Magnetic Order and Electronic Transport behaviour in Tailored made Nanostructural Co- Cr Ferrospinels

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Pandav, Sachin S. Pujari, Amit A. Bagade, Vashishtha M. Gurme, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7994297/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 28 Feb, 2026 Read the published version in Journal of Materials Science: Materials in Electronics → Version 1 posted You are reading this latest preprint version Abstract The unique size-dependent structural and physical properties of Cr³⁺-doped spinel ferrites, coupled with their wide range of applications, have garnered significant attention from the scientific community. In this work, CoCrₓFe₂₋ₓO₄ (x = 0.0, 0.5, 1.0, 1.5, and 2.0) compositions were synthesized using the citrate–gel auto-combustion method and subsequently sintered at 700°C for 6 hours. XRD analysis demonstrated that all samples crystallized in a pure cubic spinel phase. The lattice parameter was found to decrease slightly with increasing chromium content, ranging from 8.3862 Å to 8.3835 Å. The study of cation arrangement showed that Co²⁺ ions are chiefly positioned at octahedral (B) sites., while the relatively larger Cr³⁺ ions substitute for smaller Fe³⁺ ions at the same sites. FTIR spectra showed characteristic M-O stretching vibrations pertaining to the tetrahedral (A) and octahedral (B) lattice positions, further affirming the characteristic spinel phase. All dielectric parameters, such as dielectric constant, dielectric loss, and loss tangent, were found to decrease as the frequency increased. Magnetic characterization revealed that the replacement of Fe³⁺ by Cr³⁺ led to a decrease in saturation magnetization and an increase in coercivity, indicating the potential of these materials for permanent magnet applications. Rietveld refinement XRD Cr-doped Auto-combustion technique Ferrites Dielectric properties Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction In the realm of modern technological innovations and biomedical engineering, AB₂O₄-type spinel ferrites have attracted considerable scholarly interest due to their economic viability and cost efficiency, thereby rendering them exceptionally appropriate for applications in electrical and magnetic sensing [ 1 – 6 ]. Among various ferrites, cobalt ferrite (CoFe₂O₄) has become one of the most extensively studied materials. This interest arises from its ability to form numerous solid solutions when doped with transition or rare-earth elements, allowing for the fine adjustment of its physical properties. Investigating how dopants or substituents influence the magnetic and electrical characteristics of the Co-Fe system provides valuable insight into the underlying physical mechanisms [ 7 – 14 ]. Several studies have examined the substitution of different divalent and trivalent cations in CoFe₂O₄ and their effects on the material’s structural, magnetic, and dielectric behavior [ 15 ]. Replacing Co²⁺ ions with Bi³⁺, Al³⁺, Mn²⁺, Ni²⁺, or Zn²⁺ has been shown to improve both magnetic and dielectric performance [ 16 , 17 ]. In contrast, the incorporation of Cr³⁺ as a substituent result in a noticeable reduction in saturation magnetization and coercivity, highlighting the significant impact of specific cationic substitutions on the material's properties [ 17 ]. Furthermore, Cr³⁺ substitution significantly influences the dielectric properties of CoFe₂O₄, as evidenced by previous studies [ 18 , 19 ]. Cr³⁺ substitution at Co²⁺ sites have been shown to affect both the magnetic and dielectric properties of CoFe₂O₄ [ 18 ]. Impedance spectroscopy is often used to analyze the AC electrical properties of ferrites, providing essential information about charge transport and conduction mechanisms [ 20 ]. The substitution of divalent or trivalent cations at either the A-site or B-site within the spinel lattice can effectively modify these electrical characteristics [ 21 – 25 ]. Many researchers have further studied how factors such as frequency, temperature, and cationic composition affect the overall magnetic and dielectric behavior of CoFe₂O₄, leading to a better understanding of its complex properties [ 21 – 25 ]. The crystallographic configuration of CoFe 2 ​O 4​ exhibits an inverse spinel structure in its bulk phase; however, a dimensional reduction to nanoscale induces a transformation towards partial inversion spinel architecture, attributed to the redistribution of cationic species within the crystallographic framework [ 26 – 27 ]. In its bulk configuration, COFE exhibits a magnetic structure characterized by two antiferromagnetically coupled sublattices, demonstrating distinct magnetic moment orientations in opposing directions [ 28 – 29 ]. In the spinel AB₂O₄ structure, the tetrahedral (A) sites are occupied by Fe³⁺ ions (3d⁵, M = 5 µB) that are ferromagnetically aligned, forming one sub-lattice. The second sub-lattice consists of Co²⁺ (3d⁸, M = 5 µB) and Fe³⁺ (3d⁵, M = 5 µB) ions positioned at the octahedral (B) sites, also showing ferromagnetic ordering. The interaction between these two sub-lattices results in a net saturation magnetization of approximately 3 µB per formula unit [ 30 ]. Variations in the distribution of cations between tetrahedral (A) and octahedral (B) sites significantly influence the spin alignment, thereby profoundly affecting the magnetic and electrical properties of cobalt ferrite. The introduction of dopants at specific lattice sites induces changes in the magnetic moment and regulates particle growth, which in turn alters the cation distribution. These modifications ultimately govern the material's overall physical and functional behaviour. The dielectric properties of ferrites hold significant importance, not only for their wide range of practical applications as well as from a fundamental research standpoint. The dielectric behaviour observed in polycrystalline ferrite materials arises primarily due to the combined contributions of interfacial polarization and hopping conduction polarization mechanisms. Tiwari et al. [ 31 ] investigated the temperature-dependent dielectric permittivity of a Ba₀.₅Sr₀.₅Nb₂O₆/CoCr₀.₄Fe₁.₆O₄ multiferroic composite, which exhibited characteristics of a relax or ferroelectric. Panda et al. [ 30 ] conducted comprehensive investigations into the dielectric behavior of bulk CoFe₂O₄, elucidating both frequency and temperature dependencies, wherein distinct contributions from grain boundaries and intragranular regions were identified, along with the determination of characteristic relaxation frequencies Lahouli et al. [05] systematically investigated the variation of dielectric permittivity with frequency in Ni-Zn-Al ferrite systems, analyzing the correlations between frequency modulation and dielectric response characteristics. Kumar et al. [ 25 ] conducted systematic investigations on the frequency-dependent dielectric characteristics of Ni-substituted cobalt ferrite systems. Recent thermal analyses of dielectric properties have revealed critical insights into para-ferroelectric phase transitions and elucidated the fundamental nature of ferroelectric behaviour in these materials. Sekulicet. al. studied the dielectric behavior of MFe₂O₄ (where M = Mn, Ni, Zn) ferrites, analysing their dependence on both frequency and temperature [ 32 ]. The influence of Cr-ion doping on Co–Fe spinel ferrites was systematically investigated with respect to their morphological, structural, dielectric, and magnetic properties. Structural characterization was carried out using XRD and EDS. Morphological features were analysed through SEM and TEM. Magnetic behaviour was studied, while microwave absorption properties were evaluated to assess the impact of incremental Cr-ion substitution (CoFe 2 − x Cr x O 4 , x = 0.0, 0.5, 1.0, 1.5, and 2.0) within the Co-Fe ferrite lattice. 2. Experimental section 2.1. Chemicals All reagents utilized in the present work were of Analytical Reagent (AR) grade, ensuring exceptional purity and suitability for the experimental objectives, thereby eliminating the need for further purification. 2.2. Synthesis of CoCr x Fe 2−x O 4 spinels Nanoparticles ferrite with chemical formula CoCr x Fe 2−x O 4 (x = 0.0, 0.5, 1.0, 1.5, and 2.0) were prepared in air through the citrate–gel auto-combustion technique [ 33 ]. In precise stoichiometric proportions of ferric nitrate Fe(NO 3 ) 3 .9H 2 O, cobalt nitrate Co(NO 3 ) 2 .6H 2 O, chromium nitrate (Cr(NO 3 ) 3 .9H 2 O) and citric acid (C₆H₈O₇) in a 1:1 mole ratio was accurately measured and dissolved separately in a minimal volume using deionized water to obtain a homogeneous solution. Precursor mixture was gradually evaporated to dryness, resulting in a soft, porous mass. The dried precursors were then sintered in air at 700°C for 6 hours. 2.3. Material characterizations The crystallographic analysis of the powder sample was conducted using X-ray diffraction (XRD) measurements on a Rigaku Miniflex-600 diffractometer, which was equipped with Cuα1 radiation (λ = 0.15406 nm) and operated at 40 kV with a scan rate of 2° per minute. Surface morphological investigations were carried out using field emission scanning electron microscopy (FE-SEM) on a JEOL JSM-6500F instrument. The elemental composition was determined through energy dispersive spectroscopy (EDS) with an Oxford X-max detector. The magnetic properties of the synthesized samples were assessed at room temperature using a Vibrating Sample Magnetometer (EZ VSM model). 3. Results and discussion 3.1 X-ray diffraction studies Figure 1 displays the XRD profiles of sintered samples with diverse compositions, accompanied by the Rietveld refinement outcomes. All observed diffraction peaks correspond well with JCPDS No. 22-1086, confirming the formation of a pure, single-phase spinel ferrite structure. The Bragg peak positions are indicated by vertical lines. The black open circles indicate the detected intensity. The red solid line indicates the Rietveld-calculated intensity. The lower blue line shows the difference between the observation and the calculation. The major diffraction peaks are associated with the (220), (311), (222), (400), (422), (511), (440), and (533) planes. These peaks confirm the cubic spinel structure. During Rietveld refinement, the oxygen positions were treated as free parameters, whereas atomic fractional positions were kept constant. Other parameters, including lattice constants, temperature factors, occupancies, scale factors, and shape factors, were treated as free parameters. The XRD data for all samples were refined using the Fd 3 m space group, with the background corrected using the Pseudo-Voigt peak function. The position coordinates and refined occupancies of various atoms are summarized in Table 1 . The refined crystal parameters and atomic positions are also provided in Table 2 . The refined patterns show that the values of thegoodness of fit (χ²) lie between 1 and 1.5, indicating a satisfactory refinement quality. The goodness of fit (χ²) is calculated as the ratio of the weighted profile R-factor (R wp ) to the expected R-factor (R exp ). A small R exp , typically observed when data collection is overextended, results in a χ² greater than 1. Conversely, if data collection is too rapid, R exp is large and values ofχ² are almost 1. Deviations in χ² values can also stem from miscalculation of counts in the data. The final R wp obtained from a structure-free refinement serves as a reliable indicator of the best achievable profile fit, and the R wp in the Rietveld refinement should converge to this value. The Rietveld refined parameters, including χ², R wp , R exp , R B , R F , crystallite size (D), lattice constant (a), and unit cell volume (V), are summarized in Table 2 . The observed R-factor values were relatively high, likely due to the nanocrystalline nature of the samples, which may contribute to a higher signal-to-noise ratio. The average crystallite size (D), determined using Scherrer’s equation, was found to be approximately 50 nm. The lattice constant values exhibited a slight decrease from 8.3862 Å to 8.3835 Å with increasing chromium concentration ( Table 2 ) . This reduction in lattice parameter can be attributed to the smaller ionic radius of Cr³⁺ (0.68 Å) relative to that of Fe³⁺ (0.73 Å) [ 34 , 35 ]. Table 1 Position coordinates and occupancies of different atoms of CoCr x Fe 2−x O 4 (0.0 ≤ x ≥ 2.0) system Lattice sites Atoms Position coordinate Occupancy x y z x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 Tetrahedral A-site Fe (tet) 0.125 0.125 0.125 0.721 0.847 0.696 0.698 0.705 Co (tet) 0.125 0.125 0.125 0.105 0.125 0.193 0.147 0.152 Octahedral B-site Fe (oct) 0.500 0.500 0.500 1.279 1.353 1.404 1.452 1.430 Co (oct) 0.500 0.500 0.500 0.895 0.875 0.807 0.853 0.865 Cr (oct) 0.500 0.500 0.500 0.000 0.300 0.900 1.350 1.864 Table 2 Rietveld refinement factors CoCr x Fe 2−x O 4 (0.0 ≤ x ≥ 2.0) system Reitveld refinement factors CoCr x Fe 2−x O 4 (0.0 ≤ x ≥ 2.0) x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 χ 2 1.06 1.02 1.06 1.10 1.12 R B (%) 4.43 3.56 4.76 5.34 5.33 R F (%) 5.41 4.72 4.97 6.02 6.42 R wp 27.6 27.4 29.8 30.3 28.3 R exp 28.3 27.3 22.4 28.8 28.4 D (nm) 47 54 49 55 48 a (Å) 8.3862 8.3851 8.3848 8.3841 8.3835 V (Å 3 ) 590 590 588 590 589 Oxygen position (x = y = z) 0.2626 0.2622 0.2676 0.2619 0.2674 The XRD profiles demonstrated an increase in the intensity of diffraction peaks with the increasing chromium content (x), which is likely due to the improved uniformity of ion distribution within the spinel cubic lattice. The TEM image of a typical CoFe₂O₄ sample, presented in Fig. 2 , reveals that the ferrite grains are within the nanometre size range, confirming the nanocrystalline nature of the material. The average grain size is approximately 40 nm, with the particles exhibiting a predominantly spherical morphology and a narrow size distribution. Notably, the CoFe₂O₄ samples also display complex particle shapes, with some nanoparticles adopting a cube-like form. 3.2 Field emission scanning electron microscope (FESEM) and EDS studies Figure 2 . presents the FESEM images (a-e) of CoFe 2 − x Cr x O 4 samples with varying chromium concentrations (x = 0.0, 0.5, 1.0, 1.5 and 2.0). The micrographs reveal non-uniformly sized crystal grains that are randomly distributed and exhibit slight agglomeration. The grains display irregular shapes with a tendency toward spherical morphology. Grain sizes, determined using Image software, align closely with the crystallite sizes calculated from XRD, ranging from 41.50 nm to 52.25 nm. However, no consistent pattern in grain size or morphology is observed with increasing dopant concentration, indicating a non-uniform variation in grain characteristics with chromium doping levels [ 36 ]. The FESEM images reveal the porosity and grain boundaries, key microstructural characteristics that significantly affect the electrical, magnetic, and other intrinsic physical features of these nanomaterials [ 37 ]. Porosity calculations, based on XRD analysis, indicate a reduction in porosity with increasing dopant concentration [ 38 ]. Porosity has a considerable influence on determining the physical properties of materials, and its effects vary depending on the material type, pore distribution, pore size, and the intended application [ 39 ]. For instance, in materials intended for electrical applications, the inclusion of air gaps or other non-conductive phases within the pores can result in decreased electrical conductivity [ 40 ]. The elemental composition of CoCrFeO 4 was examined through Energy Dispersive X-ray Spectroscopy (EDX), as depicted in Fig. 3 . The experimentally determined metal concentrations were found to exhibit excellent agreement with the theoretical stoichiometric values, as summarized in Table 3 [ 31 ]. This consistency indicates that the synthesized compounds maintain their stoichiometric integrity even after thermal treatment at 700°C, confirming the robustness of the synthesis process. Table 3 Theoretical and observed parameters of prepared CoCr x Fe 2−x O 4 samples Composition (x) Theoretical mass % Observed mass % Co Fe Cr Co Fe Cr 0.0 25.11 62.10 - 25.34 61.86 - 0.5 25.21 46.57 14.77 24.89 45.87 13.98 1.0 25.62 31.05 29.54 24.84 29.84 28.79 1.5 25.12 15.53 44.31 25.23 15.11 43.67 2.0 26.25 - 59.08 25.08 - 58.69 Table 4 Saturation magnetization (Ms), Coercivity (Hc), Remanent magnetization (Mr) and Magnetic momentum for CoCr x Fe 2−x O 4 samples Composition (x) Saturation magnetization (Ms) emu/g Coercivity (Hc) Oe Remanent magnetization (Mr) emu/g Magnetic momentum µB (B.M.) 0.0 41.74 1303.8 22.87 1.72 0.5 24.20 199.25 7.22 0.98 1.0 19.69 131.80 3.99 0.82 1.5 7.50 504.45 1.007 0.52 2.0 1.37 436.47 1.412 0.12 3.3 High-resolution transmission electron microscope (HRTEM) studies The HRTEM analysis was conducted to elucidate the morphological and structural characteristics of the synthesized CoCr x Fe 2−x O 4 samples. HRTEM imaging, as illustrated in Fig. 4 . (a) and (b), revealed distinct crystalline domains with well-defined lattice fringes, enabling precise structural characterization at the nanoscale level. Quantitative analysis of particle dimensions indicated a diameter range between 37–54 nm with a relatively narrow size distribution, demonstrating excellent control over the synthesis parameters. The observed morphology exhibited predominantly polygonal crystallites with a quasi-random spatial distribution throughout the samples.The HRTEM findings were corroborated with X-ray Diffraction (XRD) data, demonstrating excellent agreement in terms of crystalline sizes and phase purity.These results highlight the effectiveness of HRTEM as a robust tool for characterizing the nanoscale structures of Co₀.₇Cu₀.₃Fe₂-ₓCrₓO₄ synthesized materials. 4. Magnetic properties Figure 5 illustrates the change in saturation magnetization ( Ms ) as a function of chromium content. The saturation magnetization decreases from 41.74 to 1.37 emu/g, accompanied by a reduction in the magnetic moment from 1.72 to 0.21 µB ​. This behaviour confirms the ferromagnetic nature of all the studied compositions. In spinel ferrites, the inter-sublattice exchange interaction (J AB ​) between A and B sites is stronger than the intra-sublattice interaction (J BB ​) between B-site ions. The compound CoFe₂O₄, exhibiting an Inverse spinel-type arrangement [Fe 3+ (Co 2+ Fe 3+ )O 4 ] is characterized by dominant J AB ​ interactions over J BB ​. The observed decrease in saturation magnetization and magnetic moment with increasing Cr content (x) is attributed to the substitution of Fe³⁺ ions (magnetic moment 5µB​) with Cr³⁺ ions, which possess a significantly lower magnetic moment (3µB). High concentration of Cr 3+ ions (x > 1.5), A-B interaction becomes weak while B-B interaction get strengthened to result decrease in magnetism. The high value of Hc is may be due to presence of magnetic anisotropy and reduction in particle size in nanoscale with Cr content. The non-linear trend can be described by Neel’s theory of ferrimagnetism. 5. Dielectric Study 5.1 Dielectric permittivity (ε') and Dielectric loss (tan δ) The variation of the dielectric constant (εʹ) as a function of frequency is presented in Fig. 6 . (a) and (b). A systematic increase in εʹ is noted with the gradual incorporation of Ce³⁺ ions in CoCr x Fe 2−x O 4 .The dielectric behaviour in ferrites is primarily influenced by both structural and microstructural factors. The incorporation of Ce³⁺ ions in place of Fe³⁺ ions lead to the partial reduction of Fe³⁺ to Fe²⁺ in order to maintain charge neutrality. This substitution facilitates enhanced electron hopping between Fe³⁺ and Fe²⁺ ions, resulting in reduced grain resistance. The increased electron mobility promotes the accumulation of charges at grain boundaries, thereby enhancing polarization and, consequently, the dielectric constant. At lower frequencies, the dielectric constant is significantly higher, as polarization mechanisms, such as electronic hopping and interfacial polarization, are more effective. However, with increasing frequency, these mechanisms are unable to respond to the rapid alternating field, leading to a decline in polarization. Beyond a critical frequency, εʹ attains a nearly constant value, indicating the saturation of polarization effects at higher frequencies. The inability of Fe²⁺↔ Fe³⁺ electron exchange to keep pace with the alternating electric field beyond a certain frequency threshold is well-documented [ 41 ]. The observed behaviour of εʹ can be attributed to space charge polarization, which arises due to the inhomogeneous dielectric structure of the material. This phenomenon is effectively described by the Maxwell-Wagner two-layer model [ 42 , 43 ], which considers the material to be composed of numerous well-conducting grains separated by thin, poorly conducting grain boundaries. The polarization in ferrites is predominantly influenced by the electronic exchange between Fe² and Fe³⁺ions. This exchange is governed by the localized movement of electrons under the influence of the external electric field, contributing to the overall polarization of the system. The interplay between these conducting grains and insulating boundaries plays a critical role in determining the dielectric properties of the material. The dependence of dielectric dissipation factor (tan δ) and dielectric loss (ε″) on frequency as represented in Fig. 6 (b). The values of tan δ and ε″ are influenced by various factors, including stoichiometry, Fe²⁺ content, and structural homogeneity, all of which depend on the composition and sintering temperature of the samples [ 44 ].The initial decrease in tan δ with increasing frequency can be explained using Koop’s phenomenological model [ 40 ]. As shown in Fig. 6 (b), the tan δ and ε″ versus log(f) plots for samples with x > 0.05 display anomalous dielectric behavior, marked by a distinct peak at a specific frequency. This phenomenon is more prominent in the present system than in those described previously. The frequency ( f max ) corresponding to the maxima in tan δ and ε″ corresponding to each composition can be clearly determined from Fig. 6 (b). The criteria for observing such maxima in tan δ and ε″ in dielectric materials are well established [ 45 ]. $$\:\omega\:\tau\:=1$$ 1 The relationship between the angular frequency ( \(\:\omega\:\) ) and the frequency at maximum dielectric loss \(\:({f}_{max}\) ) is given by \(\:\omega\:=2{f}_{max}\) and τ represents the relaxation time. The relaxation time is directly related to the hopping probability ( p ) per unit time and can be expressed as τ = 1/2 p or equivalently, \(\:{f}_{max}\) ​∝ p . A peak in dielectric loss occurs when the hopping frequency of electrons between Fe²⁺ and Fe³⁺ ions at neighboring B-sites matches the frequency of the applied alternating current (AC) field. This effect, known as ferromagnetic resonance, highlights the dynamic equilibrium between electron hopping and the external field frequency [ 44 ]. 5.2 AC conductivity (σ AC ) with frequency This study aims to identify the type of polaron and the underlying conduction mechanism in the samples. The electron conduction mechanism in ferrites has been previously explained by Austin and Mott [ 46 ] using the electron and polaron hopping model. Figure 7 illustrates the variation of AC conductivity (σ AC ​) on frequency and composition at room temperature. It is evident that σ AC ​ rises steadily with increasing frequency. This trend can be explained by the increased hopping of charge carriers at higher frequencies, consistent with Koops' model [ 47 ]. At low frequencies, conduction primarily occurs via grain boundary structures, whereas at higher frequencies, it is dominated by the conducting grains. In these samples, the high density of interfacial states in the nanoscale system serves as charge carriers through ionization, facilitating charge transport and enhancing conductivity. Consequently, the AC conductivity in these nanosystems is significantly higher compared to bulk materials, as noted in previous studies [ 48 ]. The observed increase in σ AC ​ ​ with frequency is consistent with the small polaron conduction mechanism, as described by Alder and Feinleib [ 49 ]. In conclusion, the conduction in all samples is predominantly governed by small polaron hopping. 5.3 Complex impedance at room temperature with frequency To investigate the relaxation phenomena, a complex impedance analysis was conducted across a varying frequency range, as illustrated in Fig. 8 . These impedance plots provide insights into the contributions from grains, grain boundaries, and other microstructural features of the material.The data are represented as Nyquist plots, showing the imaginary part of impedance (Z′′) against the real part of impedance (Z′) over a frequency range of 20 Hz to 1 MHz. The real (Z′) and imaginary (Z′′) components of the complex impedance were calculated using the following expressions: Z’ = Rg / (1 + Rg 2 ω 2 Cg 2 ) 2 Z'' = Rg 2 ω Cg / (1 + Rg 2 ω 2 Cg 2 ) 3 where, ω denotes the angular frequency, Rg is resistance and Cg is capacitance. The Z′ versus Z′′ plots exhibit a single semi-circular arc for all samples, indicating that the electrical conduction is predominantly governed by the bulk grains interior. This observation suggests that the dominant conduction mechanism in the samples originates from grain boundary contributions. 6. Conclusion Cr³⁺-doped Co–Fe ferrite nanoparticles were successfully prepared via the citrate–gel auto-combustion method. Rietveld refinement of the XRD data confirmed that the samples possessed a cubic spinel structure with a single-phase composition. SEM and TEM analyses verified the nanoscale dimensions of the synthesized particles, consistent with the XRD findings. FTIR spectra further supported the presence of the cubic spinel structure in ferrites that were sintered at 700°C for 6 hours. The addition of Cr³⁺ ions to the Co-Fe lattice led to an increase in the variation of Debye temperature between 688 K and 706 K, indicating improved structural rigidity. Magnetic characterization showed a reduction in saturation magnetization (Ms) with increasing chromium content. This reduction in ( Ms )​ is attributed to the replacement of Fe³⁺ ions by Cr³⁺ ions, which weakens the sublattice interactions and reduces the magnetic moment associated with the unit cell. Despite the decrease in magnetization, all compositions exhibited ferrimagnetic behaviour. Additionally, the introduction of Cr³⁺ ions enhanced the dielectric properties of the samples, further broadening their applicability in multifunctional devices. Declarations 9. Conflict of Interest There are no conflicts of interest to declare. 8. Funding This work was funded by the University Grants Commission (UGC), New Delhi, under the Rajiv Gandhi National Fellowship (RGNF) Scheme (No. F. 14 − 2(SC)/2010 (SA-III)). Author Contribution Dr. R. S. Pandav and Dr. U. B. Sankapal carried out an investigation and formal analysis, data curation, and original draft writing, Dr. S. S. Pujari and Amit A. Bagade provided resources and formal analysis. Dr. Vashishtha M. Gurme carried out modification, creation, and presentation and visualization of the manuscript. Dr. R. S. Pandav carried out funding acquisition, administration, supervision, manuscript editing. All persons made substantial contributions to the work reported in the manuscript. 7. Acknowledgement The authors sincerely acknowledge the University Grants Commission (UGC), New Delhi, for its support and encouragement throughout this work. References V.D. More, R.B. Borade, K.R. Desai, V.K. Barote, S.S. Kadam, V.S. Shinde, D.R. Kulkarni, R.H. 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09:21:37","extension":"html","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":149239,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/aba6a9e948f20ba21eaa1aff.html"},{"id":97667729,"identity":"44714bb5-7317-44c4-bb87-9a27a768bee2","added_by":"auto","created_at":"2025-12-08 09:24:11","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":478155,"visible":true,"origin":"","legend":"\u003cp\u003eRietveld refined X-ray diffraction patterns of CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2-x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e, (a) x = 0.0, (b) x = 0.5, (c) x = 1.0, (d) x = 1.5, (e), x = 2.0.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/b11f160fd983a8114d3c942c.png"},{"id":97417887,"identity":"586b9e65-e0c8-4442-a060-fbdd4fa5c89d","added_by":"auto","created_at":"2025-12-04 07:42:27","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":833191,"visible":true,"origin":"","legend":"\u003cp\u003eFE-SEM images of CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2-x\u003c/sub\u003eO\u003csub\u003e4 \u003c/sub\u003espinels: (a) x = 0.0, (b) x = 0.5, (c) x = 1.0, (d) x = 1.5, (e), x = 2.0 at X30000 magnification.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/fa0d45e6ff3f4e249d6a52da.png"},{"id":97417858,"identity":"801d2ce5-8781-4358-aef9-cd155ac76014","added_by":"auto","created_at":"2025-12-04 07:42:25","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":36380,"visible":true,"origin":"","legend":"\u003cp\u003eEnergy dispersive X-ray spectra of CoFeCrO\u003csub\u003e4\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/cda5d2de9f1767b7e27bd420.png"},{"id":97417859,"identity":"95384729-bdb4-4c63-baa1-3fd1e6adc295","added_by":"auto","created_at":"2025-12-04 07:42:25","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":144029,"visible":true,"origin":"","legend":"\u003cp\u003eHRTEM images of CoFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/6ef02b6531f303f97aef5693.png"},{"id":97417865,"identity":"1231bb1c-769c-49c3-958c-e2e95af5ce3d","added_by":"auto","created_at":"2025-12-04 07:42:25","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":98454,"visible":true,"origin":"","legend":"\u003cp\u003eVSM loops for CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2-x\u003c/sub\u003eO\u003csub\u003e4 \u003c/sub\u003espinels .\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/1bebb078dfc1349f337a6a25.png"},{"id":97667234,"identity":"2d4db3ef-f481-4424-a65f-e4720e29bebc","added_by":"auto","created_at":"2025-12-08 09:23:05","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":207910,"visible":true,"origin":"","legend":"\u003cp\u003eSaturation magnetization of various composition of CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2-x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003espinels.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/c411f0e1be781e40b6845d15.png"},{"id":97417879,"identity":"9d2604d2-7f22-4ff0-8835-af774afcb44a","added_by":"auto","created_at":"2025-12-04 07:42:25","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":108427,"visible":true,"origin":"","legend":"\u003cp\u003e(a) variation of dielectric permittivity (εʹ) vs. frequency, (b) variation of dielectric loss tangent with frequency for CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2-x\u003c/sub\u003eO\u003csub\u003e4\u0026nbsp;\u0026nbsp; \u003c/sub\u003esamples.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/14a232aacae9c19f6e8c38dd.png"},{"id":97666104,"identity":"8b9097c7-7c36-4fd9-9332-123a6953edfd","added_by":"auto","created_at":"2025-12-08 09:20:27","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":117060,"visible":true,"origin":"","legend":"\u003cp\u003eVariation in a. c. conductivity with frequency for CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2-x\u003c/sub\u003eO\u003csub\u003e4 \u003c/sub\u003esamples.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/81974c52506ff664bead7a75.png"},{"id":97417866,"identity":"3ad13c86-0220-47f1-8231-aed07b9377d3","added_by":"auto","created_at":"2025-12-04 07:42:25","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":121544,"visible":true,"origin":"","legend":"\u003cp\u003eNyquist plots for CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2-x\u003c/sub\u003eO\u003csub\u003e4 \u003c/sub\u003esamples.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/3563002ca7f2eb70c20cf054.png"},{"id":103765730,"identity":"b98e3b5e-3ee4-4972-b299-8c7bd03c39e2","added_by":"auto","created_at":"2026-03-02 16:08:22","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3132138,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7994297/v1/1ebd166a-4ae4-40fc-988a-f503b1bd5ff0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Magnetic Order and Electronic Transport behaviour in Tailored made Nanostructural Co- Cr Ferrospinels","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn the realm of modern technological innovations and biomedical engineering, AB₂O₄-type spinel ferrites have attracted considerable scholarly interest due to their economic viability and cost efficiency, thereby rendering them exceptionally appropriate for applications in electrical and magnetic sensing [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Among various ferrites, cobalt ferrite (CoFe₂O₄) has become one of the most extensively studied materials. This interest arises from its ability to form numerous solid solutions when doped with transition or rare-earth elements, allowing for the fine adjustment of its physical properties. Investigating how dopants or substituents influence the magnetic and electrical characteristics of the Co-Fe system provides valuable insight into the underlying physical mechanisms [\u003cspan additionalcitationids=\"CR8 CR9 CR10 CR11 CR12 CR13\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Several studies have examined the substitution of different divalent and trivalent cations in CoFe₂O₄ and their effects on the material\u0026rsquo;s structural, magnetic, and dielectric behavior [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Replacing Co\u0026sup2;⁺ ions with Bi\u0026sup3;⁺, Al\u0026sup3;⁺, Mn\u0026sup2;⁺, Ni\u0026sup2;⁺, or Zn\u0026sup2;⁺ has been shown to improve both magnetic and dielectric performance [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. In contrast, the incorporation of Cr\u0026sup3;⁺ as a substituent result in a noticeable reduction in saturation magnetization and coercivity, highlighting the significant impact of specific cationic substitutions on the material's properties [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Furthermore, Cr\u0026sup3;⁺ substitution significantly influences the dielectric properties of CoFe₂O₄, as evidenced by previous studies [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Cr\u0026sup3;⁺ substitution at Co\u0026sup2;⁺ sites have been shown to affect both the magnetic and dielectric properties of CoFe₂O₄ [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Impedance spectroscopy is often used to analyze the AC electrical properties of ferrites, providing essential information about charge transport and conduction mechanisms [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. The substitution of divalent or trivalent cations at either the A-site or B-site within the spinel lattice can effectively modify these electrical characteristics [\u003cspan additionalcitationids=\"CR22 CR23 CR24\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Many researchers have further studied how factors such as frequency, temperature, and cationic composition affect the overall magnetic and dielectric behavior of CoFe₂O₄, leading to a better understanding of its complex properties [\u003cspan additionalcitationids=\"CR22 CR23 CR24\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe crystallographic configuration of CoFe\u003csub\u003e2\u003c/sub\u003e​O\u003csub\u003e4​\u003c/sub\u003e exhibits an inverse spinel structure in its bulk phase; however, a dimensional reduction to nanoscale induces a transformation towards partial inversion spinel architecture, attributed to the redistribution of cationic species within the crystallographic framework [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. In its bulk configuration, COFE exhibits a magnetic structure characterized by two antiferromagnetically coupled sublattices, demonstrating distinct magnetic moment orientations in opposing directions [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. In the spinel AB₂O₄ structure, the tetrahedral (A) sites are occupied by Fe\u0026sup3;⁺ ions (3d⁵, M\u0026thinsp;=\u0026thinsp;5 \u0026micro;B) that are ferromagnetically aligned, forming one sub-lattice. The second sub-lattice consists of Co\u0026sup2;⁺ (3d⁸, M\u0026thinsp;=\u0026thinsp;5 \u0026micro;B) and Fe\u0026sup3;⁺ (3d⁵, M\u0026thinsp;=\u0026thinsp;5 \u0026micro;B) ions positioned at the octahedral (B) sites, also showing ferromagnetic ordering. The interaction between these two sub-lattices results in a net saturation magnetization of approximately 3 \u0026micro;B per formula unit [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Variations in the distribution of cations between tetrahedral (A) and octahedral (B) sites significantly influence the spin alignment, thereby profoundly affecting the magnetic and electrical properties of cobalt ferrite. The introduction of dopants at specific lattice sites induces changes in the magnetic moment and regulates particle growth, which in turn alters the cation distribution. These modifications ultimately govern the material's overall physical and functional behaviour.\u003c/p\u003e\u003cp\u003eThe dielectric properties of ferrites hold significant importance, not only for their wide range of practical applications as well as from a fundamental research standpoint. The dielectric behaviour observed in polycrystalline ferrite materials arises primarily due to the combined contributions of interfacial polarization and hopping conduction polarization mechanisms. Tiwari et al. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] investigated the temperature-dependent dielectric permittivity of a Ba₀.₅Sr₀.₅Nb₂O₆/CoCr₀.₄Fe₁.₆O₄ multiferroic composite, which exhibited characteristics of a relax or ferroelectric. Panda et al. [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] conducted comprehensive investigations into the dielectric behavior of bulk CoFe₂O₄, elucidating both frequency and temperature dependencies, wherein distinct contributions from grain boundaries and intragranular regions were identified, along with the determination of characteristic relaxation frequencies Lahouli et al. [05] systematically investigated the variation of dielectric permittivity with frequency in Ni-Zn-Al ferrite systems, analyzing the correlations between frequency modulation and dielectric response characteristics. Kumar et al. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] conducted systematic investigations on the frequency-dependent dielectric characteristics of Ni-substituted cobalt ferrite systems. Recent thermal analyses of dielectric properties have revealed critical insights into para-ferroelectric phase transitions and elucidated the fundamental nature of ferroelectric behaviour in these materials. Sekulicet. al. studied the dielectric behavior of MFe₂O₄ (where M\u0026thinsp;=\u0026thinsp;Mn, Ni, Zn) ferrites, analysing their dependence on both frequency and temperature [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe influence of Cr-ion doping on Co\u0026ndash;Fe spinel ferrites was systematically investigated with respect to their morphological, structural, dielectric, and magnetic properties. Structural characterization was carried out using XRD and EDS. Morphological features were analysed through SEM and TEM. Magnetic behaviour was studied, while microwave absorption properties were evaluated to assess the impact of incremental Cr-ion substitution (CoFe\u003csub\u003e2\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e, x\u0026thinsp;=\u0026thinsp;0.0, 0.5, 1.0, 1.5, and 2.0) within the Co-Fe ferrite lattice.\u003c/p\u003e"},{"header":"2. Experimental section","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Chemicals\u003c/h2\u003e\u003cp\u003eAll reagents utilized in the present work were of Analytical Reagent (AR) grade, ensuring exceptional purity and suitability for the experimental objectives, thereby eliminating the need for further purification.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Synthesis of CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2\u0026minus;x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e spinels\u003c/h2\u003e\u003cp\u003eNanoparticles ferrite with chemical formula CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2\u0026minus;x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e (x\u0026thinsp;=\u0026thinsp;0.0, 0.5, 1.0, 1.5, and 2.0) were prepared in air through the citrate\u0026ndash;gel auto-combustion technique [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. In precise stoichiometric proportions of ferric nitrate Fe(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e.9H\u003csub\u003e2\u003c/sub\u003eO, cobalt nitrate Co(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e2\u003c/sub\u003e.6H\u003csub\u003e2\u003c/sub\u003eO, chromium nitrate (Cr(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e.9H\u003csub\u003e2\u003c/sub\u003eO) and citric acid (C₆H₈O₇) in a 1:1 mole ratio was accurately measured and dissolved separately in a minimal volume using deionized water to obtain a homogeneous solution. Precursor mixture was gradually evaporated to dryness, resulting in a soft, porous mass. The dried precursors were then sintered in air at 700\u0026deg;C for 6 hours.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Material characterizations\u003c/h2\u003e\u003cp\u003eThe crystallographic analysis of the powder sample was conducted using X-ray diffraction (XRD) measurements on a Rigaku Miniflex-600 diffractometer, which was equipped with Cuα1 radiation (λ\u0026thinsp;=\u0026thinsp;0.15406 nm) and operated at 40 kV with a scan rate of 2\u0026deg; per minute. Surface morphological investigations were carried out using field emission scanning electron microscopy (FE-SEM) on a JEOL JSM-6500F instrument. The elemental composition was determined through energy dispersive spectroscopy (EDS) with an Oxford X-max detector. The magnetic properties of the synthesized samples were assessed at room temperature using a Vibrating Sample Magnetometer (EZ VSM model).\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e3.1 X-ray diffraction studies\u003c/h2\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e displays the XRD profiles of sintered samples with diverse compositions, accompanied by the Rietveld refinement outcomes. All observed diffraction peaks correspond well with JCPDS No. 22-1086, confirming the formation of a pure, single-phase spinel ferrite structure. The Bragg peak positions are indicated by vertical lines. The black open circles indicate the detected intensity. The red solid line indicates the Rietveld-calculated intensity. The lower blue line shows the difference between the observation and the calculation. The major diffraction peaks are associated with the (220), (311), (222), (400), (422), (511), (440), and (533) planes. These peaks confirm the cubic spinel structure. During Rietveld refinement, the oxygen positions were treated as free parameters, whereas atomic fractional positions were kept constant. Other parameters, including lattice constants, temperature factors, occupancies, scale factors, and shape factors, were treated as free parameters. The XRD data for all samples were refined using the Fd\u003csup\u003e3\u003c/sup\u003em space group, with the background corrected using the Pseudo-Voigt peak function. The position coordinates and refined occupancies of various atoms are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The refined crystal parameters and atomic positions are also provided in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The refined patterns show that the values of thegoodness of fit (χ\u0026sup2;) lie between 1 and 1.5, indicating a satisfactory refinement quality. The goodness of fit (χ\u0026sup2;) is calculated as the ratio of the weighted profile R-factor (R\u003csub\u003ewp\u003c/sub\u003e) to the expected R-factor (R\u003csub\u003eexp\u003c/sub\u003e). A small R\u003csub\u003eexp\u003c/sub\u003e, typically observed when data collection is overextended, results in a χ\u0026sup2; greater than 1. Conversely, if data collection is too rapid, R\u003csub\u003eexp\u003c/sub\u003e is large and values ofχ\u0026sup2; are almost 1. Deviations in χ\u0026sup2; values can also stem from miscalculation of counts in the data. The final R\u003csub\u003ewp\u003c/sub\u003e obtained from a structure-free refinement serves as a reliable indicator of the best achievable profile fit, and the R\u003csub\u003ewp\u003c/sub\u003e in the Rietveld refinement should converge to this value. The Rietveld refined parameters, including χ\u0026sup2;, R\u003csub\u003ewp\u003c/sub\u003e, R\u003csub\u003eexp\u003c/sub\u003e, R\u003csub\u003eB\u003c/sub\u003e, R\u003csub\u003eF\u003c/sub\u003e, crystallite size (D), lattice constant (a), and unit cell volume (V), are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The observed R-factor values were relatively high, likely due to the nanocrystalline nature of the samples, which may contribute to a higher signal-to-noise ratio. The average crystallite size (D), determined using Scherrer\u0026rsquo;s equation, was found to be approximately 50 nm. The lattice constant values exhibited a slight decrease from 8.3862 \u0026Aring; to 8.3835 \u0026Aring; with increasing chromium concentration \u003cb\u003e(\u003c/b\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e. This reduction in lattice parameter can be attributed to the smaller ionic radius of Cr\u0026sup3;⁺ (0.68 \u0026Aring;) relative to that of Fe\u0026sup3;⁺ (0.73 \u0026Aring;) [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePosition coordinates and occupancies of different atoms of CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2\u0026minus;x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e (0.0\u0026thinsp;\u0026le;\u0026thinsp;x\u0026thinsp;\u0026ge;\u0026thinsp;2.0) system\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"10\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eLattice sites\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eAtoms\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003ePosition coordinate\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"5\" nameend=\"c10\" namest=\"c6\"\u003e\u003cp\u003eOccupancy\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ex\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003ey\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003ez\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003ex\u0026thinsp;=\u0026thinsp;0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003ex\u0026thinsp;=\u0026thinsp;0.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003ex\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003ex\u0026thinsp;=\u0026thinsp;1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003ex\u0026thinsp;=\u0026thinsp;2.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eTetrahedral A-site\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFe (tet)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.721\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.847\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.696\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.698\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.705\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCo (tet)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.105\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.193\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.147\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.152\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003eOctahedral B-site\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFe (oct)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.279\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.353\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.404\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.452\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.430\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCo (oct)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.895\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.875\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.807\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.853\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.865\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCr (oct)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.300\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.900\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.350\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.864\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eRietveld refinement factors CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2\u0026minus;x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e (0.0\u0026thinsp;\u0026le;\u0026thinsp;x\u0026thinsp;\u0026ge;\u0026thinsp;2.0) system\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eReitveld refinement factors\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003eCoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2\u0026minus;x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e (0.0\u0026thinsp;\u0026le;\u0026thinsp;x\u0026thinsp;\u0026ge;\u0026thinsp;2.0)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ex\u0026thinsp;=\u0026thinsp;0.0\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ex\u0026thinsp;=\u0026thinsp;0.5\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003ex\u0026thinsp;=\u0026thinsp;1.0\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003ex\u0026thinsp;=\u0026thinsp;1.5\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003ex\u0026thinsp;=\u0026thinsp;2.0\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eχ\u003c/b\u003e\u003csup\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1.12\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eR\u003c/b\u003e\u003csub\u003e\u003cb\u003eB\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(%)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4.43\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e5.34\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e5.33\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eR\u003c/b\u003e\u003csub\u003e\u003cb\u003eF\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(%)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e5.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e6.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e6.42\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eR\u003c/b\u003e\u003csub\u003e\u003cb\u003ewp\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e27.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e27.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e29.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e30.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e28.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eR\u003c/b\u003e\u003csub\u003e\u003cb\u003eexp\u003c/b\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e28.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e27.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e22.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e28.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e28.4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eD\u003c/b\u003e \u003cb\u003e(nm)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e48\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003ea\u003c/b\u003e \u003cb\u003e(\u0026Aring;)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8.3862\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e8.3851\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e8.3848\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e8.3841\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e8.3835\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eV\u003c/b\u003e \u003cb\u003e(\u0026Aring;\u003c/b\u003e\u003csup\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sup\u003e\u003cb\u003e)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e590\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e590\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e588\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e590\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e589\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eOxygen position (x\u0026thinsp;=\u0026thinsp;y\u0026thinsp;=\u0026thinsp;z)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.2626\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.2622\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2676\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.2619\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.2674\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe XRD profiles demonstrated an increase in the intensity of diffraction peaks with the increasing chromium content (x), which is likely due to the improved uniformity of ion distribution within the spinel cubic lattice. The TEM image of a typical CoFe₂O₄ sample, presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e2\u003c/span\u003e, reveals that the ferrite grains are within the nanometre size range, confirming the nanocrystalline nature of the material. The average grain size is approximately 40 nm, with the particles exhibiting a predominantly spherical morphology and a narrow size distribution. Notably, the CoFe₂O₄ samples also display complex particle shapes, with some nanoparticles adopting a cube-like form.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Field emission scanning electron microscope (FESEM) and EDS studies\u003c/h2\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e2\u003c/span\u003e. presents the FESEM images (a-e) of CoFe\u003csub\u003e2\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eCr\u003csub\u003ex\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e samples with varying chromium concentrations (x\u0026thinsp;=\u0026thinsp;0.0, 0.5, 1.0, 1.5 and 2.0). The micrographs reveal non-uniformly sized crystal grains that are randomly distributed and exhibit slight agglomeration. The grains display irregular shapes with a tendency toward spherical morphology. Grain sizes, determined using Image software, align closely with the crystallite sizes calculated from XRD, ranging from 41.50 nm to 52.25 nm. However, no consistent pattern in grain size or morphology is observed with increasing dopant concentration, indicating a non-uniform variation in grain characteristics with chromium doping levels [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. The FESEM images reveal the porosity and grain boundaries, key microstructural characteristics that significantly affect the electrical, magnetic, and other intrinsic physical features of these nanomaterials [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Porosity calculations, based on XRD analysis, indicate a reduction in porosity with increasing dopant concentration [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Porosity has a considerable influence on determining the physical properties of materials, and its effects vary depending on the material type, pore distribution, pore size, and the intended application [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. For instance, in materials intended for electrical applications, the inclusion of air gaps or other non-conductive phases within the pores can result in decreased electrical conductivity [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe elemental composition of CoCrFeO\u003csub\u003e4\u003c/sub\u003e was examined through Energy Dispersive X-ray Spectroscopy (EDX), as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The experimentally determined metal concentrations were found to exhibit excellent agreement with the theoretical stoichiometric values, as summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. This consistency indicates that the synthesized compounds maintain their stoichiometric integrity even after thermal treatment at 700\u0026deg;C, confirming the robustness of the synthesis process.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eTheoretical and observed parameters of prepared CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2\u0026minus;x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e samples\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eComposition\u003c/p\u003e\u003cp\u003e(x)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003eTheoretical mass %\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e\u003cp\u003eObserved mass %\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFe\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eCr\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eCo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eFe\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eCr\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e25.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e62.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e25.34\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e61.86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e-\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e25.21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e46.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e14.77\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e24.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e45.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e13.98\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e25.62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e31.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e29.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e24.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e29.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e28.79\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e25.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e15.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e44.31\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e25.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e15.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e43.67\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e26.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e59.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e25.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e58.69\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSaturation magnetization (Ms), Coercivity (Hc), Remanent magnetization (Mr) and Magnetic momentum for CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2\u0026minus;x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e samples\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eComposition\u003c/p\u003e\u003cp\u003e(x)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSaturation magnetization (Ms) emu/g\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCoercivity (Hc) Oe\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRemanent magnetization (Mr) emu/g\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMagnetic momentum \u0026micro;B (B.M.)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e41.74\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1303.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e22.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.72\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e24.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e199.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e7.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e19.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e131.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.82\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e504.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.007\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.52\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.37\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e436.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.412\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.12\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.3 High-resolution transmission electron microscope (HRTEM) studies\u003c/h2\u003e\u003cp\u003eThe HRTEM analysis was conducted to elucidate the morphological and structural characteristics of the synthesized CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2\u0026minus;x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e samples. HRTEM imaging, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e4\u003c/span\u003e. (a) and (b), revealed distinct crystalline domains with well-defined lattice fringes, enabling precise structural characterization at the nanoscale level. Quantitative analysis of particle dimensions indicated a diameter range between 37\u0026ndash;54 nm with a relatively narrow size distribution, demonstrating excellent control over the synthesis parameters. The observed morphology exhibited predominantly polygonal crystallites with a quasi-random spatial distribution throughout the samples.The HRTEM findings were corroborated with X-ray Diffraction (XRD) data, demonstrating excellent agreement in terms of crystalline sizes and phase purity.These results highlight the effectiveness of HRTEM as a robust tool for characterizing the nanoscale structures of Co₀.₇Cu₀.₃Fe₂-ₓCrₓO₄ synthesized materials.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Magnetic properties","content":"\u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the change in saturation magnetization (\u003cem\u003eMs\u003c/em\u003e) as a function of chromium content. The saturation magnetization decreases from 41.74 to 1.37 emu/g, accompanied by a reduction in the magnetic moment from 1.72 to 0.21\u003cem\u003e\u0026micro;B\u003c/em\u003e​. This behaviour confirms the ferromagnetic nature of all the studied compositions. In spinel ferrites, the inter-sublattice exchange interaction (J\u003csub\u003eAB\u003c/sub\u003e​) between A and B sites is stronger than the intra-sublattice interaction (J\u003csub\u003eBB\u003c/sub\u003e​) between B-site ions. The compound CoFe₂O₄, exhibiting an Inverse spinel-type arrangement [Fe\u003csup\u003e3+\u003c/sup\u003e(Co\u003csup\u003e2+\u003c/sup\u003eFe\u003csup\u003e3+\u003c/sup\u003e)O\u003csub\u003e4\u003c/sub\u003e] is characterized by dominant J\u003csub\u003eAB\u003c/sub\u003e​ interactions over J\u003csub\u003eBB\u003c/sub\u003e​. The observed decrease in saturation magnetization and magnetic moment with increasing Cr content (x) is attributed to the substitution of Fe\u0026sup3;⁺ ions (magnetic moment 5\u0026micro;B​) with Cr\u0026sup3;⁺ ions, which possess a significantly lower magnetic moment (3\u0026micro;B). High concentration of Cr\u003csup\u003e3+\u003c/sup\u003e ions (x\u0026thinsp;\u0026gt;\u0026thinsp;1.5), A-B interaction becomes weak while B-B interaction get strengthened to result decrease in magnetism. The high value of Hc is may be due to presence of magnetic anisotropy and reduction in particle size in nanoscale with Cr content. The non-linear trend can be described by Neel\u0026rsquo;s theory of ferrimagnetism.\u003c/p\u003e"},{"header":"5. Dielectric Study","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e5.1 Dielectric permittivity (ε') and Dielectric loss (tan δ)\u003c/h2\u003e\u003cp\u003eThe variation of the dielectric constant (εʹ) as a function of frequency is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e6\u003c/span\u003e. (a) and (b). A systematic increase in εʹ is noted with the gradual incorporation of Ce\u0026sup3;⁺ ions in CoCr\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e2\u0026minus;x\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e.The dielectric behaviour in ferrites is primarily influenced by both structural and microstructural factors. The incorporation of Ce\u0026sup3;⁺ ions in place of Fe\u0026sup3;⁺ ions lead to the partial reduction of Fe\u0026sup3;⁺ to Fe\u0026sup2;⁺ in order to maintain charge neutrality. This substitution facilitates enhanced electron hopping between Fe\u0026sup3;⁺ and Fe\u0026sup2;⁺ ions, resulting in reduced grain resistance. The increased electron mobility promotes the accumulation of charges at grain boundaries, thereby enhancing polarization and, consequently, the dielectric constant. At lower frequencies, the dielectric constant is significantly higher, as polarization mechanisms, such as electronic hopping and interfacial polarization, are more effective. However, with increasing frequency, these mechanisms are unable to respond to the rapid alternating field, leading to a decline in polarization. Beyond a critical frequency, εʹ attains a nearly constant value, indicating the saturation of polarization effects at higher frequencies. The inability of Fe\u0026sup2;⁺\u0026harr; Fe\u0026sup3;⁺ electron exchange to keep pace with the alternating electric field beyond a certain frequency threshold is well-documented [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. The observed behaviour of εʹ can be attributed to space charge polarization, which arises due to the inhomogeneous dielectric structure of the material. This phenomenon is effectively described by the Maxwell-Wagner two-layer model [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], which considers the material to be composed of numerous well-conducting grains separated by thin, poorly conducting grain boundaries. The polarization in ferrites is predominantly influenced by the electronic exchange between Fe\u0026sup2; and Fe\u0026sup3;⁺ions. This exchange is governed by the localized movement of electrons under the influence of the external electric field, contributing to the overall polarization of the system. The interplay between these conducting grains and insulating boundaries plays a critical role in determining the dielectric properties of the material.\u003c/p\u003e\u003cp\u003eThe dependence of dielectric dissipation factor (tan δ) and dielectric loss (ε\u0026Prime;) on frequency as represented in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e6\u003c/span\u003e (b). The values of tan δ and ε\u0026Prime; are influenced by various factors, including stoichiometry, Fe\u0026sup2;⁺ content, and structural homogeneity, all of which depend on the composition and sintering temperature of the samples [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e].The initial decrease in tan δ with increasing frequency can be explained using Koop\u0026rsquo;s phenomenological model [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b), the tan δ and ε\u0026Prime; versus log(f) plots for samples with x\u0026thinsp;\u0026gt;\u0026thinsp;0.05 display anomalous dielectric behavior, marked by a distinct peak at a specific frequency. This phenomenon is more prominent in the present system than in those described previously. The frequency (\u003cem\u003ef\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e) corresponding to the maxima in tan δ and ε\u0026Prime; corresponding to each composition can be clearly determined from Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b). The criteria for observing such maxima in tan δ and ε\u0026Prime; in dielectric materials are well established [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\omega\\:\\tau\\:=1$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe relationship between the angular frequency (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\omega\\:\\)\u003c/span\u003e\u003c/span\u003e) and the frequency at maximum dielectric loss \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:({f}_{max}\\)\u003c/span\u003e\u003c/span\u003e) is given by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\omega\\:=2{f}_{max}\\)\u003c/span\u003e\u003c/span\u003e and τ represents the relaxation time. The relaxation time is directly related to the hopping probability (\u003cem\u003ep\u003c/em\u003e) per unit time and can be expressed as τ\u0026thinsp;=\u0026thinsp;1/2\u003cem\u003ep\u003c/em\u003e or equivalently, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{max}\\)\u003c/span\u003e\u003c/span\u003e​\u0026prop;\u003cem\u003ep\u003c/em\u003e. A peak in dielectric loss occurs when the hopping frequency of electrons between Fe\u0026sup2;⁺ and Fe\u0026sup3;⁺ ions at neighboring B-sites matches the frequency of the applied alternating current (AC) field. This effect, known as ferromagnetic resonance, highlights the dynamic equilibrium between electron hopping and the external field frequency [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e5.2 AC conductivity (σ\u003csub\u003eAC\u003c/sub\u003e) with frequency\u003c/h2\u003e\u003cp\u003eThis study aims to identify the type of polaron and the underlying conduction mechanism in the samples. The electron conduction mechanism in ferrites has been previously explained by Austin and Mott [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e] using the electron and polaron hopping model. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e7\u003c/span\u003e illustrates the variation of AC conductivity (σ\u003csub\u003eAC\u003c/sub\u003e​) on frequency and composition at room temperature. It is evident that σ\u003csub\u003eAC\u003c/sub\u003e​ rises steadily with increasing frequency. This trend can be explained by the increased hopping of charge carriers at higher frequencies, consistent with Koops' model [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. At low frequencies, conduction primarily occurs via grain boundary structures, whereas at higher frequencies, it is dominated by the conducting grains. In these samples, the high density of interfacial states in the nanoscale system serves as charge carriers through ionization, facilitating charge transport and enhancing conductivity. Consequently, the AC conductivity in these nanosystems is significantly higher compared to bulk materials, as noted in previous studies [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. The observed increase in σ\u003csub\u003eAC\u003c/sub\u003e​ ​ with frequency is consistent with the small polaron conduction mechanism, as described by Alder and Feinleib [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e]. In conclusion, the conduction in all samples is predominantly governed by small polaron hopping.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003e5.3 Complex impedance at room temperature with frequency\u003c/h2\u003e\u003cp\u003eTo investigate the relaxation phenomena, a complex impedance analysis was conducted across a varying frequency range, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e8\u003c/span\u003e. These impedance plots provide insights into the contributions from grains, grain boundaries, and other microstructural features of the material.The data are represented as Nyquist plots, showing the imaginary part of impedance (Z\u0026prime;\u0026prime;) against the real part of impedance (Z\u0026prime;) over a frequency range of 20 Hz to 1 MHz. The real (Z\u0026prime;) and imaginary (Z\u0026prime;\u0026prime;) components of the complex impedance were calculated using the following expressions:\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eZ\u0026rsquo; = Rg / (1\u0026thinsp;+\u0026thinsp;Rg\u003csup\u003e2\u003c/sup\u003eω\u003csup\u003e2\u003c/sup\u003eCg\u003csup\u003e2\u003c/sup\u003e) 2\u003c/p\u003e\u003cp\u003eZ'' = Rg\u003csup\u003e2\u003c/sup\u003e ω Cg / (1\u0026thinsp;+\u0026thinsp;Rg\u003csup\u003e2\u003c/sup\u003eω\u003csup\u003e2\u003c/sup\u003eCg\u003csup\u003e2\u003c/sup\u003e) 3\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere, ω denotes the angular frequency, Rg is resistance and Cg is capacitance. The Z\u0026prime; versus Z\u0026prime;\u0026prime; plots exhibit a single semi-circular arc for all samples, indicating that the electrical conduction is predominantly governed by the bulk grains interior. This observation suggests that the dominant conduction mechanism in the samples originates from grain boundary contributions.\u003c/p\u003e\u003c/div\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eCr\u0026sup3;⁺-doped Co\u0026ndash;Fe ferrite nanoparticles were successfully prepared via the citrate\u0026ndash;gel auto-combustion method. Rietveld refinement of the XRD data confirmed that the samples possessed a cubic spinel structure with a single-phase composition. SEM and TEM analyses verified the nanoscale dimensions of the synthesized particles, consistent with the XRD findings. FTIR spectra further supported the presence of the cubic spinel structure in ferrites that were sintered at 700\u0026deg;C for 6 hours. The addition of Cr\u0026sup3;⁺ ions to the Co-Fe lattice led to an increase in the variation of Debye temperature between 688 K and 706 K, indicating improved structural rigidity. Magnetic characterization showed a reduction in saturation magnetization (Ms) with increasing chromium content. This reduction in (\u003cem\u003eMs\u003c/em\u003e)​ is attributed to the replacement of Fe\u0026sup3;⁺ ions by Cr\u0026sup3;⁺ ions, which weakens the sublattice interactions and reduces the magnetic moment associated with the unit cell. Despite the decrease in magnetization, all compositions exhibited ferrimagnetic behaviour. Additionally, the introduction of Cr\u0026sup3;⁺ ions enhanced the dielectric properties of the samples, further broadening their applicability in multifunctional devices.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003e9. Conflict of Interest\u003c/h2\u003e\u003cp\u003eThere are no conflicts of interest to declare.\u003c/p\u003e\u003ch2\u003e8. Funding\u003c/h2\u003e\u003cp\u003eThis work was funded by the University Grants Commission (UGC), New Delhi, under the Rajiv Gandhi National Fellowship (RGNF) Scheme (No. F. 14\u0026thinsp;\u0026minus;\u0026thinsp;2(SC)/2010 (SA-III)).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eDr. R. S. Pandav and Dr. U. B. Sankapal carried out an investigation and formal analysis, data curation, and original draft writing, Dr. S. S. Pujari and Amit A. Bagade provided resources and formal analysis. Dr. Vashishtha M. Gurme carried out modification, creation, and presentation and visualization of the manuscript. Dr. R. S. Pandav carried out funding acquisition, administration, supervision, manuscript editing. All persons made substantial contributions to the work reported in the manuscript.\u003c/p\u003e\u003ch2\u003e7. Acknowledgement\u003c/h2\u003e\u003cp\u003eThe authors sincerely acknowledge the University Grants Commission (UGC), New Delhi, for its support and encouragement throughout this work.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eV.D. More, R.B. Borade, K.R. Desai, V.K. Barote, S.S. Kadam, V.S. Shinde, D.R. Kulkarni, R.H. Kadam, Site occupancy, surface morphology and mechanical properties of Ce3\u0026thinsp;+\u0026thinsp;added Ni-Mn-Zn ferrite nanocrystals synthesized via sol-gel route. NANO. \u003cb\u003e16\u003c/b\u003e, 2150059 (2021)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eA. Spivakov, C. Lin, E. Lin, Y. Chen, Y. Tseng, Preparation and magnetic properties of cobalt-doped FeMn\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e spinel nano-particles. Nanoscale Res. Lett. \u003cb\u003e16\u003c/b\u003e, 162 (2021)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eH.Q. Alijani, S. Iravani, S. Pourseyedi, M. Torkzadeh-Mahani, M. Barani, M. Khatami, Biosynthesis of spinel nickel ferrite nanowhiskers and their biomedical applications. Sci. Rep. \u003cb\u003e11\u003c/b\u003e(1), 17431 (2021)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eA. Spivakov, C. Lin, E. Lin, Y. Chen, Y. Tseng, Preparation and magnetic properties of cobalt-doped FeMn\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e spinel nanoparticles. Nanoscale Res. Lett. \u003cb\u003e16\u003c/b\u003e, 162 (2021)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eR. Lahouli, J. Massoudi, M. Smari, H. Rahmouni, K. Khirouni, E. Dhahri, L. Bessais, Investigation of annealing effects on the physical properties of Ni\u003csub\u003e0.6\u003c/sub\u003eZn\u003csub\u003e0.4\u003c/sub\u003eFe\u003csub\u003e1.5\u003c/sub\u003eAl\u003csub\u003e0.5\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e ferrite. 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Chavan, L.R. Naik, Chavan, X-ray diffraction studies and dielectric properties of Ni doped Mg ferrites. Vacuum. \u003cb\u003e152\u003c/b\u003e, 47\u0026ndash;49 (2018)\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Rietveld refinement; XRD, Cr-doped, Auto-combustion technique, Ferrites, Dielectric properties","lastPublishedDoi":"10.21203/rs.3.rs-7994297/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7994297/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe unique size-dependent structural and physical properties of Cr\u0026sup3;⁺-doped spinel ferrites, coupled with their wide range of applications, have garnered significant attention from the scientific community. In this work, CoCrₓFe₂₋ₓO₄ (x\u0026thinsp;=\u0026thinsp;0.0, 0.5, 1.0, 1.5, and 2.0) compositions were synthesized using the citrate\u0026ndash;gel auto-combustion method and subsequently sintered at 700\u0026deg;C for 6 hours. XRD analysis demonstrated that all samples crystallized in a pure cubic spinel phase. The lattice parameter was found to decrease slightly with increasing chromium content, ranging from 8.3862 \u0026Aring; to 8.3835 \u0026Aring;. The study of cation arrangement showed that Co\u0026sup2;⁺ ions are chiefly positioned at octahedral (B) sites., while the relatively larger Cr\u0026sup3;⁺ ions substitute for smaller Fe\u0026sup3;⁺ ions at the same sites. FTIR spectra showed characteristic M-O stretching vibrations pertaining to the tetrahedral (A) and octahedral (B) lattice positions, further affirming the characteristic spinel phase. All dielectric parameters, such as dielectric constant, dielectric loss, and loss tangent, were found to decrease as the frequency increased. Magnetic characterization revealed that the replacement of Fe\u0026sup3;⁺ by Cr\u0026sup3;⁺ led to a decrease in saturation magnetization and an increase in coercivity, indicating the potential of these materials for permanent magnet applications.\u003c/p\u003e","manuscriptTitle":"Magnetic Order and Electronic Transport behaviour in Tailored made Nanostructural Co- Cr Ferrospinels","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-04 07:42:20","doi":"10.21203/rs.3.rs-7994297/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7d052a18-3bb6-4652-8906-6c735eb71f65","owner":[],"postedDate":"December 4th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-02T16:05:10+00:00","versionOfRecord":{"articleIdentity":"rs-7994297","link":"https://doi.org/10.1007/s10854-026-16888-8","journal":{"identity":"journal-of-materials-science-materials-in-electronics","isVorOnly":false,"title":"Journal of Materials Science: Materials in Electronics"},"publishedOn":"2026-02-28 15:59:43","publishedOnDateReadable":"February 28th, 2026"},"versionCreatedAt":"2025-12-04 07:42:20","video":"","vorDoi":"10.1007/s10854-026-16888-8","vorDoiUrl":"https://doi.org/10.1007/s10854-026-16888-8","workflowStages":[]},"version":"v1","identity":"rs-7994297","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7994297","identity":"rs-7994297","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}