Structural, Morphological and Ferroelectric Properties of Sr-Cd Co-Doped Nickel Ferrite for Energy Storage Devices

Abstract

Ferroelectric materials, renowned for their capacity to demonstrate spontaneous electric polarization reversible through an external electric field, are essential in numerous technological applications owing to their distinctive characteristics. For this, a series of spinel Sr-Cd co-doped nickel ferrite nanomaterials Cd_0.5−xSr_xNi_0.5Fe₂O₄ (x = 0.0, 0.1, 0.2 and 0.3) were prepared through the standard sol-gel auto combustion method The XRD patterns showed that the prepared samples have a cubic spinel structure. The crystallite sizes of the samples vary from 29 to 40 nm. The morphology of prepared samples showed uniformly distributed spheres. Magnetic properties showed the soft magnetic nature of the prepared ferrites. The ferroelectric study revealed that Sr-Cd substituted ferrites exhibited the elliptical nature of ferroelectric loops at normal room temperature. The maximum polarization has been achieved at x = 0.3. The understanding of current and voltage (I–V) showed a slowly decreasing tendency of leakage current on both sides symmetrically against the increasing Sr content. The conductivity of the prepared spinel increases as a function of higher Sr doping. The real part of dielectric constant increases with increasing frequency. The materials show large elliptical loops indicating high asymmetric ferroelectric energy storage capability.

1. Introduction

The overuse of fossil fuels endangers the environment and hastens the depletion of nonrenewable energy supplies [1,2]. This critical situation may be addressed by updating low-cost, renewable, and environmentally friendly sustainable energy and storage technologies [3]. Developing devices that store energy, such as solar cells, supercapacitors (SCs), fuel cells and energy obtained from sustainable sources are two essential strategies for resolving the world’s energy challenge in the future [4]. A lot of attention has been paid to the inexpensive materials for electrodes utilized in SCs. Biomass energy and renewable energy technology have made significant contributions to ensuring humanity’s energy future. The rising usage of renewable energy sources will demand a significantly higher capacity for charge storage. As a result, developing effective energy storage technologies has become ever more vital [5,6,7,8].

Ferrites are the principal chemical elements of ferric oxides, especially Fe₂O₃ and FeO, which are sometimes partially substituted by oxides that contain other transition metals, which develop as powder or ceramic bodies that exhibit ferromagnetic qualities [9]. The ferrites are classified into three distinct categories based on their crystalline structure: spinel MFe₂O₄, garnet M₃Fe₅O₁₂, and hexagonal MFe₁₂O₁₉ [10]. Ferrites are attracting substantial interest and are still the topic of innumerable investigations owing to their potential application in high-density data storage mediums, magneto refrigeration systems, microwave magnetized devices, transducer cores, catalysis, and many other applications [11]. An ordinary spinel catalyst contains the chemical formula AB₂X₄, where “A” signifies a divalent ion, “B” denotes a trivalent ion, and “X” corresponds to an oxide ion [12]. Spinel ferrites have been at the forefront of nanotechnology and nanoscience in recent years due to other remarkable characteristics, such as their nanoscale size as well as super-paramagnetic behavior [13,14,15].

Ferrites are excellent materials for a variety of industrial (sensors, photoelectric devices, photo catalysis, magnetic pigments, energy storage devices, controlled signal transformation, batteries) and biomedical (drug delivery, MRI, tissue, bio-magnetic separation, tumor treatment) applications [16,17,18,19,20]. The production technique, additive calcination, and substitution procedure all affect the ferrite’s structure and physical characteristics [21]. The optical, dielectric, electrical, and magnetic features of nanoscale NiFe₂O₄ can be improved and controlled by doping with ions of transition metals, like Co²⁺, Zn²⁺, Ni²⁺ [17,22,23,24]. Doping spinel ferrite with transition metal ions alters the distribution of cations between the octahedral (B) and tetrahedral (A) sites, resulting in refined magnetic characteristics. Moreover, the doped ions may alter the energy of the grain boundaries, functioning as a catalyst for grain growth [25].

Spinel ferrites make excellent substitute materials for single-metal oxides owing to their immense impact on magnetic and electrical fields. The nanocrystalline ferrites category contains nickel ferrite (NiFe₂O₄) and is considered an appealing material [26]. NiFe₂O₄ corresponds to the cubic spinel structural compounds family, and its inverse spinel geometry comprises Fe³⁺ ions at the A sites and Ni²⁺ ions at the B sites with equal distribution [27,28]. Magnetic nanomaterials have lately gained popularity precisely because of their new material characteristics that differ dramatically from those found in their bulk counterparts [29]. Ni-based materials have received substantial investigation and are currently regarded as excellent future electrode materials for pseudo capacitors due to their exceptional specific capacitance, remarkable chemical and thermal stability, and lower price when compared to other transition metal oxides (TMOs) [30].

Nickel ferrite is a sort of soft ferrite that forms an inverse spinel via Ni²⁺ ions in the B sub-lattice and Fe³⁺ ions in both A and B sub-lattices. Because of their ability to form square bonds, Cd²⁺ and Sr²⁺ ions favor tetrahedral locations. Introducing diamagnetic Cd²⁺ and Sr²⁺ ions into the Ni ferrite lattice influences the crystal’s local shape, converting it to a mixed spinel [31]. It additionally has the potential to improve ferroelectric characteristics such as polarisation, saturation, and magnetization. Because Cd²⁺ ions are intermittent, they may produce cationic deficiencies at higher sintering temperatures. At the same time, discrepancies in ionic radii may cause crystal deformation, causing a strain in the structure and substantial spin canting. This interaction between cationic vacancies and ionic radius variations will result in a considerable shift in the value of the observed magnetic moment, suggesting further analysis [32,33,34].

The literature on Sr-Cd co-doped nickel ferrite systems is scarce. We systematically studied the effects of Cd⁺² and Sr⁺² ion doping on the structural and morphological, magnetic and ferroelectric characteristics of nickel ferrite. We have implemented the sol-gel auto combustion technique with an organic fuel mixture of glycine and urea. When compared to alternative synthesis processes such as vapor phase deposition, ball milling, etc., the sol-gel auto combustion approach ensured phase purity and particle size uniformity, as well as a lower number of imperfections [35,36]. XRD, SEM, magnetic and ferroelectric characterization of the samples were performed to evaluate the structural changes created in the samples and the morphology of nanostructures and P-E loops at normal ambient temperature. It additionally exists that trivalent ion replacement improves storage capacity. As an outcome, it becomes very exciting to substitute divalent co-doped ferrite (Cd_0.5−xSr_xNi_0.5Fe₂O₄) and investigate its structural, morphological, magnetic and ferroelectric properties for prospective use in energy storage devices.

2. Experimental Section

2.1. Materials

Urea CO(NH₂)₂, glycine [NH₂CH₂COOH], Nickel nitrate [Ni(NO₃)₂.H₂O], Strontium nitrate [Sr(NO₃)₂] Cadmium nitrate [Cd(NO₃)₂], and Iron nitrate nonahydrate [Fe(NO₃)₃.9H₂O] were purchased from Sigma-Aldrich (Taufkirchen, Germany) with listed purity of 88.9%.

2.2. Material Synthesis

Sol-gel auto combustion was employed to fabricate the spinel ferrites Cd_0.5−xSr_xNi_0.5Fe₂O₄ with (x = 0.0, 0.1, 0.2 and 0.3). The process of making ferrites involved combining urea [CH₄N₂O] and glycine [NH₂CH₂COOH] as the fuel agents with analytical-grade nickel nitrate [Ni(NO₃)₂.6H₂O], strontium nitrate [Sr(NO₃)₂] cadmium nitrate [Cd(NO₃)₂], and iron nitrate hexahydrate [Fe(NO₃)₃.9H₂O]. The stoichiometric values of the aforementioned chemicals were taken in separate beakers, and prior to combining all the components of a sample, the components were first dispersed individually in 50 mL deionized water for different values of x. The solution was stirred (50 rpm) while being heated at 80 °C and then burned until it turned into ash using a self-assisting burning technique. This process turned the solution into a gel. The pH of the solution has been maintained at 7. The burnt powder was then sintered for 4 h at 1200 °C to obtain single phase spinel ferrites. The sintered powder was further refined using mortar and piston. The refined powder thus obtained was used for X-ray diffraction using Cu-kα X-ray diffractometer (Rigaku Miniflex-II, Neu-Isenburg, Germany) with 1.54 Å wavelength. SEM images of the prepared samples were taken using (Hitachi-SU1510, Tokyo, Japan). Similarly, M-H loops were obtained using Lakhshore-7407 and P-E loops using measured at 300 K using 9 V driving voltages for PZT/LSM. The 0.8 g powdered sample Cd_0.5−xSr_xNi_0.5Fe₂O₄ at x = 0.0, and 0.3 were turned into pellets of 1mm thickness using 40 kN force for 2 min and subsequently dielectric measurements have been made using R&S ZVA 50 VNA model in the frequency range 1 to 6 GHz.

3. Results and Discussion

3.1. XRD Analysis

The study of patterns obtained from XRD reveals the development of a single-phase compound exhibiting a cubic arrangement and the lattice parameter “a” for each specimen has been determined (

Table 1. Structural parameters calculated from X-ray diffractometer.

Concentration (x)	Crystallite Size (Dp) (nm)	d-Spacing (Å)	Lattice Parameter ‘a’ (Å)	Unit Cell Volume (106 pm3)	X-ray Density (${\rho }_x$) (g/cm3)	Dislocation Dendity δ = 1/D2
Cd0.5 Sr0.0 Ni0.5Fe2O4	29.67	1.5270	4.319	80.57	5.65	0.001136
Cd0.4 Sr0.1 Ni0.5Fe2O4	35.42	1.5736	4.450	88.12	5.12	0.000797
Cd0.3 Sr0.2 Ni0.5Fe2O4	38.05	1.6256	4.597	97.14	4.96	0.000691
Cd0.2 Sr0.3 Ni0.5Fe2O4	39.93	1.7464	4.9395	120.5	4.66	0.000627

). The crystal size (D) was determined from the XRD peak widening of the (220) peak utilizing Debye-Scherer’s formula [37]. Figure 1 displays the XRD patterns of Cd_0.5−xSr_xNi_0.5Fe₂O₄. According to the JCPDS# 01-074-2081, the XRD peaks for various amounts of x, i.e., (x = 0.0, 0.1, 0.2 and 0.3), for Cd_0.5−xSr_xNi_0.5Fe₂O₄ at 2θ values of 30.29°, 35.68°, 47.46°, 53.81°, 57.37 °, 63.0° and 71.50° with (220), (311), (331), (422), (511), (440) and (620) planes have been observed (Figure 1a). The diffraction patterns demonstrate that when Sr content increases, the peak location for (220) shifts continually towards greater angles (Figure 1b).

The determination of crystallite size for high-intensity peak (220) has been done using Scherrer’s formula [37];

$$D=\frac{0.9\lambda }{\beta cos\theta }$$

(1)

The Bragg angle “$\mathsf{\theta }$”, FWHM “β”, and wavelength of the X-rays “λ” emitted from the “Cu” target are all given in the equation above. Whereas the following formula was used to compute the samples lattice parameter “a” [38]:

$$a=d\times \sqrt{h^2+k^2+l^2}$$

(2)

The Miller indices are represented by the letters “hkl” in the equation above, while the letter “d” represents the Bragg-law distance between the planes. Additionally, the following equation was used to determine the X-rays density “ρ_x” and dislocation density “δ” [39].

$${\mathsf{\rho }}_{\mathrm{x}}=\frac{Z\times M}{N_A\times V}$$

(3)

$$\mathsf{\delta }=\frac{1}{D^2}$$

(4)

The aforementioned equation uses the variables “M” for molecular weight, “N_A” for Avogadro number (6.022 × 10²³ atm mol⁻¹), “V” for the volume of the unit cell, and “Z” for molecules/unit cell.

Table 1 shows a substantial rise in the lattice parameter when the Sr²⁺ concentrations in nickel ferrite increase. Higher values for d-spacing have been achieved due to greater ionic radii of Sr²⁺ than Cd²⁺, which ultimately resulted in higher lattice parameter with doping. The widening of diffraction peaks is due to the tiny size of the produced particles. The size of the particles increased as the material composition and lattice constant increased. Cd²⁺ has an atomic radius of 0.97Å while Sr²⁺ has an atomic radius of 1.12 Å; subsequently, Cd²⁺ has a larger crystalline size than Sr²⁺ [37,40]. Higher values of lattice parameter resulted in achieving higher unit cell volume and lower X-ray density for co-doped samples. Dislocation density decreased due to increase in crystallite size.

3.2. Scanning Electron Microscopy (SEM)

The morphology of synthesized NiFe₂O₄ with different concentrations of Sr²⁺ and Cd²⁺ are depicted in Figure 2. The synthesized samples Cd_0.5−xSr_xNi_0.5Fe₂O₄ with x = 0.0 and 0.1 exhibited a uniform distribution with spherical grains morphology appearing; furthermore, cracks are quite visible in SEM images. As the substitution of Sr²⁺ is increased formation of nanoplates start to form, and finally, at x = 0.3, nanoplates are clearly visible with larger and smaller grains distributed at random due to the agglomeration of tiny particles. It is also observed that when Sr²⁺ substitution increases, then the size of particles increases. Their porous nature was not significantly changed by the substitution of Sr²⁺ from their topological view. From Image J software, the average grain size was calculated, and it came out to be 9.64 µm, 9.89 µm, 11.1 µm, and 14.1 µm for x = 0.0, 0.1, 0.2, and 0.3 respectively.

3.3. Magnetic Properties

Figure 3 depicts magnetization profiles for Cd_0.5−xSr_xNi_0.5Fe₂O₄ (with x = 0.0, 0.1, 0.2, and 0.3) along with implemented magnetic fields ranging from (+10.5 kOe to −10.5 kOe).

Table 2. Magnetic parameters saturation magnetization (M_s), magnetic remanence (M_r), squareness ration (M_r/M_s), magnetic moment (n_B), magnetic coercivity (H_c), anisotropy constant (K), and anistropic field (H_k).

X	Ms emu/g ±0.01	Mr emu/g ±0.01	Mr/Ms	nB (μB)	Hc Oe ±0.01	K ergg−1	Hk (108)
0.0	65.58	25.16	0.38	3.076448	504	34,429.5	8.75
0.1	46.10	21.28	0.46	2.137851	681	32702.19	11.82
0.2	21.80	7.73	0.35	1.003151	297	6744.375	5.15
0.3	38.16	12.12	0.31	1.735477	295	11,726.25	5.12

illustrates the computed values for fundamental magnetization characteristics, including saturation magnetization (M_s), magnetic remanence (M_r), and magnetic coercivity (H_c), based on the given M-H loops. The annealing procedures, grain development, chemical nature, and magneto-crystalline anisotropic field all have a significant influence in forming these loops [41]. Narrow S-shaped loops demonstrate the soft magnetic features of all manufactured spinel ferrites. Ferrites that possess this magnetic flexibility may be helpful in EM-absorbing substances, dielectric resonators, and monolayer chip inductors. Notably, they are also beneficial in the assimilation of fluoride ions from consumed water [42,43]. It is widely accepted that a material’s porosity increases coercivity while decreasing particle size. The size of particles corresponds oppositely, whereas porosity correlates directly to magnetized coercivity [44]. This is readily apparent when the value of x grows (i.e., x = 0.2, 0.3), whereby porosity and coercivity improve and particle size reduces. The M-H loop of the supplied sample suggests the ferrite possesses soft ferromagnetic nature with a small coercivity (<1000 Oe) [45]. It demonstrates that just a tiny magnetism needed to be created in order to eliminate magnetism from the supplied samples, revealing the soft magnetized behavior of Cd_0.5−xSr_xNi_0.5Fe₂O₄. Insufficient coercivity values are ideal for magnetically safeguarding, EMI suppression, microwave instruments, and other critical armed forces and security infrastructure [46].

As the quantity of Sr²⁺ increases, the saturation magnetization reduces in comparison to the un-doped sample. This phenomenon is mostly due to the decreasing strength of ferromagnetic interactions, as growing quantities of Fe³⁺ exhibiting elevated spin transform into Fe²⁺ with a comparatively low magnetic dipole moment [47]. The following greater saturation magnetization ensures that the manufactured ferrites may be easily removed from aqueous dispersion using a magnetic field from the exterior. Additionally, magnetized remanence improves with Sr²⁺ replacements ranging from 7.73 emu/g to 25.16 emu/g. The squareness fraction ranges from 0.32 to 0.46, indicating that the manufactured material contains a single magnetized domain [48].

The magnetic moment (n_B) of Cd_0.5−xSr_xNi_0.5Fe₂O₄ ferrites was calculated by using Equation (5) and outcomes are tabulated in table [49].

$${\mathrm{n}}_{\mathrm{B}}({\mathsf{\mu }}_{\mathrm{B}})=\frac{\mathrm{M}\times \mathrm{M}\mathrm{s}}{5585}$$

(5)

Here, Molecular weight of samples is represented by ‘M’ and saturation magnetization is denoted by ‘M_s’.

Anisotropic constant (K) and Anisotropic field (H_k) was calculated by using the Equations (6) and (7) respectively [50].

$$\mathrm{K}=\frac{\mathrm{H}\mathrm{c}\times \mathrm{M}\mathrm{s}}{0.96}$$

(6)

$${\mathrm{H}}_{\mathrm{K}}=\frac{2\mathrm{K}}{{\mathsf{\mu }}_{\mathrm{o}}\mathrm{M}\mathrm{s}}$$

(7)

Here, Coercivity is denoted by ‘H_C’ while the value of μ_o = 4π × 10⁻⁷ H/m.

The Table 2 demonstrates that as dopant concentration increases, the value of anisotropic constant (K) and anisotropic field (H_k) reduces rather than being constant, indicating that the material is anisotropic. The lowering numbers enable the substance softer to magnetize in the prospective of the easiest direction. The coercivity exhibits inverse relationship with the size of the grains. The number of grain boundaries rises with grain size, making it challenging to arrange the domains. So, the coercivity of Cd_0.5−xSr_xNi_0.5Fe₂O₄ nanoparticles decreases as grain size increases with Sr²⁺ injection [51].

3.4. Ferroelectric Analysis

Ferroelectricity is the key characteristic of these materials that have modernized the electronic realm. The phenomenon of ferroelectricity can easily be analyzed by polarization-electric field (P-E) hysteresis loop. Figure 4 demonstrated the P-E loops for the as-synthesized compositions recorded at 30 V. The elliptical nature observed in the P-E loops of the given ferrite system is indicative of hysteresis in the ferroelectric material. Hysteresis denotes a delay or lag in the response of the material when the electric field is applied or removed. The elliptical shape of the loop implies that the polarization of the material does not precisely track the applied electric field but instead retains a certain level of memory or residual polarization. The formation of an elliptical loop, rather than a perfect circle, suggests that the polarization reversal in the material lacks complete symmetry. This implies that the material may not switch back and forth with perfect balance, indicating some asymmetry in its switching behavior. Additionally, elliptical loops may also signal the occurrence of ferroelectric fatigue. Ferroelectric fatigue is a phenomenon wherein the material’s switching characteristics degrade over repeated cycles of polarization reversal. In essence, the asymmetry in loop shape or any changes observed over time may be indicative of the material undergoing fatigue, potentially impacting its long-term stability. The area under the curve for PE loops is indicative of the energy loss during the polarization process. An elliptical loop indicates a particular dissipation pattern, interestingly low energy losses as compared to other shapes. In FeRAM elliptical loops shows the faster response time that benefits faster read/write operations from the memory. They are also beneficial for multifunctional devices such as energy harvesting devices where both mechanical and electric responses are crucial.

The P-E loops incorporated that the polarization exhibits a linear dielectric behavior. Such conduct is evident from the perceived increasing trend of polarization along with the electric field strength, which also assures the ferroelectric nature of the relevant samples. Ferroelectric analyses of Cd-Sr co-doped nickel ferrite nanoparticles Cd_0.5−xSr_xNi_0.5Fe₂O₄ (x = 0.0, 0.1, 0.2 and 0.3) are represented by P-E plots at 30 V (Figure 4). As the applied electric field increases, the polarization in the material develops and dipoles align in the direction of the applied field. When the dipoles have reached the saturation level, the applied field begins to fall, resulting in a decrease in polarization. Nearly similar phenomena occur with negative electric fields. As a result, the highest coercivity value of 29.9 V/cm for Cd_0.5Ni_0.5Fe₂O₄ uniform P–E loop was obtained. The values of the coercive electric field for Cd_0.5−xSr_xNi_0.5Fe₂O₄ (where x = 0.0, 0.1, 0.2 and 0.3, respectively) are given in

Table 3. Coercive Electric Field (E_c), Recoverable Energy Density (W_R) and Energy Loss Density (W_L), Total Energy Density (W_T).

Contents X	Ec (KV/cm) ±0.02	WR (J/cm3)	WL (J/cm3)	WT (J/cm3)	Efficiency (η)
Cd0.5Sr0.0Ni0.5Fe2O4	0.02999	0.12	1.965	2.0844	5.75
Cd0.4Sr0.1Ni0.5Fe2O4	0.02802	0.426	1.045	1.471	28.95
Cd0.3Sr0.2Ni0.5Fe2O4	0.02889	0.0578	0.0876	0.1454	39.73
Cd0.2Sr0.3Ni0.5Fe2O4	0.02822	0.0734	0.0549	0.1282	57.20

. The coercivity value varies between 28 to 30V/cm with the rise in the concentration amount of doped Sr²⁺.

P-E loops revealed an open-mouth structured for all samples. This is basically due to the conducting behaviour of these materials resulting in high leakage current. The high leakage current is mainly due to oxygen vacancies or voids in the prepared spinel ferrite. The P–E loop obtained in this case represents a lossy conductor type, possibly due to the large value of the leakage current [52,53]. The increase in the doping amount of Sr²⁺ ions on lattice sites has increased the P-E loop area, which may be due to the increasing conducting behaviour of materials that leads to the rise in electrical leakage current. Cd_0.5Ni_0.5Fe₂O₄ displayed the lowest P–E loop area and the lowest leakage current. Increasing the content of Sr²⁺, host ions remarkably increased the ferroelectric nature of Cd_0.5−xSr_xNi_0.5Fe₂O₄. Saturation polarization was maximum for the highest doped sample (x = 0.30). This is because the dopant (Sr and Cd) ions had higher electrical responses than the host ions (Fe and Ni). Also, the structural changes improved the ferroelectric properties of the doped materials [54,55]. The values of maximum polarization (P_m) and remnant polarization (P_r) against varying values of Cd²⁺ and Sr²⁺ phase fractions has been shown in Figure 5. A decreasing trend of Pm, as well as Pr, was perceived with the increasing Sr₂O₃ phase fractions contributing low surface area offered by the relatively large particle size trapping numerous charge carriers [51]. With substitution, the uniform distribution of electric dipoles decreases. The simultaneous decrease in P_r and P_m in doped NiFe₂O₄ confirms short-range ordering, indicating ferroelectric phase stability. Saturation polarization increased with increasing Sr²⁺ content. Higher saturation polarization of the materials increases their energy storage capacity and makes them good candidates for use in energy storage devices. Properties like optical, electric and non-linear optics response for multi-layered capacitors LCD and storage devices can potentially be altered by altering the ferroelectric behaviors of the material, and a Cd²⁺ and Sr²⁺ doped material has potential use for such applications.

The values of recoverable energy density (W_R), energy loss density (W_L) and total energy density (W_T) and Coercive Electric Field (E_c) for Cd_0.5−xSr_xNi_0.5Fe₂O₄ (where x = 0.0, 0.1, 0.2 and 0.3), respectively at 30 V are tabulated in Table 3. Energy density can be efficiently calculated through P-E loops. Energy loss density (W_L) can be worked out by the area covered by P-E loops, whereas; plotting of the area enclosed by the discharge curve gives the value of recoverable energy density (W_R). By summarizing the values of W_L and W_R, one can determine the value of storage energy density (W_S). The values of W_L, W_R and W_S can be calculated by using Equation (8)–(10), respectively;

W_T = P_mP_r

(8)

W_R = (P_m – P_r)E_c

(9)

W_L = W_T − W_R

(10)

For x = 0.3, the variation of W_R and W_S clearly illustrates the enhanced recoverable energy density. These P-E loops also help to figure out the energy storage efficiency (η) of the material and can be calculated by using Equation (11) [56].

η = W_R/(W_R + W_L) × 100%

(11)

The efficiency of a prepared series of samples is depicted in Figure 6. The lowest efficiency has been achieved for x = 0.0. It was discovered that efficiency increased with increasing Sr²⁺ content. It is clear from the above equation that the value of efficiency (η) increased as W_R increased. This W_R value is associated with the region confined by the discharge curve and polarization axis.

The current versus voltage (I–V) curves have been keenly analyzed for the as-synthesized samples. The plotted I–V graph is displayed in Figure 7. The leakage current exhibited symmetric trends for both the positive and negative sides of the applied field. A decreasing trend of leakage current had been perceived with the increasing Sr²⁺ phase fractions. The maximum current value was determined for the sample with concentration at x = 0.30. The leakage current moved symmetrically along the positive as well as negative boundaries of the practical field. With increasing Sr²⁺ substitution, a decreasing trend in leakage current was found.

3.5. Dielectric Response

The dielectric characteristics are crucial as they could be beneficial in understanding the dielectric energy storage behavior of the prepared materials. The real and imaginary parts of the permittivity against increasing frequency in the range 1 to 6 GHz has been shown in the Figure 8 for undoped and doped sample (x = 0.3). The curves show that the real part of the permittivity which is indicative of the dielectric energy stored in the material has a higher value and increases with increasing frequency. This means that the dielectric polarization for the given material increases at high frequency. The imaginary part of dielectric constant does not show much variation with increasing frequency. This is indicative that the ferrite material dielectric losses have not increased with increasing energy. The real part of permittivity shows higher values for doped sample (x = 0.3) as compared to undoped sample.

4. Conclusions

In this work, the sol-gel auto combustion process was effectively affianced for producing Cd_0.5−xSr_xNi_0.5Fe₂O₄ (x = 0.0, 0.1, 0.2 and 0.3). A systematic study of structural, morphological and ferroelectric effects of Sr-Cd doped NFO was utilized. The XRD peaks of all the samples indicate a spinel cubic structure with a highly crystalline nature. SEM analysis revealed the presence of cracks and oblong particles with a decrease in their average size. Magnetic parameters with S-shaped loops showed typical spinel ferrite response. P-E loops were consistent with every single sample accepted the normal room temperature ferroelectric nature, and the loop has a maximum value of P_m for x = 0.3. The P_m and P_r graph shows linearly decreasing trend with Sr-Cd substitution. W_R and W_L both increase with increasing values of substitution contents and is maximum at x = 0.3. The I–V graph shows the declining trend of leakage current observed with the increasing Sr substitution. The conductivity of these materials is maximum for maximum substitution of Sr and minimum substitution of Cd. The prepared samples show high real dielectric constant for doped sample. These materials are very useful and efficient for energy storage devices due to their characteristics.