Mössbauer and Structure-Magnetic Properties Analysis of AyB1−yCxFe2−xO4 (C=Ho,Gd,Al) Ferrite Nanoparticles Optimized by Doping

AyB1−yCxFe2−xO4 (C=Ho,Gd,Al) ferrite powders have been synthesized by the sol-gel combustion route. The X-ray diffraction of the CoHoxFe2−xO4 (x = 0~0.08) results indicated the compositions of single-phase cubic ferrites. The saturation magnetisation of CoHoxFe2−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 CoHoxFe2−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 CoHoxFe2−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 Mg0.5Zn0.5CxFe2−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 AlMg0.5Zn0.5FeO4 ferrite reached a minimum value (MS = 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.


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 (CoFe 2 O 4 ) 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 Fe 3+ 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 CoFe 2 O 4 nanoparticles doped with rare earth Ho 3+ ions, where the saturation magnetisation of CoFe 2 O 4 nanoparticles increased with Ho 3+ substitution, owing to the Ho 3+ ions having a larger magnetic moment of 10.6 µ B . However, in other studies [9,10], the decrease in saturation magnetisation with Figure 1 shows the X-ray diffraction (XRD) patterns of ferrites CoHo x Fe 2−x O 4 (x = 0-0.10) calcinated at 800 • C. The XRD patterns show that the CoHo x Fe 2−x O 4 samples are single spinel-structure ferrites (JCPDS card no. . No impurity peaks are observed in these XRD patterns. Owing to the ionic radius of Fe 3+ ions (0.645 Å) being smaller than Ho 3+ ions (0.901 Å) [9,11,12], when x ≤ 0.04, the lattice constants of CoHo x Fe 2−x O 4 ferrite are larger than CoFe 2 O 4 ferrite, as shown in Table 1. When x ≥ 0.06, the lattice parameter of CoHo x Fe 2−x O 4 ferrite is no longer increasing, possibly owing to the solubility limit of Ho 3+ ions [9]. The average crystallite size of the CoHo x Fe 2−x O 4 samples estimated using the Debye-Scherrer formula [5,10,12] is between 21 and 55.6 nm. With Ho 3+ doping, the decrease in the average crystallite size can be explained using the studies by others [14][15][16]. The RE 3+ ions have an empty, half or filled 4f electron shell, such that rare earth Ho 3+ ions substituted ferrites need more energy to grow grains and complete crystallisation.
Molecules 2023, 27, x FOR PEER REVIEW 2 of 17 magnetisation of CoFe2O4 nanoparticles increased with Ho 3+ substitution, owing to the Ho 3+ ions having a larger magnetic moment of 10.6 µB. However, in other studies [9,10], the decrease in saturation magnetisation with Ho 3+ substitution is attributed to Ho being paramagnetic at room temperature, weakening exchange interactions. Panneer Muthuselvam et al. [11] synthesised CoFe1.95Ho0.05O4 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 (Mg 2+ ) ions are distributed over the octahedral (B) sites and Zinc ions (Zn 2+ ) 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 solgel method, and studied the application of samples in magnetic cores and high frequency materials. Herein, we have synthesised AyB1−yCxFe2−xO4 (C=Ho,Gd,Al) via the sol-gelcombustion method and investigated the variation of structural and magnetic properties for the ferrite sample with rare earth element substitution. Figure 1 shows the X-ray diffraction (XRD) patterns of ferrites CoHoxFe2−xO4 (x = 0-0.10) calcinated at 800 °C. The XRD patterns show that the CoHoxFe2−xO4 samples are single spinel-structure ferrites (JCPDS card no. . No impurity peaks are observed in these XRD patterns. Owing to the ionic radius of Fe 3+ ions (0.645 Å) being smaller than Ho 3+ ions (0.901 Å) [9,11,12], when x ≤ 0.04, the lattice constants of CoHoxFe2−xO4 ferrite are larger than CoFe2O4 ferrite, as shown in Table 1. When x ≥ 0.06, the lattice parameter of CoHoxFe2−xO4 ferrite is no longer increasing, possibly owing to the solubility limit of Ho 3+ ions [9]. The average crystallite size of the CoHoxFe2−xO4 samples estimated using the Debye-Scherrer formula [5,10,12] is between 21 and 55.6 nm. With Ho 3+ doping, the decrease in the average crystallite size can be explained using the studies by others [14][15][16]. The RE 3+ ions have an empty, half or filled 4f electron shell, such that rare earth Ho 3+ 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]:

X-ray Diffraction Characterisation
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 Ho 3+ substitution. So, according to Formula (1), the X-ray density tends to increase with Ho 3+ substitution because of the increase in the relative molecular mass.
The XRD patterns of the un-sintered and sintered CoHo 0.02 Fe 2−x O 4 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, the X-ray density and the lattice parameter have no noticeable changes, and the average crystallite size of CoHo 0.02 Fe 1.98 O 4 increases with increasing calcination temperature. Unlike in this study, the reported XRD diffraction peaks of CoFe 2 O 4 calcined at a low temperature are not very sharp [4,14]. This indicates that the sample has good crystallinity without calcination. The X-ray density of the sample was calculated by the following relationship [8,12,13]: 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 Ho 3+ substitution. So, according to Formula (1), the X-ray density tends to increase with Ho 3+ substitution because of the increase in the relative molecular mass.
The XRD patterns of the un-sintered and sintered CoHo0.02Fe2−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, the X-ray density and the lattice parameter have no noticeable changes, and the average crystallite size of CoHo0.02Fe1.98O4 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.     4 and Al x Mg 0.5 Zn 0.5 Fe 2−x O 4 (x = 0~0.1). No impurity peaks were found in these XRD patterns. Table 3 indicates that the Gd 0.075 Mg 0.5 Zn 0.5 Fe 1.925 O 4 ferrite has the maximum lattice constant value, due to the radius of Fe 3+ ions being smaller than the radius of Gd 3+ ions [30,33]. With the doping of rare earth Gd 3+ 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 Al 3+ ions being smaller than Fe 3+ ions [34], the lattice constant of Al x Mg 0.5 Zn 0.5 Fe 2−x O 4 ferrite is smaller than Mg 0.5 Zn 0.5 Fe 2 O 4 ferrite, and are shown in Table 4.
in these XRD patterns. Table 3 indicates that the Gd0.075Mg0.5Zn0.5Fe1.925O4 ferrite has the maximum lattice constant value, due to the radius of Fe 3+ ions being smaller than the radius of Gd 3+ ions [30,33]. With the doping of rare earth Gd 3+ 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 Al 3+ ions being smaller than Fe 3+ ions [34], the lattice constant of AlxMg0.5Zn0.5Fe2−xO4 ferrite is smaller than Mg0.5Zn0.5Fe2O4 ferrite, and are shown in Table 4.   With the investigated samples GdxMg0.5Zn0.5Fe2−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 AlxMg0.5Zn0.5Fe2−xO4 (x = 0~0.1) is between 15.8 maximum lattice constant value, due to the radius of Fe 3+ ions being smaller than the radius of Gd 3+ ions [30,33]. With the doping of rare earth Gd 3+ 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 Al 3+ ions being smaller than Fe 3+ ions [34], the lattice constant of AlxMg0.5Zn0.5Fe2−xO4 ferrite is smaller than Mg0.5Zn0.5Fe2O4 ferrite, and are shown in Table 4.   With the investigated samples GdxMg0.5Zn0.5Fe2−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 AlxMg0.5Zn0.5Fe2−xO4 (x = 0~0.1) is between 15.8  With the investigated samples Gd x Mg 0.5 Zn 0.5 Fe 2−x O 4 (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 x Mg 0.5 Zn 0.5 Fe 2−x O 4 (x = 0~0.1) is between 15.8 nm and 37.7 nm. The XRD density increases with Gd 3+ 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 x Mg 0.5 Zn 0.5 Fe 2−x O 4 is attributed to the relative molecular mass increase. Moreover, the decreases in XRD density of Al x Mg 0.5 Zn 0.5 Fe 2−x O 4 are attributed to the fact that the relative molecular mass decreases. Figures 5 and 6 are the XRD patterns of Gd 0.05 Mg 0.5 Zn 0.5 Fe 1.95 O 4 and Al 0.5 Mg 0.5 Zn 0.5 Fe 1.5 O 4 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 we know that the lattice constant and average crystallite size increases, and the XRD Density decreases with increasing the sintered temperature for the Gd 0.05 Mg 0.5 Zn 0.5 Fe 1.95 O 4 . For the Al 0.5 Mg 0.5 Zn 0.5 Fe 1.5 O 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. In other literature studies [35], the diffraction peaks of XRD is not very sharpness for CoGd 0.1 Fe 1.9 O 4 calcined at low temperature, the diffraction peaks of XRD is very sharpness for Gd 0.05 Mg 0.5 Zn 0.5 Fe 1.95 O 4 and Al 0.5 Mg 0.5 Zn 0.5 Fe 1.5 O 4 without burning. This indicates that the sample has good crystallinity without sintering.
that the relative molecular mass decreases.  6 are the XRD patterns of Gd0.05Mg0.5Zn0.5Fe1.95O4 and Al0.5Mg0.5Zn0.5Fe1.5O4 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 we know that the lattice constant and average crystallite size increases, and the XRD Density decreases with increasing the sintered temperature for the Gd0.05Mg0.5Zn0.5Fe1.95O4. For the Al0.5Mg0.5Zn0.5Fe1.5O4, 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. In other literature studies [35], the diffraction peaks of XRD is not very sharpness for CoGd0.1Fe1.9O4 calcined at low temperature, the diffraction peaks of XRD is very sharpness for Gd0.05Mg0.5Zn0.5Fe1.95O4 and Al0.5Mg0.5Zn0.5Fe1.5O4 without burning. This indicates that the sample has good crystallinity without sintering.

Temperature (°C) Lattice Constant (Å) Average Crystallite Size (Å) Density (g/cm 3 )
Un    Figure 7 shows the SEM images of CoHoxFe2−xO4 (x = 0, 0.02) annealed at 800 °C. As    Figure 7 shows the SEM images of CoHo x Fe 2−x O 4 (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 Ho 3+ substitution, some cobalt ferrite particles are agglomerated, possibly owing to the magnetic interactions between CoHo x Fe 2−x O 4 particles [15]. Figure 6. XRD patterns of Al0.5Mg0.5Zn0.5Fe1.5O4 sintered at different temperatures.  Figure 7 shows the SEM images of CoHoxFe2−xO4 (x = 0, 0.02) annealed at 800 °C shown in Figure 3, the sample is well-crystallised, and the grain size is almost unif With Ho 3+ substitution, some cobalt ferrite particles are agglomerated, possibly owi the magnetic interactions between CoHoxFe2−xO4 particles [15].  Figure 8 is the grain size distribution of CoFe2O4 and CoHo0.02Fe1.98O4. Usi statistical method, the calculated average grain size of CoFe2O4 and CoHo0.02Fe1.98O ~96.26 and ~47.15 nm, respectively. The grain size of ferrite samples is less than 100 indicating that they are nanoparticles. It is slightly larger than the average crystallite determined using an X-ray, suggesting that each ferrite particle comprises se crystallites [16,17].  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 CoHo0.02Fe1.98O4 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 CoHo0.02Fe1.98O4 particles [15], but the degree of The SEM images of CoHo 0.02 Fe 1.98 O 4 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 0.02 Fe 1.98 O 4 particles [15], but the degree of agglomeration is small. The SEM images of CoHo0.02Fe1.98O4 un-sintered and sintered at 400 °C and 800 °C ar shown in Figure 9. As the heat treatment temperature increased, the crystallinity of th 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 ferrit particles are agglomerated with the increasing heat treatment temperature, owing to th magnetic interactions between CoHo0.02Fe1.98O4 particles [15], but the degree o agglomeration is small. Figure 9. SEM images of CoHo0.02Fe1.98O4 un-sintered and sintered at 400 °C and 800 °C. Figure 10 are the SEM images of Gd0.05Mg0.5Zn0.5Fe1.95O4 and Al0.5Mg0.5Zn0.5Fe1.5O sintered 800 °C. The sample is well crystallized, and the grain size is almost uniform. With the Gd 3+ ions and Al 3+ ions substituting, some particles of cobalt ferrite are agglomerated [21]. Figure 11 are the grain size histogram of Mg0.5Zn0.5Fe2O4, Gd0.05Mg0.5Zn0.5Fe1.95O4 and Al0.5Mg0.5Zn0.5Fe1.5O4. The average grain size is approximately 90.74nm, 46.11 nm and   .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].

Magnetic Analysis
substitution, as shown in Table 7, which could be calculated according to the following relation [8,18]: where nB is the Bohr magneton and M is the molecular mass. The relative molecular mass of CoHoxFe2−xO4 increases as Ho 3+ is replaced. The Ho 3+ , Co 2+ and Fe 3+ ions are 10.6, 3 and 5 µB [8], respectively. Ho exhibits para-magnetism at 295 K [9,10]. Ho 3+ ions preferred to occupy B sites owing to the large Ho 3+ 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 (nB) decreases. Owing to the increased M and the decreased nB with the substitution of Ho 3+ ions, MS decreases according to the formula (2). These results are consistent with other literature reports [9,20].  However, Table 7 shows that MS increases with Ho 3+ concentration for x ≤ 0.02 because of a small amount of paramagnetic Ho 3+ ions occupying A sites. The coercivity (HC) variation of cobalt ferrite with the substitution of Ho 3+ ions can be explained as follows. The rare earth Ho 3+ ions have substantial magneto-crystalline anisotropy [8,19,20]. HC does not increase monotonously with the doping of rare earth Ho 3+ ions because HC is also related to the factors such as crystallinity and crystallite size [21].
Magnetic hysteresis loops of CoHo0.02Fe1.98O4 and CoHo0.10Fe1.90O4 at different sintering temperatures are shown in Figures 13 and 14, respectively. After annealing at 900 °C, CoHo0.02Fe1.98O4 and CoHo0.10Fe1.90O4 have the maximum MS value because particle size increases with the sintering temperature [22].  However, Table 7 shows that M S increases with Ho 3+ concentration for x ≤ 0.02 because of a small amount of paramagnetic Ho 3+ ions occupying A sites. The coercivity (H C ) variation of cobalt ferrite with the substitution of Ho 3+ ions can be explained as follows. The rare earth Ho 3+ ions have substantial magneto-crystalline anisotropy [8,19,20]. H C does not increase monotonously with the doping of rare earth Ho 3+ ions because H C is also related to the factors such as crystallinity and crystallite size [21].
Magnetic H C is related to grain size (D), and their relationship is H C = g − h/D 2 (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. The MS of CoHo0.02Fe1.98O4 and CoHo0.10Fe1.90O4 decrease after annealing at 400 °C because the un-sintered sample may have a good crystallinity, as determined by XRD and SEM. Tables 8 and 9 show that MS increases with Ho 3+ concentration for x = 0.02 and x = 0.10. The MS of CoHo0.02Fe1.98O4 is larger than that of CoHo0.10Fe1.90O4, owing to the small amount of paramagnetic Ho 3+ 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 Ho 3+ occupying A sites will increase MS. The HC of CoHo0.02Fe1.98O4 and CoHo0.10Fe1.90O4 initially increases, decreasing as the sintering temperature increases. HC is related to grain size (D), and their relationship is HC = g − h/D 2 (single domain region) and HC = a + b/D (multi-domain region). According to the abovementioned SEM analysis, the particle size increases with increasing calcination temperature, so the HC increases initially and then decreases as the annealing temperature increases.    The MS of CoHo0.02Fe1.98O4 and CoHo0.10Fe1.90O4 decrease after annealing at 400 °C because the un-sintered sample may have a good crystallinity, as determined by XRD and SEM. Tables 8 and 9 show that MS increases with Ho 3+ concentration for x = 0.02 and x = 0.10. The MS of CoHo0.02Fe1.98O4 is larger than that of CoHo0.10Fe1.90O4, owing to the small amount of paramagnetic Ho 3+ 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 Ho 3+ occupying A sites will increase MS. The HC of CoHo0.02Fe1.98O4 and CoHo0.10Fe1.90O4 initially increases, decreasing as the sintering temperature increases. HC is related to grain size (D), and their relationship is HC = g − h/D 2 (single domain region) and HC = a + b/D (multi-domain region). According to the abovementioned SEM analysis, the particle size increases with increasing calcination temperature, so the HC increases initially and then decreases as the annealing temperature increases.     ions and Al 3+ ions from Tables 10 and 11. As Gd 3+ replaces, the relative molecular mass of Gd x Mg 0.5 Zn 0.5 Fe 2−x O 4 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 Gd 3+ ions are considered as non-magnetic ions at 295 K [38]. Moreover, the magnetic moment of Fe 3+ ions is 5 µ B [21].  ions and Al 3+ ions from Tables 10  and 11. As Gd 3+ replaces, the relative molecular mass of GdxMg0.5Zn0.5Fe2−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 Gd 3+ ions are considered as non-magnetic ions at 295 K [38]. Moreover, the magnetic moment of Fe 3+ ions is 5 µB [21].     15 and 16 show the magnetic hysteresis curve of GdxMg0.5Zn0.5Fe measured at 295 K. The magnetization nearly reaches saturation at 5000 Oe. The satura magnetization decreases with the substitution of Gd 3+ ions and Al 3+ ions from Table  and 11. As Gd 3+ replaces, the relative molecular mass of GdxMg0.5Zn0.5Fe2−xO4 incre The magnetic moments of rare earth ions generally come from localized 4f electron solids, and the magnetic ordering temperature is low, and the Gd rare-earth element the Curie temperature of 293.2 K, close to RT(295 K) [36,37]. The magnetic di orientation is disordered at 295 K, and the rare-earth ion doping has no contributio magnetization. Therefore, the Gd 3+ ions are considered as non-magnetic ions at 295 K Moreover, the magnetic moment of Fe 3+ ions is 5 µB [21].    Due to the relative molecular mass increase and the magnetic moment n B decrease with the doping of Gd 3+ 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 x Mg 0.5 Zn 0.5 Fe 2−x O 4 , as the Al 3+ 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 x Mg 0.5 Zn 0.5 Fe 2−x O 4 is larger than that of the Mg 0.5 Zn 0.5 Fe 2 O 4 from Table 10. The variation of coercivity with Gd 3+ ions substituted MgZn ferrite can be explained as follows. Rare earth ions (Gd 3+ ) have stronger magnetocrystalline anisotropy [33,39].
Magnetic hysteresis loops of Gd 0.05 Mg 0.5 Zn 0.5 Fe 1.95 O 4 at different sintering temperatures are shown in Figure 17. Table 12 indicates that Gd 0.05 Mg 0.5 Zn 0.5 Fe 1.95 O 4 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 0.05 Mg 0.5 Zn 0.5 Fe 1.95 O 4 decreases as sintering temperature increases. The coercivity (H C ) is related to grain size (D), and their relationship is H C = g − h/D 2 (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 0.05 Mg 0.5 Zn 0.5 Fe 1.95 O 4 sintered at different temperatures is the multidomain region, so the coercivity decreases as annealing temperature increases. Due to the relative molecular mass increase and the magnetic moment nB decrease with the doping of Gd 3+ 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 nB will decrease. For the AlxMg0.5Zn0.5Fe2−xO4, as the Al 3+ are replaced the relative molecular mass and the total magnetic moment nB decreases, and the influence of the magnetic moment is greater than the relative molecular mass, so the saturation magnetization decreases. The coercivity of GdxMg0.5Zn0.5Fe2−xO4 is larger than that of the Mg0.5Zn0.5Fe2O4 from Table 10. The variation of coercivity with Gd 3+ ions substituted MgZn ferrite can be explained as follows. Rare earth ions (Gd 3+ ) have stronger magnetocrystalline anisotropy [33,39].  Figure 17. Table 12 indicates that Gd0.05Mg0.5Zn0.5Fe1.95O4 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 Gd0.05Mg0.5Zn0.5Fe1.95O4 decreases as sintering temperature increases. The coercivity (HC) is related to grain size (D), and their relationship is HC = g − h/D 2 (single domain region) and HC = 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 Gd0.05Mg0.5Zn0.5Fe1.95O4 sintered at different temperatures is the multidomain region, so the coercivity decreases as annealing temperature increases.    Figure 18 shows the Mössbauer spectra of CoHo x Fe 2−x O 4 (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, the changes in I.S. values are relatively small with the effects of Ho 3+ substitution, and Ho 3+ doping has no apparent impact on the s-electron charge distribution of Fe nuclei [24]. According to other reports, the I.S. values of Fe 3+ 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 Fe 3+ . Table 13 shows that the magnetic hyperfine field (H) tends to decrease by Ho 3+ substitution, owing to the decrease of the A-B super-exchange by the paramagnetic rare-earth Ho 3+ ions [27,28]. The value of the quadrupole shift is very small in the specimens of CoHo x Fe 2−x O 4 , 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 x Fe 2−x O 4 has changed with increasing Ho substitution, which indicates that Ho 3+ substitution influences the Fe 3+ fraction at tetrahedral A and octahedral B sites.

°C
27.54 55.79 3.79 Figure 18 shows the Mössbauer spectra of CoHoxFe2−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, the changes in I.S. values are relatively small with the effects of Ho 3+ substitution, and Ho 3+ doping has no apparent impact on the s-electron charge distribution of Fe nuclei [24]. According to other reports, the I.S. values of Fe 3+ 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 Fe 3+ . Table 13 shows that the magnetic hyperfine field (H) tends to decrease by Ho 3+ substitution, owing to the decrease of the A-B super-exchange by the paramagnetic rareearth Ho 3+ ions [27,28]. The value of the quadrupole shift is very small in the specimens of CoHoxFe2−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 CoHoxFe2−xO4 has changed with increasing Ho substitution, which indicates that Ho 3+ substitution influences the Fe 3+ fraction at tetrahedral A and octahedral B sites.     4 , 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 Fe 3+ ions are 0.1-0.5 mm/s [27,36]. From Tables 14 and 15, the isomer shifts values indicate that iron is in the form of Fe 3+ ions. The value of the quadrupole shift is relatively small with effects of Gd 3+ and Al 3+ ions substitution, and Gd 3+ 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 Gd 3+ ions and Al 3+ ions substitution. mm/s [27,36]. From Tables 14 and 15, the isomer shifts values indicate that iron is in form of Fe 3+ ions. The value of the quadrupole shift is relatively small with effects of G and Al 3+ ions substitution, and Gd 3+ doping has no obvious effect on the s-electron cha distribution of Fe nuclei [25,27]. The magnetic hyperfine field of the Zeeman-split se spectra decreases with rare earth Gd 3+ ions and Al 3+ ions substitution.        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.

Conclusions
A y B 1−y C x Fe 2−x O 4 (C=Ho,Gd,Al) ferrite powders were synthesised via the sol-gelcombustion route. The XRD results show that CoHo x Fe 2−x O 4 are single spinel-structured ferrites, and the CoHo 0.02 Fe 1.98 O 4 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 x Fe 2−x O 4 displayed ferromagnetic behaviour. Mössbauer spectra of CoHo 0.02 Fe 1.98 O 4 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 0.5 Zn 0.5 C x Fe 2−x O 4 (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 Gd 3+ ions; that the sample exhibited paramagnetic character with the replaced Al 3+ ions; and that the isomer shift values indicated that iron is in the form of Fe 3+ ions.