Effect of ferrite content and temperature on the magnetic properties of Fe@SiO2@Mn-Zn-ferrite SMC materials

Abstract

Building upon previous studies that have reported promising soft magnetic performance of Fe/Mn-Zn ferrite-based soft magnetic composites (SMCs), the present work focuses on effect of ferrite content and temperature on the magnetic properties of Fe@SiO2@Mn-Zn-ferrite SMC materials. A series of five Fe/SiO₂/Mn-Zn SMCs were fabricated using powder metallurgy and compaction. Structural characterization and detailed magnetic property measurements were performed to assess their soft magnetic behavior. The composites were synthesized with varying mass ratios of Fe/SiO₂ to Mn-Zn ferrite powders, specifically 100:0, 99:1, 98:2, 97:3, 96:4, and 90:10. Key magnetic parameters evaluated included complex permeability, maximum permeability, total core loss, and its components: hysteresis loss, classical eddy current loss, and excess loss. Furthermore, frequency–temperature loss maps were constructed to evaluate the magnetic performance under different thermal and frequency conditions. Considering the specific operational frequency requirements, the optimal ferrite concentration within the composite was determined to be in the range of 2–4%. The investigation highlighted the influence of excess magnetic losses, especially within the medium-frequency range. The modified composites demonstrated improved thermal stability, retaining favorable soft magnetic properties after thermal cycling up to 200 °C. These results highlight the potential applicability of the developed composites in environments demanding reliable high-temperature magnetic performance.

Introduction

Soft magnetic materials in the form of powder cores have attracted significant attention for use in electrical equipment such as inductors, transformers, and reactors^1,2, owing to their advantageous properties including isotropic microstructure, high saturation magnetization, and low energy loss at high frequencies. Soft magnetic composites (SMCs), typically composed of magnetic powders embedded in an insulating matrix and fabricated through powder metallurgy, are designed to suppress eddy current losses, which are the primary contributors to frequency-dependent energy dissipation^3,4. This suppression is achieved by applying electrically insulating coatings on the surfaces of individual powder particles, effectively restricting eddy current paths within isolated regions of the material. However, even with electrical insulation at the particle level, interparticle electrical contacts can persist, potentially enabling macroscopic eddy current loops across particle clusters or within the composite’s cross-section^5,6.

Achieving high electrical resistivity through uniform, thin, and stable insulating coatings is therefore crucial for optimizing the magnetic performance of SMCs. The quality and integrity of the insulating layer critically affect magnetic characteristics, particularly total core loss⁷. Various types of insulation coatings have been employed, including organic materials (e.g., thermoplastics, thermosets), inorganic compounds (e.g., phosphates, oxides, sulfates), and hybrid systems^8–11. While these coatings can effectively reduce eddy current losses, they often introduce a magnetic dilution effect, and the presence of air gaps in the insulating phase can degrade permeability and static magnetic performance. Because traditional insulating materials tend to weaken magnetic coupling and lower magnetic conductivity, there is growing interest in using magnetic ferrites as functional insulating layers^12–15. Hybrid composite architectures consisting of a ferromagnetic matrix coated with an insulating ferrimagnetic phase offer a promising approach to enhancing performance. This configuration enables the insulating ferrite layer to contribute to overall magnetization while preserving high electrical resistivity. A recent methodological advancement involves the use of the first-order reversal curve (FORC) technique to assess the quality of ferrite coatings and the degree of magnetic coupling between iron and ferrite phases in hybrid SMCs¹⁶.

Thermal effects can significantly influence the magnetic behavior of SMCs, necessitating the inclusion of temperature-dependent analysis in the modeling and prediction of permeability and core losses¹⁷. This consideration is particularly critical in the design of high-speed electric motors¹⁸. Despite the relevance, relatively few studies have systematically examined the impact of temperature on the magnetic properties of SMCs^19–23. Consequently, while SMCs demonstrate substantial potential in electromagnetic applications, further investigation and optimization of their thermal behavior—especially as it relates to the insulation layer—are warranted.

In this work, a non-conductive ceramic ferrite matrix with inherent magnetic moment was applied to iron particles via a dry mechanofusion process, resulting in significantly enhanced permeability at high frequencies. Accordingly, Fe/SiO₂/Mn–Zn ferrite soft magnetic composites were developed. The key innovation relative to prior research lies in the application of a SiO₂ interlayer combined with a sintered Mn–Zn spinel ferrite, synthesized via a solid-state reaction route, to form a multifunctional coating architecture.

Materials and methods

Preparation and characterization of the SMCs

In this study, ferro–ferrite composites comprising iron particles coated with a bilayer of SiO₂ and Mn–Zn ferrite were synthesized. The ferromagnetic core material employed in the fabrication of soft magnetic composite (SMC) samples was ASC100.29 grade iron powder (Höganäs AB), with particle sizes in the range of 100–160 mm. The Mn–Zn ferrite was synthesized via a conventional solid-state reaction method, using a precursor mixture consisting of 71.2 wt% Fe₂O₃, 21.6 wt% MnO, and 7.2 wt% ZnO. The starting powders were accurately weighed, dry-mixed, and subjected to a pre-sintering (calcination) process at 850 °C for 4 h, employing a heating rate of 4 °C/min. Following the pre-firing step, TiO₂ and CoO were introduced as dopants at concentrations of 1000 ppm and 3000 ppm, respectively. The doped ferrite powders were then wet-milled in a water-based dispersion medium for 9 h, followed by drying at 90 °C for 24 h. Final sintering was performed at 1300 °C for 3 h under a controlled atmosphere, following thermal profiles based on the Morineau–Paulus equation. This sintering protocol was optimized to yield a dense, homogeneously structured spinel-type Mn–Zn ferrite suitable for coating applications. Particle size distribution was measured using a Mastersizer 3000 (Malvern Instruments), which utilizes laser diffraction for precise particle sizing. To achieve a target ferrite particle size of ≤ 40 mm, the sintered Mn–Zn ferrite powder was subjected to an additional milling process lasting 12 h. The morphological and compositional characteristics of the powders and soft magnetic composite (SMC) samples were analyzed using scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), and particle size distribution techniques. The spatial distribution of the secondary phase was evaluated from light optical micrographs using digital image analysis and spatial statistics. To evaluate spatial regularity and clustering, several quantitative metrics were employed: the nearest-neighbor distance for each data point and its mean value, the expected mean distance for a spatially random (Poisson) distribution of identical density, and the Clark–Evans R-index, defined as the ratio of the observed to the theoretical mean nearest-neighbor distance. In situ temperature-dependent X-ray diffraction (XRD) analysis was performed using a Rigaku Ultima IV powder diffractometer equipped with Cu Ka_1,2 radiation (l = 0.1541 nm), coupled with an Anton Paar HTK 1200N high-temperature chamber. The measurements were conducted in the temperature range of 30–200 °C, with a heating rate of 2 °C/min. After reaching each target temperature, a stabilization period of 2 min was employed prior to data acquisition to ensure thermal equilibrium. Composite powders were prepared by blending Fe/SiO₂ and Mn–Zn ferrite powders at varying mass ratios (100:0, 99:1, 98:2, 97:3, 96:4, and 90:10) using a planetary mill operated without milling media, applying the mechanofusion technique. This method promotes the coating of larger iron particles with smaller ferrite particles via high-energy mechanical interaction. The planetary mill operated at 500 rpm, with the rotation direction reversed every 5 min. The blending process was performed under dry conditions for 1 h. During this procedure, repeated mechanical collisions caused the fine ferrite particles to adhere to the surface of the larger, mechanically softer iron particles.

Experimental methods

Electrical resistivity measurements were conducted using a non-contact method, as described in reference ²⁴. The complex magnetic permeability was evaluated over the frequency range of 1–40 MHz using an impedance/gain-phase analyzer (HP4194A). Normal magnetization curves were obtained with an AMH-1K-S permeameter (Laboratorio Elettrofisico), while total power losses in the frequency range of 100 Hz to 1 kHz were determined from hysteresis loops measured at a peak magnetic induction of 0.2 T. For frequencies ranging from 1 to 100 kHz, total losses were measured using MATS-2010SA AC hysteresisgraph.

Results and discussion

Characterization of the structure of Fe/SiO₂/Mn-Zn ferrite samples

The ferrite powders predominantly exhibited particle sizes ranging from 1 to several micrometers, as illustrated in Fig. 1a. Although larger ferrite particles (up to ~ 10 mm) were occasionally observed, they were found to be well-dispersed and non-agglomerated. The iron powder particles exhibited sizes between 100 and 160 mm (Fig. 1b). A representative SEM image of SiO₂-coated iron particles is shown in Fig. 1c. SEM micrographs of the various composite powders with increasing ferrite content are shown in Fig. 1d, e, f, g and h. A higher-magnification image of the Fe/SiO₂/Mn–Zn composite containing 3 wt% ferrite is presented in Fig. 1i. The interaction between the mechanically hard ferrite and mechanically softer iron matrix led to surface smoothing of the iron particles, thereby enhancing ferrite adhesion.

Fig. 1.

SEM of (a) Mn-Zn ferrite, (b) iron particles, (c) iron particles coated with SiO₂, (d) Fe/SiO₂/Mn-Zn 1%, (e) 2%, (f) 3%, (g) 4%, (h) 10% of Mn–Zn ferrite and (i) Fe/SiO₂/Mn-Zn 3% of Mn–Zn ferrite at higher magnification level.

A series of Fe/SiO₂/Mn–Zn soft magnetic composites were fabricated under high-pressure compaction conditions. The compaction was carried out at a pressure of 1.7 GPa, with a pressing speed of 5 mm/min and a peak pressure dwell time of 90 s, conducted in ambient air at room temperature. The composites were formed into ring-shaped samples using a die, yielding specimens with approximate dimensions of 24 mm outer diameter, 18 mm inner diameter, and 2.5 mm height. A reference sample without a SiO₂ interlayer was also prepared under identical processing conditions for comparative analysis. Previous studies²⁵ have demonstrated that the thickness of the SiO₂ layer formed on Fe particles via the Stöber method is influenced by several factors, including the concentrations of TEOS and NH₃, reaction temperature, processing duration, as well as the size and surface morphology of the Fe particles. Typically, the SiO₂ layer produced using this method ranges from approximately 5–10 nm to just under 1 mm in thickness. In the present study, the selected synthesis parameters yielded SiO₂ coatings with thicknesses between 50 and 200 nm, consistent with findings reported in earlier work²⁶. Although the coating is not uniformly distributed, it predominantly lies within the 10–250 nm range. In contrast, the secondary ferrite layer exhibits a substantially greater thickness. Importantly, the spatial distribution of the ferrite phase, its tendency to cluster, and the resulting porosity have a more pronounced influence on the composite’s overall electrical and magnetic properties.

The mass of the resulting samples ranged from 3.0 to 3.4 g, corresponding to calculated densities between 6.60 g/cm³ and 7.46 g/cm³. SEM micrographs taken perpendicular to the compaction direction for samples containing 1%, 2%, 3%, 4%, and 10% Mn–Zn ferrite are shown in Fig. 2. These images demonstrate that with increasing ferrite content, a more pronounced and continuous insulating layer forms around the iron particles. An R-index value (see Supplementary Fig S1a), indicates clustering, while values approaching 1 suggest a random spatial distribution. All calculated R-values were less than 1, confirming a general tendency toward clustering. Among the tested samples, the sample containing 2 wt% ferrite exhibited the highest R-index, indicating the most random distribution, whereas the 3 wt% sample displayed the strongest clustering tendency. A higher degree of randomness implies that the ferrite is primarily distributed over the surfaces of Fe particles, with minimal or no accumulation in the interstitial (triple point) regions. In contrast, a lower R-index suggests more pronounced clustering, potentially due to complete surface coverage of Fe/SiO2 particles accompanied by minor ferrite accumulation in the triple points. The nature of clustering varies with ferrite content. In the sample with 1 wt% ferrite, the observed clustering characterized by a larger number of smaller clusters—can be attributed to insufficient ferrite coverage, remaining below the percolation threshold. Conversely, at higher ferrite contents (4 wt% and 10 wt%), clustering likely results from excess ferrite accumulating in the triple points, forming thicker interparticle layers. In these cases, the clustering tendency is further intensified by porosity localized within the ferrite-rich regions. The value of the secondary phase’s area fraction, (see Supplementary Fig S1b), determined by image analysis, as expected, monotonically increases with the ferrite content.

Fig. 2.

SEM of microstructures of SMCs surfaces perpendicular to compaction direction with surface analysis of the (a) element distribution of the prepared Fe/SiO₂Mn–Zn ferrite, (b) 1%, (c) 2%, (d) 3%, (e) 4%, and (f) 10% of Mn–Zn ferrite in composition.

The synthesized Fe/SiO₂/Mn–Zn composites exhibited relatively dense microstructures characterized by low porosity and thin interparticle boundaries. As illustrated in Fig. 3b, an inverse correlation between sample density and ferrite content was observed. This trend is attributed to the lower intrinsic density of Mn–Zn ferrite compared to pure iron. Sample densities were calculated based on precise geometric measurements and corresponding sample mass.

Fig. 3.

(a) Electrical resistivity and (b) density of investigated Fe/SiO₂/Mn-Zn ferrite SMC samples.

In the studied composite materials, both electrical resistivity and density exhibit predominantly linear trends as a function of ferrite content, as illustrated in Fig. 3. An increase in ferrite content results in a significant enhancement of electrical resistivity, accompanied by a gradual decrease in overall density. Notably, the incorporation of 10 wt% Mn–Zn ferrite leads to approximately a tenfold increase in electrical resistivity, while simultaneously causing a reduction in density of about 10%. This behavior is attributed to the lower intrinsic density of Mn–Zn ferrite (5 g/cm³) relative to that of pure iron (7.86 g/cm³). The simultaneous increase in resistivity and decrease in density with rising ferrite content indicates a strong interrelation between these properties within the composite system.

Evaluating the magnetic properties of materials under elevated temperatures is essential for understanding their thermal stability, particularly for applications operating in high-temperature environments. Prior studies on hybrid composite systems composed of iron and sintered ferrite have highlighted the critical relationship between the thermal stability of the composite’s magnetic properties and the Curie temperature of the ferrite-based insulating layer¹⁹. The use of ferrites with high Curie temperatures can extend the functional temperature range of iron/ferrite composites²³. However, iron composites coated with pure Mn–Zn ferrite, in the absence of non-magnetic binders, exhibit irreversible changes in magnetic permeability upon thermal exposure. This behavior is demonstrated in Fig. 4a and b, where the real and imaginary components of complex permeability are shown before heating (pre-heating), and after thermal cycling to 200 °C followed by cooling to room temperature. Such thermal fluctuations, reflective of practical operating conditions, lead to pronounced degradation of magnetic performance. While the real permeability remains relatively stable at lower frequencies, frequencies above 100 kHz exhibit a marked reduction in the real component and a downward shift in the peak frequency of the imaginary component. This deterioration stands in contrast to the favorable influence of incorporating a ferrite-based coating that serves both as a magnetic and dielectric insulator, such as sintered ferrite grains. Although the permeability tends to stabilize after several heating cycles, the stabilized values remain inferior to those observed in the initial, unheated state.

Fig. 4.

Effect of a thermal cycling on real and imaginary parts of complex permeability of (a), (b) Fe/Mn-Zn ferrite and (c), (d) Fe/SiO₂/Mn-Zn ferrite composites.

In comparison, as shown in Fig. 4c and d, the introduction of a silica (SiO₂) interlayer effectively mitigates thermally induced microstructural changes in the compressed iron particles. The silica acts as a barrier to thermal expansion or contraction that could otherwise create unintended interparticle electrical pathways, thereby preserving the composite’s magnetic integrity across thermal cycles.

To investigate the structural changes occurring in samples lacking the SiO₂ interlayer, in situ X-ray diffraction (XRD) measurements were conducted under increasing temperature conditions. The results for the Fe/Mn–Zn ferrite composite, presented in Fig. 5, reveal a clear trend: the Bragg reflections corresponding to the body-centered cubic (bcc) phase of iron progressively shift towards lower 2θ angles with increasing temperature. This shift is attributed to thermal expansion of the iron crystal lattice. In addition to changes in peak position, a noticeable reduction in peak broadening is observed with temperature elevation. The narrowing of the diffraction peaks suggests the occurrence of structural relaxation processes within the composite material during heating.

Fig. 5.

X-ray diffraction patterns with increasing temperature for Fe/Mn-Zn ferrite composite sample.

A comparison of the X-ray diffraction (XRD) patterns of Fe/Mn–Zn ferrite composites obtained at ambient temperature (25 °C), both before and after in situ annealing (Fig. 6), reveals minimal changes in the peak profiles corresponding to the Fe-bcc phase. This observation suggests that thermal treatment induces structural relaxation without significant alteration to the overall phase structure.

Fig. 6.

Comparison of X-ray diffraction patterns acquired at ambient temperature (25 °C) before and after in-situ annealing XRD experiment at 200 °C.

The structural relaxation induced by thermal treatment is evident in the reduction of the Full Width at Half Maximum (FWHM) of the strongest Bragg reflection (110) corresponding to the Fe-bcc phase. Initially, the FWHM is stable at 0.23 degrees. However, as the temperature increases to 70 °C, the FWHM gradually decreases, reaching a minimum value of 0.185 degrees at 200 °C. Upon cooling back to 25 °C, the FWHM remains at 0.185 degrees, which significantly deviates from the initial value of 0.23 degrees, indicating a notable structural change.

Characterization of the magnetic properties of Fe/SiO₂/Mn-Zn ferrite samples

In Fig. 7, the DC real component of permeability is plotted as a function of temperature for all evaluated composites. Remarkably, a discernible linear increase in permeability is observed spanning from –30 to 200 °C. This temperature-induced trend is likely attributed to the diminishing effective anisotropy K₁ inherent to the materials as temperatures rise, as outlined by Yanagimoto et al. ²⁷. In this context, the rise in permeability with temperature suggests a concurrent reduction in the material’s anisotropy upon heating. The revealed linear trajectory underscores that within the probed temperature range, the permeability of these composites can be adeptly modulated by temperature adjustments.

Fig. 7.

Temperature dependence of DC real component of permeability in Fe/SiO₂/Mn-Zn ferrite composites with different content of ferrite.

Figure 8 depicts the variation in the complex permeability spectra of the examined composites as a function of ferrite insulation content, ranging from 0 to 10 wt%. The real component of permeability transitions from DC conditions to approximately 10 kHz, exhibiting a slight decrease when moving from a ferrite-free sample to one containing 1% ferrite. However, this reduction in permeability is reversed in composites containing 2% and 3% ferrite. As the ferrite content increases further, a continued decline in permeability is observed.

Fig. 8.

(a) Real and (b) imaginary part of complex permeability of Fe/SiO₂/Mn-Zn ferrite samples at different ferrite content.

The incorporation of ferrite into the Fe/SiO₂ composite system demonstrates significant benefits in the medium-frequency range, spanning from 100 kHz to several tens of MHz. Here, both the real and imaginary components of permeability improve with increasing ferrite content, in accordance with the measured electrical resistivity values. Notably, for samples with higher ferrite content, the real component of permeability reaches an equivalent value at a higher magnetizing frequency. Similarly, the peak of the imaginary permeability shifts to a higher frequency with increasing ferrite content. The broad maximum observed in Fig. 8 results from the relaxation of magnetization processes, including both the viscous motion of domain walls and spin rotation. The relaxation dispersion of permeability is influenced by the electrical resistivity and magnetic anisotropy of the material. In contrast, pure sintered Mn-Zn ferrites typically exhibit a strong contribution from spin rotation, characterized by resonance energy absorption at several MHz, which is often accompanied by a less prominent domain wall permeability dispersion, especially at low peak inductions.

At the lowest ferrite concentration (1%), introduced into the Fe/SiO₂ composite without ferrite, the rigid and brittle ferrite particles disrupt the composite’s structure, causing a mild degradation in magnetic properties. However, at higher concentrations (2–3%), this negative effect is mitigated. The ferrite grains effectively neutralize the free magnetic poles of the more sparsely distributed iron particles through magnetic coupling. This coupling mechanism, as elucidated in our previous study via detailed analysis of first-order reversal curve diagrams ¹⁶, suggests that a more homogeneous ferrite coating, along with enhanced magnetic interactions in the 2% and 3% ferrite samples, plays a crucial role in enhancing the DC real component of complex permeability. It is noteworthy that composites with 4% and 10% ferrite content exhibited significantly reduced densities, which in turn diminished the DC real component of complex permeability. The reduced density negatively impacted on the magnetic properties, leading to a decrease in the DC real component of complex permeability. The magnetic coupling provided by the ferrite particles in these compositions was insufficient to offset these adverse effects.

The fundamental magnetic behavior of the fabricated composite materials is reflected in their peak permeability, as shown in Fig. 9. This peak permeability, denoted as m = B_p/H_p, is derived from the peak induction (B_p) and peak magnetic field (H_p) observed in the hysteresis loop under specified magnetizing conditions.

Fig. 9.

Peak relative permeability as a function of (a), (b) magnetic field and (c), (d) magnetic induction in the Fe/SiO₂/Mn-Zn ferrite composites determined from the hysteresis loops measured at (a), (c) DC condition and (b), (d) f = 1 kHz.

Figure 9 presents the permeability as a function of either the peak magnetic field (panels a and b) or the peak magnetic induction (panels c and d). Both relationships show an initial increase in permeability at low to moderate fields or inductions, followed by a distinct peak, after which permeability decreases. This trend indicates the attainment of maximum permeability, corresponding to the point where domain walls are largely annihilated, with subsequent processes primarily driven by magnetization rotation. When transitioning from DC conditions in the field-dependence of permeability to AC measurements at a frequency of 1 kHz (as seen by comparing Fig. 9a with 9b), a reduction in permeability is observed in samples with 4% and 10% ferrite content. In contrast, the permeability of other samples remains relatively stable, even under higher magnetic fields. Although the peak position in the permeability-field relationship remains consistent across varying ferrite concentrations, a shift toward lower inductions is observed in the permeability-induction relationship as ferrite content increases. Specifically, the induction shifts from approximately 0.4 T at 0% ferrite to about 0.2 T at 10% ferrite, a trend that persists even at a frequency of 1 kHz. The decrease in permeability with induction following its peak is more pronounced than the decrease with respect to the field, which can be attributed to the more significant nonlinearity of induction in relation to the magnetic field.

Figure 10 illustrates the relationship between power loss and frequency, ranging from DC to 100 kHz, for samples containing different proportions of Mn-Zn ferrite under a maximum induction of 0.2 T. A reduction in magnetic loss is observed as ferrite concentration increases across all frequencies, until a threshold of 4% ferrite is reached.

Fig. 10.

Power loss as a function of frequency in the range DC—100 kHz at maximum induction of 0.2 T of investigated Fe/SiO₂/Mn-Zn ferrite SMC samples.

Notably, the composite with the highest ferrite content (10%) exhibits higher power loss than the 4% ferrite composite up to approximately 85 kHz, after which it shows the lowest power loss. The factors contributing to power loss in these soft magnetic composites are complex and include hysteresis losses, intra-particle eddy current losses within the conductive iron grains, inter-particle eddy current losses due to electrical connections between particles, and additional losses near the mobile domain walls. In our analysis, we applied the Statistical Theory of Losses ²⁸ to provide a more detailed explanation of the origin of these losses in our composites. According to this framework, the measured losses are considered as the sum of three mechanisms: hysteresis loss (W_h), classical loss (W_class), and excess loss (W_exc).

In the comprehensive analysis of loss separation conducted in this study (Fig. 11), it was observed that hysteresis loss dominated the total loss up to frequencies in the kilohertz range. Hysteresis loss refers to the energy dissipated during the magnetization and demagnetization processes of the material. However, as the frequency increased, excess loss began to exceed hysteresis loss. Micro-eddy current losses, caused by currents circulating within individual iron particles, remained consistent across all samples, likely due to the uniformity of the iron particles coated with SiO₂ in each case. Macro eddy current losses showed a moderate decrease with increasing ferrite content in the composite. This reduction is attributed to the higher electrical resistivity, which impedes the flow of eddy currents, thereby reducing the losses.

Fig. 11.

Energy loss separation for Fe/SiO₂/Mn-Zn ferrite composites with (a) 0%, (b) 1%, (c) 2%, (d) 3%, (e) 4% and (f) 10% of ferrite in composition.

It is important to note that at even higher frequencies, particularly in the megahertz range, eddy current losses are expected to surpass both hysteresis and excess losses. This is because eddy current losses are proportional to the square of the frequency, meaning that at higher frequencies, eddy currents circulate more rapidly, resulting in greater energy losses.

Figure 12 presents the AC hysteresis loops of the synthesized samples at magnetization frequencies of 10 kHz and 90 kHz, subjected to a peak induction of 0.2 T. This figure clearly illustrates the evolution of the hysteresis loops as the frequency increases. A more pronounced slope in the hysteresis curve suggests an increase in permeability, indicating enhanced magnetic responsiveness. In contrast, a larger area within the hysteresis loop as the frequency rises signifies a higher degree of energy dissipation, suggesting that eddy currents within the material become more significant at higher frequencies. Notably, while the materials exhibit a consistent coercive field at 10 kHz, the sample with 4% ferrite content demonstrates the lowest coercive field at the 90 kHz frequency.

Fig. 12.

Hysteresis loops of the Fe/SiO₂/Mn-Zn ferrite SMC samples measured at frequencies of (a) 10 kHz and (b) 90 kHz at maximum induction 0.2 T.

Figure 13 demonstrates that the increase in loss with higher frequencies is mitigated under elevated temperature conditions. The temperature-dependent loss trajectory of the samples highlights the significant influence of thermal effects on their magnetic properties. Elevated temperatures lead to a decrease in magnetic anisotropy, which subsequently results in a reduction in energy dissipation and lower loss values. A notable decrease in loss is observed in the lower-right quadrant of the frequency-temperature plot, particularly for ferrite concentrations of 3% and 4%. This observation underscores the importance of considering thermal effects when evaluating the performance of soft magnetic composites based on iron and Mn-Zn ferrite matrices.

Fig. 13.

Frequency–temperature maps of energy loss in composites with 0 vol%, 1 vol%, 2 vol%, 3 vol%, 4 vol% and 10 vol% of Mn-Zn ferrite measured at peak induction of 0.2 T.

Conclusions

The synthesized Fe/SiO₂/Mn-Zn ferrite composite demonstrated improved soft magnetic properties while maintaining structural stability under thermal variations up to 200 °C. Elevated temperatures led to an increase in magnetic permeability and a reduction in magnetic loss, primarily due to the temperature-induced decrease in magnetic anisotropy. However, the addition of the non-magnetic SiO2 layer slightly reduced the permeability compared to the composites without it. Despite this, the composite demonstrated stable permeability and relaxation dispersion profiles even after thermal cycling under operational conditions. At ferrite concentrations greater than 3 wt%, a decrease in the DC component of real permeability was observed, while magnetic loss decreased across the frequency range up to 100 kHz as ferrite content increased, reaching a minimum at 4%.

For specific operational frequency requirements, the optimal ferrite concentration for the composite was found to be between 2 and 4%. The study highlighted the significant influence of excess loss, particularly in the medium-frequency range.

Author contributions

J.F.: Conceptualization, Investigation, Writing, Supervision, Project administration, Funding acquisition; S.D.: Conceptualization, Methodology, Formal analysis, Investigation, Writing; S.V.: Formal analysis, Investigation, Methodology; J.B.: Methodology, Formal analysis, Investigation; R.B.: Methodology, Investigation; M.F.: Methodology, Investigation; P.K.: Methodology, Project administration, Funding acquisition; V.T.: Methodology, Formal analysis, Investigation; V.Z.: Methodology, Formal analysis, Investigation.

Funding

This work was funded by the Slovak Research & Development Agency (APVV-20–0072), by the Scientific Grant Agency of the Ministry of Education, Science, Research & Sport of the Slovak Republic and the Slovak Academy of Sciences (VEGA 1/0132/24 and VEGA 1/0016/24), and by the EU NextGenerationEU through the Recovery and Resilience Plan for Slovakia under the project No. 09I03-03-V03-00034.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare that they have no competing interests.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-13494-2.