Effects of Nonmagnetic Zn2+ Ion and RE Ion Substitution on the Magnetic Properties of Functional Nanomaterials Co1−yZnyRExFe2−xO4 (RE = La, Sm, Gd) by Sol–Gel

Magnetic Functional Nanomaterials Co1−yZnyRExFe2−xO4 (RE (rare-earth) = La,Sm,Gd) were prepared using the sol–gel combustion method. XRD characterization confirms that the ferrite samples we synthesized are single-phase cubic structures. The variation in the average crystalline size and lattice parameter is related to RE ion doping. The Mössbauer spectra of CoRExFe2−xO4 are two sets of magnetic six-wire peaks that indicate the ferrimagnetic behavior of the sample. The calcination temperature greatly influences the absorption area of Mössbauer for CoFe2O4, indicating that the calcination temperature affects the iron ion content at the octahedral B and tetrahedral A sites. Additionally, scanning electron microscopy measurements of the substituted specimens reveal that the ferrite powders are nanoparticles. With an increase in RE ions, the coercivity increases, and the saturation magnetization changes obviously. The XRD characterization of Co0.7Zn0.3LaxFe2−xO4 shows that the main crystalline phase of the sample is the cubic spinel structure phase, and there are fewer secondary crystalline phases. The lattice parameter tends to decrease with the substitution of La3+ ions. The average grain size decreased significantly with the increase in La content. From ferrimagnetic state transition to relaxation behavior, the hyperfine magnetic field decreases in La concentration by room temperature Mössbauer spectra. With the substitution of La3+ ions, both the saturation magnetization and coercivity of the samples were reduced, and the coercivity of all samples was lower.


Introduction
CoFe 2 O 4 is an important magnetostriction and magnetic material [1][2][3][4].CoFe 2 O 4 has been widely used as magnetic recording material [5][6][7][8].Mössbauer effect spectra are a suitable technique to detect the local environment of iron nuclei around various divalent cations consisting of a close-packed oxygen arrangement [9][10][11][12][13].The rare-earth ions exhibit interesting magnetic and magnetostrictive properties [14][15][16][17][18], playing an essential role in the magnetocrystalline anisotropy of ferrite.The RE ions of 4f elements substitute Fe 3+ ions of 3d elements in ferrites, exhibiting the strong 3d-4f spin-orbital coupling [19][20][21][22][23]. Kumar et al. [10] studied the magnet anisotropy on the La 3+ substitution effect of CoFe 2−x La x O 4 ferrites.Mariano et al. [11] synthesized the magnetic nanoparticles Fe 2−x CoSm x O 4 and analyzed the variation of physical and magnetic properties with Sm content.Simultaneously, Rana et al. [12] investigated the dielectric properties, revealing a strong dependence on Gd 3+ substitution in nano cobalt ferrite.Mixed ferrite has vast applications in a wide range, from frequencies to radio microwaves [24][25][26][27].They play an irreplaceable role in magnetic recording, computer memory, and microwave devices due to their low eddy current loss and high resistivity [28][29][30][31].In nanomaterials containing transition metals with 3D band structures, magnetic carriers are 3D shell electrons that migrate from one atom to another [32][33][34][35].The magnetic moments are localized in individual atoms [36,37].The dielectric constants and permeability of Co 0.5 Zn 0.5 Fe 2 O 4 in the range of 10 MHz to 1.0 GHz show the potential of the material as an electromagnetic interference absorber [38].For Co 1−x Zn x Fe 2 O 4+γ of the composition x = 0.6, its paramagnetic transition temperature is 310-334 K, indicating that magnetic fluid hyperthermia is suitable for self-control states [39].For synthesizing nanometer ferrite powder, the sol-gel method is a simple and economical process.
To sum up, the substitution of nonmagnetic Zn 2+ ions and rare-earth ions will have a greater impact on magnetic properties.The above literature mainly studies the influence of Zn ion or rare-earth ion single-component doping on sample properties, while some of the literature has focused on the influence of co-doped cobalt ferrite with nonmagnetic Zn ions and rare-earth ions on sample magnetism.Therefore, the co-doping of nonmagnetic Zn ions and rare-earth ions will be studied in this paper.It has many advantages, for example, inexpensive raw material, low external energy consumption, homogenous highly reactive powder, and good crystallinity [40].In this paper, Co 1−y Zn y RE x Fe 2−x O 4 (RE = La, Sm, Gd) functional nanomaterials were prepared by sol-gel auto combustion method, and the effects of nonmagnetic zinc ion and rare-earth ion substitution on their structural magnetic properties were studied.

The XRD Analysis
Figure 1 shows the XRD diffraction pattern of CoFe 2 O 4 sintered at different temperatures, from which no impurity peak is observed, confirming that CoFe 2 O 4 possesses a single spinel-structure ferrite.The average crystallite size increased, and the lattice parameter showed changes for CoFe 2 O 4 sintered at different temperatures, as indicated in Table 1.
Previous studies [4,20,21] have shown that the diffraction peaks of XRD are not sharp for CoFe 2 O 4 calcined at low temperatures.
strong dependence on Gd 3+ substitution in nano cobalt ferrite.Mixed ferrite has vast applications in a wide range, from frequencies to radio microwaves [24][25][26][27].They play an irreplaceable role in magnetic recording, computer memory, and microwave devices due to their low eddy current loss and high resistivity [28][29][30][31].In nanomaterials containing transition metals with 3D band structures, magnetic carriers are 3D shell electrons that migrate from one atom to another [32][33][34][35].The magnetic moments are localized in individual atoms [36,37].The dielectric constants and permeability of Co0.5Zn0.5Fe2O4 in the range of 10 MHz to 1.0 GHz show the potential of the material as an electromagnetic interference absorber [38].For Co1-xZnxFe2O4+γ of the composition x = 0.6, its paramagnetic transition temperature is 310-334 K, indicating that magnetic fluid hyperthermia is suitable for self-control states [39].For synthesizing nanometer ferrite powder, the sol-gel method is a simple and economical process.
To sum up, the substitution of nonmagnetic Zn 2+ ions and rare-earth ions will have a greater impact on magnetic properties.The above literature mainly studies the influence of Zn ion or rare-earth ion single-component doping on sample properties, while some of the literature has focused on the influence of co-doped cobalt ferrite with nonmagnetic Zn ions and rare-earth ions on sample magnetism.Therefore, the co-doping of nonmagnetic Zn ions and rare-earth ions will be studied in this paper.It has many advantages, for example, inexpensive raw material, low external energy consumption, homogenous highly reactive powder, and good crystallinity [40].In this paper, Co1-yZnyRExFe2-xO4 (RE = La, Sm, Gd) functional nanomaterials were prepared by sol-gel auto combustion method, and the effects of nonmagnetic zinc ion and rare-earth ion substitution on their structural magnetic properties were studied.

The XRD Analysis
Figure 1 shows the XRD diffraction pattern of CoFe2O4 sintered at different temperatures, from which no impurity peak is observed, confirming that CoFe2O4 possesses a single spinel-structure ferrite.The average crystallite size increased, and the lattice parameter showed changes for CoFe2O4 sintered at different temperatures, as indicated in Table 1.
Previous studies [4,20,21] have shown that the diffraction peaks of XRD are not sharp for CoFe2O4 calcined at low temperatures.Ferrite doped with nonmagnetic rare-earth ions exhibits strong spin-orbit coupling (3d-4f) since the rare-earth ions plan an important role in determining the magnetocrystalline anisotropy [8][9][10][11].In our results, however, the diffraction peaks of XRD are sharp for CoFe2O4 without burning.The samples without calcination still display excellent crystallinity.Ferrite doped with nonmagnetic rare-earth ions exhibits strong spin-orbit coupling (3d-4f) since the rare-earth ions plan an important role in determining the magnetocrystalline anisotropy [8][9][10][11].In our results, however, the diffraction peaks of XRD are sharp for CoFe 2 O 4 without burning.The samples without calcination still display excellent crystallinity.

Content (x) Lattice Parameter (Å) Average Crystallite Size (Å) Density (g/cm
where M is the relative molecular mass, N is Avogadro's number, and a is the lattice parameter.The XRD density decreases with RE 3+ substitution, as shown in Table 2. Doping RE ions leads to an increase in relative molecular mass, and according to Equation (1), the lattice parameter will also increase.The decrease in XRD density can be attributed to the increasing lattice parameter.The XRD density is calculated using the formula [17][18][19]: where M is the relative molecular mass, N is Avogadro's number, and a is the lattice parameter.The XRD density decreases with RE 3+ substitution, as shown in Table 2. Doping RE ions leads to an increase in relative molecular mass, and according to Equation (1), the lattice parameter will also increase.The decrease in XRD density can be attributed to the increasing lattice parameter.Figure 3 displays the XRD patterns of Co 0.7 Zn 0.3 La x Fe 2−x O 4 (x = 0~0.20)ferrites calcined at 800 • C for 3 h.For all the samples with 0 ≤ x ≤ 0.05, the XRD patterns shown are single phase with spinel structure.When 0.07 ≤ x ≤ 0.20, XRD results confirm that the main phase is the cubic spinel phase, and there is a small amount of LaFeO 3 in the impurity phase.The XRD intensity of LaFeO 3 increases by increasing the La content, which is due to the La 3+ ions having bigger ionic radii and very low solubility in spinel lattice [41].  ) ferrites calcined at 800 °C for 3 h.For all the samples with 0 ≤ x ≤ 0.05, the XRD patterns shown are single phase with spinel structure.When 0.07 ≤ x ≤ 0.20, XRD results confirm that the main phase is the cubic spinel phase, and there is a small amount of LaFeO3 in the impurity phase.The XRD intensity of LaFeO3 increases by increasing the La content, which is due to the La 3+ ions having bigger ionic radii and very low solubility in spinel lattice [41].Table 3 indicate XRD data for Co0.7Zn0.3LaxFe2-xO4calcined at 800 °C .Figure 4 indicate that the lattice parameter tends to decrease with the substitution of La 3+ ions.It may be that there are secondary phases forming in the grain boundary.Other articles have reported similar results for rare-earth substituted ferrites [10].Average crystallite size tends to decrease with the substitution of La 3+ ions; similar results are introduced in the other literature [15].Due to the lower bond energy of Fe 3+ -O 2 compared to La 3+ -O 2− , the entry of La 3+ ions into the lattice to form La 3+ -O 2 bonds requires more energy.Therefore, for ferrite replaced by La 3+ ions, more energy is required to complete crystallization and grain growth.Table 3 shows the trend that density decreases with La 3+ concentration for all samples.The relative atomic weight of La is greater than that of Fe, so the relative molecular weight of the sample increases with the increase in La doping amount.The increase in X-ray density is attributed to an increase in relative molecular weight and a decrease in lattice parameters [42].The increase in X-ray density also indicates improved densification [43].Figure 4 indicate that the lattice parameter tends to decrease with the substitution of La 3+ ions.It may be that there are secondary phases forming in the grain boundary.Other articles have reported similar results for rare-earth substituted ferrites [10].Average crystallite size tends to decrease with the substitution of La 3+ ions; similar results are introduced in the other literature [15].Due to the lower bond energy of Fe 3+ -O 2 compared to La 3+ -O 2− , the entry of La 3+ ions into the lattice to form La 3+ -O 2 bonds requires more energy.Therefore, for ferrite replaced by La 3+ ions, more energy is required to complete crystallization and grain growth.Table 3 shows the trend that density decreases with La 3+ concentration for all samples.The relative atomic weight of La is greater than that of Fe, so the relative molecular weight of the sample increases with the increase in La doping amount.The increase in X-ray density is attributed to an increase in relative molecular weight and a decrease in lattice parameters [42].The increase in X-ray density also indicates improved densification [43].The X-ray patterns of Co0.7Zn0.3La0.01Fe1.99O4calcined at different temperatures are displayed in Figure 5 and Table 4.The samples are all single-phase structures of spinel ferrite, and no other impurities were found.The lattice parameters of all samples showed no significant changes, but the average crystallite size showed an increasing trend with the increase in calcination temperature.The diffraction peaks of Co0.7Zn0.3La0.01Fe1.99O4without burning are very sharp.The samples without calcination still display excellent crystallinity.The X-ray patterns of Co 0.7 Zn 0.3 La 0.01 Fe 1.99 O 4 calcined at different temperatures are displayed in Figure 5 and Table 4.The samples are all single-phase structures of spinel ferrite, and no other impurities were found.The lattice parameters of all samples showed no significant changes, but the average crystallite size showed an increasing trend with the increase in calcination temperature.The diffraction peaks of Co 0.7 Zn 0.3 La 0.01 Fe 1.99 O 4 without burning are very sharp.The samples without calcination still display excellent crystallinity.The X-ray patterns of Co0.7Zn0.3La0.01Fe1.99O4calcined at different temperatures are displayed in Figure 5 and Table 4.The samples are all single-phase structures of spinel ferrite, and no other impurities were found.The lattice parameters of all samples showed no significant changes, but the average crystallite size showed an increasing trend with the increase in calcination temperature.The diffraction peaks of Co0.7Zn0.3La0.01Fe1.99O4without burning are very sharp.The samples without calcination still display excellent crystallinity.   .From this, it can be seen that the ferrite samples we prepared are nanoparticles, as their average grain size is less than 100 nm.They are slightly larger than the average crystallite size of X-ray, so each particle is composed of several crystallites [22].

Structures and Grain Sizes
Molecules 2023, 28, x FOR PEER REVIEW 6 of 18 become agglomerated, which may be due to the magnetic interactions between CoRExFe2−xO4 particles [11].Figure 7 shows a histogram of the grain size distribution of CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd).Statistical methods were used to analyze the average grain size of CoFe2O4, CoLa0.02Fe1.98O4,CoSm0.02Fe1.98O4,and CoGd0.02Fe1.98O4,which were estimated as approximately 96.26, 54.18, 57.36, and 46.15 nm, respectively.From this, it can be seen that the ferrite samples we prepared are nanoparticles, as their average grain size is less than 100 nm.They are slightly larger than the average crystallite size of X-ray, so each particle is composed of several crystallites [22].The SEM micrographs and grain size distribution diagram of CoFe2O4 sintered at 1000 °C are depicted in Figure 8.The average grain size of CoFe2O4 ferrite sintered at 1000 °C is estimated to be approximately 137.5 nm, which is larger than the average grain size become agglomerated, which may be due to the magnetic interactions between CoRExFe2−xO4 particles [11].Figure 7 shows a histogram of the grain size distribution of CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd From this, it can be seen that the ferrite samples we prepared are nanoparticles, as their average grain size is less than 100 nm.They are slightly larger than the average crystallite size of X-ray, so each particle is composed of several crystallites [22].The SEM micrographs and grain size distribution diagram of CoFe2O4 sintered at 1000 °C are depicted in Figure 8.The average grain size of CoFe2O4 ferrite sintered at 1000 °C is estimated to be approximately 137.5 nm, which is larger than the average grain size (96.26nm) of the cobalt ferrite annealed at 800 °C.This indicates that the average grain size of the CoFe2O4 sample increases with an increase in the calcining temperature.Figure 9 shows the SEM microphotographs of Co0.7Zn0.3LaxFe2-xO4(x = 0.05, 0.10) annealed at 800 °C.The sample Co0.7Zn0.3La0.05Fe1.95O4we prepared has a relatively uniform grain distribution and good crystallinity, while Co0.7Zn0.3La0.10Fe1.90O4has lower crystallinity.Figure 10 shows the histogram of the grain size distribution of Co0.7Zn0.3LaxFe2-xO4(x = 0.05, 0.10) ferrites.The significant decrease in the average grain size with increasing La content may be due to the growth of grain being inhibited with LaFeO3 [18].The average grain size of Co0.7Zn0.3La0.05Fe1.95O4and Co0.7Zn0.3La0.10Fe1.90O4estimated by a statistical method is approximately 35.21 and 30.90 nm, respectively.The average grain size is slightly larger than the average crystallite size of X-ray, so each particle is composed of several crystallites [22].(x = 0.05, 0.10) ferrites.The significant decrease in the average grain size with increasing La content may be due to the growth of grain being inhibited with LaFeO 3 [18].The average grain size of Co 0.7 Zn 0.3 La 0.05 Fe 1.95 O 4 and Co 0.7 Zn 0.3 La 0.10 Fe 1.90 O 4 estimated by a statistical method is approximately 35.21 and 30.90 nm, respectively.The average grain size is slightly larger than the average crystallite size of X-ray, so each particle is composed of several crystallites [22].
(96.26 nm) of the cobalt ferrite annealed at 800 °C.This indicates that the average grain size of the CoFe2O4 sample increases with an increase in the calcining temperature.Figure 9 shows the SEM microphotographs of Co0.7Zn0.3LaxFe2-xO4(x = 0.05, 0.10) annealed at 800 °C.The sample Co0.7Zn0.3La0.05Fe1.95O4we prepared has a relatively uniform grain distribution and good crystallinity, while Co0.7Zn0.3La0.10Fe1.90O4has lower crystallinity.Figure 10 shows the histogram of the grain size distribution of Co0.7Zn0.3LaxFe2-xO4(x = 0.05, 0.10) ferrites.The significant decrease in the average grain size with increasing La content may be due to the growth of grain being inhibited with LaFeO3 [18].The average grain size of Co0.7Zn0.3La0.05Fe1.95O4and Co0.7Zn0.3La0.10Fe1.90O4estimated by a statistical method is approximately 35.21 and 30.90 nm, respectively.The average grain size is slightly larger than the average crystallite size of X-ray, so each particle is composed of several crystallites [22].

Room Temperature Mössbauer Spectra
Figure 11 shows the room temperature Mössbauer spectroscopy curve for CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 °C.We used the Mösswinn 3.0 program to fit the measured Mössbauer spectrum, which consists of two sets of six-line peaks.The six linear peaks with a large isomer shift (I.S.) correspond to the iron ions at position B, while the other set of six linear peaks with a smaller isomer shift (I.S.) correspond to the iron ions at position A. This difference is due to the varying internuclear separations between Fe 3+ and O 2− ions [23,24].The changes in I.S. values due to RE 3+ substitution are relatively small, and the effect of RE 3+ doping on the charge distribution around Fe 3+ is not significant [24].According to other reports, the I.S. values for Fe 3+ ions range from 0.1 mm/s to 0.5 mm/s [25].Therefore, the I.S. values indicate that the iron in our sample is Fe 3+ ions (Table 5).The magnetic hyperfine field (H) does not appear to be affected by RE 3+ substitution.Figure 12

Room Temperature Mössbauer Spectra
Figure 11 shows the room temperature Mössbauer spectroscopy curve for CoRE x Fe 2−x O 4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 • C. We used the Mösswinn 3.0 program to fit the measured Mössbauer spectrum, which consists of two sets of six-line peaks.The six linear peaks with a large isomer shift (I.S.) correspond to the iron ions at position B, while the other set of six linear peaks with a smaller isomer shift (I.S.) correspond to the iron ions at position A. This difference is due to the varying internuclear separations between Fe 3+ and O 2− ions [23,24].The changes in I.S. values due to RE 3+ substitution are relatively small, and the effect of RE 3+ doping on the charge distribution around Fe 3+ is not significant [24].According to other reports, the I.S. values for Fe 3+ ions range from 0.1 mm/s to 0.5 mm/s [25].Therefore, the I.S. values indicate that the iron in our sample is Fe 3+ ions (Table 5).The magnetic hyperfine field (H) does not appear to be affected by RE 3+ substitution.Figure 12

Room Temperature Mössbauer Spectra
Figure 11 shows the room temperature Mössbauer spectroscopy curve for CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 °C.We used the Mösswinn 3.0 program to fit the measured Mössbauer spectrum, which consists of two sets of six-line peaks.The six linear peaks with a large isomer shift (I.S.) correspond to the iron ions at position B, while the other set of six linear peaks with a smaller isomer shift (I.S.) correspond to the iron ions at position A. This difference is due to the varying internuclear separations between Fe 3+ and O 2− ions [23,24].The changes in I.S. values due to RE 3+ substitution are relatively small, and the effect of RE 3+ doping on the charge distribution around Fe 3+ is not significant [24].According to other reports, the I.S. values for Fe 3+ ions range from 0.1 mm/s to 0.5 mm/s [25].Therefore, the I.S. values indicate that the iron in our sample is Fe 3+ ions (Table 5).The magnetic hyperfine field (H) does not appear to be affected by RE 3+ substitution.Figure 12      Figure 13 displays the room temperature Mössbauer spectra of Co0.7Zn0.3LaxFe2-xO4.The spectra of Co0.7Zn0.3Fe2O4,fitted with two sextets of Zeeman-split, are attributed to Fe 3+ at tetrahedral and octahedral sites, indicating the ferrimagnetic behavior of the samples.The six linear peaks with a large I.S. correspond to the iron ions at position B, while the other set of six linear peaks with a smaller I.S. correspond to the iron ions at position A [20].When 0.01 ≤ x ≤ 0.15, the Mössbauer spectrum of Co0.7Zn0.3LaxFe2-xO4only shows a set of magnetic six-line peaks, corresponding to the six-line peaks at the B site, indicating that Fe 3+ ions only occupy the octahedral B site [44].The Mössbauer spectrum of x = 0.20 was fitted with one single sextet and a central paramagnetic doublet, and it shows the relaxation effects features.The A-B exchange interaction decreases with the substitution of nonmagnetic La 3+ ions, resulting in a decrease in the magnetic hyperfine field value [8].The large isomer shift (I.S.) value of Fe 2+ ions is 0.1-0.5 mm/s, while for Fe 3+ , it is 0.6-1.7 mm/s [44].From the isomer shift (I.S.) values in Table 6, we know that the iron ions in our sample are in the Fe 3+ state.Figure 14 displays the A site of the tetrahedral lattice and the B site of the octahedral lattice.The quadrupole shift of the magnetic sextet for A and B sites is very small, which indicates that the charge distribution of atomic nuclei is close to spherical symmetry.Mössbauer spectrum of Co0.7Zn0.3La0.2Fe1.8O4was fitted with one single sextet and a central paramagnetic doublet, which shows the relaxation effects features [45].only shows a set of magnetic six-line peaks, corresponding to the six-line peaks at the B site, indicating that Fe 3+ ions only occupy the octahedral B site [44].The Mössbauer spectrum of x = 0.20 was fitted with one single sextet and a central paramagnetic doublet, and it shows the relaxation effects features.The A-B exchange interaction decreases with the substitution of nonmagnetic La 3+ ions, resulting in a decrease in the magnetic hyperfine field value [8].The large isomer shift (I.S.) value of Fe 2+ ions is 0.1-0.5 mm/s, while for Fe 3+ , it is 0.6-1.7 mm/s [44].From the isomer shift (I.S.) values in Table 6, we know that the iron ions in our sample are in the Fe 3+ state.Figure 14 displays the A site of the tetrahedral lattice and the B site of the octahedral lattice.The quadrupole shift of the magnetic sextet for A and B sites is very small, which indicates that the charge distribution of atomic nuclei is close to spherical symmetry.Mössbauer spectrum of Co 0.7 Zn 0.3 La 0.2 Fe 1.8 O 4 was fitted with one single sextet and a central paramagnetic doublet, which shows the relaxation effects features [45].Figure 15 depicts the room temperature (RT) Mössbauer spectroscopy curve for CoFe2O4 powders that were calcined at 400, 800, and 1000 °C.The spectra comprise two sets of Zeeman sextet splits.Table 7 indicates that there were no significant changes in     Figure 15 depicts the room temperature (RT) Mössbauer spectroscopy curve for CoFe2O4 powders that were calcined at 400, 800, and 1000 °C.The spectra comprise two sets of Zeeman sextet splits.Table 7 indicates that there were no significant changes in   7 indicates that there were no significant changes in Mössbauer data for CoFe 2 O 4 samples that were calcined at various temperatures.The H remained constant with increasing annealing temperature.This may be due to the high crystallinity of the samples without calcination, as observed in the XRD patterns.However, there were changes in the Mössbauer absorption area, indicating that the calcination temperature affected iron ions at the tetrahedral A and octahedral B sites.
Molecules 2023, 28, x FOR PEER REVIEW 11 of 18 Mössbauer data for CoFe2O4 samples that were calcined at various temperatures.The H remained constant with increasing annealing temperature.This may be due to the high crystallinity of the samples without calcination, as observed in the XRD patterns.However, there were changes in the Mössbauer absorption area, indicating that the calcination temperature affected iron ions at the tetrahedral A and octahedral B sites.  Figure 16 shows the room temperature Mössbauer spectrum of Co0.7Zn0.3La0.01Fe1.99O4ferrite.The spectra of all ferrites sintered at different temperatures were fitted using a sixbaryon pattern.Table 8 shows no significant change in the Mössbauer parameters of Co0.7Zn0.3La0.01Fe1.99O4calcined at different temperatures (unsintered and sintered at 400, 800 °C).The magnetic hyperfine field does not vary with annealing temperature.From the XRD spectrum, this may be due to the good crystallinity of the uncalcined sample.Figure 16 shows the room temperature Mössbauer spectrum of Co 0.7 Zn 0.3 La 0.01 Fe 1.99 O 4 ferrite.The spectra of all ferrites sintered at different temperatures were fitted using a six-baryon pattern.Table 8 shows no significant change in the Mössbauer parameters of Co 0.7 Zn 0.3 La 0.01 Fe 1.99 O 4 calcined at different temperatures (unsintered and sintered at 400, 800 • C).The magnetic hyperfine field does not vary with annealing temperature.From the XRD spectrum, this may be due to the good crystallinity of the uncalcined sample.

Magnetic Property of Particles
The RT magnetic hysteresis curves of CoFe2O4 calcined at 800 and 1000 °C are presented in Figure 17.Table 9 shows that the saturation magnetization of CoFe2O4 increases with the annealing temperature, which is a result of the effect of calcination temperature on particle size [4].The SEM results reveal that the higher calcination temperature led to greater crystallinity and larger average grain size of the CoFe2O4 sample.The coercivity of CoFe2O4 decreases as the annealing temperature increases [10].The coercivity (HC) of the sample is related to the grain size (D) of the sample.When the sample is a single domain, their relationship is HC = g -h/D 2 , and when the sample is multi-domain, their relationship is HC = a + b/D.In the single-domain region, the coercive force increases with the increase in grain size, while in the multi-domain region, the coercive force decreases with the increase in particle diameter.The critical size of cobalt ferrite is approximately 70 nm [13,21].Based on SEM analysis, the particle size of our sample belongs to a multi-domain region, and the coercive force decreases with the increase in annealing temperature.

Magnetic Property of Particles
The RT magnetic hysteresis curves of CoFe 2 O 4 calcined at 800 and 1000 • C are presented in Figure 17.Table 9 shows that the saturation magnetization of CoFe 2 O 4 increases with the annealing temperature, which is a result of the effect of calcination temperature on particle size [4].The SEM results reveal that the higher calcination temperature led to greater crystallinity and larger average grain size of the CoFe 2 O 4 sample.The coercivity of CoFe 2 O 4 decreases as the annealing temperature increases [10].The coercivity (H C ) of the sample is related to the grain size (D) of the sample.When the sample is a single domain, their relationship is H C = gh/D 2 , and when the sample is multi-domain, their relationship is H C = a + b/D.In the single-domain region, the coercive force increases with the increase in grain size, while in the multi-domain region, the coercive force decreases with the increase in particle diameter.The critical size of cobalt ferrite is approximately 70 nm [13,21].Based on SEM analysis, the particle size of our sample belongs to a multi-domain region, and the coercive force decreases with the increase in annealing temperature.Figure 18 displays the RT magnetic hysteresis curve of CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd) measured at 295K.The magnetization of CoRExFe2−xO4 approaches saturation at 10,000 Oe.The magnetism of rare-earth elements mainly comes from the magnetic moment of their 4f electrons.Due to the inner arrangement of 4f electrons, their magnetic moment is very stable, allowing the magnetism of rare-earth elements to remain stable over a wide temperature range [16,29].The Gd element has a Curie temperature of 293.2 K, close to RT (295 K) [18].The magnetic dipoles are arranged disorderly at the temperature of 295 K; therefore, RE ion doping does not contribute to magnetization.From Table 10, the substitution of RE 3+ ions results in a reduction in the saturation magnetization, which can be calculated using the following equation [26,27]:  Oe.The magnetism of rare-earth elements mainly comes from the magnetic moment of their 4f electrons.Due to the inner arrangement of 4f electrons, their magnetic moment is very stable, allowing the magnetism of rare-earth elements to remain stable over a wide temperature range [16,29].The Gd element has a Curie temperature of 293.2 K, close to RT (295 K) [18].The magnetic dipoles are arranged disorderly at the temperature of 295 K; therefore, RE ion doping does not contribute to magnetization.  Figure 18 displays the RT magnetic hysteresis curve of CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd) measured at 295K.The magnetization of CoRExFe2−xO4 approaches saturation at 10,000 Oe.The magnetism of rare-earth elements mainly comes from the magnetic moment of their 4f electrons.Due to the inner arrangement of 4f electrons, their magnetic moment is very stable, allowing the magnetism of rare-earth elements to remain stable over a wide temperature range [16,29].The Gd element has a Curie temperature of 293.2 K, close to RT (295 K) [18].The magnetic dipoles are arranged disorderly at the temperature of 295 K; therefore, RE ion doping does not contribute to magnetization.From Table 10, the substitution of RE 3+ ions results in a reduction in the saturation magnetization, which can be calculated using the following equation [26,27]: From Table 10, the substitution of RE 3+ ions results in a reduction in the saturation magnetization, which can be calculated using the following equation [26,27]: where M is the molecular mass, and n B is the Bohr magneton.As RE 3+ was replaced, the relative molecular mass of CoRE x Fe 2−x O 4 increased.La 3+ , Sm 3+ , Gd 3+ , Co 2+ , and Fe 3+ ions have magnetic moments of 0µ B , 1.7µ B , 7.94µ B , 3µ B , and 5µ B [11,15,17,18,28], respectively.As a result, RE ions (La 3+ , Sm 3+ and Gd 3+ ) are considered nonmagnetic at 295 K. Co 2+ ions prefer to occupy the B sites, and RE 3+ ions only occupy the B sites due to their large ionic radius [6,7,18,30,31].According to the Neel theory, the magnetic moment n B of (Fe) A [CoRE x Fe 1−x ] B O 4 can be expressed as [20,29]: where M A and M B are the magnetic moments of the A site and B site, respectively.The substitution of RE 3+ ions leads to a decrease in the magnetic moment.The theoretical saturation magnetization also decreases, as per Equation ( 2), which is consistent with experimental results.Table 10 indicates an increase in the coercivity of CoRE x Fe 2−x O 4 with the addition of RE ions.For CoFe 2 O 4 ferrite, the large coercivity value is primarily at the B site due to the anisotropy of the cobalt ions [6].Coercivity is influenced by microstrain, magnetic particle morphology, and magnetic domain size [16,32,33].Rare-earth ions (RE = La, Sm, and Gd) exhibit stronger magnetocrystalline anisotropy; therefore, the coercivity of cobalt ferrite increases with the substitution of RE 3+ ions [7,8,21,29].Additionally, the crystallite size of RE-substituted ferrite decreases with RE 3+ ion substitution [13,16,34,35].In our research, the grain size of CoFe 2 O 4 calcined at 800 and 1000 • C falls within the multi-domain region; the grain size of the sample increases with increasing calcination temperature, so the coercivity decreases as the annealing temperature increases.
Figure 19 shows the room temperature hysteresis loop of Co 0.7 Zn 0.3 La x Fe 2−x O 4 .For all samples, the magnetization reached saturation in an external field of 10,000 Oe.

M n
where M is the molecular mass, and nB is the Bohr magneton.As RE 3+ was replaced, the relative molecular mass of CoRExFe2−xO4 increased.La 3+ , Sm 3+ , Gd 3+ , Co 2+ , and Fe 3+ ions have magnetic moments of 0µB, 1.7µB, 7.94µB, 3µB, and 5µB [11,15,17,18,28], respectively.As a result, RE ions (La 3+ , Sm 3+ and Gd 3+ ) are considered nonmagnetic at 295 K. Co 2+ ions prefer to occupy the B sites, and RE 3+ ions only occupy the B sites due to their large ionic radius [6,7,18,30,31].According to the Neel theory, the magnetic moment nB of (Fe)A[CoRExFe1−x]BO4 can be expressed as [20,29]: where MA and MB are the magnetic moments of the A site and B site, respectively.The substitution of RE 3+ ions leads to a decrease in the magnetic moment.The theoretical saturation magnetization also decreases, as per Equation ( 2), which is consistent with experimental results.Table 10 indicates an increase in the coercivity of CoRExFe2−xO4 with the addition of RE ions.For CoFe2O4 ferrite, the large coercivity value is primarily at the B site due to the anisotropy of the cobalt ions [6].Coercivity is influenced by microstrain, magnetic particle morphology, and magnetic domain size [16,32,33].Rare-earth ions (RE = La, Sm, and Gd) exhibit stronger magnetocrystalline anisotropy; therefore, the coercivity of cobalt ferrite increases with the substitution of RE 3+ ions [7,8,21,29].Additionally, the crystallite size of RE-substituted ferrite decreases with RE 3+ ion substitution [13,16,34,35].In our research, the grain size of CoFe2O4 calcined at 800 and 1000 °C falls within the multidomain region; the grain size of the sample increases with increasing calcination temperature, so the coercivity decreases as the annealing temperature increases.
Figure 19 shows the room temperature hysteresis loop of Co0.7Zn0.3LaxFe2-xO4.For all samples, the magnetization reached saturation in an external field of 10,000 Oe.In Table 11, the saturation magnetization decreases with an increase in La content.The doping of La element affects the magnetic properties of cobalt ferrite.Co 2+ prefers octahedral sites, and the Zn 2+ ion prefers tetrahedral sites, which is due to Co-Zn ferrite being an inverted spinel and La 3+ ions having strong B site preference [14,16], so the cation distribution is (Zn 0.3 Fe) A [Co 0.7 La x Fe 1−x ] B O 4 [43,44].According to the two sublattice model of Néel's theory, the magnetic moment n B is expressed by [46]: where M B and M A are the sublattice magnetic moments of the B and A positions.Figure 20 shows the changes in theoretical and experimental magnetic moments as La concentration increases.According to Figure 20, the experimental and theoretical magnetic moments decrease with an increase in La content x.According to Equation (3), the theoretical saturation magnetization decreases with an increase in La content x.
Molecules 2023, 28, x FOR PEER REVIEW 15 of 18 In Table 11, the saturation magnetization decreases with an increase in La content.The doping of La element affects the magnetic properties of cobalt ferrite.Co 2+ prefers octahedral sites, and the Zn 2+ ion prefers tetrahedral sites, which is due to Co-Zn ferrite being an inverted spinel and La 3+ ions having strong B site preference [14,16], so the cation distribution is (Zn0.3Fe)A[Co0.7LaxFe1-x]BO4[43,44].[46]: where MB and MA are the sublattice magnetic moments of the B and A positions.Figure 20 shows the changes in theoretical and experimental magnetic moments as La concentration increases.According to Figure 20, the experimental and theoretical magnetic moments decrease with an increase in La content x.According to Equation (3), the theoretical saturation magnetization decreases with an increase in La content x.For all samples, the variation in experimental saturation magnetization is well consistent with the theoretical saturation magnetization.As shown in Table 11, the coercivity of Co0.7Zn0.3LaxFe2-xO4decreases with increasing La content x.All samples display low coercivity, which shows that they are typical soft ferrites [46,47].The large coercivity essentially originates from the magnetocrystalline anisotropy of the Co 2+ ions in the octahedral site [47,48].The coercivity decreases with increasing lanthanum content, which can be due to the weakening of anisotropy when the Co 2+ ions migrate to the tetrahedral site.While x = 0.05 and x = 0.10, the coercivity has no significant changes, which may be attributed to the appearance of impurity phases LaFeO3 [47,49,50].

Experimental Method
Magnetic Functional Nanomaterials Co1-yZnyRExFe2-xO4 (RE (rare-earth) = La,Sm,Gd) were synthesized by the sol-gel combustion method.The synthetic raw material of the For all samples, the variation in experimental saturation magnetization is well consistent with the theoretical saturation magnetization.As shown in Table 11, the coercivity of Co 0.7 Zn 0.3 La x Fe 2−x O 4 decreases with increasing La content x.All samples display low coercivity, which shows that they are typical soft ferrites [46,47].The large coercivity essentially originates from the magnetocrystalline anisotropy of the Co 2+ ions in the octahedral site [47,48].The coercivity decreases with increasing lanthanum content, which can be due to the weakening of anisotropy when the Co 2+ ions migrate to the tetrahedral site.While x = 0.05 and x = 0.10, the coercivity has no significant changes, which may be attributed to the appearance of impurity phases LaFeO 3 [47,49,50].

Experimental Method
Magnetic Functional Nanomaterials Co 1−y Zn y RE x Fe 2−x O 4 (RE (rare-earth) = La,Sm,Gd) were synthesized by the sol-gel combustion method.The synthetic raw material of the sample is analytically pure nitrate Fe(NO 3 ) 3 •9H 2 O, M(NO 3 ) 2 •6H 2 O (M = Co, Zn, La, Sm, Gd), ammonia (NH 3 •H 2 O), and citric acid (C 6 H 8 O 7 •H 2 O).Add deionized water to citric acid and metal nitrate to form the solution and adjust the pH value to around 7 by adding C 6 H 8 O 7 •H 2 O and NH 3 •H 2 O. Place the mixed solution in a constant temperature water bath at 80 • C, stir it electrically until the gel is dried, dry it further in an oven at 120 • C, and ignite it in air with a small amount of alcohol as an oxidant.After self-ignition, the powder material is annealed in a muffle furnace at a specific temperature.Place the mixed solution in a constant temperature water bath at 80 • C, stir it electrically until the gel is dried, dry it further in an oven at 120 • C, and ignite it in air with a small amount of alcohol as an oxidant.After self-ignition, the powder material is annealed at a specific temperature in a muffle furnace.The various analytical techniques (XRD, SEM, Mössbauer, VSM) were used to determine the following features: the impact of different doping amounts of La, Sm, Gd ion, calcination temperature, and calcination time on the structure, chemical bonding, particle shape and size, magnetic performance, and hyperfine interaction of samples.

Conclusions
We used the sol-gel combustion method to synthesize Co 1−y Zn y RE x Fe 2−x O 4 (RE =La, Sm, Gd) nanoparticles.CoFe 2 O 4 samples calcined at different temperatures (unsintered and sintered at 400 • C, 800 • C, 1000 • C) have good crystallinity.Furthermore, the XRD results indicate that CoRE x Fe 2−x O 4 ferrites are single spinel-structured.SEM images suggest that the samples are well crystallized, with homogeneously distributed grains and composed of nanoparticles.RT Mössbauer spectroscopy of CoRE x Fe 2−x O 4 (x = 0, 0.02; RE = La, Sm, Gd) demonstrates ferrimagnetic behavior.Mössbauer spectra of CoFe 2 O 4 reveal that the magnetic properties are influenced by the calcination temperature.The magnetization curve results suggest that RE ion doping impacts the coercivity and saturation magnetization, allowing the regulation of the sample's magnetism through RE ion doping.The XRD patterns of Co 0.7 Zn 0.3 La x Fe 2−x O 4 confirm the main phase is a cubic spinel phase structure along with the appearance of impurity phases LaFeO 3 .It indicates that in spinel lattice, lanthanum has very low solubility.The average grain size decreases significantly with increasing La content.As the La content increases, the average grain size significantly decreases.The Mössbauer spectrum indicates that with the doping of nonmagnetic ions, the sample transitions from a ferrous magnetic state to a relaxed state, while the iron ions in the sample are in the Fe 3+ state.The saturation magnetization and coercivity decrease with the increase in La content x.The change in coercivity is attributed to the decrease in magnetic crystal anisotropy and the presence of impurity phases LaFeO 3 .

Figure 3
Figure3displays the XRD patterns of Co0.7Zn0.3LaxFe2-xO4(x = 0~0.20)ferrites calcined at 800 °C for 3 h.For all the samples with 0 ≤ x ≤ 0.05, the XRD patterns shown are single phase with spinel structure.When 0.07 ≤ x ≤ 0.20, XRD results confirm that the main phase is the cubic spinel phase, and there is a small amount of LaFeO3 in the impurity phase.The XRD intensity of LaFeO3 increases by increasing the La content, which is due to the La 3+ ions having bigger ionic radii and very low solubility in spinel lattice[41].Table3indicate XRD data for Co0.7Zn0.3LaxFe2-xO4calcined at 800 °C .

Figure 4 .
Figure 4.The variation of lattice parameter and average crystallite size for Co 0.7 Zn 0.3 La x Fe 2−x O 4 .

Figure 6
Figure 6 depicts the SEM images of Functional Nanomaterials CoRE x Fe 2−x O 4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 • C. The sample is well crystallized and displays almost uniform grain sizes.With the substitution of RE 3+ ions, some cobalt ferrite particles become agglomerated, which may be due to the magnetic interactions between CoRE x Fe 2−x O 4

Figure 7 .
Figure 7. Grain size of CoRE x Fe 2−x O 4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 • C. The SEM micrographs and grain size distribution diagram of CoFe 2 O 4 sintered at 1000 • C are depicted in Figure 8.The average grain size of CoFe 2 O 4 ferrite sintered at 1000 • C is estimated to be approximately 137.5 nm, which is larger than the average grain size (96.26nm) of the cobalt ferrite annealed at 800 • C.This indicates that the average grain size of the CoFe 2 O 4 sample increases with an increase in the calcining temperature.

Figure 8 .
Figure 8. Scanning electron microscopy micrographs and grain size distribution diagram for CoFe2O4 sintered at 1000 °C.

Figure 8 .
Figure 8. Scanning electron microscopy micrographs and grain size distribution diagram for CoFe 2 O 4 sintered at 1000 • C.

Figure 9
Figure 9 shows the SEM microphotographs of Co 0.7 Zn 0.3 La x Fe 2−x O 4 (x = 0.05, 0.10) annealed at 800 • C. The sample Co 0.7 Zn 0.3 La 0.05 Fe 1.95 O 4 we prepared has a relatively uniform grain distribution and good crystallinity, while Co 0.7 Zn 0.3 La 0.10 Fe 1.90 O 4 has lower crystallinity.Figure 10 shows the histogram of the grain size distribution of Co 0.7 Zn 0.3 La x Fe 2−x O 4(x = 0.05, 0.10) ferrites.The significant decrease in the average grain size with increasing La content may be due to the growth of grain being inhibited with LaFeO 3[18].The average grain size of Co 0.7 Zn 0.3 La 0.05 Fe 1.95 O 4 and Co 0.7 Zn 0.3 La 0.10 Fe 1.90 O 4 estimated by a statistical method is approximately 35.21 and 30.90 nm, respectively.The average grain size is slightly larger than the average crystallite size of X-ray, so each particle is composed of several crystallites[22].

Figure 8 .
Figure 8. Scanning electron microscopy micrographs and grain size distribution diagram for CoFe2O4 sintered at 1000 °C.
Figure11shows the room temperature Mössbauer spectroscopy curve for CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 °C.We used the Mösswinn 3.0 program to fit the measured Mössbauer spectrum, which consists of two sets of six-line peaks.The six linear peaks with a large isomer shift (I.S.) correspond to the iron ions at position B, while the other set of six linear peaks with a smaller isomer shift (I.S.) correspond to the iron ions at position A. This difference is due to the varying internuclear separations between Fe 3+ and O 2− ions[23,24].The changes in I.S. values due to RE 3+ substitution are relatively small, and the effect of RE 3+ doping on the charge distribution around Fe 3+ is not significant[24].According to other reports, the I.S. values for Fe 3+ ions range from 0.1 mm/s to 0.5 mm/s[25].Therefore, the I.S. values indicate that the iron in our sample is Fe 3+ ions (Table5).The magnetic hyperfine field (H) does not appear to be affected by RE 3+ substitution.Figure12displays the spatial structure of spinel ferrite cells.It is possible that micro-substitution is insufficient to significantly alter the H.The quadrupole displacement value in the sample CoRExFe2−xO4 is the smallest, indicating good symmetry of the electric field around the atomic nucleus in cobalt ferrite.

Figure 11 .
Figure 11.Room temperature Mössbauer spectroscopy curve for CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 °C.(The blue and purple line spectra represent the Mössbauer spectra of iron ions in the A and B lattice, while the red line spectra represent the total Mössbauer spectra)

18 Figure 10 .
Figure11shows the room temperature Mössbauer spectroscopy curve for CoRE x Fe 2−x O 4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 • C. We used the Mösswinn 3.0 program to fit the measured Mössbauer spectrum, which consists of two sets of six-line peaks.The six linear peaks with a large isomer shift (I.S.) correspond to the iron ions at position B, while the other set of six linear peaks with a smaller isomer shift (I.S.) correspond to the iron ions at position A. This difference is due to the varying internuclear separations between Fe 3+ and O 2− ions[23,24].The changes in I.S. values due to RE 3+ substitution are relatively small, and the effect of RE 3+ doping on the charge distribution around Fe 3+ is not significant[24].According to other reports, the I.S. values for Fe 3+ ions range from 0.1 mm/s to 0.5 mm/s[25].Therefore, the I.S. values indicate that the iron in our sample is Fe 3+ ions (Table5).The magnetic hyperfine field (H) does not appear to be affected by RE 3+ substitution.Figure12displays the spatial structure of spinel ferrite cells.It is possible that micro-substitution is insufficient to significantly alter the H.The quadrupole displacement value in the sample CoRE x Fe 2−x O 4 is the smallest, indicating good symmetry of the electric field around the atomic nucleus in cobalt ferrite.
Figure11shows the room temperature Mössbauer spectroscopy curve for CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 °C.We used the Mösswinn 3.0 program to fit the measured Mössbauer spectrum, which consists of two sets of six-line peaks.The six linear peaks with a large isomer shift (I.S.) correspond to the iron ions at position B, while the other set of six linear peaks with a smaller isomer shift (I.S.) correspond to the iron ions at position A. This difference is due to the varying internuclear separations between Fe 3+ and O 2− ions[23,24].The changes in I.S. values due to RE 3+ substitution are relatively small, and the effect of RE 3+ doping on the charge distribution around Fe 3+ is not significant[24].According to other reports, the I.S. values for Fe 3+ ions range from 0.1 mm/s to 0.5 mm/s[25].Therefore, the I.S. values indicate that the iron in our sample is Fe 3+ ions (Table5).The magnetic hyperfine field (H) does not appear to be affected by RE 3+ substitution.Figure12displays the spatial structure of spinel ferrite cells.It is possible that micro-substitution is insufficient to significantly alter the H.The quadrupole displacement value in the sample CoRExFe2−xO4 is the smallest, indicating good symmetry of the electric field around the atomic nucleus in cobalt ferrite.

Figure 11 .Figure 11 .
Figure 11.Room temperature Mössbauer spectroscopy curve for CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 °C.(The blue and purple line spectra represent the Mössbauer spectra of iron ions in the A and B lattice, while the red line spectra represent the total Mössbauer spectra) Figure 11.Room temperature Mössbauer spectroscopy curve for CoRE x Fe 2−x O 4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 • C. (The blue and purple line spectra represent the Mössbauer spectra of iron ions in the A and B lattice, while the red line spectra represent the total Mössbauer spectra).

Figure 12 .
Figure 12.The spatial structure of spinel ferrite cells.

Figure 12 .
Figure 12.The spatial structure of spinel ferrite cells.

Figure 13
Figure 13 displays the room temperature Mössbauer spectra of Co 0.7 Zn 0.3 La x Fe 2−x O 4 .The spectra of Co 0.7 Zn 0.3 Fe 2 O 4 , fitted with two sextets of Zeeman-split, are attributed to Fe 3+ at tetrahedral and octahedral sites, indicating the ferrimagnetic behavior of the samples.The six linear peaks with a large I.S. correspond to the iron ions at position B, while the other set of six linear peaks with a smaller I.S. correspond to the iron ions at position A[20].When 0.01 ≤ x ≤ 0.15, the Mössbauer spectrum of Co 0.7 Zn 0.3 La x Fe 2−x O 4 only shows a set of magnetic six-line peaks, corresponding to the six-line peaks at the B site, indicating that Fe 3+ ions only occupy the octahedral B site[44].The Mössbauer spectrum of x = 0.20 was fitted with one single sextet and a central paramagnetic doublet, and it shows the relaxation effects features.The A-B exchange interaction decreases with the substitution of nonmagnetic La 3+ ions, resulting in a decrease in the magnetic hyperfine field value[8].The large isomer shift (I.S.) value of Fe 2+ ions is 0.1-0.5 mm/s, while for Fe 3+ , it is 0.6-1.7 mm/s[44].From the isomer shift (I.S.) values in Table6, we know that the iron ions in our sample are in the Fe 3+ state.Figure14displays the A site of the tetrahedral lattice and the B site of the octahedral lattice.The quadrupole shift of the magnetic sextet for A and B sites is very small, which indicates that the charge distribution of atomic nuclei is close to spherical symmetry.Mössbauer spectrum of Co 0.7 Zn 0.3 La 0.2 Fe 1.8 O 4 was fitted with one single sextet and a central paramagnetic doublet, which shows the relaxation effects features[45].

Figure 13 .
Figure 13.Room temperature Mössbauer spectroscopy curve of Co0.7Zn0.3LaxFe2-xO4calcined at 800 °C.(The blue and purple line spectra represent the Mössbauer spectra of iron ions in the A and B lattice, while the red line spectra represent the total Mössbauer spectra)

Figure 14 .
Figure 14.The A site of the tetrahedral lattice and the B site of the octahedral lattice.(1-6 and a-d represent the Oxygen ion).

Figure 13 .
Figure 13.Room temperature Mössbauer spectroscopy curve of Co 0.7 Zn 0.3 La x Fe 2-x O 4 calcined at 800 • C. (The blue and purple line spectra represent the Mössbauer spectra of iron ions in the A and B lattice, while the red line spectra represent the total Mössbauer spectra).

Figure 13 .
Figure 13.Room temperature Mössbauer spectroscopy curve of Co0.7Zn0.3LaxFe2-xO4calcined at 800 °C.(The blue and purple line spectra represent the Mössbauer spectra of iron ions in the A and B lattice, while the red line spectra represent the total Mössbauer spectra)

Figure 14 .
Figure 14.The A site of the tetrahedral lattice and the B site of the octahedral lattice.(1-6 and a-d represent the Oxygen ion).

Figure 14 .
Figure 14.The A site of the tetrahedral lattice and the B site of the octahedral lattice.(1-6 and a-d represent the Oxygen ion).

Figure 15
Figure 15 depicts the room temperature (RT) Mössbauer spectroscopy curve for CoFe 2 O 4 powders that were calcined at 400, 800, and 1000 • C. The spectra comprise

Figure 15 .
Figure 15.Room temperature Mössbauer spectroscopy curve for CoFe2O4 unsintered and sintered at 400, 800, and 1000 °C.(The blue and purple line spectra represent the Mössbauer spectra of iron ions in the A and B lattice, while the red line spectra represent the total Mössbauer spectra)

Figure 15 .Table 7 .
Figure 15.Room temperature Mössbauer spectroscopy curve for CoFe 2 O 4 unsintered and sintered at 400, 800, and 1000 • C. (The blue and purple line spectra represent the Mössbauer spectra of iron ions in the A and B lattice, while the red line spectra represent the total Mössbauer spectra).

Figure 16 .
Figure 16.Room temperature Mössbauer spectroscopy curve for Co 0.7 Zn 0.3 La 0.01 Fe 1.99 O 4 sintered at 0, 400, and 800 • C. (The red line spectra represent theMössbauer spectra of iron ions in the B lattice and the total Mössbauer spectra).

Figure 18
Figure18displays the RT magnetic hysteresis curve of CoRE x Fe 2−x O 4 (x = 0, 0.02; RE = La, Sm, Gd) measured at 295K.The magnetization of CoRE x Fe 2−x O 4 approaches saturation at 10,000 Oe.The magnetism of rare-earth elements mainly comes from the magnetic moment of their 4f electrons.Due to the inner arrangement of 4f electrons, their magnetic moment is very stable, allowing the magnetism of rare-earth elements to remain stable over a wide temperature range[16,29].The Gd element has a Curie temperature of 293.2 K, close to RT (295 K)[18].The magnetic dipoles are arranged disorderly at the temperature of 295 K; therefore, RE ion doping does not contribute to magnetization.

Figure 20 .
Figure 20.Variation of theoretical and experimental magnetic moment with lanthanum substitution.

Figure 20 .
Figure 20.Variation of theoretical and experimental magnetic moment with lanthanum substitution.

Table 3 indicate
XRD data for Co 0.7 Zn 0.3 La x Fe 2−x O 4 calcined at 800 • C.

Average Cryst Size (Å) Density (g/cm 3 )
Figure 6 depicts the SEM images of Functional Nanomaterials CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 °C.The sample is well crystallized and displays almost uniform grain sizes.With the substitution of RE 3+ ions, some cobalt ferrite particles
2.2.Structures and Grain SizesFigure 6 depicts the SEM images of Functional Nanomaterials CoRExFe2−xO4 (x = 0, 0.02; RE = La, Sm, Gd) sintered at 800 °C.The sample is well crystallized and displays almost uniform grain sizes.With the substitution of RE 3+ ions, some cobalt ferrite particles

Table 4 .
XRD pattern data for Co 0.7 Zn 0.3 La 0.01 Fe 1.99 O 4 calcined at different temperatures.

Table 6 .
The room temperature Mössbauer spectroscopy data of Co 0.7 Zn 0.3 La x Fe 2−x O 4 calcined at 800 • C.

Table 8 .
The room temperature Mössbauer spectroscopy data of Co 0.7 Zn 0.3 La 0.01 Fe 1.99 O 4 calcined at 800 • C.

Table 9 .
Magnetic data for CoFe 2 O 4 sintered at 800 • C and 1000 • C.

Table 9 .
Magnetic data for CoFe2O4 sintered at 800 °C and 1000 °C.

Table 9 .
Magnetic data for CoFe2O4 sintered at 800 °C and 1000 °C.

Table 11 .
Magnetic data for Co 0.7 Zn 0.3 La x Fe 2−x O 4 calcined at 800 • C.