Mössbauer and Structure-Magnetic Properties Analysis of A_yB_1−yC_xFe_2−xO₄ (C=Ho,Gd,Al) Ferrite Nanoparticles Optimized by Doping

Abstract

A_yB_1−yC_xFe_2−xO₄ (C=Ho,Gd,Al) ferrite powders have been synthesized by the sol-gel combustion route. The X-ray diffraction of the CoHo_xFe_2−xO₄ (x = 0~0.08) results indicated the compositions of single-phase cubic ferrites. The saturation magnetisation of CoHo_xFe_2−xO₄ decreased by the Ho³⁺ ions, and the coercivity increased initially and then decreased with the increase of the calcination temperature. The Mössbauer spectra indicated that CoHo_xFe_2−xO₄ displays a ferrimagnetic behaviour with two normal split Zeeman sextets. The magnetic hyperfine field tends to decrease by Ho³⁺ substitution owing to the decrease of the A–B super-exchange by the paramagnetic rare earth Ho³⁺ ions. The value of the quadrupole shift was very small in the CoHo_xFe_2−xO₄ specimens, indicating that the symmetry of the electric field around the nucleus is good in the cobalt ferrites. The absorption area of the Mössbauer spectra changed with increasing Ho³⁺ substitution, indicating that the substitution influences the fraction of iron ions at tetrahedral A and octahedral B sites. The X-ray diffraction of Mg_0.5Zn_0.5C_xFe_2−xO₄(C=Gd,Al) results confirmed the compositions of single-phase cubic ferrites. The variation of the average crystalline size and lattice constant are related to the doping of gadolinium ions and aluminum ions. With increasing gadolinium ions and aluminum ions, the coercivity increased and the saturation magnetization underwent a significant change. The saturation magnetization of AlMg_0.5Zn_0.5FeO₄ ferrite reached a minimum value (M_S = 1.94 mu/g). The sample exhibited ferrimagnetic and paramagnetic character with the replacement with Gd³⁺ ions, that sample exhibited paramagnetic character with the replacement with Al³⁺ ions, and the isomer shift values indicated that iron is in the form of Fe³⁺ ions.

1. Introduction

Ferrite is important in various magnetic applications because it has the properties of magnetic materials and insulators [1,2,3,4]. Among the ferrite spinel structures, cobalt ferrites (CoFe₂O₄) are the important magnetic and magnetostriction materials [5,6,7,8]. As a famous hard magnetic material, cobalt ferrite has been widely used for magnetoelastic sensor applications [9,10,11,12]. The distribution of cations between tetrahedron (A) and octahedron (B) ferrite and the magnetic field interaction will affect the structure and electrical and magnetic properties [13,14,15,16]. Rare earth ions considerably affect the magneto-crystal anisotropy of ferrite by substituting Fe³⁺ ions in ferrites with the rare earth ions of 4f elements, which exhibit a strong spin-orbital (3d–4f) coupling [17,18,19]. Particularly, small amounts of rare earth holmium (Ho) elements affect the magnetic properties of cobalt ferrites [20,21,22]. Lohar et al. [8] studied the structural and magnetic properties of CoFe₂O₄ nanoparticles doped with rare earth Ho³⁺ ions, where the saturation magnetisation of CoFe₂O₄ nanoparticles increased with Ho³⁺ substitution, owing to the Ho³⁺ ions having a larger magnetic moment of 10.6 μ_B. However, in other studies [9,10], the decrease in saturation magnetisation with Ho³⁺ substitution is attributed to Ho being paramagnetic at room temperature, weakening exchange interactions. Panneer Muthuselvam et al. [11] synthesised CoFe_1.95Ho_0.05O₄ spinel ferrite annealed at different temperatures, which showed a single domain and multi-domain behaviour at a critical annealing temperature of 1050 °C. Rare earth ions will have a great influence on the magnetocrystalline anisotropy of ferrite [23,24,25,26]. Mg-Zn ferrite is important in soft magnetic materials and semiconducting magnetic materials [27,28,29]. Because Mg-Zn ferrite has low eddy current losses, high resistivity and high cost effective, it is widely used in computer memory, recording heads and loading coils [30]. Mg-Zn ferrite has a well-known cubic spinel structure, where most of the Magnesium (Mg²⁺) ions are distributed over the octahedral (B) sites and Zinc ions (Zn²⁺) tend to occupy the tetrahedral (A) sites [31]. The structure and magnetic properties of the sample are affected by the ion distribution [32]. Mukhtar et al. [6] synthesized Pr-substituted Mg-Zn ferrites by the sol-gel method, and studied the application of samples in magnetic cores and high frequency materials. Herein, we have synthesised A_yB_1−yC_xFe_2−xO₄ (C=Ho,Gd,Al) via the sol-gel-combustion method and investigated the variation of structural and magnetic properties for the ferrite sample with rare earth element substitution.

2. Results and Analysis

2.1. X-ray Diffraction Characterisation

Figure 1 shows the X-ray diffraction (XRD) patterns of ferrites CoHo_xFe_2−xO₄ (x = 0–0.10) calcinated at 800 °C. The XRD patterns show that the CoHo_xFe_2−xO₄ samples are single spinel-structure ferrites (JCPDS card no. 22-1086). No impurity peaks are observed in these XRD patterns. Owing to the ionic radius of Fe³⁺ ions (0.645 Å) being smaller than Ho³⁺ ions (0.901 Å) [9,11,12], when x ≤ 0.04, the lattice constants of CoHo_xFe_2−xO₄ ferrite are larger than CoFe₂O₄ ferrite, as shown in

Table 1. XRD date of CoHo_xFe_2−xO₄ calcined at 800 °C.

Content (x)	Lattice Parameter (Å)	Average Crystallite Size (Å)	Density (g/cm3)
0	8.35497	556	5.3468
0.02	8.38601	350	5.3342
0.04	8.40681	308	5.3434
0.06	8.38132	229	5.4415
0.08	8.37719	249	5.4989
0.10	8.38928	221	5.5243

. When x ≥ 0.06, the lattice parameter of CoHo_xFe_2−xO₄ ferrite is no longer increasing, possibly owing to the solubility limit of Ho³⁺ ions [9]. The average crystallite size of the CoHo_xFe_2−xO₄ samples estimated using the Debye–Scherrer formula [5,10,12] is between 21 and 55.6 nm. With Ho³⁺ doping, the decrease in the average crystallite size can be explained using the studies by others [14,15,16]. The RE³⁺ ions have an empty, half or filled 4f electron shell, such that rare earth Ho³⁺ ions substituted ferrites need more energy to grow grains and complete crystallisation.

The X-ray density of the sample was calculated by the following relationship [8,12,13]:

$${\rho }_x=\frac{8M}{N{a}^3}$$

(1)

where a is the lattice parameter, N is Avogadro’s constant, and M is the relative molecular mass.

Table 1 shows that the lattice parameter also tends to increase when the relative molecular mass increases with Ho³⁺ substitution. So, according to Formula (1), the X-ray density tends to increase with Ho³⁺ substitution because of the increase in the relative molecular mass.

The XRD patterns of the un-sintered and sintered CoHo_0.02Fe_2−xO₄ samples are single spinel-structured ferrites, as shown in Figure 2. No impurity peaks were found in these XRD patterns. The breadth of XRD lines decreases with increasing heat treatment temperatures. As shown in

Table 2. XRD date of CoHo_0.02Fe_1.98O₄ un-sintered and sintered at 400 °C, 800 °C.

Temperature (°C)	Lattice Parameter (Å)	Average Crystallite Size (Å)	Density (g/cm3)
Un-sintered	8.38379	249	5.3384
400	8.39279	293	5.3212
800	8.38601	350	5.3342

, the X-ray density and the lattice parameter have no noticeable changes, and the average crystallite size of CoHo_0.02Fe_1.98O₄ increases with increasing calcination temperature. Unlike in this study, the reported XRD diffraction peaks of CoFe₂O₄ calcined at a low temperature are not very sharp [4,14]. This indicates that the sample has good crystallinity without calcination.

Figure 3 and Figure 4 show the X-ray diffraction (XRD) characterization of ferrites Gd_xMg_0.5Zn_0.5Fe_2−xO₄ and Al_xMg_0.5Zn_0.5Fe_2−xO₄ (x = 0~0.1). No impurity peaks were found in these XRD patterns.

Table 3. XRD date of Gd_xMg_0.5Zn_0.5Fe_2−xO₄ sintered at 800 °C.

Content (x)	Lattice Constant (Å)	Average Crystallite Size (Å)	Density (g/cm3)
0	8.43133	377	4.8879
0.025	8.42094	344	4.9624
0.05	8.43047	301	5.0018
0.075	8.44593	290	5.0303
0.1	8.42142	214	5.1307

indicates that the Gd_0.075Mg_0.5Zn_0.5Fe_1.925O₄ ferrite has the maximum lattice constant value, due to the radius of Fe³⁺ ions being smaller than the radius of Gd³⁺ ions [30,33]. With the doping of rare earth Gd³⁺ ions, the lattice constant does not increase monotonously, due to the larger rare earth ionic radius leading to the lattice distortion of Mg-Zn ferrite [31,32]. Due to the radius of Al³⁺ ions being smaller than Fe³⁺ ions [34], the lattice constant of Al_xMg_0.5Zn_0.5Fe_2−xO₄ ferrite is smaller than Mg_0.5Zn_0.5Fe₂O₄ ferrite, and are shown in

Table 4. XRD date of Al_xMg_0.5Zn_0.5Fe_2−xO₄ sintered at 800 °C.

Content (x)	Lattice Parameter (Å)	Average Crystallite Size (Å)	Density (g/cm3)
0	8.43133	377	4.8879
0.25	8.39110	290	4.7963
0.5	8.36480	202	4.6779
0.75	8.31315	158	4.5988
1.0	8.25874	179	4.5201

.

With the investigated samples Gd_xMg_0.5Zn_0.5Fe_2−xO₄ (x = 0~0.1), the average crystallite size estimated by the Debye-Scherrer formula is between 21.4 nm and 37.7 nm [29,30]. Additionally, the average crystallite size of Al_xMg_0.5Zn_0.5Fe_2−xO₄ (x = 0~0.1) is between 15.8 nm and 37.7 nm. The XRD density increases with Gd³⁺ substitution from Table 3. The doping of rare earth Gd ions will cause the relative molecular mass to increase, and the lattice constant of Mg-Zn ferrite has no significant change. Therefore, the increases in XRD density of Gd_xMg_0.5Zn_0.5Fe_2−xO₄ is attributed to the relative molecular mass increase. Moreover, the decreases in XRD density of Al_xMg_0.5Zn_0.5Fe_2−xO₄ are attributed to the fact that the relative molecular mass decreases.

Figure 5 and Figure 6 are the XRD patterns of Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄ and Al_0.5Mg_0.5Zn_0.5Fe_1.5O₄ sintered at different temperatures. No impurity peaks were found in these XRD patterns. The breadth of XRD lines trends to decrease with increasing heat treatment temperatures. From

Table 5. XRD date of Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄ sintered at different temperatures.

Temperature (°C)	Lattice Constant (Å)	Average Crystallite Size (Å)	Density (g/cm3)
Un-sintered	8.41517	228	5.0292
400 °C	8.41829	233	5.0236
800 °C	8.43047	301	5.0018

we know that the lattice constant and average crystallite size increases, and the XRD Density decreases with increasing the sintered temperature for the Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄. For the Al_0.5Mg_0.5Zn_0.5Fe_1.5O_4, the lattice parameter decreases and the X-ray density increases, and average crystallite size is trend to increase with increasing the sintering temperature from

Table 6. XRD date of Al_0.5Mg_0.5Zn_0.5Fe_1.5O₄ sintered at different temperatures.

Temperature (°C)	Lattice Parameter (Å)	Average Crystallite Size (Å)	Density (g/cm3)
Un-sintered	8.38226	165	4.6487
400 °C	8.36985	137	4.6694
800 °C	8.36480	202	4.6779

. In other literature studies [35], the diffraction peaks of XRD is not very sharpness for CoGd_0.1Fe_1.9O₄ calcined at low temperature, the diffraction peaks of XRD is very sharpness for Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄ and Al_0.5Mg_0.5Zn_0.5Fe_1.5O₄ without burning. This indicates that the sample has good crystallinity without sintering.

2.2. Scanning Electron Microscopy (SEM)

Figure 7 shows the SEM images of CoHo_xFe_2−xO₄ (x = 0, 0.02) annealed at 800 °C. As shown in Figure 3, the sample is well-crystallised, and the grain size is almost uniform. With Ho³⁺ substitution, some cobalt ferrite particles are agglomerated, possibly owing to the magnetic interactions between CoHo_xFe_2−xO₄ particles [15].

Figure 8 is the grain size distribution of CoFe₂O₄ and CoHo_0.02Fe_1.98O₄. Using a statistical method, the calculated average grain size of CoFe₂O₄ and CoHo_0.02Fe_1.98O₄ are ~96.26 and ~47.15 nm, respectively. The grain size of ferrite samples is less than 100 nm, indicating that they are nanoparticles. It is slightly larger than the average crystallite size determined using an X-ray, suggesting that each ferrite particle comprises several crystallites [16,17].

The SEM images of CoHo_0.02Fe_1.98O₄ un-sintered and sintered at 400 °C and 800 °C are shown in Figure 9. As the heat treatment temperature increased, the crystallinity of the sample was improved, and the grain size increased. But the ferrite powders have a good crystallinity without heat treatment, consistent with the XRD analysis. Some cobalt ferrite particles are agglomerated with the increasing heat treatment temperature, owing to the magnetic interactions between CoHo_0.02Fe_1.98O₄ particles [15], but the degree of agglomeration is small.

Figure 10 are the SEM images of Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄ and Al_0.5Mg_0.5Zn_0.5Fe_1.5O₄ sintered 800 °C. The sample is well crystallized, and the grain size is almost uniform. With the Gd³⁺ ions and Al³⁺ ions substituting, some particles of cobalt ferrite are agglomerated [21]. Figure 11 are the grain size histogram of Mg_0.5Zn_0.5Fe₂O₄, Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄ and Al_0.5Mg_0.5Zn_0.5Fe_1.5O₄. The average grain size is approximately 90.74nm, 46.11 nm and 44.84nm, respectively, and by a statistical method, the aluminum ion doping can make the grain size of the sample smaller. The grain size of ferrite samples is less than 100 nanometers, indicating that they are nanoparticles. However, they are slightly bigger than average crystallite size for an X-ray. Therefore, each particle is made up of several crystallites [17].

2.3. Magnetic Analysis

Figure 12 shows the RT (at 295 K) magnetic hysteresis curve of CoHo_xFe_2−xO₄ measured at 295 K. The magnetisation of CoHo_xFe_2−xO₄ (x = 0–0.10) nearly reaches saturation at 10,000 Oe. The saturation magnetisation (M_S) decreases with Ho³⁺ substitution, as shown in

Table 7. Magnetic data for CoHo_xFe_2−xO₄ calcined at 800 °C.

Content (x)	MS (emu/g)	HC (Oe)	Mr (emu/g)
0	70.58	1005	34.71
0.02	72.54	1351	37.77
0.04	67.58	1266	35.06
0.06	64.64	1158	31.90
0.08	61.82	1094	30.24
0.10	57.96	1016	26.28

, which could be calculated according to the following relation [8,18]:

$$M_S=\frac{5585\times n_B}{M}$$

(2)

where n_B is the Bohr magneton and M is the molecular mass. The relative molecular mass of CoHo_xFe_2−xO₄ increases as Ho³⁺ is replaced. The Ho³⁺, Co²⁺ and Fe³⁺ ions are 10.6, 3 and 5 μ_B [8], respectively. Ho exhibits para-magnetism at 295 K [9,10]. Ho³⁺ ions preferred to occupy B sites owing to the large Ho³⁺ ionic radius. Thus, the magnetic moment of the octahedral B site will decrease as the iron is replaced by holmium; this combined with the Néel theory, the total magnetic moment (n_B) decreases. Owing to the increased M and the decreased n_B with the substitution of Ho³⁺ ions, M_S decreases according to the Formula (2). These results are consistent with other literature reports [9,20].

However, Table 7 shows that M_S increases with Ho³⁺ concentration for x ≤ 0.02 because of a small amount of paramagnetic Ho³⁺ ions occupying A sites. The coercivity (H_C) variation of cobalt ferrite with the substitution of Ho³⁺ ions can be explained as follows. The rare earth Ho³⁺ ions have substantial magneto-crystalline anisotropy [8,19,20]. H_C does not increase monotonously with the doping of rare earth Ho³⁺ ions because H_C is also related to the factors such as crystallinity and crystallite size [21].

Magnetic hysteresis loops of CoHo_0.02Fe_1.98O₄ and CoHo_0.10Fe_1.90O₄ at different sintering temperatures are shown in Figure 13 and Figure 14, respectively. After annealing at 900 °C, CoHo_0.02Fe_1.98O₄ and CoHo_0.10Fe_1.90O₄ have the maximum M_S value because particle size increases with the sintering temperature [22].

The M_S of CoHo_0.02Fe_1.98O₄ and CoHo_0.10Fe_1.90O₄ decrease after annealing at 400 °C because the un-sintered sample may have a good crystallinity, as determined by XRD and SEM.

Table 8. Magnetic data of CoHo_0.02Fe_1.98O₄ at different sintering temperatures.

Temperature (°C)	MS (emu/g)	HC (Oe)	Mr (emu/g)
Un-sintered	60.01	1301	29.98
400	55.80	2234	29.62
500	61.10	1944	32.37
600	63.52	1655	33.56
700	69.21	1426	36.91
800	72.54	1351	37.77
900	76.16	1152	40.99

and

Table 9. Magnetic data of CoHo_0.10Fe_1.90O₄ at different sintering temperatures.

Temperature (°C)	MS (emu/g)	HC (Oe)	Mr (emu/g)
Un-sintered	47.89	1290	20.68
400	39.75	2052	18.83
500	45.72	1533	20.42
600	50.30	1174	21.50
700	57.05	1014	25.13
800	57.96	1016	26.28
900	66.12	914	33.8

show that M_S increases with Ho³⁺ concentration for x = 0.02 and x = 0.10. The M_S of CoHo_0.02Fe_1.98O₄ is larger than that of CoHo_0.10Fe_1.90O₄, owing to the small amount of paramagnetic Ho³⁺ occupying A sites and the decreasing of the magnetic moment at the tetrahedral A site as the iron is replaced by holmium. According to Néel theory, the paramagnetic Ho³⁺ occupying A sites will increase M_S. The H_C of CoHo_0.02Fe_1.98O₄ and CoHo_0.10Fe_1.90O₄ initially increases, decreasing as the sintering temperature increases. H_C is related to grain size (D), and their relationship is H_C = g − h/D² (single domain region) and H_C = a + b/D (multi-domain region). According to the above-mentioned SEM analysis, the particle size increases with increasing calcination temperature, so the H_C increases initially and then decreases as the annealing temperature increases.

Figure 15 and Figure 16 show the magnetic hysteresis curve of Gd_xMg_0.5Zn_0.5Fe_2−xO₄ measured at 295 K. The magnetization nearly reaches saturation at 5000 Oe. The saturation magnetization decreases with the substitution of Gd³⁺ ions and Al³⁺ ions from

Table 10. Magnetic data for Gd_xMg_0.5Zn_0.5Fe_2−xO₄ sintered at 800 °C.

Content (x)	MS (emu/g)	HC (Oe)	Mr (emu/g)
0	34.98	13.64	1.10
0.025	31.38	62.52	4.67
0.05	27.54	55.79	3.79
0.075	28.17	62.99	4.36
0.1	24.67	50.52	2.61

and

Table 11. Magnetic data for Al_xMg_0.5Zn_0.5Fe_2−xO₄ calcined at 800 °C.

Content (x)	MS (emu/g)	HC (Oe)	Mr (emu/g)
0	34.98	13.64	1.10
0.25	15.39	50.37	1.38
0.5	6.26	53.56	0.54
0.75	3.96	50.37	0.33
1	1.94	59.06	0.16

. As Gd³⁺ replaces, the relative molecular mass of Gd_xMg_0.5Zn_0.5Fe_2−xO₄ increases. The magnetic moments of rare earth ions generally come from localized 4f electrons in solids, and the magnetic ordering temperature is low, and the Gd rare-earth element has the Curie temperature of 293.2 K, close to RT(295 K) [36,37]. The magnetic dipole orientation is disordered at 295 K, and the rare-earth ion doping has no contribution to magnetization. Therefore, the Gd³⁺ ions are considered as non-magnetic ions at 295 K [38]. Moreover, the magnetic moment of Fe³⁺ ions is 5 μ_B [21].

Due to the relative molecular mass increase and the magnetic moment n_B decrease with the doping of Gd³⁺ ions, the saturation magnetization decreases. Therefore, the magnetic moment of the octahedral B site will decrease as the iron is replaced by gadolinium and according to Neel theory the total magnetic moment n_B will decrease. For the Al_xMg_0.5Zn_0.5Fe_2−xO₄, as the Al³⁺ are replaced the relative molecular mass and the total magnetic moment n_B decreases, and the influence of the magnetic moment is greater than the relative molecular mass, so the saturation magnetization decreases. The coercivity of Gd_xMg_0.5Zn_0.5Fe_2−xO₄ is larger than that of the Mg_0.5Zn_0.5Fe₂O₄ from Table 10. The variation of coercivity with Gd³⁺ ions substituted MgZn ferrite can be explained as follows. Rare earth ions (Gd³⁺) have stronger magnetocrystalline anisotropy [33,39].

Magnetic hysteresis loops of Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄ at different sintering temperatures are shown in Figure 17.

Table 12. Magnetic data for Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄ sintered at different temperatures.

Temperature (°C)	MS (emu/g)	HC (Oe)	Mr (emu/g)
Un-sintered	25.29	71.92	4.39
400 °C	22.93	69.58	3.73
800 °C	27.54	55.79	3.79

indicates that Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄ after annealing at 800 °C has the maximum value for saturation magnetization, because particle size increases with an increase in sintering temperature [29]. The coercivity of Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄ decreases as sintering temperature increases. The coercivity (H_C) is related to grain size (D), and their relationship is H_C = g − h/D² (single domain region) and H_C = a + b/D (multidomain region) [30]. The coercivity increases with grain diameter increases in the single domain region, and the coercivity decreases as the grain size increases in the multidomain region. The grain size of Gd_0.05Mg_0.5Zn_0.5Fe_1.95O₄ sintered at different temperatures is the multidomain region, so the coercivity decreases as annealing temperature increases.

2.4. Mössbauer Spectroscopy

Figure 18 shows the Mössbauer spectra of CoHo_xFe_2−xO₄ (x = 0, 0.04 and 0.08) polycrystalline ferrite powders measured at room temperature. All Mössbauer spectra were fitted using the Mösswinn 3.0 programme, and the spectra consist of two split Zeeman sextets, which indicates that the samples are ferrimagnetic. The six-line magnetic pattern with a larger isomer shift (I.S.) corresponds to the iron ion at position B, while the other six-line peak corresponds to the iron ion at position A [23,24]. As shown in

Table 13. Mössbauer parameters of CoHo_xFe_2−xO₄ calcined at 800 °C.

Content (x)	Component	I.S. (mm/s)	Q.S. (mm/s)	H (T)	Γ (mm/s)	A0 (%)
0	Sextet (A)	0.237	−0.004	48.946	0.360	32.4
	Sextet (B)	0.375	−0.024	45.695	0.322	67.6
0.04	Sextet (A)	0.126	−0.050	48.613	0.387	22.2
	Sextet (B)	0.316	0.151	44.156	0.429	77.8
0.08	Sextet (A)	0.157	0.061	48.546	0.463	24.5
	Sextet (B)	0.224	−0.137	43.641	0.740	75.5

, the changes in I.S. values are relatively small with the effects of Ho³⁺ substitution, and Ho³⁺ doping has no apparent impact on the s-electron charge distribution of Fe nuclei [24]. According to other reports, the I.S. values of Fe³⁺ ions are 0.1–0.5 mm/s [25,26]. From Table 13, the I.S. values indicate that the iron in the samples of this study is in the form Fe³⁺. Table 13 shows that the magnetic hyperfine field (H) tends to decrease by Ho³⁺ substitution, owing to the decrease of the A–B super-exchange by the paramagnetic rare-earth Ho³⁺ ions [27,28]. The value of the quadrupole shift is very small in the specimens of CoHo_xFe_2−xO₄, indicating that the symmetry of the electric field around the nucleus is good in the cobalt ferrites. The absorption area of Mössbauer spectra for CoHo_xFe_2−xO₄ has changed with increasing Ho substitution, which indicates that Ho³⁺ substitution influences the Fe³⁺ fraction at tetrahedral A and octahedral B sites.

Figure 19 and Figure 20 show the Mössbauer spectroscopy curve for Gd_xMg_0.5Zn_0.5Fe_2−xO₄ and Al_xMg_0.5Zn_0.5Fe_2−xO₄ polycrystalline ferrite powders measured at room temperature. For the Mg_0.5Zn_0.5Fe₂O₄, the spectra analyzed were a Zeeman-sextets-split, which shows features of relaxation effects. For the Gd_xMg_0.5Zn_0.5Fe_2−xO₄, when x = 0.05, 0.1, spectra of the samples fit a Zeeman-sextets-split and a central paramagnetic doublet [24,25,40]. According to other reports, the isomer shifts (I.S.) values of Fe³⁺ ions are 0.1–0.5 mm/s [27,36]. From

Table 14. Mössbauer parameters of Gd_xMg_0.5Zn_0.5Fe_2−xO₄ sintered at 800 °C.

Content (x)	Component	I.S. (mm/s)	Q.S. (mm/s)	H (T)	Γ (mm/s)	A0 (mm/s)
0	Sextet (B)	0.318	0.005	24.234	0.268	100
0.05	Sextet (B)	0.302	−0.173	30.350	0.334	93.1
	Doublet	0.301	0.409	-	0.327	6.9
0.1	Sextet (B)	0.116	−0.029	38.679	0.528	79.4
	Doublet	0.348	0.627	-	0.537	20.6

and

Table 15. Mössbauer parameters of Al_xMg_0.5Zn_0.5Fe_2−xO₄ sintered at 800 °C.

Content (x)	Component	I.S. (mm/s)	Q.S. (mm/s)	H (T)	Γ (mm/s)	A0 (mm/s)
0	Sextet (B)	0.318	0.005	24.234	0.268	100
0.5	Double	0.322	0.568	-	0.417	100
1	Double	0.292	0.672	-	0.414	100

, the isomer shifts values indicate that iron is in the form of Fe³⁺ ions. The value of the quadrupole shift is relatively small with effects of Gd³⁺ and Al³⁺ ions substitution, and Gd³⁺ doping has no obvious effect on the s-electron charge distribution of Fe nuclei [25,27]. The magnetic hyperfine field of the Zeeman-split sextet spectra decreases with rare earth Gd³⁺ ions and Al³⁺ ions substitution.

3. Experimental

A_yB_1−yC_xFe_2−xO₄ (C=Ho,Gd,Al) ferrite powders were synthesised via the sol-gel- combustion route. The synthetic raw materials of the sample are analytically pure nitrates (Co(NO₃)₂·6H₂O, Fe(NO₃)₃·9H₂O,Mg(NO₃)₂·6H₂O, Zn(NO₃)₂·6H₂O, Gd(N O₃)₃·9H₂O, Al(NO₃)₃·9H₂O and Ho(NO₃)₃·6H₂O), ammonia (NH₃·H₂O) and citric acid (C₆H₈O₇·H₂O). Deionised water was added to form separate solutions of citric acid and metal nitrates. Then, citric acid and metal nitrates were mixed while adjusting the pH value at ~7 with ammonia. This solution mixture was kept on a thermostat water bath at 80 °C while electrically stirring the solution until it became a dried gel. The gel was further dried in the drying oven at 120 °C and ignited in the air with a small amount of alcohol as an oxidant. After spontaneous combustion, the material was annealed in the muffle furnace according to the specific temperature (400–900 °C). The crystalline structure was investigated by X-ray diffraction (D/max-2500V/PC, Rigaku, Tokyo, Japan). The micrographs were obtained by scanning electron microscopy (NoVa^TM Nano SEM 430, Diamond Bar, CA, USA). The Mössbauer spectrum was performed at room temperature, using a conventional Mössbauer spectrometer (Fast Com Tec PC-mossII, Oberhaching, Germany). Magnetization measurements were carried out with vibrating sample magnetometer (JDAW-2000D, Changchun INPRO Magneto-electric Technology Co., Ltd., Changchun, China) at room temperature.

4. Conclusions

A_yB_1−yC_xFe_2−xO₄ (C=Ho,Gd,Al) ferrite powders were synthesised via the sol-gel- combustion route. The XRD results show that CoHo_xFe_2−xO₄ are single spinel-structured ferrites, and the CoHo_0.02Fe_1.98O₄ samples calcined at different temperatures have good crystallinity. The SEM images further confirmed that the sample was well-crystallised, the grain was distributed homogeneously, and the sample comprised nanoparticles. The RT Mössbauer spectroscopy of CoHo_xFe_2−xO₄ displayed ferromagnetic behaviour. Mössbauer spectra of CoHo_0.02Fe_1.98O₄ showed that the calcination temperature affected the magnetic properties. The magnetisation results showed that rare-earth ion doping affects magnetic parameters, such as coercivity and saturation magnetisation, so the magnetic properties of samples can be regulated by rare-earth ion doping. Mg_0.5Zn_0.5C_xFe_2−xO₄(C=Gd,Al) ferrite sintered at different temperatures have good crystallinity. The rare-earth ion and aluminum ion doping, and sintering process had an effect on magnetic parameters such as coercivity and saturation magnetization. The Mössbauer spectra showed that the sample exhibited ferrimagnetic and paramagnetic character with the replaced Gd³⁺ ions; that the sample exhibited paramagnetic character with the replaced Al³⁺ ions; and that the isomer shift values indicated that iron is in the form of Fe³⁺ ions.