepared at different annealing temperature.

Sample	BaFe12O19 (%)	Fe2O3 (%)	a (Å)	c (Å)	L (nm)
B-700	69.7	31.3	5.870	23.239	32.88
B-800	82.2	17.8	5.875	23.206	34.76
B-900	91.0	9.0	5.809	23.234	35.45
B-1000	100	0.0	5.893	23.132	36.08

Figure 2 shows XRD patterns of hexaferrite BaFe_12-xHg_xO₁₉ nanoparticles annealed at 1000°C for 4 h, x = 0.00, 0.05, 0.10, 0.20 and 0.30. All diffraction peaks in the pattern were belonging to those of M-type barium hexaferrite BaFe₁₂O₁₉ with space group P63/mmc (194) from JCPDS card number 01-084-0757. From the diffraction patterns, they show the crystallite as single phase of the prepared samples, with no impurity phases. The calculated lattice parameters for undoped sample, $a$ = 5.893 Å and $c$ = 23.132 Å, are consistent with JCPDS card number 01-084-0757 [24]. Figure 3 shows the lattice parameters variation versus x. It is seen that the lattice parameter $c$ increases with increasing x, while the lattice parameter $a$ slightly decreases. The increase in $c$ can be attributed to the partial substitution of the smaller ionic radius Fe³⁺ ions (0.64 Å) by larger ionic radius Hg²⁺ ions (1.02 Å). More variation is observed for lattice parameter $c$ because of c-axis is easy axis which the spins can freely rotate around this axis, comparing with a-axis. The ratio $c/a$ has been calculated for all the prepared samples and found to be in the range 3.925–3.983, confirming with Vegard’s law as the ratio $c/a$ should be less than 3.98 for M-type hexaferrite [24]. Moreover, the unit cell volume decreases from 695.688 ų for x = 0.00–688.106 ų for x = 0.30 (Table 2). This decrease is due to the strongly dependence of unit cell volume on $a$ ($V$ α $a^2$) more than $c.$ The calculated values of X-ray density (${\rho }_x$), bulk density (${\rho }_b$) and percentage of porosity ($P\mathrm{\%}$) are listed in Table 2 versus Hg⁺² ions content. It is displayed the increase of (${\rho }_x$) and (${\rho }_b$) with increasing x, which is attributed to the larger atomic weight and density of Hg 200.59 g mol⁻¹ and 13.56 g cm⁻³, respectively, comparing with Fe of density 7.87 g cm⁻³ and atomic weight 55.84 g mol⁻¹. It is observed that ${\rho }_x$ is higher than ${\rho }_b$ due to the presence of pores which affected by sintering temperature [25] and the syntheses conditions [26]. The results showed that porosity follows the inverse behaviour of ${\rho }_x$, it is found to increase as the Hg²⁺ ion content increases. The increase in porosity may be attributed to the diminution of oxygen vacancies or the formation of a solid solution [27].

Figure 2. XRD patterns of BaFe_12-xHg_xO₁₉ nanoparticles annealed at 1000°C for 4 h.

Figure 3. The variation of the lattice parameters $a$ and $c$ versus Hg²⁺ ions content.

Table 2. XRD parameters of BaFe_12-xHg_xO₁₉ nanoparticles annealed at 1000°C for 4 h.

Hg^2+ ions content (x)	a (Å)	c (Å)	c/a	$V$ (Å^3)	${\rho }_x$ (g/cm^3)	${\rho }_b$ (g/cm^3)	$P$%	L (nm)	w (nm)
0.00	5.893	23.132	3.925	695.688	5.31	3.76	28.94	36.077	46.955
0.05	5.883	23.138	3.933	693.512	5.36	3.89	27.20	37.294	48.835
0.10	5.876	23.239	3.955	694.883	5.38	4.08	24.14	37.544	53.296
0.20	5.860	23.257	3.969	691.639	5.48	4.35	20.47	32.784	47.921
0.30	5.852	23.261	3.974	689.871	5.56	4.67	15.82	26.971	41.860

The average crystallite size (L) for the prepared samples is estimated by taking the average value of the most intense diffraction peaks using the Debye Scherrer formula [28] and their values are tabulated in Table 2. The average crystallite size is calculated from Scherer equation and is found to increase from 36.077 nm at x = 0.00 to 37.544 nm at x=0.10 and then it decreases to minimum value 26.971 nm at x = 0.30. The decreasing trend of crystallite size may be due to the high concentration of Hg²⁺ ions content which reduces the grain growth because of isolation on or close to the grain boundary which impedes its movement.

The morphologies of hexaferrite BaFe_12-xHg_xO₁₉ nanoparticles are shown in Figure 4. It is clear that the samples are composed of approximately lamellar grains. There are agglomerations between the particles which may be due to the high magnetization and the magnetic interaction between the particles [29] or related to particles chemical reaction at the time of calcination procedure. The particle size (w) of BaFe_12-xHg_xO₁₉ nanoparticles obtained at 1000°C, is mainly between 41.86 and 53.29 nm. Table 2 shows that the values of w are slightly higher than those obtained from XRD (L). This is because of X-rays can detect the individual crystallite parts into the nanoparticle, as TEM deals with the grain which might consist of a number of crystallites. As present in Table 2, it is clear that w has the same behaviour of L with Hg²⁺ ions content.

Figure 4. TEM images of BaFe_12-xHg_xO₁₉ nanoparticles.

The elemental analysis of BaFe_12-xHg_xO₁₉ nanoparticles is investigated by Energy dispersive X-ray analysis (EDS). The results indicate the presence of Ba, Fe, Hg, and O peaks as seen in Figure 5, affirming the formation of BaFe_12-xHg_xO₁₉ solid solution and indicates Hg²⁺ ions incorporation in the BaFe₁₂O₁₉ host lattice. Experimental and theoretical atomic percentages (%) of BaFe_12-xHg_xO₁₉ nanoparticles, x = 0.00, 0.10 and 0.30, are inserted in the EDS Figs. It is clear the rapprochement between the calculated and experimental values of the atomic percentages for all elements. FTIR absorption spectra of M-type hexaferrite BaFe_12-xHg_xO₁₉ nanoparticles recorded in range of 400–4000 cm⁻¹ are seen in Figure 6(a). Two main absorption bands υ₁ and υ₂ in the ranges 560–590 cm⁻¹ and 430–450 cm⁻¹ are observed which are characteristic to M-type barium hexaferrite. The band υ₁ is attributed to the stretching vibrations of the tetrahedral A-site and υ₂ to the octahedral B-site vibrations [12]. It is observed that the values of υ₁ are higher than υ₂, indicating that the vibration normal mode for A-sites is larger than that of B-sites. This is attributed to shorter bond length of the A-site clusters than that of the B-site clusters [30]. Also, the band υ_A shows up in the spectra at around 880 cm⁻¹ and is attributed to increment in the concentration of divalent ions among the A-sites [30]. The appearance of this band confirms the represents the divalent metal- oxygen vibrations and may assign to the existence of Hg²⁺– O²⁻ or/and Fe²⁺– O²⁻ among A-sites. Carbonyl group (C = O) with asymmetric stretching is detected at 1633 cm⁻¹. The detection of band around 3438 cm⁻¹ is assigned to the O–H bond of water with stretching vibration which represents the appearance of hydrogen-bonded chains [31].

Figure 5. EDX spectra and elemental mapping images of BaFe_12-xHg_xO₁₉ nanoparticles, x = 0.00, 0.10 and 0.30.

Figure 6. (a) FTIR spectra of BaFe_12-xHg_xO₁₉ nanoparticles and (b) The variation of Debye temperature against Hg²⁺ ions content.

The thermal properties of M-type hexaferrite can be discussed in terms of mean value of wave number υ_av of the characteristic peaks υ₁ and υ₂ as follows [32], and their values are listed in Table 3 versus Hg⁺² ions content. (6) $T_D=\frac{\hslash \complement v_{av}}{K}$(6) where $T_D$ is Debye temperature in Kelvin and $\complement$ is the velocity of light.

The variation of $T_D$ versus Hg²⁺ ions content is shown in Figure 6(b). It is demonstrated that $T_D$ values show increment behaviour against x. The variation of $T_D$ is attributed to the variation of the mean value of the characteristic wave number υ_av of IR bands [33]. For n-type materials, according to specific heat theory, the conduction electrons can absorb part of the heat resulting in a decrease in Debye temperature. And therefore, the increasing trend of $T_D$ confirms the reduction of conduction electrons (i.e.n-type) and increment of the holes contribution (i.e.p-type) by increasing Hg²⁺ ions [34].

The magnetic hysteresis loops, at room temperature for BaFe_12-xHg_xO₁₉ nanoparticles are shown in Figure 7. The magnetic measurements are carried out under an applied field of ±20 kG. It is displayed wide hysteretic behaviour curves (large coercivity H_c) which distinguish the hard magnetic materials [35,36]. The saturation magnetization values ($M_s$) are estimated from the approximation of Stoner-Wohlfarth (S-W) using the following equation [37]: (7) $M=M_s\left[1-\frac{\alpha }{H^2}\right]$(7) According to eq. (7(7) $M=M_s\left[1-\frac{\alpha }{H^2}\right]$(7) ), the plot of $M$ versus 1/$H^2$ (Figure 8) leads to a straight line with slope = $M_s\times \alpha$. The intersection of this straight line with y-axis gives the values of saturation magnetization $M_s$. The estimated values of $M_s$ and α are displayed in Table 4 versus Hg⁺² ions content. It is observed that $M_s$ and remnant magnetization $M_r$ rise with increasing x and attained the maximum value at x = 0.10, beyond which they decrease. The increase in $M_s$ is mainly attributed to the strengthening of super-exchange interactions among nanoparticles due to the partial substitution of Fe³⁺ ions by the Hg²⁺ ions. The ions radii Hg²⁺ ions (1.02 Å) is larger than that Fe³⁺ ions (0.64 Å). This leads to decrease the different magnetic ions distances and subsequently enhance the strength of the super-exchange interactions [38]. On the other hand, the Fe³⁺ ions in barium hexaferrite have five sites are up-spins (↑), whereas two sites are down-spins (↓) [24]. The increase in $M_s$ is attributed to the occupation of Hg²⁺ ions in the down-spin states. The net spin in upward direction consequently increases, leading to enhance $M_s$ up to x = 0.10. While the decreasing of $M_s$ and $M_r$ at high Hg²⁺ ions content may be resulting from the enhancement of nonmagnetic Hg²⁺ ions concentration and existing of spin canting due to magnetic collinearity loss.

Figure 7. Room temperature magnetic hysteresis loops of BaFe_12-xHg_xO₁₉ nanoparticles, x = 0.00, 0.05, 0.10, 0.20 and 0.30.

Figure 8. The plots of $M$ versus 1/$H^2$ for BaFe_12-xHg_xO₁₉ nanoparticles.

Table 3. The distinguishing wave number υ_1, υ₂ corresponding to different vibrations and Debye temperature of BaFe_12-xHg_xO₁₉ nanoparticles.

Hg^2+ ions content (x)	υ1 (cm^−1)	υ2 (cm^−1)	υav (cm^−1)	$T_D$ (K)
0.00	590.307	438.362	514.335	739.613
0.05	591.834	443.095	517.465	744.114
0.10	592.052	444.524	518.288	745.298
0.20	593.012	445.116	519.064	746.414
0.30	593.893	446.208	520.051	747.833

Table 4. Magnetic parameters of BaFe_12-xHg_xO₁₉ nanoparticles.

Hg^2+ ions content (x)	$M_s$ (emu/g)	$M_r$ (emu/g)	$H_c$ (G)	$m_B$ (µB)	$K_{mag}$ (erg/G)	$H_i$ (G)
0.00	56.38	25.254	4943	11.22	448167.10	15898.09
0.05	57.93	26.529	4682	11.60	442169.37	15265.64
0.10	62.37	30.647	4345	12.57	440594.50	14128.64
0.20	59.99	28.707	4645	12.25	474298.17	15812.84
0.30	59.91	28.306	4900	12.34	497120.46	16595.58

The magnetic moment ($m_B$) per formula unit in Bohr magneton (µ_B) can be calculated through the following equation [39]: (8) $m_B=\frac{M_w\times M_s}{5585},$(8) where $M_w$ is the molecular weight of each composition. The obtained values of magnetic moment are presented in Table 4 versus x. It is observed that $m_B$ has the same trend with x as $M_s$. The increase in the crystallite size L and the decrease in spin canting angle lead to enhance $M_s$, $m_B$ and the strength of A–B super-exchange magnetic interactions [39].

The magneto crystalline anisotropy constant ($K_{mag}$) and the intrinsic coercivity ($H_i$) can be deduced from the following relations [40,41]: (9) $\begin{array}{rl}{K}_{mag}& =M_s{\left(\frac{15\alpha }{4}\right)}^{0.5}\end{array}$(9) (10) $\begin{array}{rl}{H}_i& =\frac{2K_{mag}}{M_s}\end{array}$(10)

The estimated values of $K_{mag}$ and $H_i$ are also presented in Table 4 versus x. It is obvious that $H_i$ slightly decreases as Hg²⁺ ions content increases till x = 0.10, and then increases with further increase in x, and become close to that of x = 0.00. The reduction in $H_i$ may be attributed to the non-magnetic Hg²⁺ ions which make the inter-sublattice interactions weak, leading to decrease the anisotropy energy and $H_i$ [30]. Coercivity$H_c$ also decreases from 4943 G at x = 0.00 to 4345 G at x = 0.10 and then rises to 4900 at x = 0.30. The variation of $H_c$ is associated with the extrinsic effect which related to porosity and the distribution of grain size, as well as the intrinsic effect which directly related to the anisotropy field [42]. From the results listed in Table 2, it is observed that $H_c$ decreases with increasing the grain size and with decreasing the porosity which improves the inter grain connectivity across the crystal lattice. The other reason of the decrease in $H_c$ may be ascribed to the decrease in magneto crystalline anisotropy. Frequently, we can use the variations in $H_i$ values to explain the $H_c$ variations [43]. The high values of $H_i$ indicate the hard magnetic behaviour of the samples. Figure 9 shows that $H_i$ of the samples is proportional to $H_c$ and depends on crystallite size. Usually, the values range of coercivity determines the application in which nanomaterials are used, for example the substances that have $H_c$<1200 G is applicable in the field of perpendicular magnetic recording media [44]. Moreover, as-prepared hexaferrites nanoparticles of $H_c$ in the range (4943–4345 G) with $H_c$ >$M_r/2$, are known as permanent magnets which have a potential candidate for numerous applications.

Figure 9. The variation of $H_c$ and $H_i$ with the crystallite size L.

The study of EPR of ferrites is very important for investigation high frequency magnetic properties as the resonance originates from the spins-electromagnetic waves interaction [45]. Figure 10 shows the first-derivative electron paramagnetic resonance absorption spectra at room temperature for BaFe_12-xHg_xO₁₉ samples with 0.00 ≤ x ≤ 0.30. EPR spectra contain an isotropic with relative narrow EPR line, characterizing Ba ferrite samples [46]. The isotropic behaviour of EPR line, for all substituted samples, reflects its symmetry about the central position. This indicates the absence of skin effect [47]. In ferrites, Fe³⁺ ions are the main responsible for EPR spectra as EPR signal for Fe²⁺ ions can be only observed at very low temperature (∼ 4 K) because of their very short spin–lattice relaxation time [48]. On the other hand, the two main sources which are responsible for the EPR signal linewidth for any ferrite material are the interaction between magnetic dipoles among particles and the super-exchange interactions between magnetic ions through the ions of oxygen [49].

Figure 10. First-derivative absorption spectra for BaFe_12-xHg_xO₁₉ nanoparticles versus the magnetic field.

The strong EPR intensity display slightly shift for the point of maximum derivative with increasing Hg substitution. This makes a slight change in g-factor. The g-factor was calculated from knowing the g-factor of CuSO₄.5H₂O [50]. The g-factor variation with x for BaFe_12-xHg_xO₁₉ samples is shown in Figure 11. The g-factor is near ≈ 2, corresponding to barium ferrite sample [46]. There is a slight increase in g-factor with increasing Hg²⁺ ions content up to x = 0.10, followed by a decrease with further increase in x. The slight reduction of g-factor for x ≥ 0.20 reflect the decrease in the magnetic interaction. Reverse behaviour for the resonance field H_r versus x is plotted in Figure 11. The EPR line intensity of peak-to-peak amplitude Y* increases with increasing Hg substitution up to 0.10, beyond which it decreases as represented in Figure 11. This enhancement indicates the enhancement of unpaired electrons in BaFe_12-xHg_xO₁₉ samples. Moreover, the variation of peak-to-peak line width Δx_pp with Hg²⁺ ions content is also shown in Figure 11. It is clear that Δx_pp increases with increasing Hg²⁺ ions content up to x = 0.10, beyond which it decreases. The increase in Δx_pp reflects the strengthening of the dipolar interaction and indicates the existence of critical grain size with 0.00 ≤ x ≤ 0.10 as the crystalline size increases up to x = 0.10. On the other hand, the decrease in Δx_pp for x ≥ 0.20 can be interpreted as the reduction of magnetic interaction effect, according to the reduction of magnetic ions (Fe³⁺ ions), confirming with the model of solid solutions with magnetic dilution; $\mathrm{\Delta }{\text{x}}_{\text{pp}}\propto (1-\text{x}{)}^{1/2}$ [51]. The number of spins N participating in the resonance are estimated from comparing the area under the absorption curve with that for CuSO₄.5H₂O [50]. N enhances as Hg²⁺ ions content increases up to x = 0.10, beyond which it decreases as listed in Table 5. This enhancement of N, as well as g-factor and $\mathrm{\Delta }{\text{x}}_{\text{pp}}$ reflects the increase of the crystalline degree for BaFe_12-xHg_xO₁₉ samples as x increases up to 0.10, which improve the dipole interaction that in turn give large $\mathrm{\Delta }{\text{x}}_{\text{pp}}$, g-factor and N [52]. The paramagnetic susceptibility χ at room temperature is calculated through the following relation [53]: (11) $\chi =N{g}^2{\mu }_B^{2}J\left(J+1\right)/3k_{B}T$(11) where ${\mu }_B$ is Bohr magneton and $J$ is total angular momentum. The values of paramagnetic susceptibility versus Hg²⁺ ions content are listed in Table 5. It is clear that χ increases with increasing x up to 0.10, confirming with the behaviour of N with x. The order of paramagnetic susceptibility is comparable with that obtained for BaFe₁₂O₁₉ sample [10]. The spin relaxation process is characterized by a time constant that is a function of magnetic field. It depends on the rate at which the energy of microwave can be emitted or absorbed to the surrounding spins. The spin–spin relaxation time constant T can be calculated through the following relation [54]: (12) $\frac{1}{T}=\frac{\text{g}\text{β}\mathrm{\Delta }{\text{x}}_{1/2}}{\text{ħ}},\mathrm{\Delta }{\text{x}}_{1/2}=\sqrt{3}\mathrm{\Delta }{\text{x}}_{\text{pp}}$(12) where $\text{β}$ is Bohr magneton, $\mathrm{\Delta }{\text{x}}_{1/2}$ is the linewidth at half height of absorption peak. The values of spin–spin relaxation time constant versus Hg²⁺ ions content for BaFe_12-xHg_xO₁₉ samples are also listed in Table 5. One can notice that T decreases with increasing Hg²⁺ ions content up to x = 0.10, followed by a decrease for further increase in x. The behaviour could be explained according to the change in electron motion and the strength of super-exchange interaction between magnetic ions through oxygen.

Figure 11. The variation of g-factor, H_r, Δx_pp and Y* versus x for BaFe_12-xHg_xO₁₉ nanoparticles.

Table 5. Variation of N, χ and τ versus x for BaFe_12-xHg_xO₁₉ nanoparticles.

x	N × 10^22 (spin/g)	χ × 10^−3 (emu/g)	τ × 10^−9 (s)
0.00	1.94	5.01	1.30
0.05	3.14	8.26	1.26
0.10	4.15	11.14	1.21
0.20	2.41	6.30	1.36
0.30	1.57	3.97	1.43

4. Conclusion

Barium hexaferrite nanoparticles were prepared at different temperature through a co-precipitation method. XRD diffraction patterns revealed that the annealing temperature played an important role in the crystallization of barium hexaferrite. A series of BaFe_12-xHg_xO₁₉ nanoparticle, 0.00 ≤x≤ 0.30 were successfully prepared at the optimum annealing temperature 1000°C. XRD and FTIR analysis confirmed the single phase formation and the absence of impurities. Lattice parameter c increased with the increase in x, whereas a slightly decreased. M-H curves displayed wide hysteretic behaviours with higher coercivity which is characteristic of the typical hard magnetic materials, leading to recommend these materials to be a potential candidate for numerous applications such as recording media applications. M-H curves indicated the enhancement in saturation magnetization values ($M_s$) and remnant magnetization $M_r$ up to x = 0.10 followed by a decrease up to x = 0.30. On the other hand the intrinsic coercivity ($H_i$) and coercivity $H_c$ diminished as Hg²⁺ content increased till x=0.10, beyond which they enhanced. The decrease in $H_c$ might be ascribed to the increase in the grain size and the decrease in magneto crystalline anisotropy. The increase of Hg²⁺ content up to 0.10 for BaFe_12-xHg_xO₁₉ nanoparticle improved the dipole interaction that in turn made an enhancement for the values of g-factor, peak-to-peak line width, number of spin and paramagnetic susceptibility. The enhancement of these EPR parameters confirmed the improvement of the crystalline degree as Hg²⁺ content increased up to 0.10, reflecting the existence of critical grain size with 0.00 ≤ x ≤ 0.10.

Disclosure statement

No potential conflict of interest was reported by the author(s).