1 Introduction

The researchers and scientists have great interest in spinel ferrites due to their utilization in many fields i.e., circulators, transformers core, data storage devices, switching, gas sensing, radio frequency circuits, antennas, microwave, drug delivery, and high-frequency appliances [1,2,3,4]. Spinel ferrites have interesting and excellent structural, electrical, dielectric, and magnetic properties. The characteristics of spinel ferrites depend upon many factors such as structure, crystallite size, density, synthesis method, and substitution of cations [5,6,7,8,9]. The cations distribution among tetrahedral and octahedral sites strongly affects the properties of synthesized ferrites. The interactions between the cations are mainly affected by magnetic properties of spinel ferrites. There are three types of super exchange interactions (A–A, B–B and A–B) present in the spinel ferrites. When A–B superexchange interaction is stronger than (A–A and B–B) then it represents a collinear spin structure. If A–A or B–B superexchange interaction is comparable with A–B exchange interaction then it leads to non-collinear spin structure [10, 11].

Copper–zinc ferrites are crystallized as spinel ferrites that exhibit ferrimagnetic and semiconducting behavior. The antiparallel spins of magnetic moment of atoms among interstitial sites give ferrimagnetic characteristics. The structural properties can be controlled by substituting various kinds of atoms having different radius, magnetization, and atomic weight in the spin–lattice [12,13,14,15]. Copper ferrites possessed an inverse spinel structure and shows ferrimagnetic at room temperature. Zinc ferrites owing normal spinel structure in bulk with TN = 10 K and exhibited antiferromagnetic below Neel's temperature (10 K). ZnFe2O4 nano ferrites become paramagnetic at room temperature. Cu2+ ions preferentially occupied at octahedral sites while Zn2+ preferentially occupied on tetrahedral sites. Fe3+ cations are disturbed among tetrahedral and octahedral sites [16, 17]. Variation in the magnetic properties of Cu–Zn nano ferrites is attributed to the distribution of iron ions on two sites with tetrahedral and octahedral coordination of oxygen ions. If divalent cations go to tetrahedral voids only while trivalent cations occupied octahedral voids, then structure was said to be normal spinel. Special attention is required to understand the structural and magnetic properties of copper–zinc ferrites.

Polymer composite is emerging field of materials and has great interest due to wide range of applications. The polymer composites are used in many fields such as light emitting diode, transistors, radar applications, sensors and materials batteries. From different types of composites, solid polymers are important due to variety of application in different fields such as solar cells, electro chromic windows, fuel cells and energy storage devices. The important parameter which controls the various properties of combined matrix of composites is degree of miscibility [18,19,20].

Novel synthesis techniques are applied to attain definite structural and magnetic properties [21,22,23]. The various methods are used to synthesis spinel ferrites, but some most common methods are hydrothermal, co-precipitation, solid-state reaction, sol–gel, and micro-emulsion route [11, 24,25,26,27]. Sol–gel auto-combustion route offers various advantages over other methods including definite particle size, lab friendly, cost-effective, and processed at low temperature with the best homogeneity. Single-phase Cu–Zn nano ferrites can be obtained by sol–gel auto-combustion method [28]. The variation in structural and magnetic parameters of copper–zinc ferrites is observed by the substitution of indium ions. There is no report on indium incorporated copper–zinc ferrites in our best knowledge. The researchers prepared spinel ferrites at high temperature and reported the value of crystallite size, dielectric constant and dielectric losses are very high. We synthesized In3+ incorporated Cu–Zn ferrites at low temperature 500 °C. The value of crystallite size remains in the range 9.37–14.76 nm. The value of dielectric constant and dielectric losses is very small as compared to reported literature [29,30,31].

The objective of this research work is to explore the influence of indium on structural, spectral, dielectric and magnetic properties of Cu0.5Zn0.5InxFe2−xO4 ferrites. These ferrites are synthesized by novel synthesis route (sol–gel auto-combustion). Here we reported our results on structural, spectral bands/bond length, magnetic and dielectric properties which are characterized by XRD, FTIR, VSM, and dielectric.

2 Experimental procedure

The indium incorporated Cu–Zn nanocrystalline ferrites were synthesized by sol–gel auto-combustion route. The analytical grades copper nitrate, zinc nitrate, iron nitrate, indium nitrate, and citric acid were utilized without any purification in 1:1 stoichiometric ratio of metals nitrate to citric acid. All the reagents were weighed and dissolved in deionized water. Furthermore, all solutions were heated at 45 °C with continuous stirring. The pH value was maintained by adding ammonia solution ~ 7. Moreover, all the solution mixture was continuously stirred as well as heating at the temperature 90 °C. The water molecules were evaporated, and the formation of sol was developed. The gel was obtained by stirring the solutions for 3 h at 90 °C. The gel was self-ignited and burned entirely by auto-combustion method to make fluffy powder. Finally, the prepared powder was sintered at 500 °C for 4.30 h to remove organic matter and to form spinel phase. Polyvinyl alcohol (PVA) 5% was added to calcined powder as binder. The powder was pressed by hydraulic pressure to obtain a pellet of diameter 7 mm. The pellet was heated at 160 °C for 2 h. D8 Advance Bruker, Cu Kα was used for the crystal structure of sintered powder. FTIR spectra were recorded by Nicolet TM 5700 spectrophotometer. The dielectric property of synthesized ferrites was carried out by Keithley LCR meter model-197. M–H loops were obtained using vibrating sample magnetometer (VSM) Lakeshore model-7300.

3 Results and discussion

3.1 Thermal analysis

The phase transformation of copper–zinc ferrite sample was studied by thermal analysis. Thermal analysis of pure ferrite depicted in Fig. 1. The weight loss in TGA and DTA curves occurred in four successive steps. There are four peaks observed in TGA and DTA curves due to disintegration of residual components. First weight loss of ~ 2% was observed due to water evaporation. Second weight loss ~ 3% and third weight loss ~ 2% was observed due to disintegration of residual components. After that very small weight loss was observed that indicated the spinel phase formation. The first exothermic peak which appeared below 100 °C was due to moisture or water trapped in the pores of prepared ferrite. The exothermic peaks that occurred at 115 °C and 148 °C were due to decomposition of metal nitrates. The overall weight loss observed in the thermal analysis was 8%. TGA curve shows the spinel phase formation occurred after 400 °C. Three exothermic peaks appeared in DSC curve are associated with DTA peaks. DSC analysis provides information about reactions i.e., exothermic or endothermic. DSC curve revealed that decomposition process is strongly exothermic. The sintering temperature for indium substituted copper ferrites was estimated from TGA curve. The sintering of synthesized nano ferrites was carried out at 500 °C for 430 h [32, 33].

Fig. 1
figure 1

Thermal analysis of Cu0.5Zn0.5Fe2O4 ferrites

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3.2 Structural analysis

X-ray diffraction (XRD) patterns of Cu0.5Zn0.5InxFe2−xO4 nanocrystalline ferrites are displayed in Fig. 2. XRD pattern of pure sample exhibited only spinel phase and no additional phase appeared during sintering process. All the peaks (111), (220), (311), (400), (422), (511) and (440) were well indexed and matched with the ICDD card No. 01-089-7409. All the samples possessed spinel structure having cubic symmetry with space group Fd3m [34]. The various parameters such as crystallites size, lattice constant, and cell volume are calculated from XRD data and listed in Table 1. Lattice parameter increases with the substitution of In3+ up to x = 0.16 and decreases afterward. The variation occurred in the lattice parameter is ascribed by ionic radii. The increase in lattice parameter is due to incorporation of higher ionic radius In3+ ions instead of Fe3+ ions and decrease due to the presence of an additional phase [35].

Fig. 2
figure 2

XRD patterns of Cu–Zn–In–Fe–O system

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Table 1 The structural parameters of In–Cu–Zn–Fe–O ferrites
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The crystallite size (D) determined from Scherrer’s relation using (311) Bragg’s reflection peak decreases monotonically with the increase of indium contents and shown in Fig. 3. The value of ‘D’ remains in the range of 9.37–14.76 nm. The decrease in ‘D’ produces an increase in strain. When higher ionic radii In3+ are replaced with Fe3+ ions, the lattice strain is produced because larger ions enter the spinel lattice of copper–zinc ferrites produced internal stress [36]. It was observed that most intense peak (311) was shifted towards a lower angle which may be due to an increase in cell volume and lattice constant. When indium concentration increases, In3+ ions isolate from the crystal structure of Cu0.5Zn0.5Fe2O4 and form InFeO3 phase. The extra phase appeared in XRD patterns was InFeO3 and matched with the ICDD no. 01-085-2306. The impurity phase appeared in XRD patterns were indicated by (*). The cell volume increases with the inclusion of In3+ ions and decrease for higher concentration. Initially the indium ions enter into the lattice of Cu–Zn and isolated from the lattice for higher x. The increase in cell volume due to expand of volume and decrease in cell volume ascribed due to contract of cell volume.

Fig. 3
figure 3

Lattice parameter and crystallite size versus In3+ contents

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Rietveld refinement of In3+ substituted Cu–Zn ferrites was carried out by MAUD (materials analysis using diffraction) software. Figure 4 reveals Rietveld refined XRD patterns of all samples. It was observed that experimental data and standard data are matched. The pure sample exhibited single phase spinel structure while indium substituted samples showed some extra peaks of InFeO3 which elaborated by (*). The refined parameters of XRD patterns for all samples are listed in Table 2. R-factor described the quality and refinement of prepared samples. The quality of synthesized samples can be obtained by determining Rwp, Rb, Rwpnb, Rexp and GOF. GOF (goodness of fit) is simply the ratio of Rwp and Rexp. The refinement quality was considered reliable only when 1 ≤ χ2 < 2. The best refined structure is demonstrated by sig value close to one. The value of GOF is in the range of 1–2 which shows the reliability of present study. The values of lattice parameter and cell volume calculated from the refined patterns are close to experimental one and listed in Table 2 [37,38,39,40,41].

Fig. 4
figure 4

XRD patterns of Cu–Zn–In–Fe–O system

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Table 2 Rietveld refined parameters of Cu–Zn–In–Fe–O system
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X-ray density increases with the increase of indium content and displayed in Fig. 5. The increase in X-ray density is due to the denser ions replaced with lighter ions. It was expected that theoretical density will increase with the substitution of indium ions due to high molecular weight and density of In3+ ions. The bulk density is calculated by following relation ρb = m/πr2h. The bulk density has nonlinear behavior. Overall bulk density is increased with the increase of dopant concentration. The value of bulk density is smaller than X-ray density due to occurrence of pores during sintering process. Dislocation density, strain tetrahedral and octahedral radii, and hopping length were calculated from XRD data. Strain is calculated from William–Hall plots and listed in Table 3. It can be seen that strain increases with the substitution of In3+ ions. The increase in strain may be due to increase of internal stress of large ionic radii incorporation. It may be due to presence of secondary phases in the crystal structure. Dislocation density has direct relation with strain an inverse relation with crystallite size. The behavior of dislocation density is explained on the basis of crystallite size and strain. The value of dislocation density increases due to rise in strain. The behavior of dislocation density is in accordance with the D and ε. The hopping length of tetrahedral sites (LA) and octahedral sites (LB) is determined from structural data. The LA is the distance between magnetic ions at tetrahedral sites and LB is the distance between ions at octahedral sites. The hopping length improved as the percentage of indium increases and reduced for higher x. An increase in hopping length indicated that charge carriers required more energy for the hopping between one cation sides to another. Sometimes hopping was also called the distance between centers of adjacent ions. The behavior of these radii is the same as of lattice constant [42, 43].

Fig. 5
figure 5

X-ray density and strain versus In3+ contents

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Table 3 The various structural parameters of indium incorporated copper–zinc ferrites
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3.3 Spectral analysis

The structural and chemical changes occurred during combustion were investigated by spectroscopic analysis. The combustion reaction phenomenon can be studied with the help of infrared analysis. Figure 6 shows the infrared spectra of indium substituted copper–zinc ferrites. The band υ1 (539–560 cm−1) and υ2 (454–464 cm−1) correspond to cubic spinel structure [27, 44, 45]. The band υ1 occurred due to stretching vibration of metal–oxygen (Mtetra-O) at tetrahedral sites while octahedral band υ2 in the FTIR spectra was attributed to vibration of Mocta-O at octahedral sites. FTIR analysis also confirmed the spinel structure of synthesized ferrites [46]. The high-frequency band tilted towards low frequency with the substitution of In3+ ions. There is an inverse relationship between both bands. The shifting of bands depends upon cations mass, lattice parameter, and bonding of cations with oxygen. The shifting of bands towards lower frequency may be due to the decrease in metal stretching vibrations energies. As a result, covalent bonding between metal–oxygen decreased.

Fig. 6
figure 6

FTIR spectra of In3+ inclusion Cu–Zn ferrites

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The value of absorption band υ1 was high as compared to υ2 due to variation in bond length [47]. The bond length exhibited an increasing behavior for x ≤ 0.16 and decrease for higher x. The peak appeared around 1638 cm−1 attributed to O–H stretching vibrations [48]. The variation in the lattice parameter related to the expansion and contraction of the metal–oxygen bond length of crystallographic sites [49]. The incorporation of indium in copper–zinc ferrites may transfer ferric ions from B sites to A-sites. It is the reason why the vibrational frequency of the B site increases and A-site decreases [50]. The force constant behavior described on the basis of vibrational frequencies. Table 4 reveals the force constant of tetrahedral site followed by the vibrational frequencies of metals oxygen at tetrahedral sites and having the same behavior. The force constant of octahedral sites altered with variations of vibrational frequency of metals–oxygen bonds at octahedral sites [51].

Table 4 The spectral parameters of In3+ substituted Cu–Zn ferrites
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3.4 VSM analysis

The magnetic behavior of synthesized ferrites was estimated from M–H loops recorded at room temperature by VSM. The synthesized nano ferrites exhibited narrow hysteresis loops with a small value of coercivity which is evidence for the soft nature of prepared samples. It is clear from Fig. 7 that pure and substituted Cu–Zn ferrites revealed ferromagnetic nature. All the magnetic parameters are determined from hysteresis loops and presented in Table 5. The variations in magnetization as a function of applied field are studied and depicted in Fig. 7. The value of saturation magnetization decreases with the inclusion of indium [52]. The decrease in Ms attributed to the nonmagnetic In3+ ions entering into the lattice of copper–zinc ferrites at B sites and reduces the number of Fe3+ ions on octahedral sites. It decreases the magnetic moment of octahedral sites. The migration of ferroic ions from tetrahedral sites to octahedral sites increases the magnetic moment of A-sites. As a result net magnetization decreases with the inclusion of non-magnetic ions in the spinel lattice of Cu–Zn nanoferrites. Present results are resembled with the previously reported results [53]. The decrease in Ms can be described by Neel’s two sub lattice model given by: (1)

$$M = M_{{\text{B}}} - M_{{\text{A}}} .$$
(1)
Table 5 The magnetic parameters of Cu–Zn–In–Fe–O system
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Fig. 7
figure 7

M–H loops of Cu0.5Zn0.5InxFe2-xO4 ferrites

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MB and MA are magnetic moments of octahedral and tetrahedral sites, respectively. The magnetic moment is originated due to the spin orientation of two sub lattices which are aligned in an antiparallel direction. The exchange interactions present in the spinel ferrites are A–A, B–B and A–B. In the spinel lattice A–B exchange interaction is predominant than the other two types. If nonmagnetic In3+ ions preferred octahedral sites and replaced magnetic ions Fe3+ from B site. The magnetic moment of B sites reduces even if the magnetic moment of the A-site remains the same which may cause a decrease in saturation magnetization. This decrease in saturation magnetization may be due to the appearance of secondary phases. When secondary phase appeared it distort the structure and charge carriers are piles up at grain boundaries. Moreover, iron ions are isolated from the lattice which decreases the magnetization. Bohr’s magnetron decreases due to an increase of In3+ content and depicted in Fig. 8. It is another reason for the decrease in Ms [43].

Fig. 8
figure 8

The variation in anisotropy constant and Bohr’s magneton as function of indium concentration

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The small value of MR and Hc indicated the presence of single-domain particles [54]. The variations in Ms, Hc, and MR are shown in Fig. 9. The decrease in coercivity with the substitution of In3+ ions is observed. This decrease is attributed to the effect of magnetocrystalline anisotropy. The indium has zero angular momentum and did not take part in magnetocrystalline anisotropy. When In3+ ions were replaced with iron, spin–orbit coupling decreases which reduced the coercivity value [55]. The anisotropy constant is calculated and depicted in Table 5. The anisotropy constant is reduced with the inclusion of In3+ ions. This happened due to indium having a smaller value of anisotropy constant than iron. As a result, the value of coercivity was decreased. The decrease in the value of the anisotropy constant was due to decrease in domain wall energy [56]. The squareness ratio estimated from remanence and saturation magnetization. The value of MR and Ms are declined which decreases the squareness ratio. The value of squareness ratio is very small which suggested that indium incorporated copper–zinc ferrites are useful for high-frequency applications [57].

Fig. 9
figure 9

The deviation in Ms, MR and Hc of In3+ substituted copper zinc ferrites

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3.5 Dielectric studies

The dielectric constant (ε′) is used to elucidate the speed of electromagnetic wave travel through the medium. The materials that possessed a high value of ε′ were used to store charge [58]. The dielectric parameters are recorded in the frequency range of 1 MHz to 3 GHz. Figure 10 shows the frequency-dependent dielectric constant. The ε′ has a large value at a low frequency while small value at high-frequency which is the general behavior of ferrites materials. Dielectric constant at low frequency decreases rapidly while it reduces slowly at high-frequency and became almost frequency independent. The resonance peaks are observed above 2.5 GHz. The behavior of dielectric constant is associated with space charge polarization [59]. The dielectric constant behavior is ascribed by Maxwell–Wagner model. The polarization phenomenon occurred due to hopping between ferrous and ferric ions. When frequency reaches up to a definite point, the charge carrier cannot follow the variation in the AC applied field. As a result, the dielectric constant exhibited frequency-independent behavior [60].

Fig. 10
figure 10

Dielectric constant versus frequency of indium substituted Cu–Zn ferrites

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The relaxation phenomenon that appeared in the dielectric constant directly related to the polarization of substances. The space charge polarization occurred between Fe2+ and Fe3+ due to hopping phenomenon. According to Koop's theory, two conducting grains layers are separated by a resistive layer known as grain boundaries [61]. The charges pile up at grain boundaries which mainly contribute to the dielectric constant. The concentration of ferrous ions increased at octahedral sites which may increase space charge polarization. As a result dielectric constant increased. Resonance peaks beyond 2.5 GHz occurred due to the matching of charge carrier’s frequency with the externally applied field frequency. Peaking behavior is observed when the frequency of charge carriers matched with the AC applied field. It increases power loss and resonance peak appeared [62]. The dielectric loss of indium incorporated Cu–Zn nano ferrites is depicted in Fig. 11. It was seen that dielectric loss was found to decrease as the externally applied field increased [63].

Fig. 11
figure 11

Dielectric loss as function of frequency of Cu–Zn ferrites

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In dielectric material, a dielectric loss estimated the dissipation of energy. The material that possessed high conductivity also has a high dielectric loss and vice versa. The resonance peaks observed in the high-frequency region were explained briefly in the above section. The dielectric loss tangent of indium inclusion copper–zinc ferrites is displayed in Fig. 12. It is the ratio of dielectric loss to dielectric constant. The variation in tanδ depends upon various factors such as compositions, annealing temperature, and surface morphology. The value of tanδ is reduced with the increase in frequency [64]. The dielectric losses are low at high-frequency due to charge carriers no longer obey the applied field. The resonance phenomenon is observed due to the coinciding of hopping frequency with externally applied field frequency. If the content of In3+ is added in a fixed ratio then the conduction mechanism is proportional to concentration of iron ions which is responsible for a decrease in tan loss. All the results of indium substituted Cu–Zn nano ferrites matched with the reported results and suggested these materials are beneficial for microwave appliances at high-frequency [65]. AC conductivity is calculated by following relation. (2)

$$\sigma {}_{{{\text{ac}}}} = \varepsilon _{{\text{o}}} \varepsilon ^{\prime}\omega \tan \delta .$$
(2)
Fig. 12
figure 12

Frequency dependent tan loss of indium substituted Cu–Zn ferrites

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Deviation in AC conductivity versus frequency shows in Fig. 13. The variation in σac was mainly depends upon on frequency. AC conductivity increase with the increase of frequency. The behavior of AC conductivity is described with the help of Koop's theory. The behavior of grains and grain boundaries is different at different frequencies and exhibited frequency-dependent behavior. The grain boundaries are active at a low frequency produced obstruction and exhibited a decrease in the mobility of charge carriers. Thus conductivity is small at low frequency [66]. At higher frequency, grains are active that are less resistive than grain boundaries. The conduction mechanism is increased due to a rise in frequency which caused an increase in σac. The increasing field frequency increases the hopping frequency between Fe2+ and Fe3+ ions consequently AC conductivity increased. The resonance peak is observed in AC conductivity attributed to the homogenous structure of prepared ferrites material. The rapid decrease in Ac conductivity is due to lag behind phenomenon of charges and applied field [67].

Fig. 13
figure 13

AC conductivity of In3+ incorporated Cu–Zn ferrites

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The variation in M′ versus frequency is displayed in Fig. 14. The difference in grains and grain boundaries contribution is analyzed from the electric modulus [68]. It also gives information about the conduction and relaxation process. The value of M′ is directly proportional to frequency. After a certain frequency, its value approaches the maximum and becomes almost constant. This phenomenon is caused due to the conduction process of electrons of long-range mobility. The short-range mobility of charge carriers is responsible for saturating the value of M′ into an asymptotic single value. This happened due to a decrease in hopping length at B sites [69, 70]. Figure 15 reveals the frequency-dependent imaginary part of modulus. It decreases with the increase of frequency while the resonance peak is observed at higher frequencies. The value of resonance peak increases with the increase of indium content. The region below the maximum value of M″ due to long-range mobility of charge carriers while above this value charge carriers were restricted to a shorter distance and confined into the potential well [71].

Fig. 14
figure 14

Frequency dependent M′ of In3+ incorporated Cu–Zn ferrites

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Fig. 15
figure 15

M″ versus frequency of indium substituted copper–zinc ferrites

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3.6 SEM analysis

The morphology of prepared ferrites is analyzed by SEM (scanning electron microscopy) and images are shown in Fig. 16. The micrograph exhibited agglomeration of grain structure. The agglomeration in these ferrites is due to magnetic interaction between the particles. It is observed from SEM micrograph that grain size decreases with the substitution of indium in Cu–Zn ferrites. All the samples revealed crack free and regular structure. The variation in grain size indicated the fabrication of indium substituted copper–zinc ferrites [72,73,74].

Fig. 16
figure 16

SEM images of In3+ included Cu–Zn ferrites

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4 Conclusions

Indium (In3+) incorporated Cu–Zn magnetic oxides were synthesized via sol–gel auto-combustion technique. The structural analysis revealed the cubic spinel structure of all samples. Initially, the lattice constant increased for x ≤ 0.16 and reduced thereafter. The value of crystallite size was monotonically decreased and found in the range of 9.37–14.76 nm. X-ray density increased from 5.30 to 5.69 and bulk density remained in the range of 2.66 to 3.06 g/cm3. Strain and dislocation densities were increased (0.113–0.179 and 0.013–0.033) with the incorporation of In3+ ions in Cu–Zn magnetic oxides. Force constants and band position variation confirmed the substitution of indium in these materials. Various concentrations of In3+ ions greatly affected the values of magnetic parameters. The value of Ms, MR, and Hc was decreased with the increase of dopant concentration. The magnetic analysis revealed that the value of squareness ratio and anisotropy constant decreased with In3+ content. The dielectric parameters were found to increase as indium contents were increased. The value of Bohr’s magnetron also decreased from 1.08 to 0.44 μB. The small value of squareness ratio and anisotropy constant with moderate saturation magnetization may suggest that prepared materials may have potential in switching and high-frequency applications (Figs. 14, 15, 16).