Exploration through Structural, Electrical, and Magnetic Properties of Al³⁺ Doped Ni–Zn–Co Nanospinel Ferrites

Abstract

The exploration of aluminum (Al³⁺) ion substituted nickel–zinc–cobalt (Ni–Zn–Co) nanoferrites is still at the infancy stage, although the structural, electrical, and magnetic properties have been widely investigated. Single-phase cubic nanospinel ferrites of Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) with space group Fd3m were confirmed by the Rietveld refinement X-ray diffraction (XRD) data. Lattice constants displayed a declining trend with compositions x. The average particle size was found to range from 29 to 25 nm. Selected area electron diffraction (SAED) patterns were indexed according to space group Fd3m, indicating that nanoparticles are well crystallized. Samples’ modes of vibrations swung between redshift and blueshifts as detected in the Raman spectra. The saturation magnetizations (M_s) were in the range of 59.85–86.39 emu/g. Frequency-dependent dielectric constants (ε′) and ac resistivity (ρ) measurement suggested that samples were highly resistive. These resistive nanoferrites with high saturation magnetizations may function effectively for multifaceted electronic devices.

1. Introduction

Nanocrystalline magnetic ferrites have attracted tremendous attention due to their wide range of hi-tech applications like nuclear magnetic resonance to generate cross-sectional images of the human body for diagnostic resolves, spintronics devices, magnetic switches, multilayer chip inductors, information storage, biosensors, ferrofluids, magneto-caloric refrigeration, fluid hyperthermia, etc.¹⁻⁸ The steady alterations inside the ferrites’ chemical compositions could create apparent differences in the cation distributions.^6,9 The cation distribution depends on existing ions’ atomic sizes, valences, and crystal fields.⁶ Doping with divalent and trivalent cations inside the voids can significantly tune ferrites’ structural, electrical, dielectric, and magnetic properties.^2,3,6 Besides, the properties of nanoferrites can be modified by the fabrication technique, sintering temperature, and chemical compositions.^6,10 Recently, with the growth of nanoscience and nanotechnology, the nanospinel ferrites have gained much consideration because of their extraordinarily diverse properties than their bulk mates.^3,11

Several ferrimagnetic materials have prime market share and manufacturing kits because of their response with ac magnetic fields until 1 MHz.¹² However, Ni–Zn cubic ferrites are candidates for high-frequency operating devices like power electronics, telecommunications, inductors, and transformer core.^12,13 Due to their high electrical resistivity, low power losses, and high magnetic responses, these Ni–Zn spinels are ideal contenders in the high-frequency regime. Adding Co in Ni–Zn ferrites prolongs the high-frequency operational bands to operate with low loss and cost above the frequency zone 1 MHz.^12,14 Ni–Zn–Co ferrites have exceptional electromagnetic properties like high resistivity, low eddy current loss, high permeability, high Curie temperature, and high saturation magnetization.^1,14 It is industrially essential due to its implementation in targeted drug delivery systems, sensors, catalysis, magnetic recording, microwave absorber or electromagnetic interference (EMI) shielding, etc.^1,14

The addition of Al³⁺ in nickel ferrite impedes particle growth and enhances ferrites’ mechanical power.⁶ Besides, dopping of Al³⁺ increases resistivity and decreases dielectric losses. Thus, Al³⁺ ions can have the desired influence at a low level to avoid dropping the electrical strength of the ferrite and hinder grain growth.⁷ Moreover, magnetic coercivity shows a decreasing value after Al³⁺ doping, building them softer for high-frequency devices.⁶ Therefore, nickel ferrites with Al doping are effective for microwave devices that work at L, S, and C band frequencies with low intersection losses.¹ Cobalt (Co²⁺)- and aluminum (Al³⁺)-based ferrites are subjected to extensive research due to a wide range of scientific and technological exploitation. Introducing Al³⁺ into Co ferrite reduces the magnetic hardness turns on high electrical resistivity and diverse dielectric characteristics.^7,15 Hence, it has versatile uses in antennas, radio-frequency coil, radar absorbing materials, and supercapacitors.⁷

In the present research, Al³⁺-substituted Ni–Zn–Co nanospinel mixed ferrites were fabricated through the sol–gel method. The research on the nanoscaleʼs of the Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) compositions sounds intriguing because explorations with these nanocompositions have been in the infant stage. Thus, it is expected that introducing Al³⁺ in Ni–Zn–Co nanoferrites makes them highly resistive while retaining the high magnetizations that potentially function for the growing electronics devices in the nanometer range.

2. Results and Discussion

2.1. Structural Analysis

X-ray diffraction (XRD) analyses were conducted to explore the crystallographic belongings of the Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) nanospinel ferrites. Figure 1 displays the Rietveld refinement XRD patterns of the prepared nanostructures fabricated through the sol–gel method. The existing peaks indexed as (110), (220), (311), (222), (400), (422), (511), (440), (620), (533), (622), and (444) represent the single-phase cubic spinel nanostructures with space group Fd3m formed (JCPDS card no. 52-0277, JCPDS card no. 08-0234).¹

Figure 1.

Rietveld refinement XRD spectra of Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) nanospinel ferrites.

Nanospinel phaseʼs structural parameters are explored through the Rietveld refinement technique conducted by the FULLPROF software programs. Peak shapes and background refinements were carried through the pseudo-Voigt functions and six-coefficient polynomial, respectively. Experimental lattice constants (a_NR) were obtained through the N–R corrections.¹ Experimental lattice constants’ values match the lattice constants found from Rietveld refinements (a_RV) and theoretical calculations (a_TH).¹ With minor differences, lattice parameters (a_TH, a_NR, and a_RV) decrease with Al contents x. The smaller ionic radii of Al³⁺ (0.535 Å) switch to the larger ionic radii of Fe³⁺ (0.645 Å), showing a decline in the compositions’ lattice constants.¹

The highest peak angle shifting with Al contents confirms the formation of a new composite (Figure 1). The crystallite size (D_XRD) of the synthesized nanospinel ferrites is estimated through the Debye–Scherrer formula [D_XRD = 0.9λ/β cos θ, where the full width at half-maximum (FWHM) (β) showed the most substantial diffraction peak (311)].¹⁶ The crystallite sizes decrease from 27 to 24.5 nm for the compositions with x = 0–0.12. Thus, reducing crystallite sizes enhances the surface-to-volume ratio with Al contents x, indicating that the new composites apply to gas sensing applications (Table 1).¹⁷ The volume of the unit cell (V = a³ ų) and specific surface area (S = 6000/ρ_x × D_XRD) were calculated¹⁷ that are shown in Table 1. The volumes of a unit cell composition’s lattice constants follow the same decreasing trend. The crystalline structure of the Ni_0.4Zn_0.35Co_0.25Fe_1.88Al_0.12O₄ nanospinel ferrite is shown in Figure 2. The interpretation of bond angles (θ₁, θ₂, θ₃, θ₄, θ₅) with compositions signifies that the magnetic interactions (A–O–A, A–O–B, B–O–B) weaken and strengthen between the cations and anions inside the sublattices (Table 2).^16,18 The bond angles θ₁ and θ₂ represent the A–O–B interaction between the voids, whereas θ₃ and θ₄ signify the bond angles between the B–O–B exchange interactions, and θ₅ corresponds to the A–O–A interactions inside the complexes.¹⁹ The variations of these angles attribute that cations are rearranged with Al contents with different superexchange interactions.²⁰

Table 1. Reliability Factors (R_p, R_wp, R_exp, R_Bragg, R_F, and χ²) from Rietveld Refinement Fitting and Lattice Parameters [Experimental (a_NR), Theoretical (a_TH), and Rietveld Refinement Method (a_RV)], Crystallite Size (D_XRD), Unit Cell Volume (V), and Specific Surface Area (S) of the Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) Nanospinel Ferrites.

							lattice parameters
compositions	Rp	Rwp	Rexp	RBragg	RF	χ2	aNR (Å)	aTH (Å)	aRV (Å)	DXRD (nm)	V (Å3)	S × 103 (m2/g)
x = 0.00	15.0	9.39	9.15	3.264	2.786	1.05	8.3807	8.3802	8.3859	26.9	588.84	57.2
x = 0.02	16.0	9.25	8.54	2.957	2.948	1.17	8.3809	8.3795	8.3821	26.5	589.81	58.4
x = 0.05	14.2	8.92	8.75	2.952	2.183	1.04	8.3818	8.3804	8.3851	27.0	587.99	57.4
x = 0.07	16.3	9.76	8.58	2.626	2.468	1.29	8.3809	8.3803	8.3849	26.0	587.30	62.7
x = 0.10	16.0	9.99	9.16	3.665	5.644	1.19	8.3767	8.3754	8.3817	25.0	586.06	68.4
x = 0.12	16.5	9.34	8.93	2.378	2.307	1.09	8.3757	8.3745	8.3801	24.5	585.41	76.1

Figure 2.

Crystalline structure of the Ni_0.4Zn_0.35Co_0.25Fe_1.88Al_0.12O₄ nanospinel ferrite.

Table 2. Values of Bond Angles (θ₁, θ₂, θ₃, θ₄, and θ₅) of the Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) Nanoferrites.

compositions	θ1	θ2	θ3	θ4	θ5
x = 0.00	123.67	146.45	92.34	125.80	75.39
x = 0.02	123.54	145.86	92.54	125.85	75.04
x = 0.05	123.43	145.36	92.71	125.89	74.73
x = 0.07	123.45	145.48	92.67	125.88	74.80
x = 0.10	123.69	146.52	92.31	125.80	75.43
x = 0.12	123.65	146.37	92.37	125.81	75.34

2.2. Raman Spectra Studies

Raman spectroscopic measurements explore all of the ferrites samples’ cation–anion (M–O) bonding inside the nanocrystallites at room temperature (Figure 3). E_g, T_2g (1), T_2g (2), A_1g (1), and A_1g (2) are the five first-order Raman-active modes of the space group Fd3m predicted from the group theory analysis.²¹ The tetrahedral AO₄ group represents the vibration modes above 600 cm^–1. Besides, the octahedral BO₆ groupʼs vibration mode wavenumber is in the range below 600 cm^–1.¹

Figure 3.

Raman spectra of the Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (x = 0, x = 0.02, x = 0.05, x = 0.07, x = 0.1, and x = 0.12) nanospinel ferrites.

A_1g (1) and A_1g (2) modes indicate the symmetric stretching vibrations of oxygen and metal (Fe, Zn, Co, and Al) ions inside the A site and found in the range 718–770 and 629–665 cm^–1, respectively.¹ Simultaneously, T_2g (2) and T_2g (3) modes lie in between 334–452 and 562–571 cm^–1, correspondingly representing the asymmetric stretching and bending of Fe (Ni, Zn, Co, and Al)–O bonds inside the octahedral voids.¹ E_g modes fall in the range 245–348 cm^–1, corresponding to the symmetric bending of oxygen anions with metal cations (Fe). The whole tetrahedronʼs translational motion (metal ions at the A site together with four oxygen) of the AO₄ group in the nanoferrites x characterizes the T_2g (1) mode obtained at 152–223 cm^–1. All of the five first-order Raman-active modes are present inside the Raman spectra of ferrite samples (Figure 3). Because cations (Ni, Zn, Co, Fe, and Al) have different ionic radii, some shoulder peaks appear around the intense peak, indicating that several M–O bonds are present inside the complexes.

Both the redshift and blueshifts occur for the vibrational modes of ferrite samples x that identify the changing of cation–anion bonding with samples x.¹ Cations are rearranged using the electronʼs hopping mechanism during synthesis for all of the compositions.¹ Due to hopping, instability occurs inside the ferrites, and the surrounding cations stabilize the system by interchanging their position between the sublattices.¹ Hence, new anion–cation bonding generates inside the compositions. Therefore, M–O bonds correspond to several vibration modes with various Raman shifts for the samples having cations with different radii and atomic weights.¹ Thus, these modes swing with redshift and blueshift visible in the Raman spectra of all of the ferrite samples (Figure 3). The vibrational fluctuations indicate that new M–O bonds are formed inside the sublattice with Al doping x.

2.3. Transmission Electron Microscopy (TEM) Analysis

Figure 4a displays the TEM micrographs and reveals that particles are irregular, most likely cubic in shape, and agglomerated. The average particle size measured through TEM images reduced with compositions x is in the range of 29–25 nm (Figure 4d). The existence of the agglomerated particles on some level indicates the intermagnetic interface between the nanoparticles.²² Also, agglomeration occurs due to the magnetic dipole–dipole interaction between the synthesized nanoparticles.²³ Besides, a decrease in surface energy is another reason for nanoparticles agglomeration.²⁴

Figure 4.

(a) TEM micrographs, (b) selected area electron diffraction (SAED) pattern, (c) high-resolution transmission electron microscopy (HR-TEM) image, and (d) Variation of particle size (nm) with compositions x of the Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (x = 0, x = 0.02, x = 0.05, x = 0.07, x = 0.1, and x = 0.12) nanospinel ferrites.

The HR-TEM micrograph (Figure 4b) reveals highly ordered lattice fringes with the d-spacings of 0.25, 0.29, 0.48, and 0.16 nm measured through ImageJ software, representing the (311), (220), (111), and (511) planes of a cubic phase for the compositions x = 0.00, 0.02, 0.05, 0.07, 0.1, and 0.12, respectively. Besides, this shows that the nanoparticles are well crystallized. These values are well matched with the d-spacing values determined from the analysis of the XRD spectra. The lattice images of a single grain display equally spaced lattice rows implying that the areas are well-crystalline and free from any lattice defects.²²

The selected area (electron) diffraction (SAED) pattern of the ferrite samples x (Figure 4c) represents the bright or dark bands caused by beams of light that are in phase or out of phase with one another.²⁵ The diffraction rings of the SAED patterns indexed with reflections correspond to the space group Fd3m of the spinel-cubic lattice.²³

2.4. Magnetic Hysteresis Studies

The M–H loops are disclosed in Figure 5, and magnetic parameters are presented in Table 3. The saturation magnetization (M_s) was found from the extrapolation of M vs 1/H to 1/H = 0 (at the high magnetic field).²⁶ However, the magnetic properties of nanospinel ferrites depend on several factors, including the synthesis route, crystallite size, sintering temperature, and rearrangement of cations inside the voids.⁷

Figure 5.

Hysteresis loops of the Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) nanocompositions.

Table 3. Cation Distributions, Experimental (m_Bex) and Theoretical Magnetic Moments (m_Bth), Saturation Magnetization (M_s), Remanent Magnetization (M_r), and Coercivity (H_c) of Al-Substituted Ni–Zn–Co Nanoferrites.

	cations distribution		magnetic parameters
compositions	A site	B site	mBex (μB)	mBth (μB)	Ms (emu/g)	Mr (emu/g)	Hc (Oe)
x = 0.00	Zn0.35Fe0.65	Ni0.4Co0.25Fe1.35	1.85	5.05	59.85	1.274	143.7
x = 0.02	Zn0.35Co0.05Fe0.6	Ni0.4Co0.2Fe1.38Al0.02	2.07	5.15	67.05	3.99	69.65
x = 0.05	Zn0.35Co0.1 Fe0.55	Ni0.4Co0.15Fe1.4Al0.05	2.14	5.2	69.64	5.673	162.74
x = 0.07	Zn0.35Co0.02Fe0.58Al0.05	Ni0.4Co0.23Fe1.35Al0.02	2.52	5.28	82.32	0.473	14.7
x = 0.10	Zn0.35Co0.02Fe0.57Al0.06	Ni0.4Co0.23Fe1.33Al0.04	2.1	5.23	68.97	6.026	91.42
x = 0.12	Zn0.35Co0.04Fe0.54Al0.07	Ni0.4Co0.21Fe1.34Al0.05	2.62	5.31	86.39	2.098	21.68

In the present work, the saturation magnetization increases from 59.85 to 82.32 emu/g until the samples with x = 0.07. After that, M_s decreased to 68.97 emu/g for the ferrite with x = 0.1, and the highest magnetization, 86.39 emu/g, was obtained for the x = 0.12 composition. The increase and decrease of M_s with compositions x are interpreted based on Neelʼs model.²² The proposed cation distribution model was established through the Rietveld refinement analysis. Moreover, the magnetic moments (m_Bth and m_Bex) and saturation magnetizations (M_s) following the same trend are exhibited in Table 3. Al³⁺ and Fe³⁺ have possibilities to take positions in both sublattices. While Zn²⁺ tends to occupy the A site, Ni²⁺ can reside in the B site. The partial occupancy of Al³⁺ for Fe³⁺ at the B site redistributes the cations inside the sublattices. The residents of Fe³⁺ increase in the B site to strengthen the superexchange interactions between the magnetic ions of the sublattices intermediated by anions O^2–.²⁷ Al³⁺ substitution for the x = 0.02 and 0.05 samples rearrange the fewer Co²⁺ (3 μ_B) to migrate from the B site to the A site replacing Fe³⁺ (5 μ_B) from the A site (Table 3). The compositionʼs cations are reordered for the x = 0.02 and 0.05 samples that gradually increase the net magnetic moment (Table 3). But for ferrite samples with x = 0.07 and 0.12, Al³⁺ resides in both the sublattices. Thus, the net magnetic moments rise from 59.85 to 86.39 emu/g (Table 3). The highest magnetization of 86.39 emu/g is obtained for the composition with x = 0.12. Further, Al content substitution with x = 0.1 decreases the net magnetic moment because magnetic dilution occurs inside the voids.¹⁵ Thus, M_s reduces to 68.97 emu/g for the x = 0.1 ferrite. Moreover, the compositionʼs grain size with x = 0.1 reduces and structural distortion occurs in the external surface. The surface effect and migration of cations generate strains that can break the surface exchange bonds in the exterior surface give rise to disorder spin states inside the sublattices.^28,29 Thus, the canted spin structure deteriorates the A and B sites’ magnetic cation superexchange interactions, decreasing M_s for x = 0.1 samples.^7,28

It is revealed from the M–H loops that all of the nanoferrites had low remanence (M_r) and coercivity (H_c) values. Thus, it endorses the ferrimagnetic properties inside the soft ferrite materials with superparamagnetic nature.^26,28 Coercivity depends on grain size, cation distribution, magnetocrystalline anisotropy, and saturation magnetization.³⁰ The variation of H_c can be interpreted through the solitary domain behavior.⁷ It is observed that all of the nanosamples’ coercivity from x = 0 to 0.12 except x = 0.1 is directly proportional to the grain sizes due to the single domain nature.²⁶ Due to Al doping, a thin layer of Al–O–Al structure forms around the grain and hinders grain walls’ movement,¹⁵ increasing H_c for the x = 0.1 sample. Some unwanted magnetic construction, including blocked particles induced inside the nanoparticles’ grains, enhances the sample’s coercivity.²⁸ These clogged particles in the nanosamples can exhibit both ferromagnetic and superparamagnetic mechanisms. These characteristics of the nanoferrites can cause changes in H_c with compositions x.²⁸

2.5. Permittivity and Loss Tangent Studies

Figure 6a displays the frequency-dependent dielectric constants (ε′) of all of the nanosamples. The dielectric response of the studied samples under exploration was interpreted as a component of Al³⁺ concentration and frequency. The dielectric nature of ferrite nanocrystals is significantly dependent on some aspects, including synthesis method, cation distribution, sintering temperature, oxygen parameter, stoichiometry, porosity, ionic charge, and proportion of cations.⁷ The frequency dependence of the dielectric constant can be explained based on space-charge polarization launched to the highly conducting grains disconnecting through the nonconducting grain borders. The space-charge polarization gathering at the detaching grain margin is a primary feature for the dielectric constant and induces electric field applications.⁷ We notice that the difference of dielectric constant depending on frequency could be endorsed to the space-charge separation that is the reason for dielectric formation inside the compositions.⁷ The Maxwell–Wagner model of interfacial polarization explains the samples’ dielectric behaviors, agreeing with Koopʼs theory.^29,31 It assumes that electron hopping happens between cations (Fe³⁺, Co²⁺, etc.) and O₂ in a network that generates interactions.^32,33 But when the electrons try to overcome the insulating margins, electrons face an obstacle and trapped electrons generate the space charge.^32,33 Moreover, oxygen ion vacancies and free charge carriers may induce inside the voids during sintering that participate in space charge separation.³¹ At a low frequency, the electrons get enough time to travel across the grains following the ac field. Hence, it can participate in space charge polarization and ε′ exhibits a high value. However, due to the rapid fluctuation of the ac field at high frequencies, the electrons try to change their direction too quickly and cannot follow the ac field. They cannot accumulate across the grain margins, and space charge polarization disappears inside the grains. Therefore, as frequency increases, the polarization gradually reduces and is independent in the high-frequency range.^31,32

Figure 6.

Variation of (a) dielectric constants (ε′) and (b) loss tangent (tan δ) with the frequency of Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) nanospinel ferrites.

Dispersion occurs for the dielectric constant in the low-frequency region. Adding Al³⁺ decreases the samples’ particle size, increasing the surface area.³³ Smaller grain offers a large number of grain margins. The well-developed grain borders can accumulate more carriers on the barriers, and enhancement occurs in dielectric constants ε′.³² However, due to the differences of the grain margins’ interfacial regions, ε′ shows variation with compositions x.³³ Besides, variations in ε′ could be attributed to the rearrangement of cations occupancy inside the sublattices. It may create variations in superexchange communication between cations.⁷ Hence, the concentration of surface charge polarization starts varying with composition and dispersion occurs in permittivities.

Figure 6b exhibits that the loss tangent (tan δ) declines with the frequency of the applied field that followed Koop’s model. The tan δ values decline with an increase in frequency in the studied nanocompositions obeying specific dispersion in a lesser frequency zone. The space-charge polarization separates highly resistant grain boundaries for encircling conducting grains in ferrite. Highly resistant grain margins in ferrite proved the idea of space-charge separation for surrounding grains.⁷ It develops at low frequencies affected by the high resistive grain borders, and a maximum amount of energy is necessary to exchange cations.⁷ Moreover, enough time is available for the movement of charge carrier inside the sublattices in a low-frequency zone.³¹ Thus, high resistive loss appears that leads to a high tangent loss value in the low-frequency region.³¹ The lessening loss tangent with Al contents in Ni–Zn–Co nanoferrites is suitable for high-frequency devices.⁷ The low loss tangent value at a high frequency indicates that the resistive loss minimizes because hopping electrons cannot follow the ac field’s swing and relaxation loss contributes.³² Thus, the lowest energy loss occurs around 10⁶ Hz for all of the samples.

2.6. Resistivity and Impedance Studies

Figure 7a shows the variation of ac resistivity (ac) as a function of applied frequency recorded at room temperature for Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) nanospinel ferrites. All of the samples’ ac resistivities decrease with increasing frequencies and progress independently in the high-frequency zone. The Maxwell–Wanger double layer model for ferrites can interpret the samples’ resistive manner with frequencies.³⁴ The conducting grains inside the samples are enclosed by the highly resistive grain margins.³⁴ The hopping carriers pile up across the barriers at low frequencies and hinder the conduction of electrons between the grains.³⁴ Hence, ferrites act as a high resistive material in the low-frequency regime. But as the frequency increases, the conductive grains become more active, generating electron hopping between the grains.³⁴ Thus, conductions occur inside ferrite samples and resistivity displays a decreasing trend with higher frequencies. The dispersion of resistivity occurs in the low-frequency area because of cation concentration differences inside the samples’ sublattices.³⁵ Besides, a thin Al–O–Al structure formed around the grain with Al substitution may create differences in electron conduction inside the voids.¹ Hence, resistivities show variations at low frequencies depending upon the above factors. However, the increase in resistivity hinders the movement of charge carriers that obstructs the buildup of space charge separation at the grain margin, and the lowest dielectric constant appears.³⁶ As a consequence, compositions with x = 0.12 yield the highest resistivity with the lowest dielectric constant in the low-frequency region.

Figure 7.

(a) Variation of ac resistivity with frequency and (b) Cole–Cole plot of reactive part with the resistive part of impedance for the Al-substituted Ni–Zn–Co nanospinel ferrites.

Figure 7b discloses the Cole–Cole graph (Z″ vs Z′ plot) of impedance to evaluate the microstructural (grain and grain boundary) resistances with the samples’ electrical response. At room temperature, the impedance spectra display semicircular arcs representing the resistance of relaxation effects present inside the ferrite samples.³³ As Al content was substituted in the compositions, the particle size decreased. The formation of the Al–O–Al layer at the grain boundary hinders the grain growth mechanism, enhancing resistance significantly in the low-frequency region.³⁷ Due to highly resistive grain margins, electron hopping is delayed across the grain borders and relaxed compared to the grain interior in the low-frequency area.³³ However, the samples with x = 0.12 show the highest grain boundary resistances with the lowest dielectric constant, and an almost inverse relation followed between the parameters (Figures 6a and 7b).³⁸ Moreover, the radius of the semicircle arc increased gradually with ferrite compositions x, indicating that the conductivity decreases with Al concentrations because of the insulating area (Al–O–Al) around the grain margins.³⁹ Thus, grains are highly conducting at high frequencies and show negligible resistance on the Z′ axis (left-hand side) on the Cole–Cole plots.³³ Only one semicircle is displayed in the present study that confirms only one relaxation mechanism inside the systems.^33,40 Moreover, significantly apparent one semicircle for all of the compositions indicates that the grain boundary effects lead the conduction mechanism while the contribution from the grains is too weak to distinguish.³³

2.7. Electric Modulus Analysis

To interpret the dielectric relaxation processes of the ferrite samples,⁴¹ the frequency-dependent real part (M′) and imaginary part (M″) of electric modulus (M*) are plotted in Figure 8a,b, respectively. Low values of M′ (ω) are observed in the low-frequency zone <10⁴ Hz and increase with higher frequencies around 10⁶ Hz. Dispersion with maxima is found for all of the samples, and then downfall is observed with frequencies up to 10⁷ Hz. The short-range mobility charge carrier’s conduction process is responsible for the continuous dispersion with increasing frequency.⁴¹ This short-range charge carrier mobility under the induced electric fieldʼs influence may occur because of restoring force deficiency inside the samples’ sublattices.⁴² Moreover, asymmetric peaks at higher frequencies indicate space charge separation for all of the ferrite samples. The variation of maxima confirms the differences in space charge polarization with compositions x.⁴³ In contrast, the low values of M′ (ω) in the low-frequency regime generate the conduction process due to the long-range mobility of charge carriers.⁴⁴

Figure 8.

(a) Variation of real part complex electrical modulus with frequency, (b) variation of imaginary part complex electrical modulus with frequency, and (c) Cole–Cole plot (M″ vs M′) of electric modulus for Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) nanospinel ferrites.

M″(ω) shows slight asymmetric peaks for all of the six compositions x (Figure 8b). The charge carriers can move over the long range toward the peak in the low-frequency zone.⁴⁵ Carriers can hop through the grains by jumping long distances.^41,45 In contrast, peaks of M″(ω) in the high-frequency regime indicate the short-range movement of charge carriers.⁴⁵ In this zone, carriers are confined in a potential well and can move horizontally within the well.⁴⁵ The peaks are observed for all samples around 10⁵ Hz, indicating the transition of the charge carrier mobility from long-range to short-range distances.¹⁴ Furthermore, peaks in M″(ω) signify the real dielectric relaxation process.⁴⁴

All Cole–Cole (M″ vs M′) plots exhibiting single semicircles are presented in Figure 8c. When the grain boundary area engages a large volume, the action between M″ and M′(ω) gives a better interpretation of semicircles than the Z″ vs Z′ plot.⁴⁶ The semicircleʼs area of all samples varies with intercepts in different positions over the M′ axis, confirming the capacitance values of different ferrite samples. The areas of the semicircles differ with compositions because of the grain size effect and differences in the ionic radii of the cations. Further, the semicircles found in the Cole–Cole plots of all samples disclose the presence of Debye relaxation. Due to the small size of the nanoferrite samples, the grain margins are highly dense.⁴⁶ Fe-ion deficiencies with an irregular placement of cations around the grain boundaries might be likely for higher grain boundary values.⁴⁶ The existence of a single semicircle in all of the ferrites indicates that the influence of the grain boundaries is more prominent than the outcome of grains in the conduction process.^42,47

3. Conclusions

In the present study, Al³⁺-substituted Ni–Zn–Co nanocompositions were successfully synthesized through the sol–gel technique. Rietveld refinement X-ray diffraction data evidenced the formation of the nanospinel structure with phase group Fd3m for all of the compositions. The cation distributions were established through the Rietveld refinement technique. Average particle sizes were in the regime of 25–29 nm, as demonstrated by TEM examinations. Thin areas of Al–O–Al structures were formed around the grain boundaries that hindered particle growth. The vibrational modes’ characteristic peaks are red-shifted and blue-shifted, as exhibited in the samples’ Raman spectra. Enhanced M_s with low values of H_c and M_r was found for the compositions. Magnetic outcomes revealed that the prepared nanocompositions are soft ferromagnetic materials and suitable for numerous technological applications. Frequency-dependent dielectric constants and ac resistivity indicated that the ferrites were highly resistive. Introducing Al³⁺ in Ni–Zn–Co ferrites makes the nanosamples highly resistive while maintaining the high magnetizations 86.39 emu/g for the x = 0.12 compositions. Maxwell–Wagner and Koopʼs phenomenological models can interpret the dielectric behavior based on the electron hopping mechanism and space-charge polarization. Al³⁺ doping plays a crucial role in tuning the electromagnetic properties of Ni–Zn–Co nanocrystals that can be potential candidates for multifunctional electronic devices in the nanometer range.

4. Experimental Section

4.1. Methodology

Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) nanospinel ferrites were fabricated through the sol–gel technique. The nitrates [Ni(NO₃)₂·6H₂O, Zn(NO₃)₂·6H₂O, Co(NO₃)₂·6H₂O, Fe(NO₃)₂·9H₂O, and Al(NO₃)₂·9H₂O] obtained from Merck, Germany, with 99.98% purity were measured according to the stoichiometric ratio and preserved in a beaker. Ethanol (50 mL) was substituted and stirred in a magnetic stirrer at a constant speed (300 rpm) for 1 h at room temperature for melting the nitrates to make the solution. A small amount of ammonia (NH₃) was dropped gently in the solution to maintain pH level 7. As a result, the solution transformed into a brown viscous gel. The gel was retained over in the magnetic stirrer at 80 °C for 21 h. The dried gel was crushed in an agate mortar and pestle for 10 min. The crushed powder was presintering at 200 °C for 2 h. The powder inside the furnace was then cooled at room temperature. Further, the residue was milled for 10 min. Finally, the product was sintered at 700° C for 4 h and underwent different characterizations. The schematic diagram of the fabrication technique of the Al-substituted Ni–Zn–Co nanoferrites is shown in Figure 9. The mechanism of the chemical synthesis in equation form is given below:

Figure 9.

Stepwise sol–gel fabrication technique for Ni_0.4Zn_0.35Co_0.25Fe_2–xAl_xO₄ (0 ≤ x ≤ 0.12) nanospinel ferrites.

4.2. Characterizations

An X-ray diffractometer (model: SmartLab SE, Rigaku Corporation, Japan) with Cu Kα radiation of wavelengths 1.54059 and 1.54441 Å was used to record the X-ray diffraction spectra of all samples at room temperature. Raman spectroscopy (Mono Vista CRS+ S&I, Germany) examined the Raman spectra range of 200–800 cm^–1. A high-resolution transmission electron microscope (TEM) (model: Talos F200X, Thermo Fisher Scientific) functioning at an accelerated voltage of 200 kV was used to display the morphology of all of the compositions. The absorption spectra of wavelength 190–1100 cm^–1 were recorded by a Dual Beam UV–vis spectrophotometer (model no: U-2900, Hitachi High-Tech Corporation, Tokyo, Japan). Physical properties measurement system (PPMS) from Quantum Design was used to record the M–H plot at room temperature. Electrical properties measurements were carried out through an impedance analyzer (Wayne Kerr 6500B).

Author Contributions

N.J. contributed to conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing—original draft, visualization, and writing—review and editing. M.N.I.K. contributed to supervision, writing—review and editing. J.I.K. contributed to supervision and writing—review and editing.

The authors declare no competing financial interest.