The influence of Co doping on the structure and magnetic properties of Ni0.5Zn0.5-xCoxFe2O4 ferrites

The influence of Co doping on the structure and magnetic properties of Ni0.5Zn0.5-xCoxFe2O4 ferrites | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The influence of Co doping on the structure and magnetic properties of Ni0.5Zn0.5-xCoxFe2O4 ferrites Hui Liu, Jie Li, Xinfang Zhang, Qing Wang, Yuekang Zhu, Xiang An, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8687585/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Apr, 2026 Read the published version in Journal of Materials Science: Materials in Electronics → Version 1 posted You are reading this latest preprint version Abstract This study investigates the effect of Co doping on the magnetic properties of Ni 0.5 Zn 0.5− x Co x Fe 2 O 4 and explores its potential applications at high frequencies. Co-doped NiZn spinel ferrite powders, Ni 0.5 Zn 0.5− x Co x Fe 2 O 4 (0.00 ≤ x ≤ 0.10), were synthesized using the solid-state reaction method.The effects of Co-doped NiZn ferrite powders on the material structure and properties were investigated using X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), vibrating sample magnetometry (VSM), and precision impedance analysis (LCR).The results indicate that with the increase in Co substitution, the phase structure of the NiZn ferrite samples remains unchanged, with all samples exhibiting a single NiZn ferrite phase. The lattice constant of the samples first decreases and then increases.The saturation magnetization (Ms) first increases and then decreases with the increase in Co doping level ( x ), while the coercive force (Hc) initially decreases and then increases as the Co doping level ( x ) rises.Simultaneously, with the increase in Co doping, the initial permeability (µ') of the samples exhibits a trend of first decreasing, then increasing, and finally decreasing again. Meanwhile, the quality factor ( Q ) and the cutoff frequency ( f r) of the samples gradually increase.When the Co doping level ( x ) is 0.08, the sample achieves the highest saturation magnetization, with values of 82.2 emu/g for saturation magnetization and 15.2 Oe for coercive force. The quality factor ( Q ) and cutoff frequency ( f r) reach 219.69 and 73.71 MHz, respectively.This study provides theoretical guidance on the effects of Co substitution in NiZn ferrites on their material structure, magnetic properties, and high-frequency applications. Soft magnetic ferrites Magnetic properties Element doping Solid-state sintering Cutoff frequency Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 1. Introduction Nickel-zinc ferrite is a non-metallic soft magnetic material that boasts advantages such as high resistivity, low temperature coefficient, high Curie temperature, excellent high-frequency performance, and low production cost, making it easy to synthesize [ 1 – 3 ]. It plays a significant role in the research and development of magnetic materials, including transformers, high-frequency inductive cores, magnetic recording materials, and microwave absorption materials [ 4 ]. Spinel ferrites are widely used in electronic products such as tablets, telecommunications, meters, motors, memory devices, photocatalysts, humidity sensors, and the aerospace sector. Their magnetic properties can typically be enhanced through process improvements and element doping [ 5 , 6 ]. NiZn ferrites are a class of typical spinel-structured soft magnetic ferrites [ 7 ]. Spinel ferrites are generally represented by the chemical formula AB 2 O 4 , where A denotes a divalent metal cation, such as Ni²⁺, Zn²⁺, Cu²⁺, Fe²⁺, etc., and B represents a trivalent metal cation, usually Fe³⁺ [ 8 ].In this structure, oxygen ions are densely packed in a face-centered cubic (FCC) arrangement, forming two types of interstitial sites: tetrahedral (A) and octahedral (B) positions [ 9 , 10 ]. As shown in the unit cell in Fig. 1 , it contains eight small cubes, each cube having four oxygen atoms densely packed, creating two types of voids: tetrahedral and octahedral [ 11 , 12 ].The doping and substitution in ferrites are primarily facilitated by the presence of oxygen ion vacancies, which contribute to the enhancement of the ferrite's properties [ 13 , 14 ]. The main methods for synthesizing spinel ferrites currently include: solid-state synthesis, self-propagating high-temperature synthesis, low-temperature solid-state chemical reaction, hydrothermal synthesis, chemical co-precipitation [ 15 – 16 ], sol-gel method [ 17 – 18 ], and other techniques for ferrite synthesis [ 19 ]. J.S. Ghodake, Rahul C. Kambale [ 20 ], and others synthesized cobalt-substituted nickel-zinc ferrites using the citrate-nitrate combustion method. They observed that the coercive force increased with the cobalt content, while both the real and imaginary parts of the initial permeability decreased.Xiao-Hui Wu, Zheng-Xiong Tao [ 21 ], and others successfully prepared nickel-zinc-cobalt ferrites using the solid-state synthesis method. At a doping level of x = 0.05, the samples exhibited the best overall performance, with a relatively high saturation magnetization of 78.25 emu/g and a low coercive force of 13.25 Oe.However, the permeability and quality factor ( Q ) were not thoroughly investigated. Therefore, we successfully prepared Co-doped NiZn ferrites using the solid-state reaction method, which has the advantages of a low sintering temperature and a simple preparation process.Co was doped into NiZn ferrites ( x = 0.00-0.10) to prepare Ni 0.5 Zn 0.5− x Co x Fe 2 O 4 , and the variations in its magnetic properties, permeability, quality factor ( Q ), and cutoff frequency ( f r) were examined. 2. Experiment 2.1 Experimental Materials The materials used in this experiment include nickel oxide (NiO, 99%), zinc oxide (ZnO, 99%), iron oxide (Fe₂O₃, 99%), and cobalt monoxide (CoO, 99%).The materials were weighed using an electronic balance, and the solid-state sintering of Co-doped nickel-zinc ferrites was conducted in a laboratory muffle furnace. The sintering temperature was set at 1180°C with a holding time of 2 hours, resulting in the preparation of Ni 0.5 Zn 0.5− x Co x Fe 2 O 4 ferrites. According to the equation: NiO+(1-2 x )ZnO+2 x CoO+2Fe 2 O 3 →2Ni 0.5 Zn 0.5− x Co x Fe 2 O 4 + x O 2 ↑ The doping levels ( x ) were set at 0.00, 0.02, 0.04, 0.06, 0.08, and 0.10. The materials were weighed using an electronic balance, and Ni 0.5 Zn 0.5− x Co x Fe 2 O 4 was synthesized using the solid-state sintering method.The masses of the raw materials are shown in Table 2.1 . Table 2.1 Weighed Mass of Raw Materials for Different Co Doping Levels x 成分 NiO(g) ZnO(g) Fe 2 O 3 (g) CoO(g) 0.00 Ni 0.5 Zn 0.5 Fe 2 O 4 5.4981 5.9914 23.5105 0 0.02 Ni 0.5 Zn 0.48 Co 0.02 Fe 2 O 4 5.5011 5.7548 23.5233 0.2208 0.04 Ni 0.5 Zn 0.46 Co 0.04 Fe 2 O 4 5.5041 5.5180 23.5361 0.4418 0.06 Ni 0.5 Zn 0.44 Co 0.06 Fe 2 O 4 5.5071 5.2810 23.5489 0.6630 0.08 Ni 0.5 Zn 0.42 Co 0.08 Fe 2 O 4 5.5101 5.0437 23.5617 0.8845 0.10 Ni 0.5 Zn 0.40 Co 0.10 Fe 2 O 4 5.5131 4.8061 23.5746 1.1062 2.2 Experimental Methods The Ni 0.5 Zn 0.5− x Co x Fe 2 O 4 ( x = 0.00-0.10) ferrite samples were prepared using the solid-state synthesis method.After accurately weighing the balls and raw materials in a 10:1 mass ratio, they were placed into a planetary ball mill (ND7-2L, Nanjing Nanda Tianzun Electronics Co., Ltd.) jar, and an appropriate amount of anhydrous ethanol was added as a process control agent and mixing medium.The ball mill speed and milling duration were set to 150 r/min and 6 hours, respectively. Afterward, the resulting material was treated in a blast drying oven (101-2A, Tianjin Test Instrument Co., Ltd.) at 90°C for 4 hours.The pressed powder was heated in a muffle furnace at a rate of 5°C/min until reaching 900°C, where it was held for 3 hours. Afterward, the sample was cooled to room temperature, crushed, and subjected to a secondary ball milling. Then, 6% PVA was added for granulation. Discs weighing 8 g and rings weighing 2 g were pressed under 15 MPa pressure.The pressed discs and rings were then heated in a muffle furnace (SX13-20×50×18, Baotou Yunje Electric Furnace Factory) at a rate of 5°C/min until reaching 550°C, where the samples were held for 2 hours to remove the binder. The temperature was then increased to 1180°C, and the samples were maintained at this temperature for 2 hours before being cooled. Subsequently, the samples were ground into a powder with a particle size of 100 µm for analysis. 2.3 Structural and Performance Testing The crystal structure and phases of the powder were determined using X-ray powder diffraction (XRD) (Smartlab, Japan) within a 2θ scanning range of 20° to 70°.The bulk samples were gold-coated, and their surface morphology was observed using a field emission scanning electron microscope (FESEM) (Zeiss, Supra 55 FE-SEM, Netherlands).Energy dispersive spectroscopy (EDS) was then performed to determine the distribution of elements on the sample surface and to calculate the weight percentage of each element.The changes in the chemical bonds of the samples were detected using Fourier-transform infrared (FTIR) spectroscopy (Bruker, VERTEX 70, Germany). KBr (spectral grade) was used as the carrier, and the sample was mixed with KBr in a 1:150 ratio, then ground in a mortar until the particle size was less than 2 µm. Scans were conducted over the wavenumber range of 2000–400 cm⁻¹, with a resolution of 4 cm⁻¹ and a scanning speed of 2.5 kHz.The magnetic properties of the samples were measured using a vibrating sample magnetometer (VSM) (VersaLab, USA). Based on the hysteresis loop of the samples, the saturation magnetization (Ms), remanent magnetization (Mr), coercive force (Hc), and magnetic moment ( n B ) were calculated.The permeability of the samples was measured using a precision impedance analyzer (LCR) (Agilent E4991A, USA). The quality factor ( Q ) and cutoff frequency ( f r) were calculated based on the real and imaginary components of the permeability. 3. Results and Discussion 3.1 XRD Analysis Nickel-zinc ferrites were prepared by solid-state sintering at 1180°C with a holding time of 2 hours, with the samples doped with varying amounts of Co. The XRD patterns of the samples are shown in Fig. 2 . By comparing the diffraction peaks of the samples with the standard PDF card for spinel-type ferrites, all samples exhibit the main diffraction peaks corresponding to the spinel structure (NiZnFe 2 O 4 ).As shown in Fig. 2 , it is clearly evident that during the doping process, the increase in Co content does not alter the NiZn ferrite phase structure. From x = 0.00 to x = 0.10, all samples exhibit a single NiZn ferrite phase. The diffraction peaks of the prepared samples were indexed and compared using the standard PDF card in Jade software. All the diffraction peaks perfectly matched, thereby confirming the formation of nickel-zinc ferrite.As the doping amount of Co increases, the intensity of the diffraction peaks of NiZnFe 2 O 4 remains relatively unchanged, indicating that the crystal structure of NiZnFe 2 O 4 is not disrupted at this doping level. Figure 3 illustrates the XRD refinement spectra of the samples with varying Co doping levels, obtained using the Rietveld method.In Fig. 3 , "Exp" represents the experimental data, "Cal" denotes the fit of the theoretical data, and "Dif" indicates the deviation between the experimental and theoretical data fit [ 22 – 24 ].By fitting and separating the overlapping peaks, the crystallographic indices of the diffraction peaks can be accurately identified. This method enables precise measurement of the lattice parameters, which are listed in Table 3.1 after refinement.The lattice constant (a) fluctuates slightly within the range of 0.8390–0.8396 nm. However, with increasing doping levels, the lattice constant (a) shows a gradual decreasing trend. This reduction correlates with the increased substitution amount, resulting in a corresponding decrease in the unit cell volume.However, the range of this variation is relatively small, as the ionic radius of Co²⁺ (0.745 Å) is only slightly larger than that of Zn²⁺ (0.74 Å), indicating that the Co doping has not significantly altered the crystal structure.As shown in the table, the parameters a, b, and c are equal. After refinement, both the overall profile factor Rp and the weighted profile factor Rwp are less than 10, with the fitting goodness χ² also being very small. This indicates that the calculated values from the fit are in close agreement with the true values of the material, suggesting that the synthesized samples are of high quality [ 25 ]. Table 3.1 lists the lattice constant a, unit cell volume (vcell), Rp (%), Rwp (%), and χ² for samples with varying Co doping levels. x a(nm) v cell R p (%) R wp (%) χ2 0.00 8.395271 591.70 1.75 2.28 1.677 0.02 8.394380 591.52 1.85 2.49 1.835 0.04 8.392717 591.16 1.73 2.29 1.742 0.06 8.391376 590.88 1.70 2.24 1.592 0.08 8.391807 590.97 1.65 2.13 1.577 0.10 8.390637 590.72 1.60 2.04 1.279 3.2 Morphological and Compositional Analysis The SEM images in Fig. 4 , taken at a magnification of 30,000x, clearly reveal the grain structure and grain boundaries.As the doping level increases, the internal structure of the material remains unchanged.The particle size distribution was statistically analyzed using Nano Measurer software, and the resulting histogram is shown in Fig. 5 .The figure illustrates that the grain size initially increases, and then, when x > 0.06, it first decreases and subsequently levels off.The SEM images show that as the Co doping level increases, the grain size of the samples gradually increases. At x = 0.06, the grain size is at its maximum. This is because CoO acts as an effective sintering aid [ 26 ]; during high-temperature sintering, CoO can form a low-melting eutectic phase with the ferrite components or increase lattice defects (such as cation vacancies), significantly enhancing the bulk and grain boundary diffusion rates of the material.This accelerates the mass transport, facilitating the removal of pores and leading to a more dense material, which provides a better thermodynamic driving force for grain growth.However, as the doping level continues to increase, the grain size gradually decreases and eventually levels off. The grains become more uniform and tightly packed. To determine the chemical composition of the material and the doping position of Co, EDS was used for material characterization. Figure 6 shows the EDS spectra of the samples with varying Co doping levels. No elements other than the doped ones were detected in the nickel-zinc ferrite, confirming the purity of the synthesized samples.Table 3.2 presents the trend of mass percentage variations of different elements at each doping level.With the increase in Co doping, the percentage of Co detected by EDS also rises, while the substituted Zn element shows a linear decrease. Other elements exhibit little to no significant change.This indicates that the actual material aligns with the theoretical design, confirming the formation of Ni 0.5 Zn 0.5− x Co x Fe 2 O 4 . These findings suggest that Co has replaced Zn in the nickel-zinc ferrite, which is consistent with the original theoretical design. Table 3.2 Elemental composition of the samples with varying Co doping levels. x 成分 Ni Zn Fe Co O C All 0.00 Ni 0.5 Zn 0.5 Fe 2 O 4 10.4 11.4 41.0 0.0 29.1 8.1 100.0 0.02 Ni 0.5 Zn 0.48 Co 0.02 Fe 2 O 4 11.1 10.9 42.4 0.4 28.3 6.9 100.0 0.04 Ni 0.5 Zn 0.46 Co 0.04 Fe 2 O 4 11.2 10.2 42.7 0.9 27.6 7.4 100.0 0.06 Ni 0.5 Zn 0.44 Co 0.06 Fe 2 O 4 10.4 9.6 40.4 1.5 29.4 8.7 100.0 0.08 Ni 0.5 Zn 0.42 Co 0.08 Fe 2 O 4 10.7 9.0 41.9 1.9 28.6 7.9 100.0 0.10 Ni 0.5 Zn 0.40 Co 0.10 Fe 2 O 4 10.5 8.7 41.0 2.4 29.4 8.0 100.0 3.3 Spectral Analysis Figure 7 shows the infrared spectra of Ni 0.5 Zn 0.5− x Co x Fe 2 O 4 ( x = 0.00–0.10) in the 400–2000 cm⁻¹ wavenumber range at room temperature. It can be observed that absorption peaks corresponding to the vibrations of Fe³⁺-O²⁻ bonds are present at 583 cm⁻¹ (associated with the tetrahedral (A) position) and at 418 cm⁻¹ (associated with the octahedral (B) position).In the spinel structure of the ferrite, the tetrahedral and octahedral positions are occupied by metal ions. The two distinct characteristic absorption peaks confirm the formation of the ferrite spinel phase [ 27 , 28 ].Due to the shorter bond length of the Fe³⁺-O²⁻ bond in the tetrahedral lattice compared to the octahedral lattice, more energy is required to vibrate the bonds corresponding to the tetrahedral lattice. As a result, the absorption band at the tetrahedral position appears at a higher wavenumber than the absorption band at the octahedral position.The peak near 1008 cm⁻¹ is attributed to the vibration of the C-O bond.In the spinel structure of the ferrite, the tetrahedral and octahedral positions are occupied by metal ions. The two distinct characteristic absorption peaks confirm the formation of the nickel-zinc ferrite spinel phase.These two main metal-oxygen bonds were observed in the FT-IR spectra of all the samples with different doping levels, confirming the formation of the spinel structure [ 29 ]. 3.4 Magnetic Property Analysis VSM tests were conducted on the samples under a 30 kOe magnetic field with varying Co doping levels. Figure 8 shows the hysteresis loops of the samples with different Co doping amounts. The corresponding magnetic parameters are listed in Table 3.4 . Table 3.4 Magnetic properties of the samples with varying Co doping levels. x Ms (emu/g) Mr (emu/g) Mr / Ms Hc (Oe) n B 0.00 77.34596 15.75147 0.204 40.9404 3.318 0.02 78.8948 1.8684 0.024 29.3216 3.378 0.04 79.41102 1.73877 0.022 28.5174 3.400 0.06 80.62515 1.3236 0.016 15.1775 3.449 0.08 82.17341 1.2102 0.015 16.3674 3.511 0.10 81.70985 4.2626 0.052 22.3933 3.488 Figure 9 shows the variation trends of the saturation magnetization (Ms) and remanent magnetization (Mr) with different Co doping levels. As the Co content increases from 0.00 to 0.10, Ms initially increases and then decreases, reaching a maximum value of 82.2 emu/g at x = 0.08.The introduction of Co²⁺ optimizes the distribution of Fe³⁺ at the A and B sites, enhancing the superexchange interaction between the A and B sites. This results in a more ordered antiferromagnetic coupling, thereby increasing the net magnetic moment to some extent, which is reflected in the rise of Ms.However, an excess of Co²⁺ occupies the octahedral sites (B sites), displacing some Fe³⁺ ions to the tetrahedral sites (A sites). This disrupts the Fe³⁺-O²⁻-Fe³⁺ superexchange pathway, resulting in a decrease in Ms.As the Co content increases, Mr first decreases and then increases. The minimum Mr value of 1.210 is reached at x = 0.01, while the maximum Mr value of 15.751 occurs at x = 0.00.For high-frequency applications, hysteresis loss is a significant component of the total loss. High remanent magnetization (Mr) can substantially reduce device efficiency and lead to heating, whereas reducing Mr helps to lower hysteresis loss [ 30 – 32 ].As shown in Table 3.4 , the Mr/Ms values for samples with different Co doping levels are all less than 0.5, which confirms the formation of a multidomain structure, where the movement of domain walls dominates the magnetization process [ 33 ]. The number of Bohr magnetons, nB, is shown in Table 3.4 and Fig. 10 . The Bohr magneton number, n B , is calculated as: n B = \(\:\:\frac{M.W\times\:Ms}{5585}\) (Eq. 3.1) The number of Bohr magnetons, n B , is shown in Table 3.4 and Fig. 10 . The Bohr magneton number, n B , is calculated as:Since n B is positively correlated with Ms, the value of n B increases and then decreases with increasing Co doping levels, following a similar trend to that of Ms. The maximum value of n B , 3.511, is reached at x = 0.08, after which n B decreases when x > 0.08.A higher n B value indicates a larger net magnetic moment, meaning the material has a stronger ability to generate a magnetic field at the atomic level. The variation in the number of n B is primarily a result of changes in the superexchange interactions between different sites in the ferrite [ 34 , 35 ]. As shown in Fig. 11 , the coercivity (Hc) first decreases and then increases. With the increase in Co doping, Hc initially decreases and then rises, reaching a maximum value of 40.9 Oe at x = 0.00 and a minimum value of 15.2 Oe at x = 0.06. The dramatic decrease in coercivity is attributed to the increased number of grain boundaries, which reduce domain wall movement resistance and magnetic moment rotation resistance. 3.5 Permeability Analysis Figure 12 shows the variation trends of the real and imaginary parts of the magnetic permeability of samples with different Co doping levels, measured using the Agilent-E4991A (USA) at room temperature in the frequency range of 1 MHz to 1 GHz. In the low to mid-frequency range (1 MHz–10 MHz), the real part of the magnetic permeability is relatively high, while the imaginary part is lower and exhibits little variation with frequency. The primary loss mechanisms are hysteresis loss and remanent loss. However, due to losses caused by factors such as size resonance and magnetic resonance, there is a sudden increase in loss, leading to a peak in the imaginary part of the magnetic permeability [ 36 , 37 ]. In the high-frequency range (10 MHz–100 MHz), due to domain wall resonance or relaxation, the real part of the magnetic permeability rapidly decreases, while the imaginary part increases sharply, resulting in the appearance of a resonance peak. In the ultra-high-frequency range (100 MHz–1000 MHz), as the frequency continues to increase, natural resonance occurs, causing the real part of the magnetic permeability to decrease further, while the imaginary part exhibits resonance [ 38 ]. Figure 13 shows that as the Co doping level increases, the initial magnetic permeability first decreases, then increases, and subsequently decreases again. This behavior may be attributed to the fact that at lower doping levels, the positive magnetostrictive coefficient (λs) of Co²⁺ conflicts with the negative λs of the matrix, introducing additional internal stress. This internal stress can pin the magnetic domain walls, making their movement more difficult.The magnetic permeability µ i is inversely proportional to the internal stress σ. Therefore, the initially increased stress leads to a decrease in µ i . When x = 0.06, magnetocrystalline anisotropy compensation begins to dominate, making domain wall movement easier and driving an increase in µ i . When x > 0.06, positive anisotropy becomes dominant, leading to a decrease in µ i . The quality factor ( Q ) of all samples is shown in Fig. 15 . As the Co content increases from 0.00 to 0.10, the Q value gradually increases. At x = 0.08, the Q value of the sample is 219.69, indicating a relatively high Q value. When x = 0.10, the Q value reaches its maximum of 262.88. The Q value can be obtained using the following formula: Q = \(\:\frac{\mu\:{\prime\:}}{\mu\:{\prime\:}{\prime\:}}\) , (Eq. 3.2) In the mid-to-high frequency range (1 MHz–10 MHz), where NiZn ferrites perform well, their extremely low eddy current losses make the total loss primarily dominated by hysteresis loss [ 39 , 40 ]. At this point, the magnitude of the Q value mainly reflects the size of the material's hysteresis loss[ 41 ]. In higher frequency ranges (100 MHz–1000 MHz), remanent loss (especially domain wall resonance) may become dominant, causing the Q value to reach a peak and then drop sharply [ 42 ]. At this point, the height of the Q value peak and the frequency at which it occurs are important indicators for evaluating the material's high-frequency limits [ 43 , 44 ]. The frequency corresponding to the maximum value of the imaginary part of the magnetic permeability (µ'') is the cutoff frequency ( f r). The cutoff frequencies ( f r) of all samples are shown in Fig. 16 . As the Co content increases from 0.00 to 0.10, the Q value shows an increasing trend. When x > 0.06, fr increases sharply. At x = 0.08, the sample's fr reaches 73.71 MHz, and at x = 0.10, the sample's fr reaches the maximum value of 104.11 MHz. Funding: North Rare Earth Project(BFXT-2023-D-0044-1), First-Class Discipline Research Special Project (YLXKZX-NKD-042), Inner Mongolia Natural Science Foundation(2025MS05088) 4. Conclusion Nickel-zinc ferrite Ni 0.5 Zn 0.5− x Co x Fe 2 O 4 was prepared via solid-state sintering, and the influence mechanism of Co doping on the composition, structure, and magnetic properties of the samples was analyzed.As the doping level increased, the nickel-zinc ferrite phase structure of the samples remained unchanged. Throughout the doping process, from x = 0.00 to x = 0.10, all samples exhibited a single-phase nickel-zinc ferrite structure.The FTIR spectral results show two characteristic peaks at 583 cm⁻¹ and 418 cm⁻¹, which correspond to the tetrahedral and octahedral positions, respectively. These are common features of all spinel structures, further confirming the structural formation of the samples we prepared.The SEM results indicate that as the Co doping level increases, the grain size of the samples first increases, then decreases, and eventually levels off. The grains become more uniform and closely packed.The EDS analysis shows that no new elements were detected on the sample surface, confirming their purity and the successful substitution of Zn²⁺ ions with Co²⁺ ions.The VSM test results show that the saturation magnetization initially increases and then decreases, while the coercivity first decreases and then increases, and the remanent magnetization initially decreases and then increases.The saturation magnetization reaches its maximum value of 82.2 emu/g at x = 0.08, with a coercivity of 16.37 Oe. At this point, the remanent magnetization is at its lowest, measuring 1.21 emu/g.The dielectric performance test results show that the initial magnetic permeability of the samples first decreases, then increases, and subsequently drops sharply to 45.39.The quality factor ( Q ) and cutoff frequency ( f r) both increase with the Co doping level, with a sharp rise occurring when x > 0.06. At x = 0.10, Q reaches its maximum value of 262.88, and fr reaches 104.11 MHz.When the doping level is 0.08, the quality factor ( Q ) is 147.34 and the cutoff frequency ( f r) is 73.71 MHz. Overall, a doping level of x = 0.08 is considered the optimal doping amount.In addition, the samples demonstrate enhanced magnetic properties, making them compatible with various magnetic applications. This is of significant importance for the fabrication of nickel-zinc-cobalt ferrite soft magnetic materials with high quality factors, high saturation magnetization, and suitability for high-frequency applications. Declarations Author Contribution HuiLiu : Conceptualization, Data curation, Formal analysis, Writing – original draft, Writing – review & editing. Jie Li : Funding acquisition. XinFang Zhang : Funding acquisition. Qing Wang : Validation. YueKang Zhu :Software. Xiang An : Investigation. YueYang Zhang : Methodology. References R. Kumar, H. Kumar, R.R. 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Jaber, Structural and elastic properties of nickel–zinc ferrite nano-particles doped with lithium[J]. J. Brazilian Soc. Mech. Sci. Eng. 40 (5), 250 (2018) B. Ghosh, M. Sardar, S. Banerjee, Effect of antisite formation on magnetic properties of nickel zinc ferrite particles[J]. J. Appl. Phys., 2013, 114 (18) R. Kumar, H. Kumar, R.R. Singh et al., Structural analysis of emerging ferrite: Doped nickel zinc ferrite[C]//AIP Conference Proceedings. AIP Publishing LLC, 2015, 1675(1): 030003 N. Chandamma, G. Shankarmurthy, S.M. ,Kumar et al., Structural and electrical properties of zinc doped nickel ferrites nanoparticles prepared via facile combustion technique[J]. J. Alloys Compd.,2016,702479–702488 J.S. Ghodake, R.C. Kambale, T.J. Shinde et al., Magnetic and microwave absorbing properties of Co2 + substituted nickel–zinc ferrites with the emphasis on initial permeability studies[J]. J. Magn. Magn. Mater. 401 , 938–942 (2016) X.H. Wu, Z.X. Tao, L.Z. Li et al., Crystal structure and enhanced magneto-electric properties of cobalt-substituted nickel–zinc ferrite[J]. J. Mater. Sci.: Mater. Electron. 31 (22), 20277–20284 (2020) H. Choi, S. Lee, T. Kouh et al., Synthesis and characterization of Co-Zn ferrite nanoparticles for application to magnetic hyperthermia[J]. J. Korean Phys. Soc. 70 (1), 89–92 (2017) N. Parkansky, B. Alterkop, R. ,Boxman et al., Magnetic properties of carbon nano-particles produced by a pulsed arc submerged in ethanol[J].Carbon,2007, 46 (2):215–219 V. Kapse, S. Ghosh, F. ,Raghuwanshi et al., Nanocrystalline Ni 0.6 Zn 0.4 Fe 2 O 4 : A novel semiconducting material for ethanol detection[J].Talanta,2008, 78 (1):19–25 L.V. Savithri, G.S. V,Sunita, ,Ch.S.L.N. S et al., Evidence of Superparamagnetism in nano phased copper doped nickel zinc ferrites synthesized by Hydrothermal Method[J].Optik,2021,247 K.J. Khan, M. Khalid, D.A. ,Chandio et al., Properties of Al 3 + substituted nickel ferrite (NiAlxFe2-xO4) nanoparticles synthesised using wet sol-gel auto-combustion[J]. J. Sol-Gel Sci. Technol. 2020 (prepublish):1–12 M. Sorescu, L. Diamandescu, R. ,Peelamedu et al., Structural and magnetic properties of NiZn ferrites prepared by microwave sintering[J]. J. Magnetism Magn. Mater. 2004, 279 (2):195–201 L. Kumar, M. Kar, Effect of Ho 3+ substitution on the cation distribution, crystal structure and magnetocrystalline anisotropy of nanocrystalline cobalt ferrite [J]. J. Exp. Nanosci. 9 (4), 362–374 (2012) R.K. Singh, J. Shah, R.K. Kotnala, Magnetic and dielectric properties of rare earth substituted Ni 0.5 Zn 0.5 Fe 1.95 R 0.05 O 4 (R = Pr, Sm and La) ferrite nanoparticles [J]. Mater. Sci. Engineering: B 210 , 64–69 (2016) K.K. Bamzai, G. Kour, B. Kaur et al., Effect of cation distribution on structural and magnetic properties of Dy substituted magnesium ferrite [J]. J. Magn. Magn. Mater. 327 , 159–166 (2013) S.E. Jacobo, M. Arana, P.G. Bercoff, Gadolinium substitution effect on the thermomagnetic properties of Ni ferrite ferrofluids [J]. J. Magn. Magn. Mater. 415 , 30–34 (2016) M.A. Almessiere, Y. Slimani, A. Demir Korkmaz et al., Sonochemical synthesis of Dy 3+ substituted Mn 0.5 Zn 0.5 Fe 2–x O 4 nanoparticles: Structural, magnetic and optical characterizations [J]. Ultrason. Sonochem. 61 , 104836–104836 (2019) R. Qindeel, Synthesis and characterization of Co-Zn based spinel ferrites [J]. Mater. Res. Express. 5 (8), 086101 (2018) S. Shuo, L. Jie, Z. Xuan et al., Magnetic properties of Sm-doped M-type barium ferrite by high-energy ball mill-assisted solid-phase reaction method [J][J]. J. Magn. Magn. Mater., 2024, 589 S. Pi, J. Li, Y. Zhang et al., Effects of Ce doping on the structure, morphology, and magnetic properties of M-type strontium ferrite[J]. J. Supercond. Novel Magn. 37 (11), 1801–1813 (2024) M.H. Abdellatif, G.M. El-Komy, A.A. Azab, Magnetic characterization of rare earth doped spinel ferrite [J]. J. Magn. Magn. Mater. 442 , 445–452 (2017) M. Shoba, S. Kaleemulla, C. Krishnamoorthi et al., Effect of Er 3+ substitution on structural and magnetic properties of narrow size distributed ZnFe 2–x Er x O 4 nanoparticles[J]. Appl. Phys. A 125 (3), 1–11 (2019) P. Thakur, R. Sharma, K. Manoj et al., Structural, morphological, magnetic and optical study of coprecipitated Nd 3+ doped Mn-Zn ferrite nanoparticles[J]. J. Magn. Magn. Mater. 479 , 317–325 (2019) B. Sun, F. Chen, W. Yang et al., Effects of nano-TiO 2 and normal size TiO 2 additions on the microstructure and magnetic properties of manganese-zinc power ferrites[J]. J. Magn. Magn. Mater. 349 , 180–187 (2014) X.Y. Guo, X.R. Yan, X.L. Cui, J.P. Wang, T. Bai, Preparation and study of lanthanum doped MnZn ferrite[J]. Chin. J. Inorg. Chem. 20 (8), 910 (2004) F. Chen, J. Zhang, X. Liu et al., The effect of ions doping on the rheological properties of ferrite ferrofluids[J]. Front. Mater. 10 , 1264049 (2023) M.N. Akhtar, M. Alelyani, M. Babar et al., Magnetodielectric, elastic, Rietveld refinement and absorption properties of Nd–Cu co-doped Co–Zn nano ferrites: development of meta-absorbers for wide frequency regime[J]. Ceram. Int. 50 (8), 12890–12904 (2024) X. Wu, W. Chen, W. Wu et al., Improvement of the magnetic moment of NiZn ferrites induced by substitution of Nd3 + ions for Fe3 + ions[J]. J. Magn. Magn. Mater. 453 , 246–253 (2018) A. Miszczyk, Protective and suppressing electromagnetic interference properties of epoxy coatings containing nano-sized NiZn ferrites[J]. Front. Mater. 7 , 183 (2020) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Apr, 2026 Read the published version in Journal of Materials Science: Materials in Electronics → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8687585","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":585534530,"identity":"ed710fc0-ac82-4eed-9c29-bdbbea4cb4b9","order_by":0,"name":"Hui Liu","email":"","orcid":"","institution":"Inner Mongolia University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Hui","middleName":"","lastName":"Liu","suffix":""},{"id":585534531,"identity":"43039241-15c1-4084-9cfb-1cf97c163dc8","order_by":1,"name":"Jie Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAv0lEQVRIiWNgGAWjYFCCA4wHEngkGPiZmQ8+IFYLA1iLZDtbsgHx9oAIg/M8ZgJEKTc4ePzBgQcyFnLGhxnMGBhqbKIJazlwxgDkMGOzwwxpDxiOpeU2EKEF7JfEbYcZjhswNhwmRgvQYUAt9ZubGdskiNRyAOywBANmZjbitEhC/WI44zAbs0ECMX7hu3H84cOfPXXy/P3nPz74UGNDWIvCjQMMDIw9UF4CIeUgIN8PMvUHMUpHwSgYBaNgxAIAT/dFn/TPUpYAAAAASUVORK5CYII=","orcid":"","institution":"Inner Mongolia University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Jie","middleName":"","lastName":"Li","suffix":""},{"id":585534532,"identity":"5157b5c4-0eec-4fa7-a84d-224068288c8e","order_by":2,"name":"Xinfang Zhang","email":"","orcid":"","institution":"Inner Mongolia University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Xinfang","middleName":"","lastName":"Zhang","suffix":""},{"id":585534534,"identity":"1dd52cfb-fc63-4bf6-a678-7026e95bc313","order_by":3,"name":"Qing Wang","email":"","orcid":"","institution":"Inner Mongolia University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Qing","middleName":"","lastName":"Wang","suffix":""},{"id":585534536,"identity":"e85edd01-3d41-41f2-9eb8-6e1b27b4917f","order_by":4,"name":"Yuekang Zhu","email":"","orcid":"","institution":"Inner Mongolia University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yuekang","middleName":"","lastName":"Zhu","suffix":""},{"id":585534538,"identity":"f0768b3c-4e2d-47f5-8c07-75555fc4dca6","order_by":5,"name":"Xiang An","email":"","orcid":"","institution":"Inner Mongolia University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Xiang","middleName":"","lastName":"An","suffix":""},{"id":585534540,"identity":"18007b12-d116-4219-89ff-06d478b7d1a0","order_by":6,"name":"Yueyang Zhang","email":"","orcid":"","institution":"Inner Mongolia University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yueyang","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2026-01-24 14:53:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8687585/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8687585/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10854-026-17083-5","type":"published","date":"2026-04-05T16:00:04+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":101935109,"identity":"14aa8207-5ca4-4d51-ae2f-e101bcbe43f2","added_by":"auto","created_at":"2026-02-05 08:25:53","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":378863,"visible":true,"origin":"","legend":"\u003cp\u003eStructure of the Spinel Ferrite\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/c8cfe57b1ab531f25ccfd3cc.png"},{"id":101934967,"identity":"10f73832-87eb-4b54-b7b9-2702386d62d4","added_by":"auto","created_at":"2026-02-05 08:25:16","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":101932,"visible":true,"origin":"","legend":"\u003cp\u003edisplays the XRD spectra of the samples with different Co doping levels\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/0103d767d01af02e5774bdc0.png"},{"id":101935544,"identity":"50dae7cf-54d5-401a-9298-a9db3b55fe6f","added_by":"auto","created_at":"2026-02-05 08:27:21","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":754999,"visible":true,"origin":"","legend":"\u003cp\u003eXRD spectra of Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e (\u003cem\u003ex\u003c/em\u003e = 0.00–0.10) samples refined using the Rietveld method\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/fc4dee58ac19e9fa5b0229c3.jpeg"},{"id":101934922,"identity":"4336ee1e-727a-4d81-aac3-704354e1ce7e","added_by":"auto","created_at":"2026-02-05 08:25:04","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1481294,"visible":true,"origin":"","legend":"\u003cp\u003eScanning electron microscope images of samples with varying Co doping levels\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/1cce0eeefef485e26a5cac29.jpeg"},{"id":101935633,"identity":"603f1cad-a0af-427f-a237-f377bf8ebdee","added_by":"auto","created_at":"2026-02-05 08:27:49","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1391233,"visible":true,"origin":"","legend":"\u003cp\u003eParticle size distribution histogram of samples with varying Co doping levels\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/12b09895a9cf0ce834ef2524.jpeg"},{"id":101935293,"identity":"f72b4757-2afe-46de-bbec-dde48e055850","added_by":"auto","created_at":"2026-02-05 08:26:36","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":228766,"visible":true,"origin":"","legend":"\u003cp\u003eEDS spectra of samples with varying Co doping levels\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/5dbafb60df3bb7dae0f8d612.jpeg"},{"id":101935285,"identity":"757d2815-6198-4d18-904a-b9c9b5022f56","added_by":"auto","created_at":"2026-02-05 08:26:30","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":98958,"visible":true,"origin":"","legend":"\u003cp\u003eInfrared spectra of samples with varying Co doping levels\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/e523226225f58dba22249303.png"},{"id":101934924,"identity":"355b4425-0aac-4483-aad3-47802392b7c4","added_by":"auto","created_at":"2026-02-05 08:25:04","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":89469,"visible":true,"origin":"","legend":"\u003cp\u003eHysteresis loops of samples with varying Co doping levels\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/9bab1e97a78cf2d8ce0c17a5.png"},{"id":101935095,"identity":"b7740b4d-97fb-49d4-8c53-31b5268348d8","added_by":"auto","created_at":"2026-02-05 08:25:45","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":73727,"visible":true,"origin":"","legend":"\u003cp\u003eVariation trends of Ms and Mr for samples with different Co doping levels\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/2c95e746ca25dde5674a4a6f.png"},{"id":101935538,"identity":"2f00733e-060b-43f0-b72c-3c46293a1fcd","added_by":"auto","created_at":"2026-02-05 08:27:20","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":46144,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e values of samples with varying Co doping levels\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/0d1a089ae46e6d99a6d5a3a9.png"},{"id":101935267,"identity":"11470bea-fbf7-4eff-a313-a38fdd19a3ee","added_by":"auto","created_at":"2026-02-05 08:26:22","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":41516,"visible":true,"origin":"","legend":"\u003cp\u003eVariation trend of coercivity (Hc) for samples with different Co doping levels\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/8995ea41b1146b2e5705d9c3.png"},{"id":101935348,"identity":"d9a18401-63f0-4ceb-b2c0-609a014cce37","added_by":"auto","created_at":"2026-02-05 08:26:51","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":140787,"visible":true,"origin":"","legend":"\u003cp\u003eVariation trends of magnetic permeability for samples with different Co doping levels\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/537352d61718dcae319b6423.png"},{"id":101935609,"identity":"c3ba2ba8-137c-4a47-bc52-3c9d9e2a80df","added_by":"auto","created_at":"2026-02-05 08:27:45","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":43572,"visible":true,"origin":"","legend":"\u003cp\u003eInitial magnetic permeability values of samples with varying Co doping levels\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/ecb8f0c5b5aa604e0edb6b8b.png"},{"id":101935082,"identity":"604ee64a-de06-41ae-b025-bb60f95b9a44","added_by":"auto","created_at":"2026-02-05 08:25:42","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":92062,"visible":true,"origin":"","legend":"\u003cp\u003eFigure 15 Variation trend of \u003cem\u003eQ\u003c/em\u003e values for samples with different Co doping levels\u003c/p\u003e","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/3c9a905ef4cf3194d0e6217b.png"},{"id":101935455,"identity":"93469cd2-2360-445a-9f1f-bd81632a2af2","added_by":"auto","created_at":"2026-02-05 08:27:07","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":44212,"visible":true,"origin":"","legend":"\u003cp\u003eFigure 16 \u003cem\u003eQ\u003c/em\u003evalues of samples with varying Co doping levels\u003c/p\u003e","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/ae16ed85410494ff3ac1e7ae.png"},{"id":106344676,"identity":"a74871d3-af32-4301-a730-8c988322fb2d","added_by":"auto","created_at":"2026-04-07 16:15:57","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6209234,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8687585/v1/df82587a-e55d-4eab-9259-f29ad752a406.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eThe influence of Co doping on the structure and magnetic properties of Ni0.5Zn0.5-xCoxFe2O4 ferrites\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eNickel-zinc ferrite is a non-metallic soft magnetic material that boasts advantages such as high resistivity, low temperature coefficient, high Curie temperature, excellent high-frequency performance, and low production cost, making it easy to synthesize [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. It plays a significant role in the research and development of magnetic materials, including transformers, high-frequency inductive cores, magnetic recording materials, and microwave absorption materials [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Spinel ferrites are widely used in electronic products such as tablets, telecommunications, meters, motors, memory devices, photocatalysts, humidity sensors, and the aerospace sector. Their magnetic properties can typically be enhanced through process improvements and element doping [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNiZn ferrites are a class of typical spinel-structured soft magnetic ferrites [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Spinel ferrites are generally represented by the chemical formula AB\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e, where A denotes a divalent metal cation, such as Ni\u0026sup2;⁺, Zn\u0026sup2;⁺, Cu\u0026sup2;⁺, Fe\u0026sup2;⁺, etc., and B represents a trivalent metal cation, usually Fe\u0026sup3;⁺ [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].In this structure, oxygen ions are densely packed in a face-centered cubic (FCC) arrangement, forming two types of interstitial sites: tetrahedral (A) and octahedral (B) positions [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. As shown in the unit cell in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, it contains eight small cubes, each cube having four oxygen atoms densely packed, creating two types of voids: tetrahedral and octahedral [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].The doping and substitution in ferrites are primarily facilitated by the presence of oxygen ion vacancies, which contribute to the enhancement of the ferrite's properties [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe main methods for synthesizing spinel ferrites currently include: solid-state synthesis, self-propagating high-temperature synthesis, low-temperature solid-state chemical reaction, hydrothermal synthesis, chemical co-precipitation [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], sol-gel method [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], and other techniques for ferrite synthesis [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eJ.S. Ghodake, Rahul C. Kambale [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], and others synthesized cobalt-substituted nickel-zinc ferrites using the citrate-nitrate combustion method. They observed that the coercive force increased with the cobalt content, while both the real and imaginary parts of the initial permeability decreased.Xiao-Hui Wu, Zheng-Xiong Tao [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], and others successfully prepared nickel-zinc-cobalt ferrites using the solid-state synthesis method. At a doping level of \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.05, the samples exhibited the best overall performance, with a relatively high saturation magnetization of 78.25 emu/g and a low coercive force of 13.25 Oe.However, the permeability and quality factor (\u003cem\u003eQ\u003c/em\u003e) were not thoroughly investigated. Therefore, we successfully prepared Co-doped NiZn ferrites using the solid-state reaction method, which has the advantages of a low sintering temperature and a simple preparation process.Co was doped into NiZn ferrites (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.00-0.10) to prepare Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e, and the variations in its magnetic properties, permeability, quality factor (\u003cem\u003eQ\u003c/em\u003e), and cutoff frequency (\u003cem\u003ef\u003c/em\u003er) were examined.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2. Experiment","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Experimental Materials\u003c/h2\u003e \u003cp\u003eThe materials used in this experiment include nickel oxide (NiO, 99%), zinc oxide (ZnO, 99%), iron oxide (Fe₂O₃, 99%), and cobalt monoxide (CoO, 99%).The materials were weighed using an electronic balance, and the solid-state sintering of Co-doped nickel-zinc ferrites was conducted in a laboratory muffle furnace. The sintering temperature was set at 1180\u0026deg;C with a holding time of 2 hours, resulting in the preparation of Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e ferrites.\u003c/p\u003e \u003cp\u003eAccording to the equation:\u003c/p\u003e \u003cp\u003eNiO+(1-2\u003cem\u003ex\u003c/em\u003e)ZnO+2\u003cem\u003ex\u003c/em\u003eCoO+2Fe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026rarr;2Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e+\u003cem\u003ex\u003c/em\u003eO\u003csub\u003e2\u003c/sub\u003e\u0026uarr;\u003c/p\u003e \u003cp\u003eThe doping levels (\u003cem\u003ex\u003c/em\u003e) were set at 0.00, 0.02, 0.04, 0.06, 0.08, and 0.10. The materials were weighed using an electronic balance, and Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e was synthesized using the solid-state sintering method.The masses of the raw materials are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e2.1\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 2.1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eWeighed Mass of Raw Materials for Different Co Doping Levels\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=\"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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e成分\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNiO(g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eZnO(g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e(g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCoO(g)\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\u003e0.00\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.4981\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.9914\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e23.5105\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.48\u003c/sub\u003eCo\u003csub\u003e0.02\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.5011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.7548\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e23.5233\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.2208\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.04\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.46\u003c/sub\u003eCo\u003csub\u003e0.04\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.5041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.5180\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e23.5361\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.4418\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.44\u003c/sub\u003eCo\u003csub\u003e0.06\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.5071\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.2810\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e23.5489\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.6630\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.42\u003c/sub\u003eCo\u003csub\u003e0.08\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.5101\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.0437\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e23.5617\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.8845\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.40\u003c/sub\u003eCo\u003csub\u003e0.10\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.5131\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.8061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e23.5746\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.1062\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=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Experimental Methods\u003c/h2\u003e \u003cp\u003eThe Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.00-0.10) ferrite samples were prepared using the solid-state synthesis method.After accurately weighing the balls and raw materials in a 10:1 mass ratio, they were placed into a planetary ball mill (ND7-2L, Nanjing Nanda Tianzun Electronics Co., Ltd.) jar, and an appropriate amount of anhydrous ethanol was added as a process control agent and mixing medium.The ball mill speed and milling duration were set to 150 r/min and 6 hours, respectively. Afterward, the resulting material was treated in a blast drying oven (101-2A, Tianjin Test Instrument Co., Ltd.) at 90\u0026deg;C for 4 hours.The pressed powder was heated in a muffle furnace at a rate of 5\u0026deg;C/min until reaching 900\u0026deg;C, where it was held for 3 hours. Afterward, the sample was cooled to room temperature, crushed, and subjected to a secondary ball milling. Then, 6% PVA was added for granulation. Discs weighing 8 g and rings weighing 2 g were pressed under 15 MPa pressure.The pressed discs and rings were then heated in a muffle furnace (SX13-20\u0026times;50\u0026times;18, Baotou Yunje Electric Furnace Factory) at a rate of 5\u0026deg;C/min until reaching 550\u0026deg;C, where the samples were held for 2 hours to remove the binder. The temperature was then increased to 1180\u0026deg;C, and the samples were maintained at this temperature for 2 hours before being cooled. Subsequently, the samples were ground into a powder with a particle size of 100 \u0026micro;m for analysis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Structural and Performance Testing\u003c/h2\u003e \u003cp\u003eThe crystal structure and phases of the powder were determined using X-ray powder diffraction (XRD) (Smartlab, Japan) within a 2θ scanning range of 20\u0026deg; to 70\u0026deg;.The bulk samples were gold-coated, and their surface morphology was observed using a field emission scanning electron microscope (FESEM) (Zeiss, Supra 55 FE-SEM, Netherlands).Energy dispersive spectroscopy (EDS) was then performed to determine the distribution of elements on the sample surface and to calculate the weight percentage of each element.The changes in the chemical bonds of the samples were detected using Fourier-transform infrared (FTIR) spectroscopy (Bruker, VERTEX 70, Germany). KBr (spectral grade) was used as the carrier, and the sample was mixed with KBr in a 1:150 ratio, then ground in a mortar until the particle size was less than 2 \u0026micro;m. Scans were conducted over the wavenumber range of 2000\u0026ndash;400 cm⁻\u0026sup1;, with a resolution of 4 cm⁻\u0026sup1; and a scanning speed of 2.5 kHz.The magnetic properties of the samples were measured using a vibrating sample magnetometer (VSM) (VersaLab, USA). Based on the hysteresis loop of the samples, the saturation magnetization (Ms), remanent magnetization (Mr), coercive force (Hc), and magnetic moment (\u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e) were calculated.The permeability of the samples was measured using a precision impedance analyzer (LCR) (Agilent E4991A, USA). The quality factor (\u003cem\u003eQ\u003c/em\u003e) and cutoff frequency (\u003cem\u003ef\u003c/em\u003er) were calculated based on the real and imaginary components of the permeability.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 XRD Analysis\u003c/h2\u003e \u003cp\u003eNickel-zinc ferrites were prepared by solid-state sintering at 1180\u0026deg;C with a holding time of 2 hours, with the samples doped with varying amounts of Co.\u003c/p\u003e \u003cp\u003eThe XRD patterns of the samples are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. By comparing the diffraction peaks of the samples with the standard PDF card for spinel-type ferrites, all samples exhibit the main diffraction peaks corresponding to the spinel structure (NiZnFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e).As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, it is clearly evident that during the doping process, the increase in Co content does not alter the NiZn ferrite phase structure. From \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.00 to \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10, all samples exhibit a single NiZn ferrite phase.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe diffraction peaks of the prepared samples were indexed and compared using the standard PDF card in Jade software. All the diffraction peaks perfectly matched, thereby confirming the formation of nickel-zinc ferrite.As the doping amount of Co increases, the intensity of the diffraction peaks of NiZnFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e remains relatively unchanged, indicating that the crystal structure of NiZnFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e is not disrupted at this doping level.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the XRD refinement spectra of the samples with varying Co doping levels, obtained using the Rietveld method.In Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, \"Exp\" represents the experimental data, \"Cal\" denotes the fit of the theoretical data, and \"Dif\" indicates the deviation between the experimental and theoretical data fit [\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].By fitting and separating the overlapping peaks, the crystallographic indices of the diffraction peaks can be accurately identified. This method enables precise measurement of the lattice parameters, which are listed in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e after refinement.The lattice constant (a) fluctuates slightly within the range of 0.8390\u0026ndash;0.8396 nm. However, with increasing doping levels, the lattice constant (a) shows a gradual decreasing trend. This reduction correlates with the increased substitution amount, resulting in a corresponding decrease in the unit cell volume.However, the range of this variation is relatively small, as the ionic radius of Co\u0026sup2;⁺ (0.745 \u0026Aring;) is only slightly larger than that of Zn\u0026sup2;⁺ (0.74 \u0026Aring;), indicating that the Co doping has not significantly altered the crystal structure.As shown in the table, the parameters a, b, and c are equal. After refinement, both the overall profile factor Rp and the weighted profile factor Rwp are less than 10, with the fitting goodness χ\u0026sup2; also being very small. This indicates that the calculated values from the fit are in close agreement with the true values of the material, suggesting that the synthesized samples are of high quality [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\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 3.1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003elists the lattice constant a, unit cell volume (vcell), Rp (%), Rwp (%), and χ\u0026sup2; for samples with varying Co doping levels.\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=\"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 \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ea(nm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ev\u003c/em\u003e\u003csub\u003ecell\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eR\u003csub\u003ep\u003c/sub\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u003csub\u003ewp\u003c/sub\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eχ2\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\u003e0.00\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.395271\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e591.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.677\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.394380\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e591.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.835\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.04\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.392717\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e591.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.742\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.391376\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e590.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.592\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.391807\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e590.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.577\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8.390637\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e590.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.279\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=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Morphological and Compositional Analysis\u003c/h2\u003e \u003cp\u003eThe SEM images in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, taken at a magnification of 30,000x, clearly reveal the grain structure and grain boundaries.As the doping level increases, the internal structure of the material remains unchanged.The particle size distribution was statistically analyzed using Nano Measurer software, and the resulting histogram is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.The figure illustrates that the grain size initially increases, and then, when \u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.06, it first decreases and subsequently levels off.The SEM images show that as the Co doping level increases, the grain size of the samples gradually increases. At \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.06, the grain size is at its maximum. This is because CoO acts as an effective sintering aid [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]; during high-temperature sintering, CoO can form a low-melting eutectic phase with the ferrite components or increase lattice defects (such as cation vacancies), significantly enhancing the bulk and grain boundary diffusion rates of the material.This accelerates the mass transport, facilitating the removal of pores and leading to a more dense material, which provides a better thermodynamic driving force for grain growth.However, as the doping level continues to increase, the grain size gradually decreases and eventually levels off. The grains become more uniform and tightly packed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo determine the chemical composition of the material and the doping position of Co, EDS was used for material characterization. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the EDS spectra of the samples with varying Co doping levels. No elements other than the doped ones were detected in the nickel-zinc ferrite, confirming the purity of the synthesized samples.Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e presents the trend of mass percentage variations of different elements at each doping level.With the increase in Co doping, the percentage of Co detected by EDS also rises, while the substituted Zn element shows a linear decrease. Other elements exhibit little to no significant change.This indicates that the actual material aligns with the theoretical design, confirming the formation of Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e. These findings suggest that Co has replaced Zn in the nickel-zinc ferrite, which is consistent with the original theoretical design.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \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 3.2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eElemental composition of the samples with varying Co doping levels.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\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=\"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 \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e成分\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNi\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eZn\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFe\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCo\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eAll\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\u003e0.00\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e11.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e41.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e29.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e8.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e100.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.48\u003c/sub\u003eCo\u003csub\u003e0.02\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e42.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e28.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e100.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.04\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.46\u003c/sub\u003eCo\u003csub\u003e0.04\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e42.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e27.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e100.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.44\u003c/sub\u003eCo\u003csub\u003e0.06\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e40.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e29.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e8.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e100.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.42\u003c/sub\u003eCo\u003csub\u003e0.08\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e41.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e28.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e100.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNi\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.40\u003c/sub\u003eCo\u003csub\u003e0.10\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e41.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e29.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e8.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e100.0\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 Spectral Analysis\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the infrared spectra of Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.00\u0026ndash;0.10) in the 400\u0026ndash;2000 cm⁻\u0026sup1; wavenumber range at room temperature. It can be observed that absorption peaks corresponding to the vibrations of Fe\u0026sup3;⁺-O\u0026sup2;⁻ bonds are present at 583 cm⁻\u0026sup1; (associated with the tetrahedral (A) position) and at 418 cm⁻\u0026sup1; (associated with the octahedral (B) position).In the spinel structure of the ferrite, the tetrahedral and octahedral positions are occupied by metal ions. The two distinct characteristic absorption peaks confirm the formation of the ferrite spinel phase [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].Due to the shorter bond length of the Fe\u0026sup3;⁺-O\u0026sup2;⁻ bond in the tetrahedral lattice compared to the octahedral lattice, more energy is required to vibrate the bonds corresponding to the tetrahedral lattice. As a result, the absorption band at the tetrahedral position appears at a higher wavenumber than the absorption band at the octahedral position.The peak near 1008 cm⁻\u0026sup1; is attributed to the vibration of the C-O bond.In the spinel structure of the ferrite, the tetrahedral and octahedral positions are occupied by metal ions. The two distinct characteristic absorption peaks confirm the formation of the nickel-zinc ferrite spinel phase.These two main metal-oxygen bonds were observed in the FT-IR spectra of all the samples with different doping levels, confirming the formation of the spinel structure [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Magnetic Property Analysis\u003c/h2\u003e \u003cp\u003eVSM tests were conducted on the samples under a 30 kOe magnetic field with varying Co doping levels. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the hysteresis loops of the samples with different Co doping amounts. The corresponding magnetic parameters are listed in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3.4\u003c/span\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 3.4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMagnetic properties of the samples with varying Co doping levels.\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=\"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 \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eMs\u003c/em\u003e(emu/g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eMr\u003c/em\u003e(emu/g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eMr\u003c/em\u003e/\u003cem\u003eMs\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eHc\u003c/em\u003e(Oe)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e\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\u003e0.00\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e77.34596\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15.75147\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.204\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e40.9404\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.318\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e78.8948\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.8684\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e29.3216\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.378\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.04\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e79.41102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.73877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e28.5174\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.400\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80.62515\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.3236\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15.1775\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.449\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e82.17341\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.2102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e16.3674\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.511\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e0.10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e81.70985\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.2626\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e22.3933\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.488\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 \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the variation trends of the saturation magnetization (Ms) and remanent magnetization (Mr) with different Co doping levels. As the Co content increases from 0.00 to 0.10, Ms initially increases and then decreases, reaching a maximum value of 82.2 emu/g at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.08.The introduction of Co\u0026sup2;⁺ optimizes the distribution of Fe\u0026sup3;⁺ at the A and B sites, enhancing the superexchange interaction between the A and B sites. This results in a more ordered antiferromagnetic coupling, thereby increasing the net magnetic moment to some extent, which is reflected in the rise of Ms.However, an excess of Co\u0026sup2;⁺ occupies the octahedral sites (B sites), displacing some Fe\u0026sup3;⁺ ions to the tetrahedral sites (A sites). This disrupts the Fe\u0026sup3;⁺-O\u0026sup2;⁻-Fe\u0026sup3;⁺ superexchange pathway, resulting in a decrease in Ms.As the Co content increases, Mr first decreases and then increases. The minimum Mr value of 1.210 is reached at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.01, while the maximum Mr value of 15.751 occurs at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.00.For high-frequency applications, hysteresis loss is a significant component of the total loss. High remanent magnetization (Mr) can substantially reduce device efficiency and lead to heating, whereas reducing Mr helps to lower hysteresis loss [\u003cspan additionalcitationids=\"CR31\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].As shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3.4\u003c/span\u003e, the Mr/Ms values for samples with different Co doping levels are all less than 0.5, which confirms the formation of a multidomain structure, where the movement of domain walls dominates the magnetization process [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe number of Bohr magnetons, nB, is shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3.4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. The Bohr magneton number, \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, is calculated as:\u003c/p\u003e \u003cp\u003e \u003cem\u003en\u003c/em\u003e \u003csub\u003e \u003cem\u003eB\u003c/em\u003e \u003c/sub\u003e=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\frac{M.W\\times\\:Ms}{5585}\\)\u003c/span\u003e\u003c/span\u003e (Eq.\u0026nbsp;3.1)\u003c/p\u003e \u003cp\u003eThe number of Bohr magnetons, \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, is shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3.4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. The Bohr magneton number, \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, is calculated as:Since \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e is positively correlated with Ms, the value of \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e increases and then decreases with increasing Co doping levels, following a similar trend to that of Ms. The maximum value of \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, 3.511, is reached at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.08, after which \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e decreases when \u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.08.A higher \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e value indicates a larger net magnetic moment, meaning the material has a stronger ability to generate a magnetic field at the atomic level. The variation in the number of \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e is primarily a result of changes in the superexchange interactions between different sites in the ferrite [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e, the coercivity (Hc) first decreases and then increases. With the increase in Co doping, Hc initially decreases and then rises, reaching a maximum value of 40.9 Oe at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.00 and a minimum value of 15.2 Oe at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.06. The dramatic decrease in coercivity is attributed to the increased number of grain boundaries, which reduce domain wall movement resistance and magnetic moment rotation resistance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Permeability Analysis\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the variation trends of the real and imaginary parts of the magnetic permeability of samples with different Co doping levels, measured using the Agilent-E4991A (USA) at room temperature in the frequency range of 1 MHz to 1 GHz.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the low to mid-frequency range (1 MHz\u0026ndash;10 MHz), the real part of the magnetic permeability is relatively high, while the imaginary part is lower and exhibits little variation with frequency. The primary loss mechanisms are hysteresis loss and remanent loss. However, due to losses caused by factors such as size resonance and magnetic resonance, there is a sudden increase in loss, leading to a peak in the imaginary part of the magnetic permeability [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn the high-frequency range (10 MHz\u0026ndash;100 MHz), due to domain wall resonance or relaxation, the real part of the magnetic permeability rapidly decreases, while the imaginary part increases sharply, resulting in the appearance of a resonance peak.\u003c/p\u003e \u003cp\u003eIn the ultra-high-frequency range (100 MHz\u0026ndash;1000 MHz), as the frequency continues to increase, natural resonance occurs, causing the real part of the magnetic permeability to decrease further, while the imaginary part exhibits resonance [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e shows that as the Co doping level increases, the initial magnetic permeability first decreases, then increases, and subsequently decreases again. This behavior may be attributed to the fact that at lower doping levels, the positive magnetostrictive coefficient (λs) of Co\u0026sup2;⁺ conflicts with the negative λs of the matrix, introducing additional internal stress. This internal stress can pin the magnetic domain walls, making their movement more difficult.The magnetic permeability \u0026micro;\u003csub\u003ei\u003c/sub\u003e is inversely proportional to the internal stress σ. Therefore, the initially increased stress leads to a decrease in \u0026micro;\u003csub\u003ei\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eWhen \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.06, magnetocrystalline anisotropy compensation begins to dominate, making domain wall movement easier and driving an increase in \u0026micro;\u003csub\u003ei\u003c/sub\u003e. When \u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.06, positive anisotropy becomes dominant, leading to a decrease in \u0026micro;\u003csub\u003ei\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe quality factor (\u003cem\u003eQ\u003c/em\u003e) of all samples is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e15\u003c/span\u003e. As the Co content increases from 0.00 to 0.10, the \u003cem\u003eQ\u003c/em\u003e value gradually increases. At \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.08, the \u003cem\u003eQ\u003c/em\u003e value of the sample is 219.69, indicating a relatively high \u003cem\u003eQ\u003c/em\u003e value. When \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10, the \u003cem\u003eQ\u003c/em\u003e value reaches its maximum of 262.88.\u003c/p\u003e \u003cp\u003eThe \u003cem\u003eQ\u003c/em\u003e value can be obtained using the following formula:\u003c/p\u003e \u003cp\u003e \u003cem\u003eQ\u003c/em\u003e=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\mu\\:{\\prime\\:}}{\\mu\\:{\\prime\\:}{\\prime\\:}}\\)\u003c/span\u003e\u003c/span\u003e, (Eq.\u0026nbsp;3.2)\u003c/p\u003e \u003cp\u003eIn the mid-to-high frequency range (1 MHz\u0026ndash;10 MHz), where NiZn ferrites perform well, their extremely low eddy current losses make the total loss primarily dominated by hysteresis loss [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. At this point, the magnitude of the \u003cem\u003eQ\u003c/em\u003e value mainly reflects the size of the material's hysteresis loss[\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn higher frequency ranges (100 MHz\u0026ndash;1000 MHz), remanent loss (especially domain wall resonance) may become dominant, causing the \u003cem\u003eQ\u003c/em\u003e value to reach a peak and then drop sharply [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. At this point, the height of the \u003cem\u003eQ\u003c/em\u003e value peak and the frequency at which it occurs are important indicators for evaluating the material's high-frequency limits [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe frequency corresponding to the maximum value of the imaginary part of the magnetic permeability (\u0026micro;'') is the cutoff frequency (\u003cem\u003ef\u003c/em\u003er). The cutoff frequencies (\u003cem\u003ef\u003c/em\u003er) of all samples are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e16\u003c/span\u003e. As the Co content increases from 0.00 to 0.10, the Q value shows an increasing trend. When \u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.06, fr increases sharply. At \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.08, the sample's fr reaches 73.71 MHz, and at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10, the sample's fr reaches the maximum value of 104.11 MHz.\u003c/p\u003e \u003cp\u003eFunding: North Rare Earth Project(BFXT-2023-D-0044-1), First-Class Discipline Research Special Project (YLXKZX-NKD-042), Inner Mongolia Natural Science Foundation(2025MS05088)\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eNickel-zinc ferrite Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e was prepared via solid-state sintering, and the influence mechanism of Co doping on the composition, structure, and magnetic properties of the samples was analyzed.As the doping level increased, the nickel-zinc ferrite phase structure of the samples remained unchanged. Throughout the doping process, from \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.00 to \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10, all samples exhibited a single-phase nickel-zinc ferrite structure.The FTIR spectral results show two characteristic peaks at 583 cm⁻\u0026sup1; and 418 cm⁻\u0026sup1;, which correspond to the tetrahedral and octahedral positions, respectively. These are common features of all spinel structures, further confirming the structural formation of the samples we prepared.The SEM results indicate that as the Co doping level increases, the grain size of the samples first increases, then decreases, and eventually levels off. The grains become more uniform and closely packed.The EDS analysis shows that no new elements were detected on the sample surface, confirming their purity and the successful substitution of Zn\u0026sup2;⁺ ions with Co\u0026sup2;⁺ ions.The VSM test results show that the saturation magnetization initially increases and then decreases, while the coercivity first decreases and then increases, and the remanent magnetization initially decreases and then increases.The saturation magnetization reaches its maximum value of 82.2 emu/g at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.08, with a coercivity of 16.37 Oe. At this point, the remanent magnetization is at its lowest, measuring 1.21 emu/g.The dielectric performance test results show that the initial magnetic permeability of the samples first decreases, then increases, and subsequently drops sharply to 45.39.The quality factor (\u003cem\u003eQ\u003c/em\u003e) and cutoff frequency (\u003cem\u003ef\u003c/em\u003er) both increase with the Co doping level, with a sharp rise occurring when \u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.06. At \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.10, \u003cem\u003eQ\u003c/em\u003e reaches its maximum value of 262.88, and fr reaches 104.11 MHz.When the doping level is 0.08, the quality factor (\u003cem\u003eQ\u003c/em\u003e) is 147.34 and the cutoff frequency (\u003cem\u003ef\u003c/em\u003er) is 73.71 MHz. Overall, a doping level of \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.08 is considered the optimal doping amount.In addition, the samples demonstrate enhanced magnetic properties, making them compatible with various magnetic applications. This is of significant importance for the fabrication of nickel-zinc-cobalt ferrite soft magnetic materials with high quality factors, high saturation magnetization, and suitability for high-frequency applications.\u003c/p\u003e "},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eHuiLiu : Conceptualization, Data curation, Formal analysis, Writing \u0026ndash; original draft, Writing \u0026ndash; review \u0026amp; editing. Jie Li : Funding acquisition. XinFang Zhang : Funding acquisition. Qing Wang : Validation. YueKang Zhu :Software. Xiang An : Investigation. YueYang Zhang : Methodology.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eR. 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Mater. \u003cb\u003e7\u003c/b\u003e, 183 (2020)\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":"Soft magnetic ferrites, Magnetic properties, Element doping, Solid-state sintering, Cutoff frequency","lastPublishedDoi":"10.21203/rs.3.rs-8687585/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8687585/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigates the effect of Co doping on the magnetic properties of Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e and explores its potential applications at high frequencies. Co-doped NiZn spinel ferrite powders, Ni\u003csub\u003e0.5\u003c/sub\u003eZn\u003csub\u003e0.5\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eCo\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eFe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e4\u003c/sub\u003e (0.00\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;0.10), were synthesized using the solid-state reaction method.The effects of Co-doped NiZn ferrite powders on the material structure and properties were investigated using X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), vibrating sample magnetometry (VSM), and precision impedance analysis (LCR).The results indicate that with the increase in Co substitution, the phase structure of the NiZn ferrite samples remains unchanged, with all samples exhibiting a single NiZn ferrite phase. The lattice constant of the samples first decreases and then increases.The saturation magnetization (Ms) first increases and then decreases with the increase in Co doping level (\u003cem\u003ex\u003c/em\u003e), while the coercive force (Hc) initially decreases and then increases as the Co doping level (\u003cem\u003ex\u003c/em\u003e) rises.Simultaneously, with the increase in Co doping, the initial permeability (\u0026micro;') of the samples exhibits a trend of first decreasing, then increasing, and finally decreasing again. Meanwhile, the quality factor (\u003cem\u003eQ\u003c/em\u003e) and the cutoff frequency (\u003cem\u003ef\u003c/em\u003er) of the samples gradually increase.When the Co doping level (\u003cem\u003ex\u003c/em\u003e) is 0.08, the sample achieves the highest saturation magnetization, with values of 82.2 emu/g for saturation magnetization and 15.2 Oe for coercive force. The quality factor (\u003cem\u003eQ\u003c/em\u003e) and cutoff frequency (\u003cem\u003ef\u003c/em\u003er) reach 219.69 and 73.71 MHz, respectively.This study provides theoretical guidance on the effects of Co substitution in NiZn ferrites on their material structure, magnetic properties, and high-frequency applications.\u003c/p\u003e","manuscriptTitle":"The influence of Co doping on the structure and magnetic properties of Ni0.5Zn0.5-xCoxFe2O4 ferrites","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-05 08:23:20","doi":"10.21203/rs.3.rs-8687585/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":"07cd3ddc-5621-4c41-8ac3-552911ce0ca4","owner":[],"postedDate":"February 5th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-07T16:12:12+00:00","versionOfRecord":{"articleIdentity":"rs-8687585","link":"https://doi.org/10.1007/s10854-026-17083-5","journal":{"identity":"journal-of-materials-science-materials-in-electronics","isVorOnly":false,"title":"Journal of Materials Science: Materials in Electronics"},"publishedOn":"2026-04-05 16:00:04","publishedOnDateReadable":"April 5th, 2026"},"versionCreatedAt":"2026-02-05 08:23:20","video":"","vorDoi":"10.1007/s10854-026-17083-5","vorDoiUrl":"https://doi.org/10.1007/s10854-026-17083-5","workflowStages":[]},"version":"v1","identity":"rs-8687585","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8687585","identity":"rs-8687585","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}