Impact of Gd³⁺ substitution on the structural, magnetic and electrical properties of cobalt ferrite nanoparticles

Abstract

In this work, we have focused on the influence of Gd³⁺ substitution on the structural, magnetic and electrical properties of cobalt ferrite synthesized using a sol–gel auto-combustion method. The powder X-ray diffraction analysis reveals that the Gd-substituted cobalt ferrites crystallize in a single phase spinel structure for lower concentrations of Gd³⁺, while a trace of GdFeO₃ appears as a minor phase for higher concentrations. Raman and Fourier transform infrared spectra confirm the formation of the spinel structure. Furthermore, Raman analysis shows that the inversion degree of cobalt ferrite decreases with Gd³⁺ doping. The field emission scanning electron microscopy images show that the substitution of small amounts of Gd³⁺ causes a considerable reduction of the grain size. Studies on the magnetic properties reveal that the coercivity of Gd-substituted cobalt ferrites enhances from 1265 Oe to 1635 Oe, the saturation magnetization decreases monotonically from 80 emu g⁻¹ to 53.8 emu g⁻¹ and the magnetocrystalline anisotropy constant increases from 5.8 × 10⁵ erg cm⁻³ to 2.23 × 10⁶ erg cm⁻³ at 300 K. The electrical properties show that the Gd³⁺ doped samples exhibit high dielectric constant (616 at 100 Hz) and ac conductivity (4.83 × 10⁻⁵ S cm⁻¹ at 100 Hz) values at room temperature. The activation energy is found to decrease from 0.408 to 0.347 eV with the rise in Gd³⁺ content. The impedance study brings out the effect of the bulk grain and the grain boundary on the electrical resistance and capacitance of cobalt ferrite. Gd substitution and the nano-size of cobalt ferrite enhance the electrical and magnetic properties which could enable a higher memory storage capability.

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Introduction

Spinel ferrites with the general formula MFe₂O₄ (M = Co, Ni, Mn and Zn etc.) are some of the most interesting magnetic oxides due to their superior electrical, magnetic and optical properties.^1–8 Among the spinel ferrites, cobalt ferrite is an attractive material due to its valuable properties, such as high coercivity, high electrical resistivity, moderate saturation magnetization, large magnetocrystalline anisotropy (∼4 × 10⁶ erg cm⁻³), good chemical stability and high Curie temperature (793 K).^9–16 It is of significant technological interest due to its potential application in targeted drug delivery systems,^17,18 microwave devices,^19,20 sensors,²¹ catalysis^22,23 and magnetic recording applications,^9,24 etc. Recently, the doping of small amounts of trivalent rare earth cations in spinel ferrites has emerged as a promising strategy to improve their magnetic and electrical properties. Moreover, these properties are governed by the antiferromagnetic superexchange interaction between Fe³⁺ and Fe³⁺ ions. Introducing small amounts of trivalent rare earth (RE) ions into the spinel ferrite lattices will also induce RE³⁺–Fe³⁺ interactions.^25–30 It is well known that the intrinsic properties of the spinel ferrite nanoparticles depend on their chemical composition and preparative methods.^31,32 Spinel ferrites are prepared by several methods, such as co-precipitation, flash combustion, citrate precursor, sol–gel, auto-combustion and ceramic techniques. Among them, the auto-combustion method is advantageous for the synthesis of nanoparticles due to the inexpensive precursors, low external energy consumption, simple equipment requirements and uniformity of particle size.³³ In the present work we aim to study the effect of Gd³⁺ substitution on the structural, magnetic and electrical properties of cobalt ferrite nanoparticles prepared using the sol–gel auto-combustion method. The results suggest that the substitution of gadolinium in cobalt ferrite has a substantial impact on the properties of the prepared samples for increasing their capacity for memory storage.

Experimental

Preparation

The nanoparticles of CoGd_xFe_2−xO₄ (x = 0.0, 0.05, 0.10, 0.15 and 0.20) were synthesized using a self-propagating sol–gel auto-combustion method. Analytical grade cobalt nitrate, ferric nitrate, gadolinium nitrate and citric acid were used as reactants. The required amount of reactants were weighed and the molar ratio of metal nitrate to citric acid was 1 : 1. The weighed metal nitrates and citric acid were separately dissolved in the minimum amount of double-distilled water. The obtained clear solutions were mixed together. The pH of the solution was adjusted to 7 with the addition of 25% ammonia solution and then magnetically stirred at ambient temperature. Its homogeneous solution was allowed to condense with continuous stirring on a hot plate, at a temperature of about 85 °C until it formed a highly viscous dried gel. Then the dried viscous gel was heated on a hot plate at 300 °C until it self-ignited. The self-ignited final product was ground well and then used for further characterization.

Characterization

The thermal analysis of the as prepared samples was carried out using a simultaneous thermogravimetric and differential thermal analysis (TG-DTA) system – Q600 SDT at a step rate of 10 °C min⁻¹ in an air atmosphere from 30 °C to 1000 °C. The powder X-ray diffraction (PXRD) patterns of all the samples were obtained using a X-ray powder diffractometer (RIGAKU, Ultima IV) employing Cu-Kα (wavelength = 1.5406 Å). Raman spectra were measured using a LASER Raman spectrophotometer (Renishaw inVia reflex) equipped with a CCD camera using an Ar ion laser (514 nm) over the range of 100–900 cm⁻¹. Fourier transform infrared (FTIR) spectra were recorded using a Shimadzu-8700 FTIR spectrometer over the range of 1200–360 cm⁻¹. The surface morphology and the elemental composition of the samples were examined using a field emission scanning electron microscope (FE-SEM, Carl Zeiss SUPRA 55) equipped with an energy dispersive spectroscopy (EDS) system. The magnetic measurements were performed using a (Quantum Design) physical property measurement system (PPMS) with a maximum applied field range of 6 T. The frequency dependence of the ac electrical properties of the samples in the form of pellets (∼10 mm in diameter and ∼1.5 mm thickness) were measured using a LCR meter (PSM 1735 COM) in the frequency range of 100 Hz to 1 MHz.

Results and discussion

Thermal analysis

The TG-DTA curves of the as-prepared CoGd_xFe_2−xO₄ (x = 0.0, 0.05, 0.1, 0.15 and 0.2) powders are shown in Fig. 1. It is seen from Fig. 1 that there are three regions for the thermal process, viz. 30–175 °C, 175–625 °C and 625–1000 °C. In the first region (30–175 °C) the initial weight loss in the TGA curves and the small endothermic peaks in the DTA curves are due to the evaporation of moisture present in the as-prepared samples. A major weight loss seen in the second region (175–625 °C) of the TGA curves and the exothermic peaks in the DTA curves could be attributed to the decomposition of unreacted reactants present in the as-prepared samples. Furthermore, in the third region (625–1000 °C) the weight loss is due to the crystallization of the self-combusted final product. It is observed that, in the third region, the temperature required for crystallization is increased for the Gd³⁺ doped samples compared with pure CoFe₂O₄. The higher the ionic radius of Gd³⁺, the higher is the thermal energy required for crystallization and hence the resulting crystallization occurs at a relatively higher temperature for the Gd³⁺ doped samples. It was concluded from the TG-DTA results that an optimal temperature of 750 °C is suitable for annealing the as-prepared samples, and thus the samples that were used for further characterization were annealed at 750 °C for 2 h.

Fig. 1 TG-DTA curves of the pristine CoGd_xFe_2−xO₄ powder samples.

Powder X-ray diffraction study

The PXRD patterns of the CoGd_xFe_2−xO₄ powders are shown in Fig. 2. All the PXRD patterns confirm that the samples have a polycrystalline cubic spinel structure and the reflection planes are perfectly indexed to cobalt ferrite (JCPDS no.: 03-0864). Furthermore, we note that there is no evidence of a secondary phase for x ≤ 0.10. This confirms that the substituted Gd³⁺ ions are completely dissolved in the cobalt ferrite lattices. The emergence of small amounts of orthoferrite phase GdFeO₃ (JCPDS no.: 74-1900) also occurs for higher Gd³⁺ content (x > 0.10). The ionic radius of the Gd³⁺ ion is 0.938 Å, which is higher than that of the Fe³⁺ ion (0.67 Å), and hence the amount of Fe³⁺ ions replaced by Gd³⁺ ions is limited and there is a solubility limit for the replacement of Fe³⁺ ions by Gd³⁺ ions. Thus, it is expected that the excess Gd³⁺ ions tend to aggregate around the grain boundaries in the form of GdFeO₃.³⁴ The optimized maximum solubility limit for the Gd³⁺ ions in cobalt ferrite in the present work is x = 0.10. Since the substitution of rare earth ions induces structural distortion by increasing crystal imperfections due to their larger size and produces micro-strain, utilizing the Williamson–Hall equation to analyze the PXRD patterns is more appropriate than using the Scherrer’s equation.^28,35,36 The full width at half maximum (FWHM) of the experimental diffracted peaks is modeled to the Gaussian shape. The actual broadening (β) of the diffraction pattern is corrected for the experimental broadening (β_ex) and the instrumental broadening (β_in) as β = β_ex² − β_in². Considering the size and strain effect, the Williamson–Hall equation for the actual broadening (β) can be modeled as follows,

β = (Kλ/D cos θ) + 4ε tan θ (1)

where (Kλ/D cos θ) is broadening due to the size (D) and 4ε tan θ is broadening due to strain (ε). The modification of eqn (1) yields,

β cos θ = (Kλ/D) + 4ε sin θ (2)

where β is the full width at half maximum of the PXRD peaks, θ is the position of the peaks, K is the Debye–Scherrer constant (0.94 for spherical nanoparticles), λ is the X-ray wavelength, D is the size of the crystallite and ε is the average micro-strain. Therefore, a linear plot of β cos θ versus 4 sin θ yields the intercept as the crystallite size and the slope as the strain. The Williamson–Hall plots for the CoGd_xFe_2−xO₄ nanoparticles are shown in Fig. 3. From Fig. 3 it is observed that the intercept values progressively increase to higher values and the slopes of the plots change from negative to positive with increasing Gd³⁺ content. The calculated values of the crystallite sizes are plotted and shown in Fig. 4. The size of the pure cobalt ferrite is 46 nm, which decreases for gadolinium doped cobalt ferrite to 24 nm (CoGd_0.05Fe_1.95O₄) and 23 nm (CoGd_0.10Fe_1.90O₄). It is observed that the growth of the CoFe₂O₄ is restricted by the substitution of Gd³⁺ ions, leading to a relatively small crystallite size compared with pure cobalt ferrite. Due to the higher bond energy of Gd³⁺–O²⁻, as compared with that of Fe³⁺–O²⁻, it is obvious that more energy is required to incorporate Gd³⁺ ions into the octahedral sites.³⁷ The energy required for this process is supplied at the expense of crystallization and therefore hinders the growth of the crystallites and a smaller crystallite size is thus observed for the Gd³⁺ doped samples. It is interesting that for higher substitution amounts (x > 0.10) of Gd³⁺, the size of the crystallites slightly increase to 24 nm (CoGd_0.15Fe_1.85O₄) and 27 nm (CoGd_0.20Fe_1.80O₄). The sudden increase of the crystallite size for higher concentrations (x > 0.10) of Gd³⁺ is expected due to the presence of a secondary GdFeO₃ phase. It is clear from the PXRD patterns of CoGd_0.15Fe_1.85O₄ and CoGd_0.20Fe_1.80O₄ that the higher concentration of Gd³⁺ favours the formation of the secondary GdFeO₃ phase. It is inferred from this observation that part of the energy required for the incorporation of Gd³⁺ ions into octahedral sites during the synthesis process is now being utilized for the growth of the crystallites. The values of the average micro-strain are measured from the slope of the lines using Fig. 3. The variation of the slope values of the pure and Gd³⁺ doped cobalt ferrites obtained from Fig. 3 is plotted in Fig. 4. We note that the slope of pure CoFe₂O₄ is negative. It is well known that for the smallest particles a negative slope indicates the presence of compressive strain in the material, while a positive slope indicates tensile strain.³⁸ The negative slope of the CoFe₂O₄ indicates the presence of compressive strain. It is interesting to note that the doping of higher amounts of Gd³⁺ ions shifts the slope values from negative to positive. This indicates that the substitution of larger sized Gd³⁺ ions is expanding the crystal lattices by changing the strain from compressive to tensile. The variation of the lattice constant of all the samples is calculated using the following relation:³⁹

a = (λ/2)*√((h² + k² + l²)/sin² θ) (3)

where a is the lattice constant, λ is the wavelength, h, k and l are Miller indices and θ is the position of the peak. The variation of the lattice constant of pure and Gd³⁺ doped cobalt ferrites is given in Table 1. For pure cobalt ferrite, the calculated value of the lattice constant is 8.371 Å, which is similar to that of the reported value for CoFe₂O₄ prepared using the solid state reaction method.³⁴ It is observed from Table 1 that Gd³⁺ substitution gradually increases the lattice constant up to x = 0.15 (8.382 Å). The ionic radius of the Gd³⁺ ion is higher than that of the Fe³⁺ ion and a linear expansion in the lattice constant is expected. The expansion of the lattice constant further supports the incorporation of Gd³⁺ into the cobalt ferrite lattice. It is observed that the value of the lattice constant is smaller for CoGd_0.20Fe_1.80O₄ (8.377 Å) compared with CoGd_0.15Fe_1.85O₄ (8.382 Å). It is clear from the PXRD patterns that the intensity of the secondary phase GdFeO₃ present in CoGd_0.20Fe_1.80O₄ is higher than that of CoGd_0.15Fe_1.85O₄. The higher substituted amount of the Gd³⁺ ions does not enter into the cobalt ferrite sub-lattices and form more of the secondary GdFeO₃ phase, and hence a reduced value of the lattice constant is observed. The values of X-ray density (d_x) have been estimated and presented in Table 1 using the relation D_hkl = (8M/Na³),³⁹ where D_hkl is the X-ray density, M is the molecular weight and N is the Avogadro number (6.023 × 10²³ mol⁻¹). The calculated value of the X-ray density is 5.313 g cm⁻³ for CoFe₂O₄. We note that the X-ray density increases with Gd³⁺ substitution. The enhanced value of X-ray density is attributed to the higher molecular weight of the samples having gadolinium ions. The density increases as the particles tend to acquire nano-sizes and pack tightly.

Fig. 2 Powder-XRD patterns of CoGd_xFe_2−xO₄ nanoparticles.

Fig. 3 Williamson–Hall plots of CoGd_xFe_2−xO₄ nanoparticles.

Fig. 4 Variation of the crystallite size and micro-strain of CoGd_xFe_2−xO₄ nanoparticles.

Table 1 Microstructural parameters: lattice constant (a), X-ray density (d_x) and IR vibrational bands from XRD and FTIR analysis of CoGd_xFe_2−xO₄ nanoparticles

Sample	a (Å)	dx (g cm^−3)	FTIR bands
			ν1 (cm^−1)	ν2 (cm^−1)
CoFe2O4	8.371	5.313	586.31	393.45
CoGd0.05Fe1.95O4	8.375	5.420	586.31	389.59
CoGd0.10Fe1.90O4	8.379	5.527	582.46	389.59
CoGd0.15Fe1.85O4	8.382	5.635	586.31	374.16
CoGd0.20Fe1.80O4	8.377	5.759	578.60	381.87

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Raman analysis

Raman spectroscopy is a powerful technique for providing more insight into the atomic structure of nanoparticles.⁴⁰ The Raman spectra of the CoGd_xFe_2−xO₄ (x = 0.0, 0.05, 0.10, 0.15 and 0.20) samples are presented in Fig. 5. For a more accurate analysis the recorded Raman spectra have been deconvoluted into individual Lorentzian peaks and the positions of the bands are given in Table 2. Cobalt ferrite has a cubic spinel structure with the Fd3m space group. From the group theory analysis, 39 normal modes of vibrations are predicted for a spinel structure, out of which five modes, A_1g (648–680 cm⁻¹), E_g (278–293 cm⁻¹) and 3T_2g (539–565, 449–471 and 163–177 cm⁻¹), are Raman active.^41,42 It is seen from Table 2 that pure cobalt ferrite shows five major bands at ∼197, ∼312, ∼471, ∼579 and ∼694 cm⁻¹. These bands are assigned to five Raman active modes of vibrations (A_1g + E_g + 3T_2g). Besides these bands, due to quantum-size effects a band around ∼621 cm⁻¹ is also detected.⁴³ Furthermore, the recorded Raman spectrum confirms the spinel structure of cobalt ferrite and rules out the existence of impurities like α-Fe₂O₃, which usually gives strong bands at ∼240 and ∼300 cm⁻¹. We note that the incorporation of the Gd³⁺ ion into the cobalt ferrite has slightly shifted the centre of the peaks towards the higher frequency side. The shifting of peaks is attributed to the development of micro-strain in the cobalt ferrite lattices due to the larger sized Gd³⁺ ion substitution and further supports the PXRD results. Moreover, it is interesting to note that the intensity of the A_1g(2) (621 cm⁻¹) vibrational mode is gradually increased with increasing Gd³⁺ substitution. The use of Raman spectroscopy to reveal the degree of inversion of the spinel ferrites has been highlighted by several authors.^42,44–48 Chandramohan et al.⁴⁷ related the decrease in the relative intensity ratio of the A_1g(1)and A_1g(2) vibrational modes to the lowering of the inversion parameter of cobalt ferrite nanoparticles of 6 nm size compared with those of 500 nm. Since the T_2g modes are assigned to vibrations within octahedral sites, whereas the A_1g modes are related to vibrations within tetrahedral sites, Fernandes et al.⁴² suggested that the contribution from the T_2g mode should also be considered for the analysis of the degree of inversion. It is further reported that for simple nanoferrites, the area ratio between the bands associated with the octahedral and tetrahedral sites, i.e., T_2g(1)/[A_1g(1) + A_1g(2)], is similar to the resultant degree of inversion. In our study, we have utilized both intensity ratio and area ratio methods and the obtained values of both ratios are depicted in Fig. 6. It is seen from Fig. 6 that both ratios are decreasing for Gd³⁺ doped cobalt ferrite nanoparticles, indicating the low degree of inversion of Gd³⁺ doped samples compared with the pure cobalt ferrite. It is well known that the vibrational modes above 600 cm⁻¹ correspond to A_1g symmetry involving symmetrical stretching vibrations of the metal–oxygen bonds of the tetrahedral group (AO₄). The substituted large-sized Gd³⁺ ions are expected to occupy only the octahedral sites⁴⁹ by transferring Co²⁺ from octahedral sites to tetrahedral sites, hence decreasing the degree of inversion, which further confirms the variation in the cation distribution compared with pure cobalt ferrite.

Fig. 5 Raman spectra of CoGd_xFe_2−xO₄ nanoparticles.

Table 2 Raman peaks of CoGd_xFe_2−xO₄ nanoparticles

Sample	A1g(1)	A1g(2)	T2g(1)	T2g(2)	Eg(1)	T2g(3)
CoFe2O4	694.83	621.21	579.20	471.49	312.31	197.3
CoGd0.05Fe1.95O4	696.08	623.89	583.57	473.89	314.74	194.00
CoGd0.10Fe1.90O4	689.06	621.98	575.05	471.50	308.54	201.61
CoGd0.15Fe1.85O4	696.15	630.13	584.83	474.69	320.30	185.61
CoGd0.20Fe1.80O4	697.39	630.72	589.14	475.43	322.70	171.04

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Fig. 6 Intensity and area ratios of the Raman bands as a function of gadolinium content.

Infrared spectral investigation

The FTIR spectra of pure and Gd³⁺ doped Co ferrite nanoparticles were also obtained and are shown in Fig. 7. The positions of the vibrational bands of the CoGd ferrites are given in Table 1. For spinel ferrites, the vibrational band around 600 cm⁻¹ corresponds to the stretching vibration of tetrahedral groups and the vibrational band around 400 cm⁻¹ corresponds to the stretching vibration of octahedral groups.⁵⁰ It is seen from Table 1 that the vibrational spectra consist of two major absorption bands, the first at about 600 cm⁻¹ (ν₁) and the second at about 400 cm⁻¹ (ν₂). These absorption bands further confirm the formation of spinel-structured cobalt ferrite. We note that with the increase of the gadolinium ion doping, a small shift in the absorption bands of the tetrahedral and octahedral sites is seen towards the lower frequency side. The substitution of Gd³⁺ ions into the octahedral site causes the migration of an equal number of Co²⁺ ions to the tetrahedral sites and, as a result, an equal number of Fe³⁺ ions migrate from tetrahedral sites to octahedral sites to relieve the strain.²⁷ The ionic radius of the Co²⁺ ion (0.82 Å) is higher than that of the Fe³⁺ ion (0.67 Å), and hence an increasing number of Co²⁺ ions in A sites increases the ionic radii of the A sites. Similarly, an increasing number of Gd³⁺ ions in B sites increases the ionic radii of the B sites. The increase of the ionic radii of the A and B sites reduced the fundamental frequency and hence the central frequency of the tetrahedral and octahedral sites shifted towards the lower frequency side. This further confirms the results discussed in the Raman analysis.

Fig. 7 The FTIR spectra of CoGd_xFe_2−xO₄ nanoparticles.

FE-SEM and EDS analysis

To analyze the surface morphological information, the FE-SEM images are observed for all the samples. Fig. 8(a–e) show the FE-SEM images of the pure and gadolinium doped cobalt ferrite samples. It is seen from the images that pure cobalt ferrite particles are agglomerated, spherical and nano-sized. Moreover, the doping of Gd³⁺ ions decreases the size of the grains. A clear difference is observed between the un-doped and doped samples. This observation is in good agreement with the size reduction observed by PXRD analysis, discussed earlier. The elemental analysis has been carried out for selected samples using energy dispersive spectroscopy with the help of FE-SEM and the results are shown in Fig. 9(a–c). The obtained results confirm the presence of Co, Gd, Fe and O elements in the prepared samples and no other traceable impurities are found within the resolution limit of EDS.

Fig. 8 (a–e) FE-SEM images of CoGd_xFe_2−xO₄ nanoparticles.

Fig. 9 (a–c) EDS spectra of CoGd_xFe_2−xO₄ (x = 0.0, 0.10 and 0.20) nanoparticles.

Magnetic study

Magnetic hysteresis loop measurements of the pure and gadolinium doped cobalt ferrite nanoparticles were carried out at 300 K and 10 K. The hysteresis loops of the CoGd_xFe_2−xO₄ (x = 0.0, 0.05, 0.10, 0.15 and 0.20) nanoparticles are shown in Fig. 10a and b. It is observed that the pure and Gd³⁺ doped cobalt ferrite nanoparticles show ferrimagnetic behavior, characterized by hysteresis loops with saturation magnetization, coercivity and remanence. The saturation magnetization (M_s), the coercivity (H_c) and the remanence magnetization (M_r) at 300 K and 10 K are given in Table 3. It is observed that the values of saturation magnetization decrease for gadolinium doped cobalt ferrites. According to Neel’s sublattice model, the spinel ferrites have three types of interactions between tetrahedral (A) and octahedral (B) interstitial sites, A–A, B–B and A–B. Among these three interactions, the A–B intra-sublattice interaction is much stronger than the other two interactions.⁵¹ It is well known that substituted rare earth ions generally occupy octahedral sites due to their larger ionic radii. The ordered magnetic moment of Gd³⁺ is evident at low temperature only (the Curie temperature of Gd is 293.2 K (ref. 52)). Therefore, the substitution of Gd³⁺ ions in cobalt ferrite lattices is equal to the substitution of non-magnetic atoms at the B sites and hence the magnetization of B sites is reduced. The total magnetization of cobalt ferrite is the difference between the magnetization of B and A sites, and consequently the magnetization is reduced at room temperature.⁵³

Fig. 10 (a and b) Hysteresis curves of CoGd_xFe_2−xO₄ nanoparticles at (a) 300 K and (b) 10 K.

Table 3 Magnetic properties of CoGd_xFe_2−xO₄ nanoparticles at 300 and 10 K: saturation magnetization (M_s), coercivity (H_c), remanence magnetization (M_r), and anisotropy constant (K₁)

Sample	300 K				10 K
	Ms (emu g^−1)	Hc (Oe)	Mr (emu g^−1)	K1 × 10^6 (erg cm^−3)	Ms (emu g^−1)	Hc (Oe)	Mr (emu g^−1)	K1 × 10^6 (erg cm^−3)
CoFe2O4	80.00	1265	41.60	0.583	86.12	6747	62.27	3.575
CoGd0.05Fe1.95O4	69.47	1466	33.55	2.080	80.71	12 400	57.77	4.008
CoGd0.10Fe1.90O4	64.66	1635	27.91	2.231	83.25	13 195	53.07	4.694
CoGd0.15Fe1.85O4	59.24	1566	25.04	2.129	82.94	13 184	48.98	5.039
CoGd0.20Fe1.80O4	53.80	1560	21.62	2.009	78.51	13 172	42.66	5.081

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It is observed that for pure cobalt ferrite with a crystallite size of 46 nm, a M_s value of 80 emu g⁻¹ is found at 300 K, which is in good agreement with the reported value (76 emu g⁻¹).⁵⁴ Moreover, the doping of Gd³⁺ ions in cobalt ferrite monotonically decreases the value of the saturation magnetization from 80 to 53.8 emu g⁻¹ when the crystallite size of the Gd³⁺ doped cobalt ferrite decreases from 40 to 23 nm. Normally, this is attributed to the surface effect of the magnetic nanoparticles due to their small crystallite size.¹² This surface effect can be elucidated by postulating the existence of a dead magnetic layer due to the surface spin disorder. It is expected that the number of spins at the surface of Gd³⁺ doped cobalt ferrite increases as the crystallite size gets smaller.⁵⁵ It is further seen from the PXRD analysis that for a higher substitution of Gd³⁺ ions, small traces of secondary phase GdFeO₃ are present. The GdFeO₃ is antiferromagnetic in nature and a decrease in the saturation magnetization is expected for higher concentrations of gadolinium.^26,56 Thus, the results of the above-mentioned effects are expected to be reflected in the saturation magnetization of the pure and gadolinium doped cobalt ferrite nanoparticles.

Moreover, it is observed that at low temperature (10 K) the saturation magnetizations of all of the samples are higher than those at 300 K. For pure cobalt ferrite, a M_s value of 86 emu g⁻¹ is found at 10 K. Such an increase in the saturation magnetization compared with that at 300 K is attributed to the decrease of the thermal fluctuation and surface spin disorder at the surface of the nanoparticle. We note that there is no enhancement in the M_s value observed for Gd³⁺ substituted cobalt ferrite. Theoretically, it is expected that the magnetization of the Gd³⁺ doped cobalt ferrite will be increased, due to the large magnetic moment of the Gd³⁺ ion (9.64 BM) at low temperature, but we have seen that the value of the saturation magnetization decreases with Gd³⁺ substitution. This could be attributed to the screening of the Gd³⁺ magnetic contribution by smaller crystallites due to Gd³⁺ doping.⁵⁷ This further indicates that the size effect plays an important role in the magnetic properties of gadolinium doped cobalt ferrite nanoparticles.

The variation in the coercivity values (at 300 K and 10 K) with Gd³⁺ substitution is given in Table 3. It is observed from Table 3 that the coercivity of the CoGd_xFe_2−xO₄ nanoparticles at 300 K increases initially with x up to x = 0.10 and then decreases for higher (x > 0.10) Gd³⁺ substitution. Pure cobalt ferrite has a coercivity of 1265 Oe, which increases to 1635 Oe for CoGd_0.10Fe_1.90O₄. The observed variation in coercivity can be explained as follows. Similar to Co²⁺ ions, Gd³⁺ ions have stronger L–S coupling and a weaker crystal field, which cause the stronger magnetocrystalline anisotropy of gadolinium doped cobalt ferrite.⁵⁸ Furthermore, it is observed that the crystallite size decreases for Gd³⁺-substituted samples. It is a well known fact that coercivity is inversely proportional to the grain size.⁵⁹ The bigger grains provide less pinning of domain walls due to the lower volume fraction of the grain boundaries.⁶⁰ The gradual enhancement of H_c with gadolinium content may be attributed to the decrease in the grain size.

On the other hand, the presence of a secondary phase also plays an important role in influencing the coercivity of magnetic materials. We have observed that for the higher concentrations of Gd³⁺ substitution (x > 0.10) the coercivity values are decreased. Generally, the secondary phases are distributed in the grain boundaries of spinel ferrites and hinder the domain wall displacement; hence one can expect an enhancement in coercivity.⁶¹ In our study, we have observed that the variation in coercivity does not follow the usual trend as mentioned above. It is well-known that in cobalt ferrite the magnetocrystalline anisotropy originates from the presence of Co²⁺ ions at the octahedral sites. As we have explained earlier in the Raman analysis, the Co²⁺ ions migrate from octahedral sites to tetrahedral sites due to the substitution of large Gd³⁺ ions. However, it is expected that the reduction in the number of Co²⁺ ions in octahedral sites might reduce the coercivity of gadolinium doped cobalt ferrite at higher concentrations. Furthermore, this clearly elucidates that the rearrangements of the cations due to Gd³⁺ substitution plays a major role in the variation of the coercivity. At low temperature (10 K), the coercivity values of all the samples are one order of magnitude increased when compared with 300 K. It is seen that pure cobalt ferrite has a coercivity of 6747 Oe, which increases to 13 195 Oe for CoGd_0.10Fe_1.90O₄. The enhanced value of coercivity is attributed to the reduced thermal fluctuation energy at 10 K, which is less effective in reducing the effects of the magnetocrystalline anisotropy energy. The substitution of rare earth ions is prone to cause magnetocrystalline anisotropy due to their larger size compared to transition elements as well as their lower value of magnetic moment. The magnetocrystalline anisotropy constant (K₁) is determined by fitting the high magnetic field data of the hysteresis loop using the relation law of approach (LA) to saturation. The law of approach describes the dependence of magnetization (M) on the applied magnetic field (H) when the applied magnetic field is much higher than the coercive field (H_c). The dependence of magnetization near saturation can be written as follows:⁶²

where M is the magnetization, M_s is the saturation magnetization, , K₁ is the cubic anisotropy constant, μ₀ is the permeability of the free space, H is the applied magnetic field and κH is the forced magnetization. The factor κH is applicable for high magnetic field and high temperature data. In our case the κH factor is not considered, since our data is at high field but not at high temperature. The calculated values of K₁ are listed in Table 3 and the results shows that the value of K₁ strongly depends on both the gadolinium content and the temperature. Furthermore, our result is comparable to earlier reports on cobalt ferrite nanoparticles.^63,64 It is observed that at 300 K, the K₁ values increase with x up to x = 0.10 and thereafter they follow a decreasing trend. This reduction in the K₁ value for higher concentrations of Gd³⁺ is attributed to the non-incorporation of higher amounts of Gd³⁺ ions into the cobalt ferrite lattices and the migration of Co²⁺ ions from octahedral sites to tetrahedral sites.

Electrical properties

Dielectric constant. The dielectric responses of all the samples were investigated to provide an insight into the electrical conduction mechanism of pure and gadolinium doped cobalt ferrite nanoparticles. The value of the dielectric constant is obtained by using the formula ε = Cε_ot/A, where C is the capacitance of the pellet, t is the thickness of the pellet and A is the area of the pellet. The frequency dependencies of the dielectric constants of pure and Gd³⁺ doped cobalt ferrites were measured at 30 °C in the frequency range of 100 Hz to 1 MHz and are depicted in Fig. 11. It is seen from Fig. 11 that the measured values of the dielectric constants strongly depend on the frequency of the applied electric field. It is further seen from Fig. 11 that the dielectric constants abruptly decrease at low frequencies and become constant at higher frequencies, hence showing a dispersion behavior at lower frequencies. The dispersion in the dielectric constants is attributed to the Maxwell–Wagner type of interfacial polarization, in agreement with Koop’s phenomenological theory.^65,66 According to this, the dielectric medium consists of well-conducting grains and poorly conducting grain boundaries. It is well known that polarization in ferrites occurs through a mechanism similar to the conduction process.⁶⁷ The polarization in cobalt ferrites is attributed to electron hopping between Fe²⁺ ↔ Fe³⁺ ions and hole hopping between Co³⁺ ↔ Co²⁺ ions and hence charge carriers reaching the grain boundaries pile up there, due to the higher resistance, and produce polarization. However, as the frequency of the applied electric field increases, the charge carriers can’t follow the frequency of the alternating applied electric field and hence decrease the polarization.⁶⁸ We note that the dielectric constant of cobalt ferrite increases with increasing Gd³⁺ substitution. Similar kinds of results are also reported in literature for cobalt ferrites.⁶⁹ This increase in the dielectric constant could be attributed to the increasing number of Fe³⁺ ions at the octahedral sites. As discussed earlier, the doping of Gd³⁺ ions causes the migration of Co²⁺ ions to tetrahedral sites and, to relieve the strain, an equal amount of Fe³⁺ ions migrate from the tetrahedral sites to octahedral sites, hence increasing the hopping of electrons between Fe²⁺ ↔ Fe³⁺ ions in the octahedral sites and enhancing the dielectric constant. It is observed that for CoGd_0.20Fe_1.80O₄, the value of the dielectric constant decreases compared with CoGd_0.15Fe_1.85O₄. Due to the non-incorporation of higher Gd³⁺ contents into CoFe₂O₄, the transfer of Fe³⁺ ions from the tetrahedral sites to the octahedral sites is limited. In addition to that, the formation of a large amount of the GdFeO₃ secondary phase in CoGd_0.20Fe_1.80O₄ decreases the number of Fe ions and ultimately the Fe²⁺ ↔ Fe³⁺ ion pairs. Hence, the availability of Fe²⁺ ↔ Fe³⁺ ion pairs decreases at the octahedral sites, and the hopping of electrons between Fe²⁺ ↔ Fe³⁺ also decreases and reduces the dielectric constant.

Fig. 11 The variation of the dielectric constant of CoGd_xFe_2−xO₄ nanoparticles with frequency at 30 °C.

AC conductivity. As mentioned earlier, the mechanism of electrical conduction is the same as that of dielectric polarization in ferrites; the enhancement of electrical polarization could be better understood in terms of ac electrical conductivity analysis. The variation of the frequency dependent ac electrical conductivity of pure and gadolinium doped cobalt ferrite nanoparticles is depicted in Fig. 12. It is obvious from Fig. 12 that the electrical conductivity of all samples increases slowly at low frequencies and rapidly increases at higher frequencies. The frequency dependent variation of the ac electrical conductivity has been explained on the basis of the Maxwell–Wagner double layer model for dielectrics. At lower frequencies the resistive grain boundaries are more active; hence hopping of charge carriers between Fe²⁺ ↔ Fe³⁺ and Co³⁺ ↔ Co²⁺ is very much hindered at lower frequencies and a constant plateau region is observed. However, at higher frequencies the conductive grains are more active and thereby support the hopping of charge carriers between neighboring ions.⁷⁰ Moreover, it is clear that the substitution of Gd³⁺ in cobalt ferrite enhances the conductivity and further supports the mechanism for the enhancement in the dielectric constant.

Fig. 12 The variation of the frequency dependent ac electrical conductivity of CoGd_xFe_2−xO₄ nanoparticles at 30 °C.

To get a clear insight into the conduction mechanism, the ac electrical conductivity of all the samples was measured at different temperatures from 30 °C to 200 °C. Fig. 13 shows the reciprocal temperature dependent electrical conductivity (σ_dc) of the CoGd_xFe_2−xO₄ nanoparticles. We note that the conductivity is found to increase with temperature as expected from the semiconducting behaviour of cobalt ferrite.^71,72 From the plot it is observed that the conductivity reveals an Arrhenius-type temperature dependence, given by the relation,

σ_dc(T) = σ_o exp(−E_dc/K_BT) (5)

where σ_o is the pre-exponential factor, E_dc is the activation energy, K_B is the Boltzmann constant and T is the temperature in Kelvin. The activation energies, E_dc, of all the samples are calculated from the slope of the least squares straight line fitting and the values of E_dc are given in Table 4. It is observed from Table 4 that the E_dc shows a dependence on the composition. It is well-known that electron hopping between Fe²⁺ ↔ Fe³⁺ ions and hole hopping between Co³⁺ ↔ Co²⁺ ions in octahedral sites are responsible for electrical conduction and dielectric polarization in cobalt ferrite. The decrease in the activation energy with the increase in the Gd³⁺ concentration supports the enhanced conductivity. Rahman et al.³⁴ prepared Gd-substituted bulk cobalt ferrite using a solid state reaction method and they found that the electrical conductivity decreased while the activation energy increased for Gd³⁺ doped samples. In this work, we found that the electrical conductivity increases and the activation energy decreases. The decrease in activation energy is attributed to the redistribution of cations due to the small particle size. The calculated values of activation energy (0.408–0.347 eV) in the present study are comparable to those reported in the literature and confirm that the hopping of electrons is primarily responsible for the electrical conduction.³⁴ We note that for CoGd_0.20Fe_1.80O₄, the electrical conductivity decreases compared with CoGd_0.15Fe_1.85O₄. Due to the non-incorporation of higher Gd³⁺ contents into CoFe₂O₄, the transfer of Fe³⁺ ions from the tetrahedral sites to the octahedral sites is limited. In addition to that, with the formation of a large amount of the GdFeO₃ secondary phase in CoGd_0.20Fe_1.80O₄, the number of Fe ions, and ultimately Fe²⁺ ↔ Fe³⁺ ion pairs, decreases. Since, the hopping of electrons between Fe²⁺ ↔ Fe³⁺ ions is responsible for electrical conduction, a decrease in Fe²⁺ ↔ Fe³⁺ ion pairs decreases the hopping of electrons and also the electrical conductivity of CoGd_0.20Fe_1.80O₄. Moreover, the higher activation energy value of CoGd_0.20Fe_1.80O₄ (0.365 eV) compared with CoGd_0.15Fe_1.85O₄ (0.347 eV) supports the above mechanism. It is concluded from the above discussions that, as the crystallite size decreases the migration of Fe³⁺ from tetrahedral sites to octahedral sites plays an important role in the conduction process of gadolinium doped cobalt ferrite nanoparticles.

Fig. 13 Arrhenius plots for the dc conductivity of CoGd_xFe_2−xO₄ nanoparticles.

Table 4 Electrical properties of CoGd_xFe_2−xO₄ nanoparticles: dielectric constant (ε′), ac conductivity (σ_ac), activation energy (E_dc), grain resistance (R_g), grain boundary resistance (R_gb), grain capacitance (CPE_g) and grain boundary capacitance (CPE_gp)

Sample	ε′ at 100 Hz	σac (S m^−1) at 100 Hz	Edc (eV)	Rg × 10^5 (Ω)	Rgb × 10^6 (Ω)	CPEg × 10^−11 (F)	CPEgp × 10^−10 (F)
CoFe2O4	230	3.97	0.408	4.55	5.44	9.77	3.52
CoGd0.05Fe1.95O4	313	8.66	0.393	2.44	1.76	0.44	7.78
CoGd0.10Fe1.90O4	465	2.34	0.365	4.48	0.69	8.54	1.67
CoGd0.15Fe1.85O4	616	4.83	0.347	1.64	0.40	9.21	3.35
CoGd0.20Fe1.80O4	501	2.37	0.365	0.376	0.72	0.10	0.173

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Impedance analysis. Impedance spectroscopy is a powerful technique for analyzing the electrical characteristics of heterogeneous materials.⁷³ The dynamics of ac electrical conductivity are further understood from analysis of the impedance spectra of the pure and gadolinium doped cobalt ferrite nanoparticles in terms of the grain and grain boundary. The measured complex impedance spectra (−Z′′ vs. Z′) of pure and gadolinium doped cobalt ferrite samples are shown in Fig. 14(a–e). The plots consist of a series array of two overlapping depressed semicircles, which represent the grain and grain boundary contributions to the conductivity. It is further observed that no other relaxation mechanism, such as an electrode effect, which is usually present at the lower frequency side of impedance spectra, is evident. The semicircle appearing in the higher frequency region is the contribution from the grain conduction of the materials, which occurs due to the parallel combination of the grain resistance and the grain capacitance of the material. The semicircle appearing in the lower frequency region is the contribution from the grain boundary conduction of the materials, which occurs due to the parallel combination of the grain boundary resistance and the grain boundary capacitance of the material. The observed semicircles in Fig. 14 were successfully modelled by an equivalent circuit model, (R_gCPE_g) (R_gbCPE_gb), where R_g and R_gb are the resistances of the grains and grain boundaries, and CPE_g and CPE_gb are the constant phase elements of the grains and grain boundaries. A constant phase element (CPE) introduced into the circuit is due to the non-ideal behaviour of the capacitance.⁷⁴ The values of R_g, R_gb, CPE_g and CPE_gb are obtained by fitting the impedance spectra to the proposed equivalent circuit model and the obtained results are presented in Table 4. It is noted that the values of R_gb and CPE_gb are higher than those of R_g and CPE_g. This indicates that the grain boundary contribution is higher than the grain contribution, which is due to the effect of small-sized crystallites. Furthermore, it is observed that the values of −Z′′ in the impedance plots for the cobalt ferrites decrease with increasing gadolinium concentration and this indicates that the overall resistance of the Gd³⁺ doped cobalt ferrite nanoparticles decreases.

Fig. 14 (a–e) The impedance plots of CoGd_xFe_2−xO₄ nanoparticles at 30 °C.

Conclusion

The substitution of Gd³⁺ ions for Fe³⁺ in cobalt ferrite reduces the crystallite size and causes an appreciable change in the structural, magnetic and electrical properties. The PXRD patterns revealed the formation of spinel CoGd_xFe_2−xO₄ ferrites with the signature of GdFeO₃ phases at higher concentrations of gadolinium. Raman and FTIR spectroscopy analyses confirmed the presence of tetrahedral and octahedral sites in the prepared samples. The inversion degree of the Gd³⁺ doped samples decreases compared with the pure cobalt ferrite nanoparticles. It is found that with the increase of gadolinium concentration, the coercivity of the cobalt ferrite nanoparticles is increased, the saturation magnetization is decreased and magnetocrystalline anisotropy constant is increased due to the crystallite size effect and cation distribution. The frequency dependent dielectric constant and the ac electrical conductivity increased with Gd-substitution. The behavior of the dielectric constant and the ac conductivity of pure and gadolinium doped cobalt ferrites was found to follow the Maxwell–Wagner model. Further, the impedance plots show the decrease of resistance in terms of the grain and grain boundary contributions. The obtained results demonstrate that the crystallite size, microstructure, magnetic and electrical properties can be tailored by tuning the gadolinium ion content in the cobalt ferrite. The enhanced coercivity (1635 Oe) of the prepared gadolinium doped cobalt ferrites with dielectric constant at room temperature is favorable for their potential use in high density recording media applications.

Acknowledgements

The authors thank the Central Instrumentation Facility, Pondicherry University for providing experimental facilities and UGC for financial support [F. No. 39-489/2010]. The authors also thank centre for nanoscience and technology (C-NST), Pondicherry University for PXRD measurements. CM thanks UGC for financial assistance in the form of Rajiv Gandhi National Fellowship (RGNF).

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