Effect of temperature on the dielectric and magnetic properties of NiFe2O4@MgFe2O4 and ZnFe2O4@MgFe2O4 core-shell

This work discusses the experimental results of the electrical and magnetic properties of the core-shell NiFe2O4@MgFe2O4 (NiF@MgF), and ZnFe2O4@MgFe2O4 (ZnF@MgF). The conductivity behavior showed semiconductor-metallic behavior, which varies between NSPT, OSPT, and CBH models depending on the temperatures and the frequencies. In addition, the dielectric showed that a mutual effect between the core and the shell materials, which increases the polarization of the space charge. From this point of view, the nanocomposites show conductive or semiconductor behavior depending on temperature, so they have the potential in many electronic devices application. The magnetization M(T) with the Faraday balance method indicates a good magnetic property of the ZnF@MgF sample. Moreover, the effective magnetic moment (μ Eff) and the Curie-Weiss constant (θ) were obtained from the protocols χ (T).

Nanocomposite has a wide range of applications, especially in multifunction devices, transducers, actuators, and sensors. The components of nanocomposites, as well as how these components accumulate with each other, have a direct impact on the physical properties of these compounds. Numerous geometric forms that accumulate in the nanocomposite, such as particles, cylindrical structures, multilayers, and shell-core nanostructures, have been studied in the literature [1][2][3][4]. The nanocomposite that consists of nanoferrites has rarely been studied although, it is one of the configurations for multisystem and that have useful physical properties by controlling their chemical composition and the size of the structure.
The synthesis, microstructure, morphological, and magnetic hysteresis loops of NiF@MgF and ZnF@MgF were previously studied [22]. So, this work is complete to the previous work to study the electrical and magnetic properties of NiF@MgF and ZnF@MgF and the relationship between the core MgF and the shell NiF or ZnF. The outcomes are discussed and compared with literature data to explicate the dielectric properties and the magnetic susceptibility of the core-shell system. angle θ, loss factor tan δ, and DC resistance (R dc ) are measured directly from the LCR meter, and the other parameters will be calculated from the relations: where ε is the dielectric constant, and σ is the conductivity, C is capacitance (in Farad), t is the thickness of the sample (m), A is the surface area of the sample (m 2 ). For temperature control, the sample was mounted in an electric oven. A Faraday balance is a device for measuring magnetic susceptibility. In this technique, the sample is suspended between electromagnet cores where a magnetic field is applied. Then, the sample is heated gradually using a non-inductive furnace. After measuring the pull of the balance (Δm), many parameters can be calculated such as the molar magnetic susceptibility (χ m ), and the molar magnetization (M m ) can be calculated using the following relations respectively: where: g is the gravity=980.6 cm s −2 , M w is the molecular weight of the sample, m is the mass of the sample, H is the magnetizing field applied, dH/dZ is the magnetic field gradient in the z-direction.

Results and discussion
3.1. Electrical conductivity Conductivity analysis saves significant information related to the transport of charge carriers. The conduction process and their response as a function of both the temperature (300-723 K) and the frequency (10 2 -8× 10 6 Hz) are presented in figures 1(A) and (B). It is easy to notice that, the conductivity behaviors are independent of the frequency applied regardless of the operating temperature. Particularly figure 1(A), for the ZnF@MgF sample at the frequency range 10 2 -9×10 5 Hz, all values of the ac conductivity are very low closed to zero. But at the MHz range of the frequency, the conductivity value increased with increasing the frequency and still coincident with each other. On the other hand, for the NiF@MgF sample in the frequency range 10 2 -9× 10 5 Hz, the values of the ac conductivity increased with increasing the temperature. But at the MHz range of the frequency, the conductivity value increased with increasing the frequency and coincident with each other. This behavior of the ac conductivity between 10 2 and 9×10 5 Hz exhibits almost frequency independent conductivity for all temperatures operated (i.e. Nearly DC conductivity σ dc ). DC conductivity values were calculated by determining the conductivity value of the frequency=0 with interpolating the curves given in figure 1(A). Figure 1(B) shows the curves of the dc conductivity σ dc calculated according to the interpolating the curves given in figure 1(A) and the measured according to equation (3) respectively, versus the temperature. It is observed that the two curves are close to each other for both samples. This means our hypothesis of the behavior of the Ac conductivity between 10 2 and 9×10 5 Hz is a DC conductivity. The behavior of the DC conductivity (σ dc ) versus the temperature (figure 1(B)) could be divided into three regions, denoted as I, II, and III. As is seen in figure 1(B), for the ZnF@MgF sample, the σ dc values decrease up to a certain temperature (first region metallic behavior) and then nearly constant (II region) and increased with temperature increased (III region semiconducting behavior). But for the NiF@MgF sample the σ dc values slowly increase up to a certain temperature denoted as T s (semiconducting behavior), then start to (the second II) decrease up to another certain temperature T m i.e., metallic behavior, and finally (the third III) increases with increasing temperature (semiconducting behavior again) which may be the ferrielectric-paraelectric transition or the Curie temperature (T c ). The T s and T m temperatures correspond to the transition temperatures from semiconducting to metallic, and metallic to semiconducting regions, respectively. The value of the T s is 523 K and the T m is 593 K for the NiF@MgF sample, but the ZnF@MgF has the value of T m =383 K. So, the Curie temperature T c for the ZnF@MgF is 383 K and for NiF@MgF=593 K (as presented in table 1).
The phenomenon of semiconducting and metallic conduction is similar to many cases of ferrites [23,24]. The explanation of this behavior, the composite contains two different materials with different properties: one of these materials may be affected by the second, and this effect may be an enhancement or non-enhancement of  the composite properties [25]. Therefore, the σ-T curves can be explained based on the type interactions (enhancement or non-enhancement) between the core (MF) and the shell (ZF or NiF). As shown in figure 1(B), at low temperatures, the metallic behavior of ZnF@MgF is predominant, but the behavior of NiF@MgF is semiconductors. Also, the transition temperature of NiF@MgF is lower than that of NF (T C =850 K) [24]. As for ZnF@MgF, the situation is different, whereas the transition temperature of ZnF is lower than the room temperature. This means that the net conduction of NiF@MgF will be increased and decrease the transition temperature, also the net conduction and the transition temperature of ZnF@MgF are increased concerning ZnF. Therefore the effect of MgF on both NiF and ZnF is an enhancement of the electrical properties.
Since the relation between the conductivity and the frequency is linearly related as in figure 1 so, these samples under investigation are obeyed to the dynamical power law, which was proposed by Jonscher [26]: where ω=2πf is the angular frequency, A is a constant and has units of σ, and (S) is dimensionless. The value of (S<1) can be determined from the slope of ln σ versus ln ω plots at different temperatures. The conductivity mechanism for any material could be explained by the temperature-dependent behavior of (S). In other words, the relation between the temperature and the value of (S) gives good knowledge about the charge transport mechanism in dielectric substances. According to the relation between the value of (S) and the temperature, several models are proposed in the literature [27][28][29][30]. Figure 2 shows the relation between the (S<1) value and the temperature. It is observed that there is a variation of this relation, indicating different conducting mechanisms dependent on the temperature and the frequency. Here, there are two different values of (S) for each sample, i.e., for the sample ZnF@MgF, it's clear that the exponent (S) increased with increasing the temperature to the transition temperature (383 K), and then decreased. So the non-overlapping small polaron tunneling (NSPT) is appropriate in the range 300-383 K. But at high 383 K, the ZnF@MgF has the correlated barrier hopping (CBH) model, where the value of Sis decreased with increasing the temperature. On the other hand, for the NiF@MgF the exponent (S) is decreased and then slowly increased with temperature, so it tends to propose the overlapping small polaron tunneling (OSPT) model of conduction in the range of temperature 300-543 K. At high temperatures, the exponent value (S) decreased with increasing the temperature, so the CBH model is appropriate at high temperatures.
As shown in figure 3, the ac conductivity values of all samples are increased with increasing the temperature i.e., it is dependent on the temperature. In 10 2 -9×10 2 Hz, the Ac conductivity of all samples is independent of the frequency for all temperatures operated, and the three regions are observed clearly. So, the Ac conductivity has a thermally activated process dependent on the temperature, and obeyed to Arrhenius relation [23]: where A is constant, E a is the activation energy, which is the energy needed to jump an electron from an ion to a neighboring ion, so giving rise to the electrical conductivity, k is Boltzmann's constant, and T is the absolute temperature. So the activation energy can be obtained by plotting Lnσ versus 1000/T, the slope of the linear parts will be equal to (E a /k). The activation energies for these processes are calculated and presented in table 1. It is observed that the value of the activation energies (E a DC) is very low, and less than both the ionization energies of the acceptor or donor (0.1 eV) and the transition energy of Fe 2+ and Fe 3+ is (0.2 eV) [23].

Dielectric properties
The real and imaginary components of the complex permittivity (ε * ) versus frequency and temperature behaviors were shown in figures 4-8. Particularly, figure 4 shows that the behavior of the dielectric constant ε′ is sometimes dispersed and others are coincident with each other at all temperatures operated. Also observed is that the values of the dielectric constant (ε') in the range of (10 2 -9×10 5 Hz) are high at low frequency and decrease with increasing frequency at all temperatures operated. But at the highest frequency range (10 6 -8×10 6 Hz) at any given temperature, the value of the ε′ has been always low as in figure 4. So the dispersion of the dielectric constant (ε′) in the frequency region (10 2 -9×10 5 Hz) is dependent on the temperature and can be explained based on Maxwell-Wagner relaxation behavior [31,32]. The highest values of the dielectric constant ε′ in the low-frequency region are due to the contributions of all types of polarizations like dipolar, interfacial, ionic, and electronic. But in the high-frequency region (MHz region), the dipoles are unable to follow the applied electric field and the only contribution from the electronic polarization so, a lower value of the dielectric constant is obtained. Hence, only electronic polarization contributes to the dielectric constant at the high frequency; therefore the lower value of the dielectric constant is obtained. In other words, the values of dielectric constant ε′ are due to the presence of heterogeneity in the core-shell [22]. These heterogeneities are the interaction between the core (MgF) and the shell (ZnF or NiF) ferrites which give rise to space charge polarization and contribute to the dielectric constant. As the electric field is applied, the space charge created due to the shell (ZnF or NiF) accumulates at the interface of the core (MgF). As the conductivity and permittivity of the constituent phases at the interface are different, the space charge polarization originates. Therefore the coreshell composites have high values for the dielectric constant created due to the space charge.
Also, according to 'the larger grains possess a higher value of the dielectric constant' [33], the increase in grain size may be the reason for a significant increase in the dielectric constant, where the value of the grain size ZnF@MgF, and NiF@MgF samples is 36, and 159 nm, respectively [22]. Generally, the difference between the charge carriers in the grain interior and grain boundaries produces an interfacial polarization that may be causing the overall dielectric constant to increase [34][35][36]. Similar behavior has also been reported in different materials such as the core-shell CuO/CuFe 2 O 4 [23], the nanocrystalline CoGd x Fe 2−x O 4 [37], and the multiferroic composites BaTiO 3 -NiFe 2 O 4 [32]. Figure 5 shows the dependence of the dielectric constant (ε') on the temperature in the frequency range 10 2 -8×10 6 Hz of both samples. The dielectric permittivity data show behavior different from the usual behavior of the ferrites as is shown in figure 5. Three different regions of dispersion can be easily identified at all frequencies operated (like the conductivity). At low temperatures (300-380 K), the dielectric spectra are governed by conductivity effects which are seen as abnormal behavior of the dielectric permittivity curves. At temperatures above 380 K, the dielectric spectra are constant and coincident with each other at low frequencies (10 2 -9×10 3 Hz). But at high frequency (10 4 -9×10 5 Hz), another kind of dispersion moves to make a peak depending on the frequencies. The main feature of this dispersion is the peaks seen in the dielectric constant, which appear at higher temperatures with the increase of frequency. It is worth noting that similar anomalies have been in the literature [38]. The authors attributed this phenomenon to a space-charge polarization in which free carriers are stored at two dielectric electrode interfaces. In the case of multi-phase materials, the interfacial inhomogeneities cause additional local variations of polarization which create local space charges (mobile ions, electrons, etc) confined in the inner or outer interfaces and possessing some limited mobility. In other words, the polarization mechanism in the core-shell composites can be explained by the dielectric behavior of ferrites and is described by the conduction process. Since the charge carriers are constant in ferrites, so band theory fails to explain conduction. However, the hopping model considers that conductivity is due to a change in mobility of constant charge carrier electron, exchanging between Fe 2+ and Fe 3+ with temperature. In the literature, generally, they have referred to Maxwell-Wagner polarization mechanism may be predominating in the total conduction of ceramic materials as in [39] and for other composites.
The frequency and temperature behaviors for the imaginary component (ε″) of the complex permittivity (ε * ) were observed in figures 6 and 7, respectively. Here the dispersion is clear at different frequencies, where at low frequencies, the dielectric constant decreases with the frequencies and increases as temperature increases. At low temperatures, the charge carriers cannot get more energy to orient themselves in the direction of an applied electric field, so the response to polarization is small and hence to dielectric constant. As the temperature increases, the charges get more than enough thermal energy to set free and move with large mobility toward an applied electric field, since space charge polarization increases leading to an increase in dielectric constant. This behavior is attributed due to the effect of temperature, which has more dominant on the interfacial than dipolar polarization due to the generation of crystal defects with increasing temperature. To go further into the analysis of the dielectric result, the dielectric loss (tan δ) must be explained. The tan δ value indicates the loss of electrical energy in the sample. So, the variation of loss tangent (tan δ) as a function of temperature at frequency range (10 2 -8×10 6 Hz) is shown in figure 8. For the ZnF@MgF sample, the dielectric loss has small values close to zero at low temperatures and increases with increasing frequency (10 2 -9×10 4 Hz). In the frequency range (10 5 -9×10 5 Hz) the dielectric loss is decreased with increasing the temperature to reach the smallest value at 383 K and then start up to increase with increasing the temperature. In the MHz region, the dielectric loss is almost constant at all temperatures operated. An increase in the dielectric loss with the temperature may be due to a thermally activated relaxation mechanism [40]. Moreover, an increase in the value of dielectric loss around 383 K can be corroborated with ferroelectric to paraelectric phase change (as seen in conductivity). But for the NiF@MgF sample, for all frequencies operated the value of the dielectric loss is very low sometimes close to zero value. Besides, two losses peaks at low frequencies (10 2 -9×10 3 Hz) around the temperatures 533 K and 623 K are shown as in figure 8, which supports the conductivity behavior with temperature. These peaks are decaying with increasing the frequency where the first disappeared at the frequency 1MHz, and the second disappeared at the frequency 500 Hz. These peaks are not shifted towards higher temperature as the frequency was increased, which indicates the thermally activated relaxation mechanism has not occurred. In other words, the relaxation is thermally activated, when the frequency of the maximum of the relaxation peak is shifted towards a higher frequency with increased temperature. At 580 K and 10 3 Hz, the dielectric loss starts up to increase with increasing the temperature to reach the maximum value. The increase in dielectric loss is attributed to decreasing resistivity with temperature and is expected because as the temperature increases the resistivity decreases. The dielectric loss is found to increase the value of the NiF@MgF than the value of the ZnF@MgF.

Dielectric modulus
The dielectric relaxation and polarization mechanism (space charge, short-range, and long-range polarization) can be well understood by studying the dielectric modulus formalism [41]. The complex electric modulus is defined by the complex dielectric permittivity as: ( ) Figure 9 shows the variation of the real part M′ as a function of frequency (10 2 -8×10 6 Hz) at the temperature range 300 to 723 K for both samples. The dielectric modulus for both samples almost has the same behavior. In an overview of figure 9, we notice that the values of M′ are nearly around zero at the lower frequencies (10 2 -9×10 2 Hz) in the temperature range (303-543 K). With increasing the frequencies, the dispersion of M′ moves towards higher frequencies continuously to reach a maximum value at 1 MHz due to the short-range mobility of charge carriers. Above 1 MHz, the dispersion of M′ moves towards decreased, indicating the long-range mobility of charge carriers. In other words, the short-range and long-range mobilities of charge carriers are associated with frequency, which agrees with other composites [42][43][44][45]. In addition, the value of M' is found to have different behavior with temperature, sometimes increases, and others decrease, and sometimes coincide with each other.
The imaginary part of the electrical modulus M″ with frequency plots at a temperature range (300-723 K) is shown in figure 10. For the sample ZnF@MgF, the M″ spectra are characterized by two relaxation peaks at intermediate and high frequencies for all temperatures operated. These peaks are attributed to both the shortrange and the long-range hopping of charge carriers from one ionic site to the neighboring ionic site in grain boundaries. In addition, at the higher temperatures, the appearance of a long tail in the low-frequency region, due to the large capacitance related to the electrode at lower frequencies. On the other hand, the M″ of NiF@MgF is characterized by a large dispersion region with increasing frequency and tends to reach a maximum at higher frequencies, and showed the non-Debye relaxations. To support this data, we have also plotted the variation of  figure 11. It is observed that there are semicircles connected to the grain and grain boundary effects of the sample. In addition, at high temperatures for NiF@MgF the centers of the semicircular arcs will be laid behind the M″ -axis, which supports the assumption the relaxations may be non-Debye type [46].

Temperature and frequency dependence of Z′ and Z″
The temperature and frequency dependence on the real (Z′) and the imaginary (Z″) part of complex impedance (Z * ) is generally written as: Where j denotes the phase. The variation of Z′ with applied frequency at the temperatures (303-773 K) is depicted in figure 12 for both samples. It can be seen from figure 12 that, Z′ is a higher value at lower frequencies, and decreases with increasing frequency, and then merges to a small value for all temperatures operated. Higher values of Z′ at lower frequencies can be attributed to the space charge effects [47][48][49]. Also, it is an observed fact that Z′ is decreasing with temperature. This happens due to the lower density of trapped charges and enhancement of immobile species at lower frequencies [50]. Also, the variation of Z″ with frequency in temperatures (303-773 K) is shown in figure 13. It is observed from figure 13 peak shifts to higher frequencies with increasing temperatures. This indicates a fact that both samples exhibit a temperature-dependent relaxation process. These relaxations can be formed due to all the charge carriers for a particular temperature will acquire sufficient energy and; will be accumulated at the grain boundary interface. So, the polarization has a maximum at this point. Therefore, the Z″ maybe have a larger extent in numerical value, which made the peaking behavior of those parameters. However, the maximum frequency can be obtained from Z″ versus frequency (including temperature) plots as depicted in figure 13. Furthermore, the relaxation time (τ) is evaluated using an equation: τ=(2πf max ) −1 , where f max is the maximum frequency. The relaxation (maximum) frequency increases with temperature and consequently, the relaxation time decreases with temperature. Similar behavior was observed in the literature [18,51]. Therefore, the variation of τ with temperature (T) obeys the Arrhenius law: τ=τ 0 exp (−E a /K b T), where τ 0 is a pre-exponential factor, K b is the Boltzmann constant, and T is the absolute temperature [52]. The Arrhenius plots (lnτ versus 1000/T plots) are drawn ( figure 14) to find the activation energies of the core-shell ZnF@MgF and NiF@MgF. The curves show three linear slopes related to the conductivity regions. The slope change is usually occurring in ferrites due to either ferri-paramagnetic transitions or due to an increase in thermally activated charge carriers having two simultaneous hopping mechanisms as mentioned above. The estimated activation energies (EI, EII, and EIII) are reported in table 1. It is observed from the results that the energies of the high-temperature region are more than that of the low-temperature region. This can be attributed to the conduction process of the core and shell. Similar slope changes in more than one region are reported in the literature [18,53]. The existence of these three relaxation processes is analyzed using complex impedance spectra (Z′versus Z″). The complex impedance spectra of both the core-shell samples for various temperatures are shown in figure 15. The plots of both the core-shell samples show different depressed semicircles, indicating the grain and the grain boundary contribution of both the core-shell samples to the impedance. The Nyquist plots are semicircular with their center lying below the real impedance axis depicting that the composites demonstrate Maxwell Wagner's relaxation behavior. It is observed that as the temperature increases the intercept point on the real axis shifts towards the origin, which indicates the decrease in the resistive property [35,54]. The asymmetry and depressed nature of semicircle arcs indicate the non-Debye nature of relaxations present in the core-shell. The radius of semicircular arcs is equivalent to the resistance of the material which is decreasing with temperature due to increasing conductivity. It is also observed that for NiF@MgF the impedance plots tend to become linear, indicating a decrease in the capacitive nature of the NiF@MgF core-shell. As also reported earlier a linear relation is obtained of other composites [35,55].

The magnetic susceptibility
The measurement of magnetic susceptibility is an interesting method for determining phase boundaries in magnetic systems as there is a distinct variation in magnetic properties that occurred during a phase transition. The temperature dependence of the magnetization M(T) for both samples is shown in figure 16. The temperature plots are obtained in a magnetic field of 0.8mT in the range of 300-500K. The data reveal the normal trend of ferrimagnetic materials; the M(T) decreases with the temperature increasing to reach the paramagnetic region where the magnetocrystalline anisotropy ceases, and then magnetization drops at the well- known Curie point. In the paramagnetic region, the thermal energy increases the entropy and the spin becomes in a random orientation where the forces overcome the magnetocrystalline energy. Also notice that the magnetization of the core-shell ZnF@MgF is high, which confirmed the previous work [22]. The increase of the magnetization for the core-shell ZnF@MgF can be explained by: • The canting angle between the moments in the B-site may be decreased, which leads to an increase in the magnetization [25].
• The increase of the value of the total magnetic moments in the octahedral site contributes to an increase in magnetization.
These factors appear to interact with one another and cause magnetization to increase for ZnF@MgF. Therefore, the sample ZnF@MgF is a ferrimagnetic substance.
From the experimental data, M(T) as shown in figure 16, with increasing the temperature, a smooth drop in the magnetization occurred. The temperature at which magnetization drops is considered as the Curie temperature; at this temperature (T Cm ), the material will be transferred from ferromagnetic to paramagnetic. In other words, the smooth transition at the Curie temperature T Cm can be used as an indicator of the degree of compositional homogeneity in both samples. The Curie temperature (T Cm ) is an important magnetic property and is a compositional-dependent parameter. The Curie temperature (T Cm ) was calculated from the plot of the first derivative of magnetization (dM/dT) versus temperature (T) as shown inset of figure 16 and listed in table 1. The transition temperature T Cm for ZnF@MgF and NiF@MgF is 426.5 K, and 483K respectively, which is different from the transition temperature of the electrical conductivity (T C ). This may be due to the magnetic interaction is less than the electrical interaction between the core (MgF) and the shell (NiF or ZnF), so the magnetic transition temperature (T Cm ) is different from the electrical transition temperature (T C ). In other words, the mutual magnetic effect between MgF and NiF or ZnF leads to a lower magnetic transition temperature. Similar variations of the T Cm and T C values were noticed in the literature [27,56]. Figure 17 shows the relation between the reciprocal magnetic susceptibility (χ M -1 ) and the temperature (T) for both samples. The relation obeyed the well-known Curie-Weiss law in the paramagnetic region. So the experimental effective magnetic moments μ eff and the Curie Weiss constant (ϴ) values can be calculated from the plot of χ M -1 versus T using the relation: where C is the Curie constant equal to the slope of the line in the paramagnetic region and presented in table 1. The variation of μ eff with the substituted ions depends on its grain size. In general, can say that the decrease in grain size leads to minimizing the magnetization [57]. Also, the net magnetic moment is strongly dependent on the Fe 3+ ions on the (B) sites. This means that the magnetic interaction between the MgF and the ZnF is an

Conclusion
From this work, the mutual effect between the core MgF and the shell ZnF / NiF improved the physical properties of NiF and ZnF. In other words, it can be comprehended that due to the magnetic cations and electric charges for both the core and the shell, the electrical and properties magnetic will be greatly varied. The effect of MgF on both NiF and ZnF is an enhancement of the electrical properties as follows: • Where the net conduction of NiF@MgF will be increased and decrease the transition temperature, also the net conduction and the transition temperature of ZnF@MgF are increased concerning ZnF. • The behavior of the conductivity is metallic semiconducting behavior depending on the value of (S), for ZnF@MgF the non-overlapping small polaron tunneling (NSPT) is appropriate in the range 300-383 K and above 383 the correlated barrier hopping (CBH) model. On the other hand, for the NiF@MgF the overlapping small polaron tunneling (OSPT) model in the range of temperature 300-543 K and at T>543K, the CBH model is appropriate.
• The values of dielectric constant ε′ are due to the presence of heterogeneity in the core-shell, which gives rise to space charge polarization.
• The variation of M′ versus M″, there are semicircles connected to the grain and grain boundary effects of the sample. The centers of the semicircular arcs for NiF@MgF will be laid behind the M' -axis, which supports the assumption the relaxations may be the non-Debye type.
• The variation of Z′-versus Z″ plots of both the core-shell samples show different depressed semicircles, indicating the grain and the grain boundary contribution of both the core-shell samples to the impedance.
• The mutual effect on the magnetic properties is more strong, where all samples have magnetic ordering in the temperature range 300-500K. The novelty in this work is an unexpected behavior of ZnF@MgF which possesses magnetization higher than the pure ferrite phase (MgFe 2 O 4 ), and Curie temperature (T Cm ) higher than the room temperature. Therefore, the sample ZnF@MgF is a ferrimagnetic substance.