Magnetic and structural properties of single-phase Gd³⁺-substituted Co–Mg ferrite nanoparticles

Abstract

Nanocrystalline Gd³⁺-doped Co–Mg ferrite nanoparticles with the chemical formula Co_0.7Mg_0.3Fe_(2−x)Gd_xO₄ (x = 0.02) were prepared by coprecipitation for the first time. The properties of the nanoparticles were investigated by X-ray diffraction, confirming a single-phase, highly crystalline cubic spinel structure in the space group Fd3̄m and an average crystallite size of 54 nm. The Fourier-transform infrared spectrum showed two fundamental absorption bands in the wavenumber range of 437–748 cm⁻¹ attributed to the stretching vibration of tetrahedral and octahedral sites in the spinel structure. Scanning electron microscopy analysis showed that the nanoparticles are different in shape and slightly agglomerated. Energy-dispersive X-ray spectroscopy demonstrated the purity of the nano-ferrite powder. Magnetic measurements revealed ferrimagnetic behavior at room and low temperatures with high coercivity and a high saturation magnetization of 95.68 emu g⁻¹, larger than that of pure bulk cobalt ferrite (80.8 emu g⁻¹). Only ferrite cobalt synthesized sonochemically has been reported to have a higher saturation magnetization (92.5 emu g⁻¹).

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Introduction

Research in the past decades has suggested that nanotechnology will have crucial long-term effects on all industrial sectors. Compared to bulk materials, nanomaterials have increased reactivity due to their increased solubility and higher proportion of surface atoms. The magnetic, electrical, mechanical, and optical properties along with the specific electronic states of nanomaterials are also totally different from those of the equivalent bulk materials.

The specific properties of nanomaterials give them a variety of physical and chemical functionalities that are highly desirable for applications in numerous industrial sectors.^1–3 The unique structural characteristics, energetics, tailoring, and production strategies of nanostructures constitute the experimental and conceptual background for the field of nanoscience. The suitable control of nanostructure properties and activity can lead to new devices and technologies. The deviation of the properties of nanosized materials from those of the corresponding bulk materials is related to surface effects, which mainly depend upon the ratio of surface area to volume, the particle size, the chemical composition, and interactions between the particles. It should be noted that rapid developments in the field of nanotechnology have opened up vast possibilities for understanding and using magnetic materials.

In addition, many physical phenomena become more noticeable as the size of the system approaches the nanoscale. In recent years, a lot of work has been done on nanocrystalline materials because of their unusual and interesting properties compared to bulk materials.^4,5 Several research groups are investigating spinel oxide nanoparticles and particularly nano-ferrites because of their potential applications in magnetic devices, microwave technology, high-density magnetic recording media, cancer treatment, drug delivery systems, magnetic resonance imaging, and other fields.

The composition and synthetic method play crucial roles in determining the physical and chemical properties of ferrites. Several researchers have synthesized substituted nanoscale ferrites using the standard ceramic technique,⁶ solid-state methods,⁷ coprecipitation,^8,9 sol–gel methods,¹⁰ molten salt routes,¹¹ electrodeposition,¹² and mecanosynthesis.¹³ Other studies have focused on improving the physical properties of these nanomaterials. For example, Li et al. have shown that at the nanoscale, the shape, particle size, and cationic distribution play crucial roles in determining the physical properties of spinel ferrite.^14,15 They also demonstrated that the magneto-resistance of spinel ferrite decreases as the average grain size is reduced.^16,17

Liu et al.¹⁴ established a correlation between the coupling of the orbital angular momentum of electron spin in CoFe₂O₄ and the superparamagnetic properties of spinel ferrite nanoparticles (MgFe₂O₄) and deduced that due to the strong magnetic coupling of the Co²⁺ lattice sites, the blocking temperature of the CoFe₂O₄ nanoparticles was at least 150 °C higher than that of MgFe₂O₄ nanoparticles of the same size. On the other hand, rare earth (RE) elements possess high magnetic moments, high magneto-crystalline anisotropy, and very high magnetostriction at low temperature due to the localized nature of 4f electrons. Thus, doping with small quantities of REs can improve the magnetic properties of nano-ferrites, particularly the magnetic coercivity, making them suitable for different applications (e.g., the treatment of hyperthermia and other biomedical applications).^17,18 Although numerous nanometric cobalt ferrites have been produced by coprecipitation, few studies have been compared the cationic distributions and magnetic properties of RE-substituted cobalt powders. To our knowledge, the cation distributions and microstructural distributions of RE-doped Co–Mg nano-ferrites have not been reported. Despite the different synthetic techniques, no reports are available on gadolinium-substituted Co–Mg nano-ferrites. In this study, a coprecipitation method was used to synthesize Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ nano-ferrites. This method was chosen for its simplicity, short reaction time, low cost, and ability to product fine and homogeneous crystalline powders without any risk of contamination.

The objective of this work was to determine the effects of doping with Gd³⁺ on the structural, magnetic, and morphological properties of Co_0.7Mg_0.3Fe_(2−x)Gd_xO₄ (x = 0.02) nanoparticles prepared via coprecipitation. To the best of our knowledge, no similar work has been reported to date.

Characterization

The synthesized powder was characterized by X-ray diffraction (XRD; PANalytical PW3050/60) to determine the crystalline phase. The lattice parameters and crystallite sizes were calculated using Rietveld refinement and the Debye–Scherrer formula, respectively. Fourier-transform infrared (FTIR) spectra were recorded on a VERTEX 70 FTIR spectrometer over the range of 400–4000 cm⁻¹. Scanning electron microscopy (SEM; Quanta 200) coupled with energy-dispersive X-ray spectrometry (EDS) was used to determine the particle morphology and the chemical composition of the sample. Magnetic measurements were conducted using a Magnetic Property Measurement System (Quantum Design MPMS-XL-7AC SQUID) to study the magnetic behavior.

Experimental details

Gd³⁺-doped Co–Mg ferrite with the chemical formula Co_0.7Mg_0.3Fe_2−xGd_xO₄ (x = 0.02) was synthesized by chemical coprecipitation. First, CoCl₂·5H₂O (≥98% pure, Sigma-Aldrich), FeCl₃ (≥99.0% pure, Sigma-Aldrich), Gd(NO₃)₃·6H₂O (≥99.0% pure, Sigma-Aldrich), and Mg(NO₃)₂ (≥99.0% pure, Sigma-Aldrich) were dissolved stoichiometrically in deionized water. The mixture was stirred with a magnetic stirrer until the solution became homogeneous. The pH of the solution was adjusted to 12 via the dropwise addition of sodium hydroxide under constant stirring. The coprecipitated products were washed several times with deionized water to remove unwanted residual salts. The precipitates were then filtered and dried overnight in an oven at 100 °C. The resulting powders were calcined at 800 °C and 900 °C.

Results and discussion

XRD analysis

The powder XRD patterns of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ calcined at 800 °C and 900 °C are shown in Fig. 1. The patterns of both samples indicate a highly pure, single-phase spinel crystal structure. The spectrum of the powder calcined at 800 °C has a parasitic peak corresponding to GdFeO₃ impurity, which is attributed to incomplete crystallization. In the spectrum of the powder calcined at 900 °C, the diffraction peaks located at 2θ values of 18.41°, 30.24°, 35.65°, 37.25°, 43.22°, 53.60°, and 57.16° correspond to the (111), (220), (311), (222), (400), (422), and (511) planes, respectively, which match exactly with the ICDD data card no #01-080-6487 (for CoFe₂O₄). These results confirm the formation of single-phase products. Thus, all dopants simply replaced the Co²⁺–Fe³⁺ ions without distorting the cubic symmetry of the host cobalt ferrite, resulting in a single-phase cubic spinel structure (space group Fd3̄m); no other impurities were detected in the high-purity cobalt ferrite both with and without gadolinium doping.

Fig. 1 XRD patterns of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ calcined at 800 and 900 °C.

The Rietveld refinement of the average intensity profiles of nanocrystalline CoFe₂O₄ and Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ calcined at 900 °C was carried out using the program FULLPROF to determine the structural properties. The fitted patterns are in good agreement with the respective experimental data with good fitting parameters; the obtained lattice parameters a are 8.3784 and 8.3805 Å for CoFe₂O₄ and Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄, respectively. All the peaks can be indexed to a spinel structure with space group Fd3̄m. Fig. 2 and 3 show the typical refinements for CoFe₂O₄ and Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ after the final cycle of Rietveld refinement.

Fig. 2 Typical Rietveld-refined XRD pattern for the CoFe₂O₄ sample.

Fig. 3 Typical Rietveld-refined XRD pattern for the Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ sample.

The average crystallite size D of each sample was determined from the full width at half maximum (FWHM) using the Debye–Scherrer formula:¹⁹

where λ is the wavelength of Cu(Kα) radiation, β is the FWHM, and θ is the Bragg diffraction angle.

The theoretical density ρ_X-ray is determined by the following relation:²⁰

where M is the molecular weight of the sample, N is Avogadro's number, and a is the lattice parameter.

The values of D and ρ_X-ray determined from eqn (1) and (2) along with the a values calculated by Rietveld refinement are listed in Table 1.

Table 1 Crystallite size (D), lattice parameter (a), and X-ray density (ρ_X-ray) values for CoFe₂O₄ and Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄

Sample	Lattice parameter a (Å)	Average crystallite size D (nm)	Theoretical density ρX-ray (g cm^−3)	Reference
CoFe2O4	8.378	81	5.299	Present work
Co0.7Mg0.3Fe1.98Gd0.02O4	8.380	54	5.295
CoFe2O4	8.355	56	5.347	21
Co0.7Mg0.3Fe2O4	8.387	48	5.050
CoFe2O4	8.354	55	5.346	22
CoFe1.96Gd0.04O4	8.397	34	5.353

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The lattice parameter a = 8.3805 Å for Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ was larger than that of CoFe₂O₄ (a = 8.3784 Å). This can be attributed to the larger ionic radii of Gd³⁺ (0.094 nm) and Co²⁺ (0.074 nm) at the octahedral site compared to the radii of Fe³⁺ (0.067 nm) and Mg²⁺ (0.072 nm), which resulted in an overall expansion of the lattice.

As shown in Table 1, The calculated value of the average crystallite size (D), of the doped sample Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ is smaller than that of the undoped cobalt ferrite CoFe₂O₄, a result that is similar to those reported for RE-doped ferrites. Indeed, by comparing our results with those found in the literature, we noticed that we observed similar structural behavior with that described in previous work, in terms of an increase in the lattice parameter and decrease in the average crystallite size, but totally different magnetic behavior.^21–24 Indeed, in the case of the two substitutions by magnesium and gadolinium, the saturation magnetization and coercivity decrease, whereas in our case the saturation magnetization and coercivity increase drastically despite having been doped with a low concentration of gadolinium. This phenomenon will be better elucidated later when discussing the magnetic properties.

From a structural point of view, this situation can result from the fact that the higher binding energy of Gd³⁺–O²⁻ compared to Fe³⁺–O²⁻. In fact, a large amount of energy is necessary to replace Fe³⁺ with Gd³⁺. As a result, Gd³⁺-substituted ferrites have higher thermal stability than pure cobalt ferrites. The smaller crystallite size may also be related to the pressure created by the larger crystals of Gd³⁺ ions (large ionic rays) on the grain boundaries.^25,26

The calculated ρ_X-ray value of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ is small compared to that of pure CoFe₂O₄. This can be explained by the decrease in molecular weight upon doping with Gd³⁺ and Mg²⁺. The relative molecular weight decreases as more Co²⁺ is replaced by Mg²⁺ since the atomic weight of Co²⁺ is greater than that of Mg. In addition, the atomic percentage of Gd³⁺ in this compound is much smaller than that of Mg²⁺.

Bulk cobalt ferrite has an inverse spinel structure that shifts to a partially inverted structure in the case of nano-ferrites. In the inverse spinel, eight of the tetrahedral sites are occupied by Fe³⁺, and half of the octahedral sites are occupied by Co²⁺ and Fe³⁺. When the size is reduced to the nanoscale, some of the Co²⁺ ions at the octahedral site migrate to the tetrahedral site, leading to a partially inverted structure. Cobalt ferrite belongs to space group Fd3̄m, and the lattice parameter is typically close to 8.39 Å.²⁷

In the literature, MgFe₂O₄ has been reported to have a partially inverted spinel ferrite structure.²⁸ The distribution of metal ions in MgFe₂O₄ is given as (Mg_1−xFe_x)[Mg_xFe_2−x]O₄, where the parenthesis and square brackets denote cation sites of tetrahedral (A-sites) and octahedral [B-sites] coordination, respectively.²⁹

Studies have been conducted on the effects of the substitution of Co by Mg on the physicochemical properties of cobalt ferrite and vice versa. Several studies have been reported on the effect of metal ion substitution on the structure and magnetic properties of MgFe₂O₄. The main objective of these studies was to synthesize pure nanocrystalline powders with the general formula Mg_xCo_1−xFe₂O₄ (0.00 ≤ x ≤ 1.00).

The structural, morphological, electrical, dielectric, and magnetic properties of Co–Mg ferrite have been studied³⁰ while continuing to verify and improve the quality of ferrite for various applications. Several experimental techniques have been used to evaluate the degree of inversion in these spinel systems, including X-ray absorption, neutron and X-ray diffraction, and Raman and Mössbauer spectroscopy. However, these methods alone cannot determine the cation distribution in Co_xMg_1−xFe₂O₄ because they only target iron ions (reported results are summarized in Table 2). Therefore, it is interesting to study the properties of Co–Mg ferrite nanoparticles doped with gadolinium because the expected improvement in the structure can lead to the improvement of the magnetic properties.

Table 2 Cation distributions found in the literature

	Site A	Site B	Method	Reference
Coprecipitation	[Mg0.1Fe0.9]	[Co0.7Mg0.2Fe1.08Gd0.02]	Mathematical model	Present work
	[Mg0.1Fe0.9]	[Mg0.4Co0.5Fe1.1]	XRD	31
	[Co0.31Fe0.69]	[Co0.69Gd0.03Fe1.28]	Rietveld analysis	32
Sol–gel	[Co0.106Mg0.049Fe0.85]	[Mg0.007Co0.85Fe1.2]	Mössbauer spectroscopy	33
	[Mg0.51Fe0.49]	[Mg0.29Co0.2Fe1.51]	Mathematical model	34
	[Mg0.159Fe0.841]	[Mg0.841Fe1.159]	Rietveld analysis	35
	[Mg0.15Fe0.85]	[Mg0.86Fe1.15]	Mössbauer spectroscopy	36
	[Mg0.14Fe0.86]	[Mg0.87Fe1.13]	Raman spectroscopy
Ceramic method	[Zn0.5Mg0.08Fe0.62]	[Mg0.62Fe1.38]	Mössbauer spectroscopy	37

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According to the literature and in the light of the considerations mentioned above, the suggested cation distribution for the Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ samples in this study can be written as

[Mg_δFe_1−δ]^A[Co_1−δ−γMg_γFe_0.98+δGd_0.02]^BO₄,

where γ is the concentration of Mg²⁺ ions, and δ is the degree of inversion represented by the percentages of Mg²⁺ and Fe³⁺ at tetrahedral and octahedral sites.

The mean ionic radii of ions at the tetrahedral site r_tet and octahedral site r_oct can be described in terms of their concentrations as

r_tet = [δr_Mg²⁺ + (1 − δ)r_Fe³⁺], (3)

andwhere r_Fe³⁺, r_Co²⁺, r_Gd³⁺, and r_Mg²⁺ are the radii of Fe³⁺, Co²⁺, Gd³⁺, and Mg²⁺ ions, respectively.

The lattice parameter can be calculated theoretically by the following equation:³⁸

where R_O is the radius of oxygen ion (R_O = 1.32 Å), and r_A and r_B are the radii of the tetrahedral and octahedral sites, respectively.

A mathematical model based on the formula proposed for cation distribution was constructed to search for the best match between the theoretical and experimental values of the lattice constant for the sample by optimizing the values of the parameters δ and γ over the tetrahedral and octahedral sites; the obtained cation distribution is shown in Table 3.

Table 3 Cation distribution of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄

aexp	ath	rA	rB	Cation distribution
				A-site	B-site
8.3805	8.38016	0.6750	0.7022	Mg0.1Fe0.9	Co0.7Mg0.2Fe1.08Gd0.02

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The results obtained from the proposed model are in very good agreement with those obtained experimentally by Nakagomi et al.³⁶ using Mössbauer and Raman spectroscopy.

From the results reported previously, it is clear that the tetrahedral site A is mainly occupied by Fe³⁺ ions and a low percentage of Mg²⁺ ions, while the octahedral site B is occupied by Fe³⁺, Gd³⁺, Co²⁺, and Mg²⁺ ions, in good agreement with other results obtained by different experimental methods (Table 2).

The spinel structure has a cubic arrangement of O²⁻ ions (fcc); each unit cell contains eight AB₂O₄ units with the space group Fd3̄m. The atom locations in the spinel depend on the choice of the origin in the space group Fd3̄m. The conventional choices for the origin in the cells of the spinel unit are either a cation site A with 4̄3m symmetry or an octahedral vacancy with 3̄m symmetry.³⁹

If the cation site A with 4̄3m symmetry is taken as the origin, the oxygen position parameter or the anionic parameter u, which is the distance between the oxygen ion and the face of the edge along the cube diagonal of the spinel lattice, is calculated by⁴⁰

where r_A is the ionic radius of the A-site, and R_O is the ionic radius of oxygen ion.

The calculated values of u(4̄3m) are 0.37886 and 0.3874 Å for the CoFe₂O₄ and Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ samples, respectively. The decrease in the oxygen positional parameter can be explained by the occupation of the Gd³⁺ only the octahedral sites but Mg²⁺ ions at the octahedral and tetrahedral sites. Consequently, the distance between the A and O²⁻ ions decreased, while that between B and O²⁻ increased.⁴¹

FTIR spectra

FTIR spectroscopy makes it possible to predict the presence of the different bonds in a crystal. The FTIR spectra of the CoFe₂O₄ and Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ samples were recorded at room temperature in the wavenumber range of 400–4000 cm⁻¹ (Fig. 4).

Fig. 4 FTIR spectra of samples Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ and CoFe₂O₄.

The positions of the vibrational bands of CoFe₂O₄ and Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ are given in Table 4. For spinel ferrites, the vibrational band at around 750–850 cm⁻¹ corresponds to the stretching vibration of the tetrahedral site, while the vibrational band at around 400–500 cm⁻¹ corresponds to the stretching vibration of the octahedral site.^33,42

Table 4 FTIR vibrational bands of CoFe₂O₄ and Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄

	ν1 (cm^−1)	ν2 (cm^−1)	ν3 (cm^−1)
CoFe2O4	437.0807	779.7678	—
Co0.7Mg0.3Fe1.98Gd0.02O4	445.28849	812.0047	1165.5477

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Table 4 indicates that the vibrational spectra consist of two main bands (ν₁ = 437.0807 cm⁻¹ and ν₂ = 779.7678 cm⁻¹) for CoFe₂O₄ and three bands (ν₁ = 445.28849 cm⁻¹, ν₂ = 812.0047 cm⁻¹, and ν₃ = 1165.5477 cm⁻¹) for Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄. The absorption band ν₁ is assigned to the stretching vibration mode of metal–oxygen at tetrahedral sites, whereas ν₂ is attributed to octahedral sites. The positions of the two strong bands are clearly related to the difference in the Fe–O bond lengths at the A- and B-sites. The presence of the band ν₃ in Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ is related to the stretching vibration of the nitrate group (NO₃).⁴³

Compared to CoFe₂O₄, the FTIR bands of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ are shifted toward higher frequency, as indicated in the inset of Fig. 4 (v₁ = 437–445 cm⁻¹ and v₂ = 749–812 cm⁻¹). These shifts are explained by the changes in the bond strength, bond length, and broadening of the tetrahedral and octahedral sites.⁴⁴

The changes in the octahedral site were greater than those in the tetrahedral site after doping with gadolinium. Thus, it can be concluded that the gadolinium ions have a greater effect on the octahedral sites. The doping ions can increase the absorption band length of the tetrahedral and octahedral site lattice. In addition, Fe³⁺, Co²⁺, Mg²⁺, and Gd³⁺ mainly occupy the B-sites in the spinel structure, inducing stress at the octahedral and tetrahedral sites. This leads to an increase in the ionic rays at both sites, leading to a change in frequency.

Morphological study

The external morphology of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ was visualized by SEM (Fig. 5). The nanoparticles agglomerated due to their mutual magnetic interactions and high surface energy. The shapes of the particles appeared to be non-spherical.

Fig. 5 SEM image of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ nanoparticles and the corresponding particle size distribution.

The particle size distribution was analyzed using ImageJ software. The particle size at the surface was roughly estimated to be in the range of 30–70 nm for the Gd-doped ferrite sample, close to the value of D obtained by XRD analysis (Scherrer's method) for the same sample.

The elemental composition of the Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ nanomaterial sample was investigated by EDS and the elemental mapping is shown in Fig. 6. The EDS spectrum and elemental mapping confirm the presence of Co, Mg, Gd, Fe, and O in the synthesized nanoparticles; no other traceable impurities were detected within the resolution limit of EDS. The theoretical elemental composition x was calculated using the following formula:

where M is the molar mass of the element, M_T is the total molar mass, and z refers to the number of elements. The theoretical and experimental elemental compositions are presented in Table 6. The experimental elemental percentages agree with the theoretical values, and the crystal structure showed a homogeneous chemical composition.

Fig. 6 EDS spectrum and elemental maps of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ and the corresponding elemental composition.

Magnetic properties

The magnetic properties of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ were investigated using a magnetic property measurement system. Fig. 6 shows the measured magnetic hysteresis loops at low and room temperature (10 and 300 K) under an applied external field of ±50 kOe. The loops indicate ferrimagnetic behavior.

The M_S values of the two curves were determined by fitting the high-field (1/H → 0) data using the following function:¹⁹

where α is a fitting constant, and H is the applied magnetic field. From the hysteresis loops, the magnetic parameters [M_S, H_c, remnant magnetization (M_r), squareness (M_r/M_S), anisotropy constant (K), and magnetic moment (n_B)] were calculated (Table 5).

Table 5 Results of magnetic measurements

	Ms (emu g^−1)	Mr (emu g^−1)	Hc (Oe)	Mr/Ms	nB (μB)	K × 10^5 (erg cm^−3)
300 K	95.68	39.99	1702.28	0.41	3.87	1.69
10 K	109.53	82.58	11 959.53	0.75	4.43	13.64

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The data in Table 5 show that M_S and M_r increased with decreasing temperature from 300 to 10 K for the doped sample, and these M_S and M_r values were higher than those of undoped cobalt ferrite. In contrast, the M_S values of some RE-doped ferrites were reported to be lower compared to that of bulk cobalt ferrite.²² The M_S determined at 10 K was higher than that determined at 300 K. This can be explained by the decrease in thermal energy at low temperature, which leads to the alignment of magnetic moments parallel to the direction of the applied magnetic field, resulting in an increase in saturation.⁴⁵ The mechanism is exactly the opposite at high temperature, where the surface spins show some disordered states, weakening their response to the applied magnetic field and thus reducing magnetization. The higher values of M_S at high and low temperature are attributed to the migration of some ferric ions from the octahedral site to the tetrahedral site. This observed variation in the M_S and M_r can be understood by considering the structure of the ferrimagnetic cubic spinel. The number of octahedral sites (B-sites) is twice the number of tetrahedral sites (A-sites), and the magnetic moments on the octahedral and tetrahedral sites are antiparallel to each other, leading to a net magnetic moment M_(cal) = M_B − M_A. In addition, the increase in size can be correlated with the transformation of the multi-domain structure into a monodomain structure^40,41 upon doping the Co–Mg nano-ferrite with Gd³⁺. At tetrahedral sites further from the proposed cation distribution, magnesium and ferric ions exhibit A–A exchange interactions; in contrast, at octahedral sites, cobalt, magnesium, ferric, and gadolinium ions exhibit B–B interactions. At tetrahedral and octahedral sites, bivalent (Co²⁺ and Mg²⁺) and trivalent (Fe³⁺ and Gd³⁺) metal ions exhibit superexchange A–B interactions. The superexchange A–B interactions are practically superior to the A–A and B–B interactions at the respective sites. The superexchange A–B interactions can increased upon the addition of Gd³⁺ in spinel nano-ferrite Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄. This increase in A–B interaction implies an increase in M_S and n_B. Based on the literature, the particle size of pure cobalt ferrite synthesized via coprecipitation is between 10 and 30 nm, while M_S is in the range of 55–75 emu g⁻¹ (Table 6). In the case of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄, as demonstrated by XRD analysis, the particle size is 54 nm, indicating that M_S increases with particle size.

Table 6 Magnetic properties of pure CoFe₂O₄ prepared via coprecipitation

pH	Crystallite size (nm)	Ms (emu g^−1)	Mr (emu g^−1)	Hc (Oe)	K × 10^3 (erg cm^−3)	nB (μB)	Reference
—	13	59.74	12.68	306.90	19.10	2.51	46
<6	38.59	73.58	41.20	568	—	3.08	47
—	16.84	61	15.25	419.00	—	—	48
12	15	75	19.3	400	—	—	49

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The distances along with the angles between the ions play a crucial role in determining the magnetic exchange interactions. In general, for spinel ferrites, these binding angles and inter-ionic distances greatly affect the magnetic characteristics. Thus, the inter-ionic distances between the cation and anion (Me–O; p, q, r, and s) and between the cation and cation (Me–Me; b, c, d, e, and f) as well as the bond angles (θ₁, θ₂, θ₃, θ₄, and θ₅) between the cation and cation–anion were calculated using the equations presented in Table 7.⁴⁰

Table 7 Expressions for determining the cation–cation (Me–Me) and cation–anion (Me–O) distances along with the bond angles

Me–Me	Me–O	Bond angle

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Tables 8, 9 and 11 show that doping with Mg²⁺ and Gd³⁺ caused the bond lengths between Me–O (r, q, and s) and Me–Me (b to f) to increase, while p decreased. An increase in site radius may be expected due to the replacement of smaller Fe³⁺ (0.067 nm) by larger Mg²⁺ (0.072 nm) and Gd³⁺ (0.094 nm) at octahedral sites. The ionic radius of a Gd³⁺ (0.094 nm) is large for the tetrahedral site; therefore, Gd³⁺ ions are forced to occupy octahedral sites. Similarly, Co²⁺ (0.074 nm) prefers to occupy octahedral sites because of its site preference binding energy. Fe³⁺ partially migrates from octahedral to tetrahedral sites.θ₁ and θ₂ are related to the A–B interaction, θ₃ and θ₄ are related to the B–B interaction, and θ₅ is related to the A–A interaction. The obtained inter-ionic binding angles are given in Table 11. Doping with Mg²⁺ and Gd³⁺ caused θ₁, θ₂, and θ₅ to decrease, while θ₃ and θ₄ increased. The increase in θ₅ indicates a strengthening of A–A interactions, while the increases in θ₃ and θ₄ suggest an increase in the strength of B–B exchange interactions. Thus, we can deduce that Fe³⁺, Mg²⁺, Gd³⁺, and Co²⁺ ions at B sites along with Fe³⁺ and a low concentration of Mg²⁺ at A sites reinforce the superexchange interaction A–B, leading to increased saturation magnetization. This enhancement in magnetic properties is also attributed to the higher magnetic moment (4f⁷ orbital, S = 7/2, L = 0, J = 7/2) and spin magnetic moment of Gd³⁺ compared to Fe³⁺ (3d⁵) and Co²⁺ (3d⁷, L = 3, S = 3/2, J = 9/2) due to strong L–S coupling. Recently, many studies have been devoted to the effects of various REE dopants on the physicochemical properties of ferrites, including Li–Ni, Ni–Zn, Mn–Zn, Mg–Cu, Cu–Zn.^50–54 In most of these studies, M_S decreased upon doping. Reports of increases in M_S upon doping with REs are much rarer. Rare earth ions generally occupy octahedral sites and have limited solubility in the spinel lattice due to their large ionic rays. However, their precise solubility in the spinel network has not been determined. It should also be noted that doping with low concentrations of REs causes M_S to increase, while high dopant concentrations cause M_S to decrease.⁵⁵ Our results are in good agreement with the theoretical studies of Hou Y. H. et al.,⁵⁶ who found that the net magnetic moment of CoFe₂O₄ increased upon doping with Gd³⁺. Yu-Hua et al. also showed that the rare earth ions prefer to substitute for Fe³⁺ located at octahedral sites, and the lattice constant of CoFe_1.875RE_0.125O₄ (RE = La, Ce, Pr, Nd, Eu, and Gd) decreased due to the decreasing ionic radius of the RE with increasing atomic number. The saturation magnetization of CoFe₂O₄ increases upon doping only with Eu and Gd because there are more unpaired 4f electrons for Eu³⁺ and Gd³⁺. Similarly, Torkian et al.⁵⁵ reported that the magnetization of Gd³⁺-doped Mn–Zn ferrite increased for Gd³⁺ substitution of up to 15%. The most significant result of this work is the production of Gd-doped Co–Mg nano-ferrites with magnetization much higher than that of bulk cobalt ferrite. To the best of our knowledge, this result has not been previously reported. Similar findings have been reported for sonochemically produced CoFe₂O₄ and Zn_xCo_(1−x)Fe₂O₄ synthesized using complex precursors (Table 10).

Table 8 Calculated cation–anion (Me–O) and cation–cation (Me–Me) inter-ionic distances and bond angles in the Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ and CoFe₂O₄ samples

Parameter	b (Å)	c (Å)	d (Å)	e (Å)	f (Å)	p (Å)	q (Å)	r (Å)	s (Å)
CoFe2O4	2.9622	3.4735	3.6279	5.4419	5.1307	2.0622	1.8699	3.5807	3.6466
Co0.7Mg0.3Fe1.98Gd0.02O4	2.9629	3.4743	3.6288	5.4432	5.1319	1.9912	1.9944	3.8190	3.6888

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Table 9 Calculated bond angles of the Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ and CoFe₂O₄ samples

Parameter	θ1 (°)	θ2 (°)	θ3 (°)	θ4 (°)	θ5 (°)
CoFe2O4	124.0221	148.1105	91.8114	125.6836	76.3662
Co0.7Mg0.3Fe1.98Gd0.02O4	121.3193	136.7599	96.1482	126.6282	69.2622

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Table 10 Magnetic properties of cobalt ferrite prepared by different synthetic methods

Compound	Method of synthesis	MS (emu g^−1 at 300 K)	Ms (emu g^−1 at 5 K)	HC (Oe at 300 K)	HC (Oe at 5 K)	Mr/Ms (300 K)	Mr/Ms (5 K)	Reference
Co0.7Mg0.3Fe1.98 Gd0.02O4	Coprecipitation	95.68	109.5	1702.28	11 959.53	0.4179	0.7539	Present work
CoFe2O4	Classical ceramic method	88	—	141	—	—	—	57
CoFe2O4	—	80.8	93.9	—	25 200		—	58
CoFe2O4	Sonochemical method	92.5	—	807	—	—	—	59
CoFe2O4	Chemical complexes	92	109	—	12	—	—	60

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Table 11 Configurations of ion pairs in spinel ferrites with favorable distances and angles for effective magnetic interactions in samples Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ and CoFe₂O₄

	A–B interaction	B–B interaction	A–A interaction
CoFe2O4
Co0.7Mg0.3Fe1.98Gd0.02O4

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The experimental magnetic moment per formula unit (n_B of Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ was be calculated as follows:⁶¹

where M is the molecular weight of the sample, and M_S is the measured saturation magnetization. The value of the magnetic moment varies from 3.87 μ_B at 300 K to 4.43 μ_B at 10 K, as shown in Table 7. This change in magnetic moment is in accordance with the variation in M_S.

According to the proposed cation distribution (Mg_0.1Fe_0.9)^A[Co_0.7Mg_0.2Fe_1.08Gd_0.02]^BO₄ and using the magnetic moment values of Mg²⁺ (0 μ_B), Fe³⁺ (5 μ_B), Gd³⁺ (7 μ_B), and Co²⁺ (3 μ_B), the net magnetic moment M_(cal) was calculated as M_(cal) = M_B − M_A, where M_A and M_B represent the net magnetic moments of lattice sites A and B, respectively. The calculated value of M_(cal) is 3.14 μ_B, comparable with the determined experimental value. Further from the proposed cation distribution, at tetrahedral locations, magnesium and ferric ions exhibit A–A exchange interactions; in contrast, at octahedral sites, cobalt, magnesium, ferric, and gadolinium ions exhibit B–B interactions. At tetrahedral and octahedral sites, the metal ions (Mg²⁺ and Fe³⁺) exhibit superexchange A–B interactions with Co²⁺, Mg²⁺, Fe³⁺, and Gd³⁺. Superexchange A–B interactions are practically superior to A–A and B–B interactions at the respective sites. There may be an increase in A–B superexchange interactions with the addition of Gd³⁺ to Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ spinel nano-ferrites. This increase in A–B interaction suggests an increase in the measured values of saturation magnetization and magnetic moment. In this work, M_S and n_B increased upon the addition of Gd³⁺ in Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ ferrite spinels. This increase in magnetic parameters can be correlated with the bonding angles. The bonding angles θ₁, θ₂, and θ₅ decreased upon doping, suggesting decreased A–A interactions. Meanwhile, θ₃ and θ₄ increased, indicating an increase in B–B and A–B interactions. The complete solubility of large Gd³⁺ ions at B sites could be responsible for the change in the magnetic behavior of the Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄ nano-ferrites. This is probably why high M_S and n_B values have been obtained with low concentrations of gadolinium. For ferrites doped with high concentrations of other REs, the decrease in saturation magnetization and magnetic moment can be interpreted based on the migration of rare earth ions to the grain boundaries, resulting in weak magnetic behavior. Moreover, the magnetic parameters of spinel ferrites depend upon various factors, including the synthetic technique, sintering temperature, crystallite size, grain size, and redistribution of cations among A and B sites.

The effective anisotropy constant K can be calculated using the relationship⁶²

where H_C is the coercivity, and M_S is the saturation magnetization. The coercivity value of the sample at 300 K is given in Table 5. It can be observed from Tables 5 and 6 show that the coercivity of the sample at 300 K was higher than that of pure cobalt ferrite synthesized via coprecipitation. The observed variation in coercivity can be explained as follows. As discussed above, compared to other ions, Co²⁺ exhibits stronger L–S coupling and a weaker crystal field, resulting in stronger magneto-crystalline anisotropy related to the increase in the concentration of high-spin Co²⁺ ions at octahedral sites.⁶³ Although Gd³⁺ has zero orbital angular momentum, gadolinium has been reported to contribute to and strengthen anisotropy.⁶⁴

The coercivity of the sample increased from 1702.28 Oe at 300 K to 11 959.53 Oe at 10 K. The enhanced coercivity is attributed to the reduced thermal fluctuation energy at 10 K, which is less effective in reducing the effects of magneto-crystalline anisotropy energy. In addition, the enhanced coercivity could be interpreted as a result of the energy barriers in the nanoparticles becoming more apparent at low temperature. While these barriers always exist, they have been suggested to become more pronounced at low temperature; hence, these barriers might delay the alignment of magnetic moments in the direction of the applied magnetic field.

As indicated in Fig. 7, the hysteresis loops show “kink” behavior at 10 K. Various explanations have been suggested for these types of loops, including the magnetic coupling between two different magnetic phases with different coercivities. However, in this work, no secondary phase was observed. The kink behavior may also be explained by the oxidation of soft magnetic layers in the presence of atmospheric oxygen. Otherwise, this anomaly can only be attributed to the reordering of magnetic spins at 10 K under the influence of the applied field. These spin reorientations are responsible for constraining the M–H loop, which can be attributed to the reorientation of surface spins around particles and to the domain wall pinning of the potential wells formed by the directional order.⁶⁵

Fig. 7 Hysteresis loops of sample Co_0.7Mg_0.3Fe_1.98Gd_0.02O₄.

The squareness ratio (M_r/M_S) at 300 K (0.4179) increased to 0.7539 at 10 K. At 300 K, M_r/M_S tends towards 0.5, corresponding to randomly oriented uniaxial anisotropic ferromagnetic particles. In contrast, at 10 K, M_r/M_S approaches 1, corresponding to typical isolated single-domain ferromagnetic particles. In the same vein, Stoner and Wohlfarth⁶⁶ reported that the quadratic ratio of 0.5 indicates non-interactive, randomly oriented particles that undergo coherent rotation under the effect of the applied magnetic field. For quadratic ratios below 0.5, the particles interact only through magnetostatic interactions. Exchange coupling only manifests for a quadratic ratio of higher than 0.5.

The squareness ratio obtained at 10 K confirms that we synthesized nanosized materials with high surface area; the surface effects of the magnetic nanoparticles are responsible for their uniaxial anisotropy. Kodama⁶⁷ effectively suggested that due to the high surface areas of nanomaterials, the spins at the surfaces are canted, and Néel's model of two sublattices is no longer valid. This spin canting at the surface results in higher magneto-crystalline anisotropy in nanomaterials, in good agreement with the results of this study. Such effects may be approved by the contribution from the single-ion anisotropy of Gd³⁺ in the crystal lattice in conjunction with the surface effects resulting from the alteration of the magnetic structures on the surfaces of the nanoparticles.⁶⁸

Conclusion

In the present work, coprecipitation was found to be an economical and efficient method for the synthesis of gadolinium-doped mixed Co–Mg ferrite nanoparticles. Structural analysis indicated a single-phase cubic spinel structure of ferrite after sintering at 900 °C, while GdFeO₃ was observed as a secondary phase after sintering at 800 °C. The crystallite size calculated from the XRD data was in the order of 54 nm. Rietveld refinement of the XRD pattern indicated an increase in the lattice constant after doping with Gd³⁺, which enhanced the crystallinity and induced compression deformations. The spinel structure was further confirmed by FTIR spectroscopy. EDS spectroscopy confirmed the presence of Co, Mg, Fe, Gd, and O in the investigated sample, verifying its purity and the good reactivity of gadolinium at 900 °C. The proposed cation distribution suggests that Co²⁺ and Gd³⁺ have strong preferences for the octahedral B sites, whereas Mg²⁺ and Fe³⁺ prefer to occupy tetrahedral A sites and octahedral B sites. The experimental and theoretical lattice constants were comparable. The measured saturation magnetization values at 10 and 300 K indicated that Gd³⁺ substitution in the mixed Co–Mg ferrite enhanced the saturation magnetization, which was attributed to the higher spin magnetic moment and anisotropy of Gd³⁺ compared Fe³⁺ along with the strong L–S coupling of Co²⁺. Coercivity increased upon Gd³⁺ doping, which can be explained by the strong L–S coupling and weak crystal field of Co²⁺, resulting in stronger magneto-crystalline anisotropy related to the increase in the concentration of high-spin Co²⁺ ions at octahedral sites. The enhancements in magnetic properties (M_S and n_B) after doping with Gd³⁺ were correlated with the changes in bond angles. Finally, we note that the obtained saturation magnetization was much higher than that of bulk cobalt ferrite.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

References

1. P. M. Ajayan, M. Pulickel, L. S. Schadler, and P. V. Braun, Nanocomposite science and technology, John Wiley & Sons, 2006.
2. D. Astruc, E. Boisselier and C. Ornelas, Chem. Rev., 2010, 110, 1857–1959.
3. E. Boisselier and D. Astruc, Chem. Soc. Rev., 2009, 38, 1759.
4. C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh, A. Kirilyuk and Th. Rasing, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 73, 220402.
5. R. K. Panda and D. Behera, J. Alloys Compd., 2014, 587, 481–486.
6. A. Lakshman, P. S. V. Subba Rao and K. H. Rao, J. Magn. Magn. Mater., 2004, 284, 352–357.
7. S. K. Sharma, R. Kumar, V. V. Siva Kumar, M. Knobel, V. R. Reddy, A. Gupta and M. Singh, Nucl. Instrum. Methods Phys. Res., Sect. B, 2006, 248, 37–41.
8. M. Thomas and K. C. George, Appl. Phys., 2009, 47, 6.
9. L. Wang, J. Li, W. Ding, T. Zhou, B. Liu, W. Zhong, J. Wu and Y. Du, J. Magn. Magn. Mater., 1999, 207, 111–117.
10. P. Brown and L. J. Hope-Weeks, J. Sol-Gel Sci. Technol., 2009, 51, 238–243.
11. S. L. Darshane, R. G. Deshmukh, S. S. Suryavanshi and I. S. Mulla, J. Am. Ceram. Soc., 2008, 91, 2724–2726.
12. M. K. Roy and H. C. Verma, J. Magn. Magn. Mater., 2006, 306, 98–102.
13. T. M. Clark and B. J. Evans, IEEE Trans. Magn., 1997, 33, 3745.
14. C. Liu, B. Zou, A. J. Rondinone and Z. J. Zhang, J. Am. Chem. Soc., 2000, 122, 6263–6267.
15. J.-M. Li, X.-L. Zeng and Z.-A. Xu, Appl. Phys. Lett., 2013, 103, 232410.
16. J.-M. Li, A. C. H. Huan, L. Wang, Y.-W. Du and D. Feng, Phys. Rev. B: Condens. Matter Mater. Phys., 2000, 61, 6876–6878.
17. I. Apostolova and J. M. Wesselinowa, Solid State Commun., 2009, 149, 986–990.
18. P. Kumar, J. Chand, S. Verma and M. Singh, Int. J. Theor. Appl. Sci., 2011, 3(2), 10–12.
19. Y. Mouhib, M. Belaiche and S. Briche, Phys. Status Solidi A, 2018, 215, 1800469.
20. T. Prabhakaran, R. V. Mangalaraja, J. C. Denardin and J. A. Jiménez, J. Alloys Compd., 2017, 716, 171–183.
21. Q. Lin, Y. He, J. Lin, F. Yang, L. Wang and J. Dong, J. Magn. Magn. Mater., 2019, 469, 89–94.
22. Q. Lin, J. Lin, Y. He, R. Wang and J. Dong, J. Nanomater., 2015, 1–6.
23. M. M. Rashad, R. M. Mohamed and H. El-Shall, J. Mater. Process. Technol., 2008, 198, 139–146.
24. L. Zhao, H. Yang, L. Yu, Y. Cui, X. Zhao, Y. Yan and S. Feng, Phys. Lett. A, 2004, 332, 268–274.
25. L. Zhao, H. Yang, L. Yu, W. Sun, Y. Cui, Y. Yan and S. Feng, Phys. Status Solidi A, 2004, 3121–3128.
26. A. A. Sattar, A. M. Samy, R. S. El-Ezza and A. E. Eatah, Phys. Status Solidi A, 2002, 8, 86–93.
27. A. Franco, F. L. A. Machado and V. S. Zapf, J. Appl. Phys., 2011, 110, 53913.
28. N. Aliyan, S. M. Mirkazemi, S. M. Masoudpanah and S. Akbari, Appl. Phys. A, 2017, 123, 446.
29. S. K. Pradhan, S. Bid, M. Gateshki and V. Petkov, Mater. Chem. Phys., 2005, 93, 224–230.
30. L. Sun, R. Zhang, Q. Ni, E. Cao, W. Hao, Y. Zhang and L. Ju, Phys. B, 2018, 545, 4–11.
31. D. Varshney, K. Verma and A. Kumar, J. Mol. Struct., 2011, 1006, 447–452.
32. S. Joshi, M. Kumar, S. Chhoker, A. Kumar and M. Singh, J. Magn. Magn. Mater., 2017, 426, 252–263.
33. G. P. Nethala, R. Tadi, A. V. Anupama, S. L. Shinde and V. Veeraiah, Mater. Sci., 2018, 36, 310–319.
34. N. Thomas, P. V. Jithin, V. D. Sudheesh and V. Sebastian, Ceram. Int., 2017, 43, 7305–7310.
35. N. K. Thanh, T. T. Loan, N. P. Duong, L. N. Anh, D. T. T. Nguyet, N. H. Nam, S. Soontaranon, W. Klysubun and T. D. Hien, Phys. Status Solidi A, 2018, 215, 1700397.
36. F. Nakagomi, S. W. da Silva, V. K. Garg, A. C. Oliveira, P. C. Morais and A. Franco, J. Solid State Chem., 2009, 182, 2423–2429.
37. A. M. Gismelseed, K. A. Mohammed, H. M. Widatallah, A. D. Al-Rawas, M. E. Elzain and A. A. Yousif, J. Phys.: Conf. Ser., 2010, 217, 012138.
38. R. A. Pawar, S. M. Patange, A. R. Shitre, S. K. Gore, S. S. Jadhav and S. E. Shirsath, RSC Adv., 2018, 8, 25258–25267.
39. S. Panchal, S. Raghuvanshi, K. Gehlot, F. Mazaleyrat and S. N. Kane, AIP Adv., 2016, 6, 055930.
40. V. K. Lakhani, T. K. Pathak, N. H. Vasoya and K. B. Modi, Solid State Sci., 2011, 13, 539–547.
41. N. Najmoddin, A. Beitollahi, H. Kavas, S. Majid Mohseni, H. Rezaie, J. Åkerman and M. S. Toprak, Ceram. Int., 2014, 40, 3619–3625.
42. M. S. Khandekar, R. C. Kambale, J. Y. Patil, Y. D. Kolekar and S. S. Suryavanshi, J. Alloys Compd., 2011, 509, 1861–1865.
43. B. M. Ali, M. A. Siddig, Y. A. Alsabah, A. A. Elbadawi and A. I. Ahmed, Adv. Nanoparticles, 2018, 07, 1.
44. H. S. Mund and B. L. Ahuja, Mater. Res. Bull., 2017, 85, 228–233.
45. S. R. Naik, A. V. Salker, S. M. Yusuf and S. S. Meena, J. Alloys Compd., 2013, 566, 54–61.
46. Z. Karimi, Y. Mohammadifar, H. Shokrollahi, Sh. K. Asl, Gh. Yousefi and L. Karimi, J. Magn. Magn. Mater., 2014, 361, 150–156.
47. A. K. Nikumbh, R. A. Pawar, D. V. Nighot, G. S. Gugale, M. D. Sangale, M. B. Khanvilkar and A. V. Nagawade, J. Magn. Magn. Mater., 2014, 355, 201–209.
48. S. Amiri and H. Shokrollahi, J. Magn. Magn. Mater., 2013, 345, 18–23.
49. R. Safi, A. Ghasemi, R. Shoja-Razavi and M. Tavousi, J. Magn. Magn. Mater., 2015, 396, 288–294.
50. M. F. Al-Hilli, S. Li and K. S. Kassim, Mater. Sci. Eng., B, 2009, 158, 1–6.
51. A. C. F. M. Costa, A. P. A. Diniz, A. G. B. de Melo, R. H. G. A. Kiminami, D. R. Cornejo, A. A. Costa and L. Gama, J. Magn. Magn. Mater., 2008, 320, 742–749.
52. D. Ravinder and K. V. Kumar, Bull. Mater. Sci., 2001, 24, 505–509.
53. N. Rezlescu, E. Rezlescu, F. Tudorache and P. D. Popa, J. Optoelectron. Adv. Mater., 2004, 6, 695.
54. J. Jiang, L. Li, F. Xu and Y. Xie, Mater. Sci. Eng., B, 2007, 137, 166–169.
55. S. Torkian, A. Ghasemi and R. S. Razavi, J. Supercond. Nov. Magnetism, 2016, 29, 1617–1625.
56. Y. H. Hou, Y. L. Huang, S. J. Hou, S. C. Ma, Z. W. Liu and Y. F. Ouyang, J. Magn. Magn. Mater., 2017, 421, 300–305.
57. G. Dascalu, T. Popescu, M. Feder and O. F. Caltun, J. Magn. Magn. Mater., 2013, 333, 69–74.
58. M. Grigorova, H. J. Blythe, V. Blaskov, V. Rusanov, V. Petkov, V. Masheva, D. Nihtianova, Ll. M. Martinez, J. S. Muñoz and M. Mikhov, J. Magn. Magn. Mater., 1998, 183, 163–172.
59. M. Abbas, B. Parvatheeswara Rao, Md. Nazrul Islam, K. W. Kim, S. M. Naga, M. Takahashi and C. Kim, Ceram. Int., 2014, 40, 3269–3276.
60. V. Mameli, A. Musinu, A. Ardu, G. Ennas, D. Peddis, D. Niznansky, C. Sangregorio, C. Innocenti, N. T. K. Thanh and C. Cannas, Nanoscale, 2016, 8, 10124–10137.
61. S. E. Shirsath, M. L. Mane, S. M. Patange, S. S. Jadhav and K. M. Jadhav, J. Phys. Chem. C, 2011, 115, 20905–20912.
62. A. Nairan, M. Khan, U. Khan, M. Iqbal, S. Riaz and S. Naseem, Nanomaterials, 2016, 6, 73.
63. Modern magnetic materials: principles and applications, ed. C. Oh. Robert and O. Handley, John Wiley Sons Inc, N. Y., 2000.
64. B. A. Calhoun and M. J. Freiser, J. Appl. Phys., 1963, 34, 1140–1145.
65. Q. Gao, G. Hong, J. Ni, W. Wang, J. Tang and J. He, J. Appl. Phys., 2009, 105, 07A516.
66. E. C. Stoner and E. P. Wohlfarth, IEEE Trans. Magn., 1991, 27, 3475–3518.
67. R. H. Kodama, J. Magn. Magn. Mater., 1999, 200, 359–372.
68. R. N. Panda, J. C. Shih and T. S. Chin, J. Magn. Magn. Mater., 2003, 257, 79–86.

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