AC measurements and magnetic properties of magnesium ferrite and its composites with reduced graphene oxide (rGO) and polypyrrole (PPy)

Abstract

Nanoparticle magnesium ferrite and its three composites have been successfully synthesized. The composites incorporate 10% of rGO, 10% of PPy, and 10% of both materials, respectively, with appropriate ratios of Mg ferrite. X-ray diffraction confirmed the formation of a homogeneous spinel phase in all samples. FTIR spectra of the rGO and PPy composites revealed characteristic peaks corresponding to functional groups such as C–O, C = C, and C–H, while interaction between the aromatic rings of PPy and rGO was evident in the ternary composite. Magnetic measurements via VSM showed soft ferrimagnetic behavior for all samples. AC conductivity analysis indicated semiconducting characteristics, with a notable enhancement in the composite containing both rGO and PPy. This improvement is attributed to π–π stacking interactions that facilitate charge transport. Dielectric behavior as a function of frequency suggests that interfacial polarization plays a significant role in the observed properties. Quantitatively, the dielectric constant increased from ~ 36 for pure MgFe₂O₄ to ~ 220 for the MgFe₂O₄/10% rGO/10% PPy composite (≈ 510% enhancement), while the AC conductivity rose from ~ 8 × 10⁻⁵ S/m to ~ 6 × 10⁻⁴ S/m (≈ 650% increase). The Impedance Cole-Cole diagram of the ferrite sample shows a part of a semicircle. As the amounts of rGO or PPy have been raised, the shape of the Cole-Cole diagram becomes smaller and closer to well-observed semicircles in the ferrite/rGO/PPy composite because of the strong π-π stacking interactions mentioned above. These enhancements indicate that the composites are promising candidates for applications in supercapacitors.

Introduction

The dielectric properties of ferrite materials are crucial for various applications, including energy storage and microelectronics. The dielectric behavior indicates the nature of electrical charge carriers and the ability of the material to store electrical energy. Ferrite’s dielectric characteristics are influenced by composition, temperature, and frequency^1,2,3 Spinel ferrites have made significant advances for decades in modern applications due to their impressive magnetic properties and minimum eddy currents. These properties enhance their chances to be used in data storage, microwave devices and other electronic devices. The study of dielectric properties is essential for understanding the suitability of the material for different technological applications. One of the most exploited ferrites are Mg-based ferrites, which are reasonably priced and can be considered as soft ferrites. This is the reason why it is used in many applications such transformer cores, magnetic recording media and chip inductors^4,5.

In addition, inorganic-organic nanocomposite materials are gaining popularity since they provide novel materials that may combine distinct properties of individual constituents. Polypyrrole is chosen as one of the candidates for the present study due to its high conductivity, easily manipulated mechanical and chemical properties along with the ease of synthesis, low density and stability. Ferrite-polymer composites may be superior electromagnetic interference (EMI) suppressors^6,7,8,9. PPy-ferrite composites in particular may be promising materials for sensors, actuators, and electromagnetic interference shielding too^10,11,12,13.

Graphene composites materials with a variety of polymers and ferrites are also attracting the interest of academics due to their unique properties as well as their potential uses. Ferrite and graphene composites combine the perfect magnetic characteristics of the ferrite and the superior graphene electrical conductivity in a hetero-architecture exhibiting a distinguishable electrochemical behavior^14,15. Mariappan et al¹⁶., had used the hydrothermal synthesis approach, to hybridize rGO with ferrites and PPy and investigated their electrochemical properties. Sadiq et al¹⁷., had studied the nanocomposites of PVP (polyvinyl pyrrolidone) and PVA (polyvinyl alcohol) with rGO (reduced graphene oxide). The rGO inclusion was altered at a fixed PVP-PVA weight ratio. They observed linear change of the dielectric constant with the weight% of the rGO.

In the present work, we aim to fill an experimental gap not investigated before by Marriappan et al¹⁶., that is, by investigating the dielectric and AC electrical properties of the ferrite/rGO/PPy composites. Another point of novelty here is using Mg ferrite instead of Co ferrite in the above-mentioned reference. The effects of combining the conductive networks of rGO and PPy with the magnetic ferrite phase may show enhancement of either conductivity or dielectric response, making the materials promising for either supercapacitor or sensor applications. Moreover, it is worth mentioning that although the DC conductivity and some briefly reported structural properties of our samples have been published¹⁸, but to the best of our knowledge, no prior work has investigated or published their AC conductivity and impedance behavior (including Cole–Cole analysis). Our study uniquely addresses this gap too by correlating the dielectric and AC electrical properties enhancements with the microstructural and interfacial features of the composite.

Experimental

Synthesis procedure

The auto-combustion technique was used to prepare the magnesium ferrite. The technique is chemically based to produce a gel and to attain the combustion creating the required spinel ferrite in nanoscale. The detailed graphical illustrations of the steps used in the preparation of the Mg ferrite and the PPy are shown in Figs. 1 and 2. The pure-phase MgFe₂O₄ has been produced utilizing an inexpensive and chemical-based auto-combustion method. The high-purity reactant chemicals used were Mg (NO₃)₂.6H₂O with a purity (98%), Fe (NO₃)₃.9H₂O with a Purity (98%) and citric acid with a purity (99.5%), which have been purchased from Loba Chemie. Mg (NO₃)₂.6H₂O and Fe (NO₃)₃.9H₂O solutions in distilled water have been mixed with the citric acid solution. At room temperature, ammonia (NH₄OH) has been added drop by drop to the nitrate-citrate solution to change the pH to 6.0. This made the solution darker and thicker. The water was then evaporated on a hot plate, resulting in the formation of a viscous gel. With much more heating, a self-propagating combustion event began within the gel. The combustion continued until the entire gel was transformed into a charred ash-like powder. The rough powder was then ground in an agate mortar to produce a fine powder. The fine powder was sintered for 6 h at 900 °C then left into the furnace until being cooled to room temperature.

The pure PPY sample was created via chemical polymerization of pyrrole monomer with apurity (99.5%), which have been purchased from Sisco Research laboratories,

(with FeCl₃.6H₂O as an oxidizing agent) with a ratio of pyrrole: FeCl₃ equals 1:2.33. A solution of 1.21 mol of ferric chloride was added drop by drop to 0.52 mol of pyrrole monomers. The resultant precipitate was obtained after 24 h by filtering and washing with distilled water until it became clear. The reduced graphene oxide was bought from Nano-Gate company in Cairo - Egypt.

To prepare the composites, the required weight percentages of ferrite, polypyrrole and/or reduced graphene oxide are mixed, stirred in distilled water for an hour, sonicated for 45 min, and then dried at 80 degrees for 5 h. Finally, the powders are milled in an agate mortar for 3 hours¹⁸. This final physical mixing process of the composites is illustrated in a schematic diagram in Fig. 3.

Measurements techniques

The prepared samples are investigated by XRD (German Bruker D8 advance diffractometer, Ultima IV- XRD) (10◦ ≤ 2θ ≥ 80◦, Cu-Kα, λ = 1.5405 Å).

Fourier transform infrared (FTIR) spectra for all samples are recorded by Bruker FT-IR in the range of 400–2000 cm⁻¹ at room temperature.

The magnetic characteristics are studied using a lab-made vibrating sample magnetometer (VSM) with a maximum applied field of 8000G at room temperature¹⁹.

The samples are imaged by using SEM (scanning electron microscope, model JEOL-JMS-6510LV) to study their morphology. Energy-dispersive X-ray spectroscopy (EDX) of the samples is performed using the same microscope.

TEM (transmission electron microscope, model JEOL-100SX) has been used to obtain two- dimension images of all samples. The selected area electron diffraction (SAED) has been carried out for the four samples investigated too.

AC electrical properties are measured by using an LCR meter (LCR METER IM3536 - Hioki) throughout a frequency range of 1 kHz to 3 MHz and a temperature range from 303 K to 423 K. Finally, The EIS spectrum analyzer software is used to analyze the Nyquist plots of the present data at the ambient temperature.

Fig. 1

Schematic diagram of the synthesis route employed for preparation of nanoparticle MgFe₂O₄.

Fig. 2

Schematic diagram of the synthesis route employed for preparation of polypyrrole (in the present work n = 1).

Fig. 3

Schematic diagram of the physical mixing process for producing the composites.

Result and discussion

XRD

Figure 4 displays the XRD patterns of MgFe₂O₄, MgFe₂O₄/10%rGO, MgFe₂O₄/10%PPy, and MgFe₂O₄/10%PPy/10%rGO. As mentioned in ¹⁸, the observed diffractograms of all samples confirm the formation of the required spinel ferrite without any impurities. The characteristic peaks of spinel cubic ferrite, are in good agreement with the standard card of MgFe₂O₄ (JCPDS no. 790416)²⁰. The average crystallite size (R), the lattice constant (a), X-ray density (D_x), the measured density (D_m), the porosity (P), the tetrahedral bond length L_A-A (Å), the octahedral bond length L_B-B (Å), and the tetrahedral – octahedral bond length L_A-B (Å), the lattice strain (ε) and dislocation density (δ) have been calculated by the following set of mathematical Eq. (1) at the highest intensity peak corresponding to the (311) plane and are displayed in Table 1.

$$\begin{aligned}\:\text{R}=\frac{\text{k}{\uplambda\:}}{{\upbeta\:}\text{cos}{\uptheta\:}} \\ \text{a}=\text{d}\sqrt{{\text{h}}^{2}+{\text{k}}^{2}+{\text{l}}^{2}}\\\:\text{d}=\frac{\text{n}{\uplambda\:}}{2\text{sin}{\uptheta\:}}\\ \:{\text{D}}_{\text{x}}=\frac{8\text{M}}{{\text{N}}_{\text{A}}{\text{a}}^{3}}\\ \:{\text{D}}_{\text{m}}=\frac{\text{m}}{\text{V}\text{o}\text{l}}\\ \:\text{P}=1-\frac{{\text{D}}_{\text{m}}}{{\text{D}}_{\text{x}}}\\ {\rm L_{A-A} = a} \:\frac{\sqrt{3}}{4}\\ {\rm L_{B-B} = a} \:\frac{\sqrt{2}}{4}\\ {\rm L_{A-B} = a }\:\frac{\sqrt{11}}{8}\\ \:\epsilon\:=\frac{{\upbeta\:}}{4\:Tan\left(\theta\:\right)}\\ \:{\updelta\:}=\frac{1}{{\text{R}}^{2}}\end{aligned}$$

(1)

; where θ is the Bragg diffraction angle, β is the full width of the diffraction line at half maximum intensity, λ is the used wavelength, k (= 0.9) is a constant for cubic spinel ferrite, d is the interplanar distance, M is the molecular weight of the sample, $\:{N}_{A}$ is Avogadro’s number, a³ is the unit cell volume, m is the mass of the sample, and Vol is the measured samples’ volume^21,22,23,24.

The diffraction peaks are sharp and narrow which indicates the crystallinity of the ferrite sample²⁵. Also, there are no distinctive peaks of PPy and rGO in Fig. 1, which may be attributed to the humble ratio of both the polymer and reduced graphene oxide in relation to the ratio of the ferrite therefore the considerably higher ferrite peaks dominate.

It is worth noting that the presence of PPy and rGO combined with the ferrite nanoparticles caused only very slight variations in the ferrite crystal lattice parameters, which ranged between 8.38 and 8.40 Å for all samples. In contrast, the average crystallite size showed a clear dependence on the type of composite: it increased in the rGO-based sample (40.95 nm) compared to the PPy-based one (37.11 nm), with the ternary MgFe₂O₄/rGO/PPy composite exhibiting the largest value (41.01 nm). as shown in Table 1 in agreement with literature²⁶.

Furthermore, by adding the low-density PPy and rGO, the observed density Dm of the composites drops reliably, increasing the porosity in agreement with literature 27. Whereas there are no observable changes in LA-A, LB-B, and LA-B in consistency with the almost constant lattice parameter.

Fig. 4

X-ray diffraction patterns of the Mg ferrite and three composite samples. 

Table 1 The lattice parameter a (Å), the average crystallite size R (nm), X-ray density D_x (kg/m³), measured density D_m (kg/m³), porosity P, dislocation density δ (line/m²), lattice strain (ε), L_A-A (Å), L_B-B, (Å), L_A-B (Å).

FT-IR spectra

The detailed (FTIR) analysis is displayed in this section. As it is well known that the infrared absorption bands are used to identify the molecular vibrational motion of the bonds. It can also help to confirm the formation of new bonds between the composite’s constituents. Figure 5 shows the FTIR spectra of all investigated samples.

The characteristic peaks of PPy and rGO, which were clearly observed in the individual composites, exhibited very small shifts (about 2–3 cm⁻¹) in the ternary MgFe₂O₄/rGO/PPy composite compared to their positions in the binary composites.

According to literature, a detailed illustration of the observed absorption bands of MgFe₂O₄, PPy and rGO is displayed in Table 2. The higher absorption at the 1557 cm^-1 band occurred in the sample containing both 10% rGO and the 10% PPy10%rGO is attributed to the π-π stacking formed between the rGO and the PPy’s aromatic ring^28,29. Also, the overlapping of distinct bands belonging to both the polymer and the reduced graphene oxide sometimes makes the interpretation of FTIR spectra challenging to some extent.

Fig. 5

FTIR spectra of the four investigated samples with assigning all peaks.

Table 2 The observed FTIR characteristic bands of MgFe₂O₄, PPy and rGO in fair agreement with literature.

The vibrational wavenumber at which such bands take place can be used to calculate force constant for the ions’ bonds at the tetrahedral sites F_A and similarly, the ions’ bonds force constant at the octahedral sites F_B. As expected, a very slight change in the force constant is observed in Table 3. The set of Eq. (2) are used to calculate the force constants, F_av the average force constant, σ the Poisson’s ratio, and the stiffness constants C₁₁ and C₁₂³⁹. For solids with a cubic structure, they can be used to estimate the rigidity modulus (G), the bulk modulus (B), and Young’s modulus (E). The equations utilized in these computations are as follows^39,40:

$$\begin{aligned}\:{F}_{A}=4{\pi\:}^{2}{c}^{2}{{\nu\:}_{1}}^{2}{\mu\:}_{1}\\\:{F}_{B}=4{\pi\:}^{2}{c}^{2}{{\nu\:}_{2}}^{2}{\mu\:}_{2}\\ \sigma = 0.324 \times (1-1.043P)\\\:{C}_{11}=\frac{{F}_{AV}}{a}\\\:{C}_{12}=\frac{{\sigma\:C}_{11}}{(1-\sigma\:)}\\\:B=\frac{{2C}_{12}+{C}_{11}}{3}\\\:{V}_{l}=\sqrt{\frac{{C}_{11}}{{D}_{X}}}\\\:{V}_{s}=\frac{{V}_{l}}{\sqrt{3}}\\\:G={D}_{x}\:{V}_{s}\\\:{V}_{m}={\left(\frac{3{V}_{s}^{3}{V}_{l}^{3}}{2{V}_{l}^{3}+{V}_{s}^{3}}\right)}^{\left(\frac{1}{3}\right)}\\\:{\varTheta\:}_{D}=\frac{hc\:{v}_{av}}{2\pi\:k} \end{aligned}$$

(2)

where c denotes the velocity of light in vacuum, while µ denotes the reduced mass of the system containing oxygen and metal. h represents Plank’s constant, and k represents Boltzmann’s constant. The calculated F_A values are greater than those of F_B, indicating that metal ions and oxygen ions interact more strongly in the A-sites than in the B-sites. It is conventional to assume that a small bond length implies strong bonds. However, from Tables 2 and 3, it is observed that the force constant and the bond length both share higher values at the tetrahedral sites than the octahedral sites and this is an abnormal behavior. In spinel ferrites, the tetrahedral (A) sites often exhibit stronger covalent character due to greater overlap between oxygen 2p and metal 3 d orbitals, which raises the force constant even if the bond length is slightly longer. According to lattice-dynamics theory, the bond stiffness (and thus force constant) depends more on the electronic overlap and bond strength than on distance alone, so a longer but more covalent bond can be stiffer than a shorter, more ionic one. This abnormal trend has been observed in other mixed ferrites and is attributed to the enhanced orbital hybridization at the A‐sites⁴¹. However, this abnormal behavior had been reported too in reference⁴² and it had been ascribed to the strong bonds formed between oxygen and metal cations. It is known that Poisson’s ratio is approximately 0.1 for covalently bonded materials, 0.25 for ionically bonded materials, and 0.33 for metallically bonded materials⁴³. Poisson’s ratio for the samples investigated has been calculated and found to be between 0.159 and 0.099. The values close to 0.1, indicate that the materials contain covalent bonding whereas the values close to 0.2 may indicate the presence of some ionic bonding⁴³. In our samples, the bulk modulus (B) and rigidity modulus (G) have been decreased by increasing the ratio of PPy and rGO, specially PPy. However, Young’s modulus is significantly dependent on porosity.

Table 3 Vibrational wavenumbers of samples ν₁ & ν₂, force constants (F), poisson’s ratio (σ), rigidity modulus (G), bulk modulus (B) and young’s modulus (E).

Young’s modulus is significantly dependent on porosity. Young’s modulus of the samples tends to decrease as porosity increases in agreement with literature. The other elastic moduli follow the same trend. This is also manifested in the values of the elastic wave velocities in both longitudinal and transverse direction (V_l and V_s, respectively) and the mean velocity $\:{V}_{m}$^39,40,44. which are shown in Table 4. The slight difference in trend between the elasticity moduli and the vibrational wave velocity is due to the density behavior.

The Debye temperature $\:\varTheta\:$_D is a physical property of a solid that characterizes the vibrational properties of its crystal lattice. It’s essentially a measure of the maximum frequency of lattice vibrations (phonons) in a solid A greater $\:\varTheta\:$_D value suggests a stiffer and less deformable material. In contrast, a lower $\:\varTheta\:$_D values suggest softer, more malleable materials. Table (4) demonstrates that for all samples, the acoustic wave velocities. It is observed that along the longitudinal direction, the vibrations have higher speed which could be explained by stronger bonding. However, in the transverse direction, the vibrations has to move perpendicular to the bonding direction which is not as fast⁴⁵. The main conclusion from such calculation is the confirmation of interaction formation between rGO, PPy, and the magnesium ferrite which is a very strong base for the magnetic and electric properties discussion.

Table 4 Acoustic wave velocities (Longitudinal (V_l), transverse (V_s)), mean wave velocities (V_m) and Debye temperature ($\:{\varvec{\theta\:}}_{\varvec{D}}$).

VSM

Figure 6 shows magnetic characteristics of ferrite and their composites determined at room temperature using a vibrating sample magnetometer (VSM). The figure displays the four samples’ hysteresis loops (MgFe₂O₄, 10% PPy, 10% rGO, and 10%PPy10%rGO). Table 5 lists all the magnetic parameters. It can be shown that when the ferrite content decreases, this affects the magnetic properties of the nanocomposites. The saturation magnetization, M_s, of composites, is mostly determined by the volume fraction of magnetic ferrite particles. As a result, lowering the MgFe₂O₄ volume fraction % decreases M_s – as mentioned above - as well as the remnant magnetization M_r of the composite samples.

To understand the nature of interaction formed between nano ferrites/rGO/PPy, a careful reading of Table 5 should be performed. The value of M_s lies in the range 20–40 emu/gm, which classifies the material as a ferrimagnetic material. A material with a coercive field between 54 and 60 G (which is approximately 4.4 to 4.8 kA/m) would typically be classified as semi-hard magnetic material. Soft Magnetic Materials have coercivity of less than 1 kA/m (about 12.5 G), semi-hard magnetic materials have coercivity between 1 kA/m and 100 kA/m (about 12.5 G to 1250 G). Hard magnetic materials have coercivity greater than 100 kA/m (about 1250 G). Semi-hard materials are often used in applications where moderate resistance to demagnetization is required, such as in magnetic data storage and certain types of sensors⁴⁶.

Fig. 6

Magnetic hysteresis loops of the prepared samples.

To understand the effect of PPy and rGO content addition on the magnetic properties, two new parameters are calculated using Eq. 4, named K the anisotropy and the squareness.

$$\:K=\frac{{H}_{c\:}{M}_{s}}{0.98}$$

$${\rm Squareness} = \:\frac{{M}_{r}}{{M}_{s}}$$

(4)

During the synthesis process, the incorporation of rGO and PPy occurs at the expense of the ferrite fraction in the composite. Since rGO and PPy are essentially non-magnetic, their presence reduces the relative amount of magnetic MgFe₂O₄, leading to a decrease in the overall saturation magnetization (Ms). In addition, the partial coating and isolation of ferrite nanoparticles by these phases, as observed in SEM, further weaken the exchange interactions between magnetic domains.

A good explanation for the trend of the change of K the anisotropy and the squareness with PPy and rGO weight% is that they are submerged in-between the grains. This hinders the alignment of magnetic moments with external field in the meanwhile decreasing the anisotropy. Moreover, the presence of impurities, fractures, pores, and dislocations may be a cause of the composite samples’ magnetic distortion. Anisotropy constant K decreases because of PPy and rGO filling these surface imperfections in composite samples, resulting in a reduction in magnetic surface anisotropy. The squareness values, being low in combination with high coercive field and moderate remnant magnetization, nominate this material for data storage.

Table 5 Saturation magnetization Ms, remnant magnetization Mr, coercivity Hc of the investigated samples, the anisotropy constant K and Squareness.

SEM and EDX

The calculated x-ray average crystallite size is compared to the average size obtained from the (SEM) images shown in Fig. 7. Using the software ImageJ, the images are analyzed, and the average grain size is calculated and compared to the XRD results. It is found that they are in good agreement. The images show the distribution of the PPy and the rGO is homogenous in the composites.

Also, in the SEM images, the darker contrast regions correspond to rGO sheets, while the lighter ones are assigned to MgFe₂O₄ nanoparticles, as distinguished by their different interplanar spacings. The small, fragmented features observed are attributed to the cladding effect of the MgFe₂O₄ particles.

Furthermore, EDX scan is used to confirm the correct chemical compositions and elemental ratios. The results of the scans are summarized in Table 6.

Fig. 7

(a-d): SEM images: (a) MgFe₂O₄, (b) MgFe₂O₄/10% rGO, (c) MgFe₂O₄/10%PPy and (d) MgFe₂O₄/10%PPy/10%rGO.

Table 6 EDX results of all samples (Atomic%).

TEM

Combining several characterization techniques is critical for fully understanding the investigated samples. Therefore, TEM images have been investigated for the two samples MgFe₂O₄/10% rGO and MgFe₂O₄/10%PPy/10%rGO and have been represented in Figs. 8 and 9. Some irregular particle agglomerations have appeared along with diversity in the particle sizes. This is most likely caused by the auto combustion precursor method’s ignition stage, this can cause the creation of non-uniform particles⁴⁷. However, the average size of MgFe₂O₄/10%PPy/10% rGO and MgFe₂O₄/10%rGO obtained from the TEM images is roughly 51.2 nm and 45.7 nm, respectively. The reason for the difference between the TEM and the XRD data can be explained. The XRD data presents the well-ordered grain size whereas, the TEM images, show the size of the grains in addition to the grain boundaries. This causes a slight increase in the TEM data than the XRD calculations.

The fine particles of ~ 20 nm with lighter contrast in Fig. 9 (b) correspond to MgFe₂O₄ nanoparticles. Their lighter contrast arises from the lower electron density compared to the surrounding rGO sheets, which appear darker. The selected area electron diffraction (SAED) has been carried out too, and the observed diffraction rings in the SAED patterns suggest the sample’s strong crystallinity. These diffraction rings are indexed to (220), (311), (400), (422), (511), and (440) planes, which are assigned to the cubic phase of MgFe₂O₄ NPs. Also, these planes match well with the planes which have appeared in the XRD patterns.

Fig. 8

(a), (b), (c) TEM images of MgFe₂O₄/10%rGO nanoparticles, (d) Image of MgFe₂O₄/10%rGO in the diffraction mode.

Fig. 9

(a), (b), (c) TEM images of MgFe₂O₄/10%PPy/10%rGO nanoparticles, (d) Image of MgFe₂O₄/10%rGO/10%PPy in the diffraction mode.

Electric properties

AC conductivity (σ_AC)

The AC conductivity σ_ac, dielectric constant ε′, and loss tangent tan(δ) of the investigated samples have been measured as functions of frequency (1khertz-3Mhertz) and temperature in the range of (303–423 K), to gain a larger insight into their properties.

The σ_ac measurements are shown in Figs. 11 (a-d). The way in which the electrical conductivity of ferrites changes with frequency can be accounted for by a theory developed by Koops. This theory suggests that ferrites have a heterogeneous structure, with regions of good conductivity (grains) separated by regions of poor conductivity at (grain boundaries)⁴⁸.

In ferrites, the conduction mechanism can take place either due to electron or polaron hopping. Electron hopping increases with frequency⁴⁹. This is because higher frequencies can facilitate more hopping events, as the electrons have less time to become trapped in localized states. Additionally, at elevated temperatures, the thermal energy can assist in overcoming energy barriers for hopping, further enhancing the effect of frequency on electron mobility. For the polaron hopping, as frequency increases, the polarization effects that can trap polarons in localized states diminish. This means that polarons can move more freely, leading to an increase in hopping rates. Increased thermal energy helps polarons gain the necessary energy to hop from one site to another. Incorporating rGO and PPy modifies the conduction mechanisms more in favor of polaron conduction in case of the PPy addition. While for rGO addition, the conduction primarily involves electron hopping, polarons also can be formed in certain conditions, especially when there are significant defects.

For the fourth sample, where 10%PPy and 10% rGO are combined, the conduction mechanism has been affected by the π-π stacking formed between the rGO and the PPy’s aromatic ring that is observed in the FTIR data^34,50. Such interaction can cause an overall increase in the conductivity values in addition to a thermally activated behavior at the low frequency limit. In fact, this behavior is observed for the 10% PPy sample but becomes more pronounced for the 10% PPy/10%rGO sample due to the higher electron and polaron hopping mechanism^28,51,52. Figure 10⁵¹ shows an illustration of the electron hopping resulted in the later sample 11.

Fig. 10

Electron Transfer between PPy and rGO sheets⁵¹.

Fig. 11

(a-d): σ_ac vs. frequency (log scale), at different temperatures for all samples.

Dielectric constant (ε′) and loss tangent (tanδ)

In Figs. 12 (a-d), we observe the logarithmic scale variation of the dielectric constant, denoted as ε’, across a range of frequencies (1 kHz-3 MHz) at varying temperatures. Upon initial examination of the frequency dependence, it becomes apparent that the dielectric constant decreases as the frequency rises. Notably, this decrease is more pronounced at lower frequencies, while at higher frequencies, it occurs at a slower rate. Such a pattern of dielectric behavior is commonly observed in spinel ferrites. The interpretation of the dielectric constant and the loss factor shown in Figs. 13(a-d) can be understood in terms of grains and grain boundaries conduction. Within grains, the crystals are highly ordered. This facilitates the alignment and polarization and in turn enhances the dielectric constant and decreases losses. This effect (though being very promoting to the physical properties) is highly pronounced at low frequencies. The grain boundaries, on the other hand, being discontinuity locations hinder the polarization and increase losses. This takes place due to numerous reasons whether charge trapping or scattering. The effect of the grain boundaries is more pronounced at high frequency limit.

The large variation in the dielectric constant with frequency indicates the occurrence of interfacial polarization at low frequencies which is due to the accumulation of charge carriers between the regions of different conductivity in heterogeneous materials⁵³. Research has also shown that interfacial polarization contributes to enhanced dielectric properties⁵⁴. At lower frequencies, other factors, such as defects at the grain boundaries and the number of Fe²⁺ ions, contribute to the high dielectric constant (ε’) in a material. However, as the frequency increases, some of the dipoles responsible for the dielectric constant are unable to respond to the alternating current (AC) field. Mainly, interfacial polarization diminishes, along with the contribution of ionic polarization. Eventually, only electronic polarization remains the dominant factor, resulting in a nonzero, but lower, dielectric constant at very high frequencies^55,56,57.

This explanation becomes clearer while studying the temperature effect. It is apparent that increasing the temperature raises the dielectric constant and losses as well. The temperature rise can be thought of as thermal energy given to the electrons facilitating the alignment and polarization. The losses on the other hand rise due to dissipated energy during the polarization⁴⁷.

The rest of the samples where the addition of the rGO and the PPy are found to increase the dielectric constant and the losses, where they reach their peaks at the 10%rGO/10%PPy sample. This raise could be understood by applying two factors. The first factor is the increase in the π-π stacking which increases charge mobility and hence polarization and losses. The second factor is the grain size effect which is found to increase slightly by incorporating rGO and PPy. It is further confirmed using XRD, SEM and TEM data. This higher grain size facilitates polarization and, at the same time, increases the grain surface area which can lead to more sites for charge accumulation and hence more losses. These two collective effects enhance both conductivity and dielectric constant^53,58.

As demonstrated in Figs. 13 (a-d), the frequency dependence of tan(δ) has decreased in the current study at various temperatures with increasing frequency. This dispersion is ascribed to the low-frequency polarization process being aided by high-resistance grain boundaries. Because of this, charge carriers need more energy to move between various ferrite sites, which accounts for the high value of tan(δ). Low-resistance grains have a greater influence at high frequencies, requiring less energy to perform hopping and as a result, the dielectric loss drops⁵⁹.

Fig. 12

έ vs. frequency (log scale), at different temperatures for all samples.

Fig. 13

(a-d): Tan(δ) vs. frequency (log scale), at different temperatures for all samples.

Impedance spectroscopy analysis

The assessment of the strength of the grain size effects is performed by measuring the real and imaginary parts of impedance for the samples. It is known that the real impedance Z` is more related to the resistive losses in the material. However, the imaginary impedance Z`` represents more the energy stored in the reactive part in the system whether it is electric or magnetic field<sup>60</sup>. Figures 14, 15, 16 and 17 show the Z` and Z`` for all the samples. The figures show the Cole-Cole diagrams which help to identify the relaxation process characterizing the samples in addition the computational fitting for the diagram to obtain an insight into the significance of the grain boundary compared to the grain effect.

Figures 15, 16 and 17 show the subsequent effect for the addition of rGO and PPy. While the effect was the decrease in Z` and Z`` value with the PPy having more decrease than rGO, the more pronounced effect took place in the rGO/PPy sample. The impedance values do not only decrease by three orders of magnitude but also the shape of the curves shows interesting features. The real impedance curves show a plateau shape with a decrease at ~ 100 kHz. The imaginary impedance curves show a peak trend at about the same range (~ 100 kHz) with the peak increasing in width and decreasing in height by the temperature rise. This can be explained by recalling the interaction forces in the composites (π electrons) and grain size effect^61,62,63.

The Cole-Cole diagrams may be explained as follows: firstly, according to the high resistivity of the investigated materials, the electrodes impedance is negligible so that the semicircle representing it doesn’t exist in the figure.

Secondly, according to the well-known equivalent circuit of such heterogeneous materials, there would be two existing semicircles, one representing the grain and the other representing the grain boundary, but since only one semicircle is pronounced in Figs. 14, 15, 16 and 17 (c), it may be due to either hiding one of the semicircles under the other or the coincidence of the two semicircles. We attribute this behavior most likely due to the close similarity between the grain and grain boundary resistances.

Therefore, we have used the EIS spectrum analyzer software to analyze the Nyquist plots of the present data. The fitting is performed for only the samples measured at room temperature. The fittings are presented in Figs. 14, 15, 16 and 17 (d) and the fitting parameters are shown in Table 7. The equivalent electrical circuits consist of two RC equivalent circuits connected in series in which according to literature²⁷ at low frequency, grain boundary resistance (R_gb) and capacitance (C_gb) should dominate, while at high frequency grain resistance (R_g) and capacitance (C_g) should dominate. But by fitting the experimental points and the hypothesized curve using the EIS spectrum analyzer software, it is observed that the grain boundary resistances and capacitances are comparable to those of the grain as shown in Table 7, and this may be the reason of the appearance of one semicircle in the present work implying the coincidence of the two semicircles.

Also, the analysis of the data using the above mentioned software shows the non-Debye capacitance nature of (C_gb), and this capacitance is called a constant phase element (CPE) (i.e. non-ideal capacitor)^35,64,65.

Moreover, the Cole-Cole diagram of MgFe₂O₄ in Fig. 14 (c) depicts that the pure ferrite has a larger semicircle as compared to those of the composites shown in Figs. 15, 16 and 17 (c) where it is obviously seen that the width of semicircle decreases with the increasing percentage of graphene content or PPy content in the samples. It becomes evident that the MgFe₂O₄/10%rGO/10%PPy composite exhibits the smallest semicircles due to the strong π-π stacking interaction mentioned above between rGO and PPy, which effectively reduces the overall impedance.

Fig. 14

(a) The Z′ (real part) of impedance as a function of frequency (log scale). (b) Z′′ (imaginary part) of impedance as a function of frequency (log scale). (c) Cole-Cole diagram (Z″ vs. Z′) for all samples at different temperatures. (d) Cole-Cole (Z″ vs. Z′) plots along with fitted curves for MgFe₂O₄ sample at room temperature and EIS equivalent circuit.

Fig. 15

(a) The Z′ (real part) of impedance as a function of frequency (log scale). (b) Z′′ (imaginary part) of impedance as a function of frequency (log scale). (c) Cole-Cole diagram (Z″ vs. Z′) for all samples at different temperatures. (d) Cole-Cole (Z″ vs. Z′) plots along with fitted curves for MgFe₂O₄/10%rGO sample at room temperature and EIS equivalent circuit.

Fig. 16

(a) The Z′ (real part) of impedance as a function of frequency (log scale). (b) Z′′ (imaginary part) of impedance as a function of frequency (log scale). (c) Cole-Cole diagram (Z″ vs. Z′) for all samples at different temperatures. (d) Cole-Cole (Z″ vs. Z′) plots along with fitted curves for MgFe₂O₄/10%PPy sample at room temperature and EIS equivalent circuit.

Fig. 17

(a) The Z′ (real part) of impedance as a function of frequency (log scale). (b) Z′′ (imaginary part) of impedance as a function of frequency (log scale). (c) Cole-Cole diagram (Z″ vs. Z′) for all samples at different temperatures. (d) Cole-Cole (Z″ vs. Z′) plots along with fitted curves for MgFe₂O₄/10%rGO/10%PPy sample at room temperature and EIS equivalent circuit.

Table 7 Resistance R_g(Ω) and capacitance C_g(F) of grain, and resistance R_gb(Ω) and capacitance CPE (C_gb) of grain boundaries, of all samples at room temperature by using EIS spectrum analyzer software.

Conclusion

The present research provides a detailed and insightful examination of the composites incorporating Mg ferrites with rGO and PPy. Analyzing the samples by different techniques has shown the consistency of all results and has given a deeper insight into the microstructure of the investigated materials. The interaction between Mg ferrite, rGO and PPy in the composites gives rise to a lower saturation magnetization field but more importantly almost constant coercive field with values ranging around 58G promising for magnetic sensors and inductor cores. In other words, it is true that the composite saturation magnetization has decreased by the addition of rGO and PPy but they are still able to attain relatively high coercive field. The electric properties have shown a significant increase in the conductivity values. The real impedance shows a stable performance for a wide range of frequencies and the reactive imaginary impedance shows a resonance relaxation peak. The rGO/PPy sample shows an extremely high dielectric constant as well with an almost monotonically decreasing trend at higher frequencies.

Overall, the MgFe₂O₄/rGO/PPy composite exhibited remarkable improvements in electrical properties, with the dielectric constant enhanced by ~ 510% and the AC conductivity increased by ~ 650% compared to pure MgFe₂O₄. This highlights the strong synergistic effect of incorporating both rGO and PPy with ferrite nanoparticles. These effects can motivate us to nominate these composites for sensors’ application as mentioned above. They also motivate the study of the electrochemical behavior of this composite for supercapacitor application in future work.