Microstructural, Magnetic, Magnetocaloric, and

Journal of Superconductivity and Novel Magnetism https://doi.org/10.1007/s10948-018-4813-6

ORIGINAL PAPER

Microstructural, Magnetic, Magnetocaloric, and Electrical Properties of Ni0.4 Mg0.3 Cu0.3 Fe2 O4 Ferrite Prepared Using Sol–Gel Method Sobhi Hcini1 · Noura Kouki2 · Reema Aldawas2 · Michel Boudard3 · Abdessalem Dhahri4 · Mohamed Lamjed Bouazizi5 Received: 14 May 2018 / Accepted: 10 July 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018

Abstract Detailed investigations of the microstructural, magnetic, magnetocaloric, and electrical properties of Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite synthesized by sol-gel method have been investigated. XRD pattern indicates that sample has cubic spinel structure ¯ symmetry. The cation distribution of the sample has been determined by Rietveld refinement. Temperature with F d 3m dependence of magnetization shows that sample exhibits a second-order PM to FM phase at the Curie temperature transition reaches value of about 1.56 J TC = 690 K. From the M(μ0 H, T ) data, we found that the maximum entropy change S max M kg−1 K−1 and relative cooling power (RCP) of 136 J kg−1 at μ0 H = 5 T. From electrical conductivity curves, the estimated value of the activation energy is equal to 0.349 eV. The Nequist diagram at different temperatures reveals that the grain boundary contribution is responsible to the conduction process for the studied sample. Keywords Ferrites · Rietveld refinement · Cation distribution · Magnetic and magnetocaloric properties · Relaxation phenomenon · Grain boundary

1 Introduction At the present time, most of the magnetic refrigeration (MR) prototypes are based on gadolinium Gd even though it is quite expensive and subject to technical problems such as corrosion in aqueous environment [1]. In the last years, most of the researches have been focused on the investigation of

Sobhi Hcini

hcini [email protected] 1

Research Unit of Valorization and Optimization of Exploitation of Resources, Faculty of Science and Technology of Sidi Bouzid, University of Kairouan, University Campus Agricultural City, 9100 Sidi Bouzid, Tunisia

2

Department of Chemistry, College of Science, Qassim University, Buraydah Almolaydah, Buraydah, Saudi Arabia

3

LMGP, CNRS, University of Grenoble Alpes, 38000 Grenoble, France

4

Al-Qunfudah University College, Umm Al-Qura University, Al-Qunfudhah City, Saudi Arabia

5

College of Engineering, Prince Sattam Bin Abdulaziz University, 655, Al Kharj 11942, Saudi Arabia

some families of compounds showing the so-called giant magnetocaloric effect (MCE). In this context, many materials were elaborated and studied for MR applications (for example, the Heusler alloys [2–4] and perovskite oxides [5–7]). Comparing with the studies made on these last materials, the investigations on magnetocaloric properties of spinel ferrites are less studied in the litterature [8–15]. As per our knowledge, researchers had tried to analyze, understand, and investigate the anomalous properties of ferrite samples (i.e., structural, electrical, magnetic properties, etc.) using different experimental techniques. But an adequate explanation of the magnetocaloric properties of doped ferrites is still lacking and offers further investigations. In the other area, ferrite compounds have also found their application in many electronic devices such as memory devices, satellite communication, magnetic sensors, computer components, high-density storage, magnetic recording media, transformer cores, gas sensors, contrast enhancement in magnetic resonance imaging (MRI) [16–18]. However, the improvement of these technologies requires a deep understanding of the electrical properties of ferrite materials. In this context, many studies have been presented in the literature which are related to our research group [19–23].

J Supercond Nov Magn

On the other hand, the knowledge of cation distribution is essential to understand the physical properties of AB2 O4 ferrites. The interesting properties of ferrite materials arise from the ability of distribution of cations among the tetrahedral (A) and octahedral (B) sites. The study of cation distributions can provide a mean of developing materials with desired properties that are useful for many devices. Different methods are presented in the literature in order to estimate the cation distribution in spinel ferrites including the Mössbauer analysis [24, 25], the X-ray diffraction [26– 29], and neutron diffraction [30, 31]. Along this line, we aimed in this work at understanding the Rietveld structure refinement, cation distribution, morphological analysis, and magnetic, magnetocaloric, and electrical properties of the mixed Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite prepared using sol-gel method.

using Philips XL30 scanning electron microscopy under an accelerating voltage of 15 kV. Magnetic measurements were performed using extraction magnetometer. The variation of magnetization with temperature M(T ) in field cooled regime was measured from room temperature to 750 K under a constant magnetic field (H = 0.05 T). Isothermal M(H, T ) data were measured around the Curie temperature (TC ) in 0 T ≤ H ≤ 5 T and 650 K ≤ T ≤ 750 K magnetic field and temperature ranges, respectively. The electrical measurements were taken using impedance spectroscopy technique by means of N4L-NumetriQ (model PSM1735) in 102 Hz ≤ f ≤ 107 Hz and 300 K ≤ T ≤ 500 K frequency and temperature ranges, respectively.

3 Results and Discussions 3.1 Microstructural Properties

2 Experimental Details Ni0.4 Mg0.3 Cu0.3 Fe2 O4 sample was prepared using solgel method [19–23]. The initial chemical reagents were Ni(NO3 )2 · 6H2 O, Mg(NO3 )2 · 6H2 O, Cu(NO3 )2 · 3H2 O, and Fe(NO3 )3 · 9H2 O. The powder sample to be used for measurements was finally sintered in air at 1473 K for 24 h. Structural characterization was carried out by X-ray diffraction (XRD) using a diffractometer (X’pert ˚ Pro, PANalytical) with CuKα radiation (λ = 1.5406 A). The structural refinement was carried out by Rietveld analysis of the powder XRD pattern using the FullProf software [32]. Morphology of the sample was analyzed Fig. 1 Rietveld analysis of XRD pattern of Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite

The XRD pattern with Rietveld refinement for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite is presented in Fig. 1. This pattern presents fairly fine and intense ray sign of good crystallization of the synthesized sample. In addition, no additional peaks were observed which shows that sample has single phase. All peaks characterizing the cubic spinel ¯ space group. For ferstructure were indexed in the F d 3m rites with general formula AB2 O4 , the cation distribution among the tetrahedral (A) and octahedral (B) sites can be obtained from an analysis of the X-ray diffraction pattern. Among the methods used to estimate the cation distribution from XRD results: (i) the Bertaut method based on


the comparision of the experimental and calculated intensity ratios for reflections whose intensities are nearly independent of the oxygen parameter, vary with the cation distribution in opposite ways, and do not significantly differ [26, 27]; and (ii) the Rietveld method based on the refinement of the atomic occupancy values [28, 29]. In our case, we used the second method to estimate the cation distributions of Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite. Based on some works reported in the literature, we deduced a preliminary cation distribution for the sample. The Ni2+ and Cu2+ ions have a preference to occupy the B-site [33, 34], while Mg2+ and Fe3+ ions are distributed in both A and B sites [30, 35, 36]. Therefore, the developed formula of Ni0.4 Mg0.3 Cu0.3 Fe2 O4 sample can be written as: 3+ 2+ 2+ 2+ 3+ 2− (Mg2+ δ Fe1−δ )[Ni0.4 Mg0.3−δ Cu0.3 Fe1+δ ]O4 , where δ is the amount of Mg at the tetrahedral (A) site. In the Rietveld refinement procedure using FullProf software, we considered this cation distribution by varying the occupancy factors for different cations to get the best fit The atomic ¯ positions corresponding to the space group (F d 3m) are 8a (1/8, 1/8, 1/8) for cations occupying the tetrahedral (A) site, 16d (1/2, 1/2, 1/2) for cations occupying the octahedral (B) site, and 32e (x, y, z) for O. Figure 1 shows a good agreement between the observed (Yobs ) and the calculated (Ycalc ) profiles. The refined values of structural parameters, including occupancy factors, lattice constant (a), unit-cell volume (V ), oxygen coordinate x(O), isotropic thermal parameters (Biso ), (cation-oxygen) distances, and (cation-oxygen-cation) bond angles for the sample are given in Table 1. Results of refinement show that the refined occupancy factors for (Ni/Cu) are close to the nominal values; however, the amount of Mg at the tetrahedral (A) site is of about δ = 0.1 which leads to the following cation distribu3+ 2+ 2+ 2+ 3+ 2− tion: (Mg2+ 0.1 Fe0.9 )[Ni0.4 Mg0.2 Cu0.3 Fe1.1 ]O4 . This cation distribution is in perfect agreement with that reported by Batoo et al. [34]. The value of the goodness of fit (χ 2 ) comes out to be ∼ 1 (see Table 1), which may be considered to be very good for estimations. The obtained value of oxygen coordinate is characteristic of a spinel-type structure [37, 38] The obtained value of experimental lattice constant ˚ (see Table 1). This value can be comis aexp = 8.4242 A pared with the theoretical lattice parameter (ath ) calculated by assuming the above-suggested cation distribution using the following equation [26]: √ 8 (1) ath = √ (rA + rO ) + 3 (rB + rO ) 3 3 where rO is the radius of oxygen ion, rA and rB are ionic radii of the A and B sites, respectively (the data of ionic radii are obtained from ref. [39]). By applying ˚ This value agree well with (1), we find ath = 8.4202 A. that experimentally obtained from the Rietveld refinement. This confirms the good estimation of the cation distribution

of sample. For comparison, the obtained value of lattice constant for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite is higher than those obtained for the undoped compound Ni0.7 Cu0.3 Fe2 O4 [40, 41]. This difference in lattice constant may be related to the difference in ionic radius between Mg2+ (0.72 ˚ [39]. Also, the lattice constant ˚ and Ni2+ (0.69 A) A) for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 is higher than that previously obtained for Ni0.5 Mg0.3 Cu0.2 Fe2 O4 [19]. This is logical due ˚ compared with to the lower ionic radius of Ni2+ (0.69 A) ˚ [39]. that of Cu2+ (0.73 A) The X-ray density for the sample can be estimated with the following relation [9]: dx =

8M Na 3

(2)

where M is the molecular weight, a is the lattice constant, and N is the Avogadro number. Equation (2) gives dx = 5.011 g cm−3 (see Table 1). This value is lower than those obtained for the Ni0.7 Cu0.3 Fe2 O4 sample [40, 41]; however, it is higher than that reported for the Ni0.5 Mg0.3 Cu0.2 Fe2 O4 sample [19]. These differences are due to difference between the densities of magnesium (1.74 g cm−3 ), nickel (8.91 g cm−3 ), and copper (8.96 g cm−3 ). Using the X’Pert HighScore Plus software to analyze the XRD pattern, the volume-averaged diameter (DXRD ) of crystallites in the sample was estimated from the Scherrer equation. We found that the DXRD value is equal to 77 nm (see Table 1). The SEM image for the Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite sample is given in Fig. 2a. This image shows uniform spherical grains with an average size of about DSEM = 623 nm (see Fig. 2b; Table 1).

3.2 Magnetic and Magnetocaloric Properties The M(T ) curve at H = 0.05 T given in Fig. 3 shows that the Ni0.4 Mg0.3 Cu0.3 Fe2 O4 sample exhibits a ferromagnetic (FM) to paramagnetic (PM) transition as the temperature increases. The TC , estimated from the minimum value of (dM/dT vs. T ) curve, is found to be 690 K. For comparison, this TC value is lower than that obtained for the undoped compound Ni0.7 Cu0.3 Fe2 O4 (TC = 823 K) [40, 42] This result reflects that the substitution of the magnetic Ni2+ ion by the non-magnetic Mg2+ ion can reduce the Curie temperature of the Ni0.7 Cu0.3 Fe2 O4 system. The isotherms of magnetization M(H, T ) measured near TC in the magnetic field range of 0–5 T are showed in Fig. 4. Using these isotherms, we presented in Fig. 5 the Arrott plot M 2 vs. (H /M) [43]. From this representation, we can note that the phase transition for the sample is of second order as the M 2 vs. (H /M) curves exhibited in the vicinity of TC positive slopes [44]. An important magnetocaloric effect corresponding to the variation of the magnetic entropy SM (T , H ) is

J Supercond Nov Magn Table 1 Structural parameters obtained from Rietveld refinement for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite Sample

Ni0.4 Mg0.3 Cu0.3 Fe2 O4

Space group

¯ Fd3m

Cell parameters

˚ aexp (A) ˚ 3) Vexp (A ˚ ath (A)

Atoms

Mg/Fe1

8.4242 (3) 597.84 (4) 8.4202 (0) WP SS AP OP ˚ 2) Biso (A WP SS OP AP ˚ 2) Biso (A WP SS AP OP ˚ 2) Biso (A 1.900 (4) 2.063 (4) 123.5 (2) 92.4 (2) 5.011 77 623 18.2 25.9 10.8 1.35

Ni/Mg/Cu/Fe2

O

Structural parameters

Agreement factors

˚ d(M8a−O) (A) ˚ d(M16d−O) (A) θ(M8a−O−M8a) (deg) θ(M16d−O−M16d) (deg) dx (g cm−3 ) DXRD (nm) DSEM (nm) Rp (%) Rwp (%) RF (%) χ 2 (%)

x=y=z

x=y=z

x=y=z

8a − 43m 1/8 0.09 (2)/1.11 (2) 1.26 (1) 16d − 3m 0.39 (2)/0.21 (2)/0.30 (2)/1.10 (2) 1/2 1.04 (1) 32e 3m 0.2552 (5) 4 2.07 (2)

The numbers in parentheses are estimated standard deviations to the last significant digit

generally manifested in the vicinity of TC at which this max ). S entropy admits its maximum value (SM M (T , H ) occurring when the magnetic field varies from zero to a non-zero value of the field H , can be calculated through the measurement of the different isotherms M(T , H ) using the following equation [1]: H ∂M

SM (T , H ) = SM (T , H )−SM (T , 0) = 0

∂T

dH

H

each discrete field Hj from two measurements at succesM T +T ,Hj )−M (T ,Hj ) , sive temperatures T and T + by ( T

where M(T , Hj )denotes the magnetization measured at the temperature T for a field Hj . Then (3) can be approximated by the following equation:

M T + T , Hj − M T , Hj Hj SM (T , H ) = T (4)

(3) Since our measurements were made with discrete temperature and field steps, the integral of (3) should be replaced by a discrete sum over the set of discrete applied magnetic fields Hj and the partial derivative ∂M ∂T can be evaluated for

where j is the step variation of the magnetic field. The exploitation of the isotherms presented in Fig. 4 using (4) allowed us to determine the variation of the magnetic entropy, SM (T , H ), as a function of temperature T . Figure 6 illustrates the SM (T , H ) for


Fig. 4 M(H, T ) curves near TC for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite

Fig. 2 a SEM image and b particle size distribution of Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite

magnetic field intervals = 1, 2, 3, 4, and 5 T, respectively from bottom to top of the figure. Note in this figure, in agreement with (4), the magnetic entropy admits its max ) at a temperature close to the maximum value (SM Curie temperature TC . This maximum becomes higher as

Fig. 3 M(T ) and dM/dT curves measured at magnetic field of 0.05 T for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite

the field increases (1.56 J kg−1 K−1 at 5 T). There is also a slight displacement of this maximum toward the high temperatures as the magnetic field increases. In order to verify the order nature of the magnetic transition of the sample, we used the universal behavior proposed by Franco et al. [45]. The universal curve can be made by using the normalized entropy change max ) versus the rescaled temperature (θ) such as: (S M /SM −(T − TC )/(Tr1 − TC ), T ≤ TC (5) θ= (T − TC )/(Tr2 − TC ), T ≥ TC where Tr1 and Tr2 are the temperatures of the two reference points that have been selected as those corresponding to max From the left inset of Fig. 6, all the normalized 1/2SM entropy change curves collapse into one curve This confirms the secondorder nature of the magnetic phase transition for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite.

Fig. 5 Arrott plots around TC for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite

J Supercond Nov Magn Fig. 6 SM (T , H ) curves of Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite. The left inset shows max ) vs. (θ ) at (SM /SM different applied magnetic fields. The right inset max shows the and (RCP) variation of SM vs. applied magnetic fields

The effectiveness for application in magnetic refrigeration technology can be evaluted by the relative cooling power (RCP) given as [1]: max × δTFWHM (6) RCP = SM

sample is comparable with that of some other ferrite materials [8, 10]. The variation of the specific heat (CP ) can also evaluated from the SM (T , H ) curves as [1]:

where δTFWHM is the full width at half maximum the ofmax magnetic entropy change curve. The values of SM and RCP exhibit an almost linear rise with increasing the magnetic field as presented in the right inset of Fig. 6. max and RCP values In Table 2, we compared the SM corresponding to magnetic fields of 3 and 5 T with some other values in the literature. It is clear from Table 2 that max and RCP of Ni Mg Cu Fe O the values of SM 0.4 0.3 0.3 2 4

CP (T , μ0 H ) = CP (T , μ0 H )−CP (T , 0) = T

Table 2 Magnetocaloric properties (at magnetic fields of 5 and 3 T) for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite compared with other ferrite materials

∂ (SM (T , μ0 H )) ∂T (7)

Using (7), the CP (T , μ0 H ) curves are shown in Fig. 7. The variation of CP shows two different behaviors around the TC . The sign of values changes from negative below TC to positive above TC .

Ferrite composition

TC (K)

μ0 H (T)

max S (J kg−1 K−1 ) M

RCP (J kg−1 )

Ref.

Ni0.4 Mg0.3 Cu0.3 Fe2 O4 Zn0.6 Cu0.4 Fe2 O4 Zn0.4 Ni0.2 Cu0.4 Fe2 O4 Zn0.2 Ni0.4 Cu0.4 Fe2 O4 Cu0.4 Zn0.6 Fe2 O4 Cu0.3 Zn0.7 Fe2 O4 Cu0.2 Zn0.8 Fe2 O4 Ni0.4 Mg0.3 Cu0.3 Fe2 O4 Zn0.6 Cu0.4 Fe2 O4 Zn0.4 Ni0.2 Cu0.4 Fe2 O4 Zn0.2 Ni0.4 Cu0.4 Fe2 O4 Cu0.4 Zn0.6 Fe2 O4 Cu0.2 Zn0.8 Fe2 O4

690 305 565 705 372 272 145 690 305 565 705 373 140

3 3 3 3 3 3 3 5 5 5 5 5 5

0.97 0.71 0.92 1.01 1.27 0.91 0.77 1.56 1.16 1.41 1.61 1.77 1.17

77 158.54 81.65 131.28 36.68 36.5 37.78 136 289 141 233 – –

PW [8] [8] [8] [10] [10] [10] PW [8] [8] [8] [10] [10]

PW, present work


Fig. 7 Temperature and magnetic fields dependence of specific heat (Cp ) for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite

Fig. 9 Room temperature variation of conductivity for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite with Jonscher power law fitting. The inset shows the temperature dependence of the exponent n

3.3 Electrical Properties Figure 8 shows the variation of the conductivity for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 sample as a function of frequency and temperature. For all temperatures, an increase in conductivity with frequency was observed. With increasing frequency, the conductivity becomes more and more dependent on frequency confirming that the rate of hopping of charge carriers increases [46]. Accorging to the Jonscher’s power law, the total conductivity is given as [47]: σtot = σdc + Bωn

(8)

where σdc is the dc conductivity and A and s are the pre-exponential and exponent factors, respectively. The fitting curves using (8) reveal good agreement between the theoretical and the experimental curves (see Fig. 9 for typical example of fitting at T = 300 K). All the

fitting parameters are summarized In Table 3. It is clear that the exponent s increases when increasing temperature corresponding to a thermally activated process. In such a case, the s values are superior to unity for all the temperatures. According to Funke criterion [48], this means that the electron hopping in the prepared sample occurs between neighboring sites. The n values agree well with those reported in previous studies [19, 20, 22, 23]. on the other hand, sample seems to behave like semiconductor in all the temperature range in view of the rise of dc conductivity with the augmentation of the temperature. The variation of σdc versus temperature can be expressed by means of a well-known Arrhenius plot as [49]: Edc (9) σdc = σ0 exp − kB T where σ0 is a pre-exponential factor, Edc is the activation energy, and kB is the Boltzmann constant. The plot of Ln(σdc ) with reciprocal temperature (1000 T−1 ) is shown in Fig. 10. In all temperature range, the curve is linear Table 3 Comparison of the activation energy found for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite with those of other ferrite samples

Fig. 8 Variation of the conductivity (σ ) with frequency at various temperatures for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite

Ferrite composition

Ea (meV)

Ref.

Ni0.4 Mg0.3 Cu0.3 Fe2 O4 Ni0.5 Mg0.3 Cu0.2 Fe2 O4 Ni0.6 Co0.4 Fe2 O4 Mg0.6 Co0.4 Fe2 O4 Mg0.4 Ni0.2 Co0.4 Fe2 O4 Mg0.2 Ni0.4 Co0.4 Fe2 O4 Ni0.6 Cu0.4 Fe2 O4

0.349 0.369 0.201 0.233 0.273 0.268 0.430

PW [19] [20] [20] [21] [22] [23]

PW, present work


Fig. 10 Ln(σdc ) vs. (1000 T−1 ) for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite

which confirms that the conduction process in the sample is thermally activated. The Edc values (expected from the slope of the linear fit plots) is equal to 0.349 eV. In Table 3,

we compared the activation energy of the sample with those reported for other ferrite systems. In particular, the value achieved in this work for the sample Ni0.4 Mg0.3 Cu0.3 Fe2 O4 is lower than that obtained for the Ni0.5 Mg0.3 Cu0.2 Fe2 O4 ferrite [19]. Then, we can conclude that the increase of the amount of Cu in Ni0.5 Mg0.3 Cu0.2 Fe2 O4 ferrite system can improve its conductivity. On the other hand, the activation energy of our sample is different than those reported in refs. [2–23], which suggests that the conduction mechanism in these ferrites is deeply influenced by the type of substitutional elements and the amount of substitution, the cations distribution between interstitial sites, the difference in ionic radii, and also the synthesis conditions. Figure 11 displays the complex impedance curves (named Nyquist diagrams) at different temperatures for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite. It is obvious from the figure that the Nyquist diagrams show semicircles arcs for all temperatures. The maxima and diameters of these semicircles arcs decrease as the temperature increases. The suitable equivalent circuit used to modelize the Nyquist plots is of the type of (Rg + Rgb //Cgb ) [50, 51] where Rg

Fig. 11 Nyquist diagrams at different temperatures for Ni0.4 Mg0.3 Cu0.3 Fe2 O4 ferrite. The inset shows the proposal electrical equivalent circuit

J Supercond Nov Magn Table 4 Electrical parameters deduced from the fitting of Nequist diagrams using equivalent electrical circuit T (K)

Rg ()

Rgb ()

Cgb × 10−11 (F)

300 320 340 360 380 400 420 440 460 480 500

95 97 102 112 55 76 100 108 89 110 118

248520 93,043 38,629 17,715 8955 6455 4750 2723 1646 1020 645

5.568 5.580 5.606 5.948 6.357 6.804 6.966 7.645 8.363 9.781 13.60

and Rgb means the grain and grain boundary resistances, and the capacitance (Cgb ) modelizes the grain boundary capacitance (see the inset of Fig. 11). The Rg , Rgb , and Cgb parameters have been evaluated for each temperature by fitting the curves using Zview software (see Table 4). It could be noted that the fit (red solid lines in Fig. 11) is in harmony with the results found during experimentation. The results show a decrease in the values of the grain boundary resistance, which confirm the semiconductor behavior of the sample as it is cited previously. Moreover, it is found that the Rgb values are more important than those of Rg confirming that the conduction in the sample is basically related to the grain boundary apport [52, 53].

4 Conclusion To conclude, we have prepared in this work a ferrite sample having Ni0.4 Mg0.3 Cu0.3 Fe2 O4 composition and we studied successively its microstructural, magnetic, magnetocaloric, and electrical properties. The cations distribution of this sample has been investigated using Rietveld structure refinement of XRD pattern. The sample exhibits a FMPM phase transition with second-order nature. At 5 T, the magnetic entropy change and relative cooling power reached values of about 1.56 and 136 J kg−1 K−1 , respectively. The electrical conductivity curves show a semiconductor behavior of the sample and activation energy of about 0.349 eV. An appropriate equivalent circuit was used to fitting the Nyquist plots, and the results show that the conduction process for the sample is mainly due to the grain boundary contribution. Funding Information This work has been supported by the Tunisian Ministry of Higher Education and Scientific Research and the frame work of Tunisia-Saudi Arabia collaborations.

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