Structural, morphological, electrical, and magnetic characteristics of 20MnFe2O4-80SiO2 nanocomposite synthesized by the one-pot auto-combustion route

We report an investigation of the structural, morphological, the ac-dc electrical, magnetic, and Mössbauer spectroscopy properties of 20MnFe2O4-80SiO2 nanocomposite prepared using a one-step and facile auto-combustion approach. XRD pattern shows the formation of MnFe2O4 nanocrystallite without any crystallization of the SiO2 phase. However, the presence of a secondary phase of the nanosized α-Fe2O3 particles was also detected. The morphological analysis showed aggregation of polygonal magnetic nano-crystallites dispersed non-uniformly in a silica matrix. The dc electrical measurements performed on a wide range of temperatures from 120 to 400 K showed the semiconducting nature of the nanocomposite. The temperature dependence of dc conductivity could be perfectly fitted to the nearest neighborhood hopping model with activation energy, ΔENNH, of 0.45 eV. The Nyquist plots demonstrated a nonmonotonous thermally activated trend and non-Debye relaxation behavior. An equivalent circuit was successfully fitted to the complex impedance spectra. The variation of both grain and grain boundary conductivities as a function of temperature exhibited three distinct regions, semiconducting-metallic-semiconducting with different activation energies over the measured temperature window. The provided description of such behavior is further advocated by the ac conductivity and dielectric modulus studies. VSM measurements revealed that the nanocomposite magnetic behavior deviates from the ideal non-interacting superparamagnetic picture, due to the presence of α-Fe2O3 nanocrystalline impurities and relatively intensive exchange interactions between ions. Mössbauer spectra showed the presence of Fe3+ ions with sixfold environment and also confirmed the existence of a sextet related to α-Fe2O3 with a quantity of about 20% out of magnetic components. Fe3+ superparamagnetic doublets were also found within the fitting procedure.


Introduction
Nanostructured spinel ferrites including manganese ferrite have been vastly studied in recent years because of their superior magnetic, catalytic, chemical stability, and electrical conductivity properties [1,2]. Manganese ferrite nanoparticles (MnFe NPs) have shown a high value of the magnetic susceptibility when compared to other ferrite nanoparticles, high chemical stability, easy synthesis process, high resistivity, soft magnetic behavior, and intermediate saturation magnetization [3,4]. These unique characteristics of MnFe NPs have brought potential merits for them to be utilized in several technological applications including MRI [4], targeted drug delivery [5], microwave, inductance, magnetic recording media, electronic devices, and magnetic storage devices, [6] and gas sensors [7].
The structural characteristics of face-centered cubic (FCC) inverse-spinel manganese ferrite have been extensively investigated [8][9][10][11][12]. The studies have shown that several parameters such as the particle, size, synthesis method, doping state, and the cations distribution in spinel structure sublattices can tune the electrical and magnetic properties of the ferrite nanocrystals [13,14]. It was demonstrated that to improve the functionality of the ferrite nanocrystallites and enhance their efficiency in technological and industrial applications, a common approach is the dispersion of magnetic nanoparticles in inert organic/inorganic matrices like polymers, amorphous silica, in other words, fabrication of magnetic-silica (or polymeric) nanocomposites [15]. The addition of an amorphous silica matrix to the magnetic nanoparticles can result in a decrease in the net magnetization of the composition. The silica coating can also lead to the modulation of the cations arrangement, interparticle interactions, and surface/volume ratio of the magnetic nanoparticles, which changes the magnetic response of the nanocomposite [14,15].
On the other hand, the electrical properties of magneticsilica nanocomposites are determined by the molar ratio of each component, the degree of dispersion, and the interaction between the components [13]. It has been previously shown that the insulator/conductor transition observed in composites can be attributed to the temperature and frequency dependence of electrical parameters such as resistance and dielectric behaviors of grains and grain boundaries within the nanocomposite microstructure [13,15].
By far, there have been numerous techniques to construct magnetic ferrite nanocomposites for example Stober sol-gel process [16], co-precipitation [17], microemulsion [18], hydrothermal [19], and auto-combustion [20]. Sol-gel autocombustion is to found be a more facile and time-saving and economically efficient method than other wet-chemistry routes and the nanocomposites prepared by this method are compositionally stoichiometric, homogeneous with controlled microstructure [21]. Previously we have synthesized manganese ferrite-silica (MnFe/Si) nanocomposites using a sol-gel auto combustion route [22]. It was observed that for the stoichiometric MnFe/Si nanocomposites consisting of ≥ 20% (in mole) of magnetic component (manages ferrite), crystallization of the secondary phase of nanosized hematite particles will occur. The aim of the present work is not to investigate the phenomenological reason for the formation of this secondary phase of hematite but to study its impacts on the structure, dc and ac conduction mechanism, and magnetic characteristics of 20MnFe 2 O 4 -80SiO 2 nanocomposite. To the best of our knowledge, there is no report in which the influence of the formation of secondary phase of nanosized α-Fe 2 O 3 particles on the temperature dependence of dc-ac conduction mechanism, cation distribution, and magnetic characterization of the nanocomposite has been comprehensively studied. Therefore in this paper, various characterization techniques, including XRD, Raman, TEM, dc-ac electrical measurements, VSM, and 57 Fe Mössbauer spectrometry, were employed to logically correlate the conduction transport and the magnetic interactions occurring within the nanocomposite. Inclusively the anomalous ac-dc conductivity behavior and magnetic characteristics of the synthesized nanocomposite induced by the formation of the hematite structure as a function of temperature was investigated.

Experimental procedure
To synthesize the 20MnFe 2 O 4 -80SiO 2 nanocomposite, all raw materials, analytical grade iron nitrate (99% purity), manganese nitrate (≥ 97% purity), TEOS (≥ 98% in solution), ammonia (≈30% in solution) and citric acid (98% purity) were purchased from MERCK. An aqueous solution of metal nitrates (molar ratio of Fe: Mn = 2:1) and citric acid (CA) with 1:1 molar ratio of metals to CA were prepared using the proper amount of the starting materials. The aqueous metal nitrates and the CA solutions were stirred for 0.5 h separately and then mixed together. Then, the metal nitrates-citrate solution was continuously stirred for 1 h to have a homogenous solution. During the stirring process of the metal-citrate solution, a small quantity of ammonia was added to maintain the solution pH value at 4. To prepare the silica precursor, TEOS, water, and ethanol were mixed with a ratio of 1/10/4, respectively, and then added up to the metal nitrates-citrate solution, in appropriate proportion to have a stoichiometric manganese ferrite-silica nanocomposite. The mixed solution was constantly stirred for 24 h in the air at a temperature of 100 °C, till the water and ethanol contents were removed and the sol was transformed into a viscous gel. The xerogel was dried at 300 °C in a preheated oven and then the oven temperature increased gradually to 600 °C in when the ignition occurred the loose powder in dark brown color was formed. As of now, the composition is noted 20MnFe/Si where 20 is the molar percentage of manganese ferrite.
The X-ray diffraction patterns (XRD) were collected at room temperature, RT, over a 2θ range of 15°-120° with 0.01° steps, 1 s time exposition per step, using a 2θ-θ coupled-mode Bragg-Brentano geometry, in a Bruker D8 Advance diffractometer with a Cu tube operating at 40 kV and 40 mA. To detect CuKα radiation with λ = 1.54056 Å an N-filter with a Lynxeye silicon area detector was used. The Rietveld refinement was performed on the experimental XRD data using FullProf software. In this method, a Voigt approximation estimating both instrumental and physical (such as defects, dislocations, and internal stress) effects in the broadening of the peaks, was applied to study the XRD profile.
The morphological investigation was executed by the transmission electron microscopy (TEM) Tecnai G2 20 S-TWIN with an electron source of LaB6 emitter and accelerating voltage of 200 kV. For TEM measurements, a small quantity of 20MnFe/Si powder was dissolved in ethanol and the solution was ultrasonicated instantly. Some drops of the solution were deposited on the carbon-coated Cu grid (Agar scientific) and the TEM images were acquired from the asdried solution.
Powder pellets with a thickness and diameter of 2 and 5 mm were compressed by the molding equipment and used for performing Raman and dc-ac electrical measurements. The Raman spectroscopy was carried out in a T64000 Jobin Yvon SPEX spectrometer, using an Ar laser (λ = 532 nm) as an excitation font in a back-scattering geometry, the spectrum was obtained between 200 and 900 cm −1 at RT.
The electrodes acquired for the electrical and dielectric measurements were applied by covering both sides of the flat pellet with silver paint. The dc electrical conductivity (σ dc ) was measured by the two probe method using a Keithley 617 programmable electrometer/source. Impedance spectroscopy measurements were performed in the frequency interval of 100 Hz-1 MHz using an Agilent 4294A Network Analyzer in the C p -R p configuration. The dc electrical and impedance measurements were characterized in the temperature range between 120 and 400 K. dc magnetic measurements in zero-field cooling (ZFC)field cooling (FC) modes and also M-B plots were carried out using a Lakeshore vibrating sample magnetometer (VSM). For the magnetization vs temperature curves in ZFC and FC modes applied field was 0.1 T (1000 Oe) and the temperature ranges from 5 to 300 K. The M (B) loops were collected at various temperatures between 5 and 300 K and under an applied magnetic field of 10 T.
Mössbauer spectra were recorded at room temperature (RT) and 77 K in a transmission geometry, using a source of Co diffused in a Rh matrix with an activity of 925 MBq. The sample consists of a thin and homogeneous layer of powder containing 5 mg Fe/cm 2 . The spectra were fitted by the least squares method, with a set of Lorentzian lines determined using the MOSFIT program (unpublished home made program F. Varret J. Teillet, University of Le Mans, France). The values of isomer shifts are given relative to α-Fe measured at RT. Figure 1a shows the XRD pattern of 20Mn/Fe sample measured at room temperature confirming the formation of the cubic spinel structure of MnFe 2 O 4 in agreement with the JCPDS no. 04-016-8331. However, crystallization of the secondary phase of α-Fe 2 O 3 in the sample was also detected. Moreover, the broad and low-intense hump at observed 2θ ~ 23° corresponds to the short-range correlations in the amorphous silica phase [19].

XRD analysis: induction of a compressive strain
Based on the integral breadth method, the average particle size of nanoparticles, D Sch , was determined using the Scherrer equation [20]: where K = 0.94, λ is the wavelength of the X-ray beam, θ is the Bragg diffraction angle and β stands for the integral breadth. Considering the strain effect in the peak broadening, by means Stokes and Wilson (S-W) approach, one can calculate the apparent strain, η S-W , as [20]: Williamson and Hall proposed a modified approach to study the XRD profile in which both size and strain contributions to the peak broadening are taken into account. From the Williamson-Hall (W-H) method, the total integral breath in reciprocal space (β* = βcosθ/λ) is denoted as [23]:   Table 1. As observed in Fig. 1, the complex background primarily comes from the huge contribution of internal strain, the defects due to the existence of amorphous silica and nanocrystalline α-Fe 2 O 3 phases. Consequently, the deconvolution of XRD peaks is influenced by the proximity of coexisting hematite and manganese ferrite, and the peak broadening and the complexity of the polycrystalline composition affect the analysis of the refinement [19]. This is reflected in the high value of strain of η W-H compared with η S-W where both size and lattice strain is considered.
In addition, it can be depicted that the average crystallite size (using both methods), of MnFe 2 O 4 particles, was found close to 7 nm being much less than the value, 55 nm, determined for the reference sample, uncoated with silica, (not reported in this paper). Such reduction in crystalline size is due to the combined effect of the presence of α-Fe 2 O 3 secondary phase and amorphous silica causing extra retarding force and strain which results in the lattice shrinkage. It is worth noting that we also could determine the average particle size of the α-Fe 2 O 3 crystalline phase using the Scherrer approach; being 30 nm bigger than the one for the MnFe 2 O 4 nanocrystalline phase. This observation further is supported by TEM analysis. Moreover, The content of hematite estimated from Rietveld refinement of X-ray diffraction data was found to be 24% (in mol%) in agreement with the value deduced from Mössbauer spectrometry as later will be discussed.

Morphological studies and Raman spectroscopy
The morphological analysis of the synthesized nanocomposite was carried out through TEM study and the micrographs are shown in Fig. 2a and b. As seen in the figure polygonal and oval particles formed aggregates and were randomly dispersed in an amorphous silica matrix. To determine the size and size distribution of the nanoparticles, at least 50 particles randomly selected from the TEM micrographs were considered. It was achieved that the particle size ranges from 4 to 32 nm and by applying a log-normal function to the size distribution histogram, the average particle size, D TEM , was determined to be 7 nm in accordance with the XRD analysis. The selected area electron diffraction (SAED) pattern ( Fig. 2a) supports, that the concentric rings characterize the amorphous nature of the silica matrix surrounding the bright small, and big spots corresponding to the nanocrystalline MnFe 2 O 4 and α-Fe 2 O 3 nanoparticles, respectively. Moreover, from the HRTEM image of 20MnFe/Si the parallel lattice fringes clearly exhibits the oriented aggregation of the MnFe 2 O 4 and α-Fe 2 O 3 nanocrystallites. Typically the lattice fringe of d ≈ 0.487 nm agrees well with the separation between the (111) lattice planes of MnFe 2 O 4 is brought in Fig. 2b. Raman spectrum of 20MnFe/Si composition measured in the spectral region between 200 and 900 cm −1 at room temperature is represented in Fig. 3. First, the spectrum was baseline corrected to remove the background effect and then normalized with respect to the most intense peak in each spectrum. Identification of all possible vibration modes in the spectrum was obtained by deconvolution into individual Gaussian peaks as described precisely in [24] and labeled in alphabetic order as demonstrated in Fig. 3.
The bands a and e detected at 218 and 594 cm −1 can be assigned to the A 1g and E g modes, respectively, in hematite [25,26]. Raman analysis reveals that four out of five firstorder Raman active modes (A 1g , E g , and 3T 2g ) characteristic of the cubic inverse-spinel structure O7h (Fd3 ̅ m) space group regarded to MnFe 2 O 4 [7] could be observed. The A 1g appeared at 649 cm −1 , band f, is the symmetric stretch of tetrahedral FeO 4 . The E g at 393 cm −1 (band c) is regarded as symmetric bending of oxygen ions with respect to Fe. The T 2g (1) at 280 cm −1 is reflected in the translational motion of Fe-O in manganese ferrite. The peak at 393 cm −1 is caused by the anti-symmetric stretch of Fe and O assigned as T 2g (2) mode. The detection of T 2g (3), band d, at 489 cm −1 is due to an anti-symmetric bending of oxygen to Fe [27]. Raman feature at 810 cm −1 observed is regarded as the Si-O-Si stretching mode in the SiO 4 structure in amorphous silica [28].
The observed reduction in the number of allowed Raman bands of MnFe 2 O 4 can be related to the particle size effect and loss of symmetry induced by the non-stoichiometric composition, the presence of vacancies, and lattice defects

dc and ac electrical investigations: an anomalous semiconducting-metallic-semiconducting transition
The dc electrical conductivity measurement as a function of temperature is illustrated in Fig. 4a for 20MnFe/Si. The dc conductivity was determined using the following formula [31]: where t is the thickness of the pellet, A stands for the pellet area and R is the instantaneous resistance obtained from the dc conductivity measurement. The room temperature dc conductivity for 20MnFe/Si was achieved at 6.25 × 10 -9 (Ω.m) −1 which is 3 orders less than the bare manganese ferrite nanoparticles prepared by the same method (not reported in this paper) being 1.56 × 10 -6 (Ω.m) −1 . In fact, SiO 2 amorphous sol-gel nanopowder has a low electrical conductivity (in the order of 10 -12 -10 -15 Ω.m −1 ) due to its mesoporous conjugated network and high surface area [32]. Moreover, α-Fe 2 O 3 nanocrystalline resistivity ranges from 10 +6 to 10 +9 Ω.m which is higher than MnFe 2 O 4 nanoparticles [33]. Therefore adding insulting amorphous silica and formation of the secondary phase of hematite nanoparticles results in an abrupt reduction of conductivity in 20MnFe/ Si compared with bare MnFe 2 O 4 nanoparticles. The dc conductivity variation with a temperature of 20MnFe/Si exhibits the semiconducting behavior for 20MnFe/Si nanocomposite over the studied temperature range. Considering the insulating nature of silica, thus, it can be elucidated that the conduction mechanism is due to electron hopping conduction between Fe 3+ to Fe 2+ and Mn 3+ to Mn 2+ . According to the nearest-neighbor-hopping (NNH) conduction model, the dc conductivity (σ dc ) in 20MnFe/Si nanocomposite can be stated by the Arrhenius equation yielding [34]: where σ o is a constant, k B = 1.38 × 10 -23 J.K −1 is the Boltzmann constant, and ΔE NNH is defined as the activation energy of the nearest-neighbor hopping.
The ln σ dc plot as a function of 1000.T −1 for the investigated sample is shown in Fig. 4b. The ΔE NNH value is obtained by linear fitting of the curve to Eq. 5 and listed in Table 1. Dielectric and ac conductivity measurements were performed over a frequency range of 10 2 Hz-1 MHz and a temperature interval of 120-400 K. The variation of the real part of the dielectric constant as a function of frequency and temperature at the selected temperatures and frequencies are given in Fig. 5a and b, respectively.
According to Fig. 5a, the dielectric constant monotonously reduces with frequency reaching a plateau at the high-frequency region between 10 5 and 10 6 Hz. Moreover, as observed in Fig. 5b, the dielectric relaxation peak shifts to higher frequencies with temperature confirming the thermally active nature of the dielectric relaxation phenomena [35]. It is worth mentioning that the real part of the dielectric constant of bulk and nanosized SiO 2 is found be to 3.9 and 2.5 [36], respectively. While the dielectric constant for α-Fe 2 O 3 nanoparticles ranges from 5 to 120 [37], dependent on the size and synthesis technique, being much less than the ones for manganese ferrite which varies from 10 2 to 10 5 as the size goes from nanoscale to the bulk scale [38]. According to the the Mössbauer studies (as will be discussed in the following), 20MnFe/Si constitutes about 20% of nanosized hematite particles, therefore, the high value of the real part of the dielectric constant at the lowfrequency region, mainly results from the contributions of α-Fe 2 O 3 and MnFe 2 O 4 nanoparticles. So it can be suggested that the electrons exchanging between Fe 2+ and Fe 3+ ions and the holes that transfer between Mn 3+ and Mn 2+ ions present in different sites are responsible for conduction and dielectric polarization. The dielectric behavior of 20MnFe/ Si can be explained in terms of the Maxwell-Wagner theory of interfacial polarization [39]. In this model, the manganese ferrite-silica nanocomposite system is considered as a heterogeneous system composed of low resistive grains and high resistive grain boundaries. Based on this approach, the electrons and holes should pass through the conductive grains and the resistive grain boundaries. With a reduction in frequency, the electrons get in high resistance grain boundaries, and therefore the nanocomposite has a larger ε′ value in the low-frequency range. In addition, the defects and oxygen vacancies accumulated in the grain boundaries act as active charge carrier traps leading to the form of an enhanced space charge polarization which leads to a higher dielectric constant in the low frequencies. As while, at higher frequencies, the alternation of the applied ac electric field hinders the electron/hole exchange consequently the polarization decreases [40]. Figure 6a, b depicts the Nyquist plots (complex impedance spectra) of 20MnFe/Si composition measured at the selected temperatures. The impedance plots of 20MnFe/Si clearly show depressed single semi-circles suggesting the presence of a non-Debye type of relaxation in our composition with a relaxation time distribution due to the heterogeneous grain size and grain boundary effect [41]. Moreover, it is observed that the diameters of the semicircles decrease as the temperature increase from 250 to 320 K, showing the semiconducting nature of the samples with a negative temperature coefficient of resistance in this measured temperature range [42]. Although an anomalous trend can be detected in the temperature interval of 320-360 K, an increase in the semicircle diameter with the temperature characterizes a positive temperature coefficient of resistance, a feature of metallic behavior. With a further increase in temperature up to 400 K, the impedance spectra define a semiconducting kind of manner. To shed light on the unusual trend represented from the impedance spectra and correlate between the impedance spectra and the microstructure of the sample, we postulate an equivalent electrical circuit drawing.
The proposed equivalent circuit consists of a series combination CPE 1 ||R 1 and CPE 2 ||R 2 (CPE, R circuit element in a parallel configuration), each representing contribution of grain and grain boundary (the inset of Fig. 6a and b). The constant phase element (CPE) in the circuit suggests an unideal Debye behavior [39]. The capacitance value of the CPE element is given by C = Q 1 / n R (1−n)/n where the n value ranges from zero (indicating pure resistive behavior) to unity (for capacitative nature). As illustrated in Fig. 6a and b, the equivalent circuit perfectly fits the experimental data.
From the fitted curves, the values of grain resistance (R g ), grain boundary resistance (R gb ), interior grain capacitance (C g ) and grain boundary capacitance (C gb ) were obtained and listed in Table 2.
According to Table 2, the R g -R gb and C g -C gb variations with temperature show C gb > C g and R gb > R g over the measured temperature window.
We also could obtain the grain and grain boundary conductivity, σ g and σ gb , using the following equation [43]: where A and L are the area and thickness of the sample, respectively. The temperature variation of σ g and σ gb for all the samples are plotted in Fig. 6c.
Based on the NNH model, for a wide temperature range, the temperature dependence of σ g and σ gb can be expressed by [43]: where ΔE a(g) and ΔE a(gb) are the activation energy of the grain and grain boundary, respectively. From the slopes of the linear fittings, we have calculated the values of ΔE a(g) and ΔE a(gb) for 20MnFe/Si which are listed in Table 3. Figure 6c indicates the Ln(σ g ) and Ln (σ gb ) vs 1000/T plots for 20MnFe/Si. In the temperature range 250-320 K, referred to as region I, the observed reduction in the grain and grain boundary resistance is because of thermal activation of the localized charge carriers [39]. In manganese ferrites, conduction comes from the hopping of localized d electrons of transition metal ions residing in oxygen lattices. Due to the electrostatic interaction via superexchange paths Fe 3+ -O-Fe 3+ and Mn 2+ -O-Mn 2+ , the cation 3d level is divided into weak doubly degenerate e g levels and stable triply degenerate t 2g levels [44]. (As later will be discussed from the room temperature Mössbauer data, the iron ions (7) g,gb = g,gb(o) . exp −ΔE a(g,gb) ∕k B T present only Fe 3+ valence state). In region I, the density of hopping carriers within the grain decreases, due to the formation of the secondary phase of hematite and the absence of Fe 2+ sites. Moreover, because of electronic entanglement and surface/core spin disorders, the energy of e g electrons (E k ) is lower than that applied by the grain boundary and the charge carriers get trapped.
Goodenough's theory [45] has suggested the coexistence of both cation-cation, and cation-anion-cation interactions in transition-metal oxides (TMOs). Based on this theory, If the strong cation-anion-cation interactions overcome the weak cation-cation interactions, TMOs present semiconducting-insulating behavior. While, if the direct cation-cation interactions between octahedral B-site dominate, a transition from the semiconducting to the metallic behavior takes place with the temperature. Also, the presence of cations with bivalence states can lead to the metallic character below the Curie temperature as previously reported for nickel ferrite nanoparticles [44] ] are stronger than the cation-cation interaction causing a semiconducting behavior at the region below 320 K. According to Mössbauer spectra, due to the reduced value of the tetrahedral isomer shift compared to the octahedral isomer shift and the formation hematite secondary phase with the six-folded Fe 3+ ions, a fraction of Fe 3+ ions are transferred to the six-fold (B) sites and reversely Mn 2+ ions migrate to 4 coordinated A site. As the Fe 3+ ions shift to the B sites the distance between the ions within the B site shortens and this induces an excessive strain, confirmed by the XRD study presented previously and agreed with the results from the NiFe 2 O 4 nano-structured particles [46]. Resulting of the excessive strain, the surface exchange bonds may break, and a canted spin structure forms. The canted spins influence the [Mn 2+ -O 2− -Mn 2+ ] interactions and also weaken the AB-exchange interactions and as a consequence lower the magnetization value. Thus, it can be assumed that in the region below 320 K, the enhancement in the number of Fe 3+ cations strengthens the exchange interaction between However; beyond 320 K the tendency to oxidize/reduce Mn and Fe ions and create defects such as oxygen vacancies in the ferrite lattice may lead to the formation of Mn 3+ and Fe 2+ cations. Resultantly, in this region from 320 to 360 K, the trapped states get delocalized, and the spins are aligned leading to creating effective conductive channels of [Fe 3+ -Fe 2+ ] and [Mn 2+ -Mn 3+ ] linkages. These channels  delocalize the charge carriers and a transition from semiconducting behavior to metallic behavior occurs. Above 360 K, due to the disordering of surface/core spins and also non-magnetic elements, the localized states reformed and the semiconducting feature reoccurs in region II, with different activation energy. Figure 7a shows the frequency dependence of the real part of ac conductivity in selected temperatures. The σ ac variation with frequency can be divided into two regions: in the low-frequency region a plateau of conductivity while the conductivity is frequency dependent in the high-frequency region. The extrapolation of low-frequency σ ac gives dc conductivity σ dc which is attributed to the long-range translation motion of carriers.
The conductivity frequency-dependent feature observed in 20MnFe/Si can be assigned to the relaxation phenomena taking place within the nanocomposite due to charge carriers hopping [39]. With increasing temperature, the ac conductivity increases due to thermally generated charge carriers. Further, the ac conductivity follows the Johnscher's power law given by [35]: where σ dc is the dc conductivity, A is a constant which varies with temperature and indication of polarizability strength, ω is the angular frequency, and n (0 ≤ n ≤ 1) is an exponential factor that depends on both temperature and frequency and a scale of polaron interactions within nanocomposite structure.
The ac conductivity data were successfully fitted to Eq. 8 and the n values were obtained. Variation for universal exponent n as a function of temperature is shown in Fig. 7b. Several models have been proposed based on the behavior of n such as QMT (Quantum tunneling mechanism, where the value of 'n' is independent of temperature), OLPT (Overlapping large polaron tunneling, where n reaches a minimum followed by increases with temperature), and CBH (Correlated barrier hopping, where n decreases with temperature) [41,43,44].
According to Fig. 7b, the exponent n strongly depends on the temperature for 20MnFe/Si. First, the value of n decreases with temperature and reaches to a minimum followed by an increase in the value with further rising of the temperature up to 360 K. Above 360 K, the n is saturated and becomes constant. Therefore, in 20MnFe/Si below 360 K, the OLPT model explains the conduction process while above 360 K the mechanism obeys the QMT model. In 20MnFe/Si composite, in the temperature interval of 260-360 K, due to the annihilation of Fe 2+ valence state, the possibility of hopping charge pair, Fe 2+ −Fe 3+ , in this composite drops and the small non-overlapping polarons are not formed anymore. Therefore, in the case of a reduced number of hopping charges, the cations, Fe 3+ and Mn 2+ , surrounded by close-packed oxygen anions, O 2− , are isolated from each other, and, then the charge carrier is localized. This localization results in the creation of the polaron and the spatial extent of the polaron may broaden to several interatomic distances [43]. Hence, long-range Coulomb interaction occurs, and the neighboring sites' potentials superimpose on each other. Accordingly, the charge transport takes place via an overlapping large polaron tunneling process.
For temperatures above 360 K, the possible presence of multiple valence states of Mn and Fe ions (Mn 2+ -Mn 3+ and Fe 2+ -Fe 3+ ) and also Jahn-Teller distortion occurring in the composite creates defects the and the charge carrier may hop between site pairs over the potential barrier, the defect centers, separating them. Therefore, the correlated barrier hopping conduction mechanism is the dominant process in this temperature window [41]. To investigate the dielectric relaxation of the sample, the frequency dependence of the imaginary part of electrical modulus, M′′, at different temperatures were plotted in Fig. 8a. The plots show an asymmetric peak at each temperature indicating the spread of relaxation with a different time constant, and non-Debye behavior. Moreover, the variation of the relation with temperature presents a non-monotonous trend; first, the relation peak shifts toward to higher frequencies as the temperature increase from 260 to 320 K. From this point up to 360 K, region II, the relaxation peak shifts down to lower frequencies, again, in the temperature window of 360-400 K (region III), the relaxation peak shifts toward to higher frequencies with temperature. The relaxation time, τ, is defined as = 1 2 f max where f max is the frequency in which the relaxation peak occurs [47]. The logarithmic representation of the relaxation time, Ln(τ), versus the inverse of temperature, 1000/T, is drawn in Fig. 8b. The relaxation time as a function of temperature can be written in the form of the following Arrhenius equation and the dielectric modulus activation energy, ΔE M′′ , is extracted from the linearization of Eq. 6 to the experimnetal data and the obtained values are listed in Table 3: where τ o is a constant parameter.
According to Fig. 8b, three distinct regions can be identified which is clearly in resembling of the semiconducting → metallic → semiconducting transitions already observed in the impedance study.
In region I, the thermally activated [Fe 3+ -O 2− -Fe 3+ ] and [Mn 2+ -O 2− -Mn 2+ ] linkages are responsible for the relaxation and the charge carriers get more mobile as the temperature increases resulting in a shifting of the relaxation frequencies toward higher values. In region II, the shift of the relaxation peak toward a lower frequency supports our discussion of the delocalization of the charge carriers with the random distribution of the energy, and metallic behavior. With an increase in temperature, the lattice vibration increases, and some of the charge carriers scatter from the grain boundaries [43]. The scattering reduces the mobility of the charge carriers and the metallic feature appears. Beyond 360 K, the localization sites are reproduced and the charge carriers get trapped again so the thermal agitation increases the charge carriers' mobility originating the semiconducting feature with different activation energy.

VSM and Mössbauer spectrometry
characterization: deviation from an ideal superparamagnetic picture Figure 9a presents the temperature dependence of the magnetization recorded at a B = 1000 Oe and in ZFC/FC modes. The ZFC curve shows a relaxation peak, T b , characteristic for the superparamagnetic feature at 36 K and T irr = 257 K, the point where ZFC curve and FC curve separate from each other. The hysteresis curves measured at 5 and 300 K are given at Fig. 8b.
Due to the lower thermal fluctuation of the magnetic moments, the magnetization at 5 K is clearly larger than that at 300 K.
As illustrated in Fig. 9b, the hysteresis loops for 20MnFe/ Si measured at 300 K do not saturate even for our highest field (B) (10 T). This indicates a magnetically hard component that can be associated with the surface spin disorder [48]. The observed behavior also might be addressed to the canting of spins in the ferrimagnetically ordered Mn-ferrite and hematite particles due to fairly strong superexchange interactions. To check that if an ideal noninteracting superparamagnetic picture can satisfactorily explain the magnetic behavior of the present composition, we have carried out a comprehensive study. In fact, magnetic nanoparticles are considered to be in superparamagnetic regime if (i) the corresponding anhysteretic curves mannerly can be fitted to a single Langevin function or a weighted sum of Langevin functions and (ii) the scaling of M/Ms with the ratio M S (B/T) is observed [49].
For the 20MnFe/Si, the scaling of M/M S with the ratio M S (B/T) is not observed, as seen in Fig. 10a. Moreover, the Langevin function fitting to the experimental curve deviates, according to Fig. 10b.
Therefore, the long-range and exchange interactions between isolated magnetic moments are effective and should be considered. This shows that the ideal noninteracting superparamagnetic model cannot be matched with the magnetic behavior of 20MnFe/Si and the magnetic interactions  between the particles seem to be critical. The variation of coercivity as a function of temperature is given in Fig. 10c. The coercivity was considered as the average value between negative and positive branches of the hysteresis loops. In accordance with Néel relaxation and the Bean-Livingston approaches, for an assembly of monodispersed and noninteracting magnetic nanoparticles, the temperature dependence of the coercivity as can be described as the following [50]: where K eff is the effective anisotropy constant. It is clear to see that such an approach is in agreement with experimental results only in temperatures below 30 K, T b , where most of the particles are blocked. While above T b , the theoretical model diverges from the experimental data. It can be argued that the behavior is related to the mixture of 2 different magnetic nanoparticle phases in a wide volume distribution with distinct anisotropy axes and relatively strong interparticle interactions [48].
To support the VSM measurement, we performed a study using a local probe technique: 57 Fe Mössbauer spectrometry. The hyperfine structures obtained at 77 K and RT (as shown in Fig. 11) consist of a superposition of quadrupolar and magnetic components. At RT, the magnetic sextet with welldefined lorentzian lines can be clearly attributed to the presence of hematite (see the refined values given in Table 4). At 77 K, the magnetic component, which shows asymmetrical and strongly broadened lines, has to be decomposed into two sub-components. The outer part that can be described by a single magnetic sextet with well-defined lines corresponds unambiguously to the presence of hematite (according to the refined values in Table 4). Moreover, it is important to note that (i) its proportions in terms of Fe content at 300 and 77 K are quite similar and in good agreement with that estimated from X-ray patterns and (ii) the values of the quadrupolar shift at 300 K and 77 K suggest a poor crystallized form of hematite (defective structure, small crystalline domains, presence of Mn cations, role of silica matrix) [51]. The inner part of the magnetic component observed at 77 K must be described by means of a distribution of hyperfine fields linearly correlated to that of the isomer shift. In addition, the quadrupolar components observed at 300 and 77 K are best fitted by means of two quadrupolar doublets with two different values of isomer shift to describe the small asymmetry but their respective and accurate estimates remain difficult due to the lack of resolution of the central part: however, it can be concluded that they can be clearly attributed to Fe 3+ species located in tetrahedral and octahedral sites of MnFe 2 O 4 nanoparticles that show superparamagnetic relaxation phenomena. Such a feature is well consistent with the small size (6-7 nm) as observed above by X-ray diffraction and TEM (see above). But the inner part of the magnetic component observed at 77 K suggests clearly a distribution of size of the spinel ultrafine nanoparticles for which the superparamagnetic relaxation phenomena is fast.

Conclusion
20MnFe/Si was synthesized by a one-step auto-combustion route. XRD pattern confirmed the formation of MnFe 2 O 4 with cubic spinel structure. However, the presence of a secondary phase of hematite was also confirmed. By means of the W-H method, the average size of MnFe 2 O 4 nanocrystallites was found to be 6.5 nm. Moreover, the W-H analysis showed the compressive strain within the nanocomposite. Morphology of the nanocomposites was studied by TEM and confirmed the formation of spherical nanosized particles with a wide size distribution dispersed in amorphous silica. A detailed study on dc electrical properties of 20MnFe/ Si showed that the NNH model can represent a picture from Fig. 11 Mössbauer spectra measured at a 77 K and b RT the dc conduction mechanism in the sample. The impedance measurement revealed a non-Debye and thermally activated relaxation phenomena in 20MnFe/Si. Application of an equivalent circuit was considered to the complex impedance spectra of 20MnFe/Si assuming the grain and grain boundary contributions in conduction mechanism. A comprehensive investigation of the temperature dependence of the grain and grain boundary conductivity revealed a semiconducting-metallic-semiconducting transition over the temperature interval of 260-400 K. The transition is caused by a shift from the cation-anion-cation interaction to the cation-cation interaction occurring with the sample. By employment of the Jonscher power law to the ac conductivity of 20MnFe/Si, it was concluded that both OLPT and QMT models can explain the conduction nature over a whole measured temperature range, in agreement with the analysis given by the modulus and impedance studies.
Static magnetization measurements, VSM, were used to investigate the magnetic behavior of Mn-ferrite/silica nanocomposites. Despite the appearance of a relaxation peak at 33 K on ZFC curve characteristic of the superparamagnetic picture, the examination of the magnetization vs. magnetic field and the coercivity vs. temperature plots declared the magnetic behavior of 20MnFe/Si departs from the ideal non-interacting superparamagnetic picture. This behavior is suggested to be likely due to the particulate of small and big nanocrystallites with different magnetic anisotropy and the interparticle magnetic interactions taking place within the nanocomposite.
The room temperature and 77 K Mössbauer spectroscopy supported the VSM analysis. The Mössbauer spectrum displayed broad linewidth relaxed doublets and a magnetic sextet, this being related to the prominent superparamagnetic feature. The quantity of hematite nanocrystalline in 20MnFe/ Si was determined using the Mössbauer studies being about 20%. A good coherency was observed between the magnetic studies and the conduction mechanism explanations.