Enhancement of magnetocaloric effect around room

Journal of Alloys and Compounds 758 (2018) 237e246

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Enhancement of magnetocaloric effect around room temperature in Zn0.7Ni0.3-xCuxFe2O4 (0 x 0.2) spinel ferrites R. Felhi a, *, H. Omrani a, M. Koubaa a, b, W.Cheikhrouhou Koubaa a, A. Cheikhrouhou a Laboratoire des Technologies des Syst emes Smarts (LT2S), Centre de Recherche Numerique Sfax, Cit e El Ons, Route de Tunis, Km 9, Sfax, B.P. 275, Sakiet Ezzit, 3021 Sfax, Tunisia b Institut Sup erieur de Biotechnologie de Sfax, Universit e de Sfax, B.P 261, 3000 Sfax, Tunisia a

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 March 2018 Received in revised form 6 May 2018 Accepted 7 May 2018 Available online 8 May 2018

In this work, a profound study has been conducted on magnetocaloric effect in Zn0.7Ni0.3-xCuxFe2O4 (with x ¼ 0, 0.1 and 0.2) spinel ferrites synthesized by the sol-gel method. The Rietveld analysis of the powder X-ray diffraction shows that the samples crystallize in the cubic system with Fd3m space group. Structural analysis shows that the lattice constant and the unit cell volume increase with increasing Cu content. Magnetization measurements versus temperature in a magnetic applied field of 0.05 T show that our samples exhibit a paramagnetic (PM)-ferromagnetic (FM) transition with decreasing temperature. The partial substitution of Ni by Cu leads to a monotonic decrease in the Curie temperature (TC) of the samples from 327 K for x ¼ 0e282 K for x ¼ 0.2. Additionally, Arrott plots and Landau theory were also studied to assess magnetic phase ordering in these materials, such investigations indicate that the phase takes values transition from the PM to FM states is of second order. The magnetic entropy change DSmax M of 0.67, 0.64 and 0.62 J/kgK for x ¼ 0, 0.1 and x ¼ 0.2, respectively at 2 T. The relative cooling power (RCP) amounts 111, 117 and 124 J/kg at 2T for x ¼ 0, 0.1 and x ¼ 0.2, respectively. Because of the relatively easy possibility of tuning the TC and the interesting values of relative cooling power, these samples can be considered as suitable candidates for magnetic refrigeration at around room temperature. © 2018 Elsevier B.V. All rights reserved.

Keywords: Spinel ferrites Sol-gel method X-ray analysis Relative cooling power Magnetocaloric effect Landau theory

1. Introduction Magnetic materials are important due to their applications in many technological and versatile fields; therefore, it has become one of the main research objects of materials physics. Especially, the finding of the magnetic refrigeration (MR) technology has attracted intensive interest of research groups [1e5]. Such technology is based on the magnetocaloric effect (MCE) of a magnetic material and it has many potential advantages over the conventional gas refrigeration [6,7]. The MCE is defined as the thermal response (heating or cooling) of magnetic solids during the application or the removal of an external magnetic field. In view of this, to promote the MR, it is necessary to fabricate magnetic materials with giant MCEs. Previous studies on the MCE were concentrated mainly on rare earth samples with a large effective paramagnetic moment and high Curie temperature. The lanthanide metal gadolinium (Gd) is considered as a prototype refrigerant, with a large

* Corresponding author. E-mail address: [email protected] (R. Felhi). https://doi.org/10.1016/j.jallcom.2018.05.078 0925-8388/© 2018 Elsevier B.V. All rights reserved.

MCE around the paramagnetic (PM) e ferromagnetic (FM) transition temperature (TC ¼ 293 K) [8]. But, this metal present many drawbacks such as high cost (4000 $/kg), hard preparation, easy oxidation, etc. However, the spinel ferrites present some advantages compared to metallic alloys such as the low production costs, the ease of shaping and preparation, the tunable TC and low eddy current loss. The spinel ferrites with the general formula AB2O4 (A tetrahedral and B octahedral site) can be synthesized by different methods, among them the sol-gel method [9]. This method offers the advantages of low cost, short annealing times, good homogeneity and high purity of the products. The interesting physical and magnetic properties of spinel ferrites arise from the ability of these materials to distribute the cations among the available tetrahedral A and octahedral B-site [10,11]. In this context, a little number of spinel ferrites materials has been reported as candidate materials for magnetic cooling [12e15]. For example M. S. Anwar et al. [12] have synthesized Ni1-xZnxFe2O4 mixed ferrite by the conventional solidstate reaction method, which present large relative cooling power (RCP). The obtained RCP values are 60, 68, 161, 120 J/kg for x ¼ 0, 0.3, 0.5 and x ¼ 0.7, respectively, under a magnetic field of 2.5 T. On the

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R. Felhi et al. / Journal of Alloys and Compounds 758 (2018) 237e246

other hand, these materials have very high Curie temperatures (TC ¼ 845, 664 and 481 K for x ¼ 0, 0.3 and 0.5, respectively), which are relatively high for potential applications in magnetic refrigeration near the room-temperature except for the Zn0.7Ni0.3Fe2O4 (x ¼ 0.7) sample which has a transition temperature TC ¼ 302 K [12]. In fact, near-room-temperature refrigeration has become an indispensable technology in contemporary society. Based on these previous results, we focused our works on the composition x ¼ 0.7 in Ni1-xZnxFe2O4 with keeping in mind the effect of elaborating method and we investigated the effect of copper (Cu) introduction into the Ni-Zn ferrite system. Cation distribution in Zn-Ni-Cu ferrites has been investigated by many authors [16,17]. Therefore, the possible cation distribution for these materials can be written as 2þ 2þ 3þ 2 3þ ðZn2þ 0:7 Fe0:3 ÞA ½Ni0:3x Cux Fe1:7 B O4 where the brackets ( ) and [ ] indicate the tetrahedral A and the octahedral B sites, respectively. Hence, in this paper an effort is made to carry out the effect of Cu substitution by magnetic Ni ions in octahedral B-site with constant nonmagnetic Zn concentration on the physical properties of Zn0.7Ni0.3-xCuxFe2O4 (with x ¼ 0, 0.1 and 0.2) samples prepared by the sol-gel method. The relative cooling power, which is an important parameter for magnetic cooling is also reported. In addition to this, implications of Landau's phase transition theory and universal behavior are investigated and discussed in details. 2. Experimental details The copper (Cu) doped Zn0.7Ni0.3-xCuxFe2O4 (with x ¼ 0, 0.1 and 0.2) ferrites were synthesized by the sol-gel method. Stoichiometric amounts of high purity powder of ZnO, NiO, CuO and Fe2O3 were dissolved in nitric acid to obtain a clear solution. Citric acid (CA) and ethylene glycol (EG) were then added with suitable amounts to the solution as the complexing and polymerizing agents, respectively. Then, this solution is heating at 130 C until obtaining a homogeneous resin. The resulting gel was then dried at 170 C until its

transformation into a black fine powder. This powder was heated in air at 300 C before sintering at several temperatures (600 C and 800 C) for 12 h. After cooling, the sample was pressed into a pellets (of about 1 mm thickness and 13 mm diameter), and then sintered at 1000 C for 24 h in air with intermediate regrinding and repelling. The phase identification and structural analysis were performed using a “Panalytical X pert Pro” diffractometer with Co- Ka radiation (l ¼ 1.7890 A ). The XRD patterns were collected in the range of 20 < 2q < 100 and the data were analyzed by the Rietveld method using the FULLPROF program. The variations of the magnetization as a function of magnetic field at different temperatures have been measured between 0 and 2 T and in a temperature range around the Curie temperature (TC) using Vibrating Sample Magnetometer (VSM) J3590 mini CFM of Cryogenics. 3. Results and discussion 3.1. X-ray diffraction analysis X-ray diffraction (XRD) patterns with a good quality were obtained for the samples with nominal compositions of 2þ 2þ 2 3þ 3þ ðZn2þ 0:7 Fe0:3 ÞA ½Ni0:3x Cux Fe1:7 B O4   (0 x 0.2) using Co-Ka radiation of wavelength 1.7890 Е at room temperature are shown in Fig. 1a. The data were refined by the Rietveld technique using the FULLPROF program [18,19]. The refinement was carried out by considering the distribution of Zn/Ni/Cu/Fe ions on two available Crystallographic sites: A site (x ¼ y ¼ z ¼ 0.125) and B site (x ¼ y ¼ z ¼ 0.50), but the oxygen positions (x ¼ y ¼ z) were taken as free parameters. The obtained results reveal that all samples are single phase without any detectable secondary phases and crystallized in the cubic structure with Fd3m space group. We can note that the introducing of Cu ion does not obviously change the spinel structure. It turns out that the fitting between the experimental spectra and the calculated values is fairly good. The results of the

Fig. 1. (a): Refined X-ray powder diffraction of Zn0.7Ni0.3-xCuxFe2O4 (x ¼ 0, 0.1 and 0.20). The experimental data are represented by squares and the calculated data is the continuous line overlapping them. The lowest curve shows the difference between the experimental and the calculated patterns. The vertical bars indicate the expected reflection positions. (b): Variation of lattice parameter a with Cu content.

R. Felhi et al. / Journal of Alloys and Compounds 758 (2018) 237e246 Table 1 Structural parameters for Zn0.7Ni0.3-xCuxFe2O4 (with x ¼ 0, 0.1 and 0.2) determined from Rietveld analysis of X-ray powder diffraction data at room temperature. Materials

x¼0

x ¼ 0.1

x ¼ 0.2

Structure type Space group a ¼ b ¼ c (Å) V (Å3) dððZn;Fe1ÞO ÞA

Cubic Fd-3m 8.4123 (7) 595.3157 1.9307(13)

Cubic Fd-3m 8.4178(9) 596.4734 1.9391(17)

Cubic Fd-3m 8.4217(10) 597.2986 1.905(3)

(Å) dððNi;Cu;Fe2ÞO ÞB

2.0419(13)

2.0393(17)

2.059(3)

239

3.2. Magnetic study Fig. 3 presents the temperature dependence of the magnetization for Zn0.7Ni0.3-xCuxFe2O4 samples under an applied magnetic field of 0.05 T. With decreasing temperature the samples exhibit a paramagnetic (PM) to ferromagnetic (FM) transition at TC, which was determined from the minimum of the dM/dT versus T curves as shown in the inset of Fig. 3. The calculated transition temperatures

(Å)

qðNi;CuOFe2Þ ( ) qðFe1OFe2Þ ( ) Rp Rwp RF

c2 DSC (nm) DWH (nm) Strain 3 (%)

93.49(5)

93.73(7)

92.59(10)

122.76(5)

122.59(7)

123.41(10)

17.1 10.2 1.23 1.35 49 65 0.23

18.8 10.9 1.40 1.41 51 67 0.20

22.5 12.9 3.22 1.88 55 70 0.21

refinement are listed in Table 1. In fact, a good refinement gives a goodness of fit c2 values lower than 2. In this table, we have also reported the residuals for the weighted pattern Rwp, the pattern Rp, RB Bragg factor and the goodness of fit c2 . The reliable parameters Rwp, Rp, RB and c2 (Table 1) are reasonable for assigning the structure to the phase on the basis of the Rietveld analysis. The lattice parameter of parent compound Zn0.7Ni0.3Fe2O4 is 8.412 Å and it is increased from 8.418 Å to 8.423 Å with increasing the Cu2þ ions content. The values of the lattice parameter exhibit a linear dependence, thus obeying Vegard's law [20,21] as shown in Fig. 1b. The increasing trend in the lattice parameter is attributed to the substitution of smaller ionic radius of Ni2þ (0.69 Å) by the larger ionic radius of Cu2þ (0.72 Å) in the host system [22]. The Average crystallites sizes can be determined from the intense peak using the Scherrer's formula [23]:

DSC ¼

Kl bcosQ

(1)

where l is the X-ray radiation wavelength (l ¼ 1.7890 Å), K is the Scherrer constant (~0.9), b is the full width at half maximum (FWHM) of the most intense peak (in radians) and Q is the peak angular position. The obtained values of crystallites size ðDSC Þ are 49 nm, 51 nm and 55 nm for x ¼ 0, x ¼ 0.1 and x ¼ 0.2, respectively. We have also estimated the crystallites size DWH of our samples by analyzing the broadening of X-ray diffraction peaks, using the WilliamsoneHall approach. The WilliamsoneHall (WeH) equation is expressed as follow [24]:

bcosQ ¼

Kl þ 4ε sinQ DWH

(2)

where ε ¼ Ddd is a coefficient related to strain effect on the crystallites. From the linear fit of the bcosQ vs 4sinQ plots (Fig. 2), the crystallites size DWH was calculated from intercept with vertical axis (Kl/DWH ¼ intercept) and the strain 3 from the slop of the fit. The obtained values of crystallites size (DWH) are found to be 65 nm, 67 nm and 70 for x ¼ 0, x ¼ 0.1 and x ¼ 0.2, respectively. The crystallites size (DWH ) calculated in the present systems using the WilliamsoneHall technique are larger than those found using the Scherrer's formula. Obviously, this difference can be connected to the fact that the broadening effect due to strain is completely excluded in Scherrer technique.

Fig. 2. The Williamson-Hall analysis plots of Zn0.7Ni0.3-xCuxFe2O4 (x ¼ 0, 0.1 and 0.20) compounds.

240


Fig. 3. Temperature dependence of magnetization M (T) measured at 0.05T. The inset shows the plots of dM/dT as a function of temperature at m0H ¼ 0.05T.

are 327 K, 296 K and 282 K for x ¼ 0, 0.1 and 0.2, respectively. The substitution of Ni by Cu does not affect the ferromagnetic behavior of the sample, but it causes a displacement of Curie temperature to low temperatures. The decreased of the transition temperature TC can be interpreted in terms of the decrease in the magnetization of B sublattice. This agrees with the previous study for ZneNieCu ferrite [25] which indicated that the magnetization of B sublattice decreased as decreasing Ni2þ ions with higher magnetic moment (2mB) compared to Cu2þ (1mB) and the presence of magnetic Fe3þ ions with largest magnetic moment (5mB). The replacement of Cu2þ in place of Ni2þ decreases the number of Ni2þeO2-eNi2þ linkages at octahedral B-sites and in turn the transition temperature TC is decreased. The obtained values of TC are close to the ambient, which is useful for magnetic cooling applications. On the other hand, when comparing our TC value for Zn0.7Ni0.3Fe2O4 sample with the one reported in Ref. [12] (TC ¼ 302 K), we can observe that the value achieved in our work is superior. This variation is mainly due to the different method and conditions of sample preparation (our samples were prepared using the sol-gel technique which is different to the standard solid state reaction method used in Ref. [12]). In order to better understand the spin dynamics, we have investigated the temperature dependence of the inverse magnetic susceptibility c1 for all compounds. The c1 defined as ðM ¼ cHÞ was performed using the Curie e Weiss law:

c¼

C T Qp

(3)

where C is the Curie constant and Qp is the paramagnetic Curie temperature. The temperature dependence of the inverse magnetic susceptibility c1 ðTÞ, as function of temperature at 0.05 T is shown in Fig. 4. By fitting the linear paramagnetic region of the data, the Curie Weiss parameters C and Qp were obtained. The positive value of Curie-Weiss temperature (Table 2) further confirms the presence of ferromagnetic exchange interaction in these samples Zn0.7Ni0.3xCuxFe2O4. The Qp value is higher than TC. Generally, this difference depends on the substance and may be related to the presence of a magnetic inhomogeneity . In order to better understand the magnetic properties and to confirm the ferromagnetic behavior at low temperatures, we carried out isothermal magnetization M (m0H) measurements in

Fig. 4. The inverse magnetic susceptibility curves measured at 0.05T as a function of temperature for Zn0.7Ni0.3-xCuxFe2O4 (x ¼ 0, 0.1 and 0.20) (the solid line is the linear fit to the susceptibility data according to CurieeWeiss law above TC).

Table 2 Magnetic parameters for Zn0.7Ni0.3-xCuxFe2O4 (with x ¼ 0, 0.1 and 0.2). Materials

x¼0

x ¼ 0.1

x ¼ 0.2

TC ðKÞ Qp ðKÞ

327 338

296 313

282 291

Zn0.7Ni0.3-xCuxFe2O4 samples under an applied magnetic field of up to 2T at different temperatures, as shown in Fig. 5. It can be seen that the magnetization increases quickly at lower magnetic fields and then increases slowly at fields H > 0.5T, followed by a saturation at higher fields. With increasing temperature, non linear dependencies of M (H) in the ferromagnetic region tend to

Table 3 , RCP values for some magnetocaloric Summary of the Curie temperature TC, DSmax M materials. riaux dTFWHM RCP References TC(K) m0H DSmax Mate M (T) (Jkg1) (Jkg1K1) Zn0.7Ni0. 3Fe2O4 Zn0.7Ni0.20Cu0. 10Fe2O4 Zn0 .7Ni0. 10Cu0.20Fe2O4 Gd Zn0.7Ni0.3Fe2O4 Zn0,5Ni0. 5Fe2O4 Zn0.7Cu0.3Fe2O4 La0.65Dy0.05Sr0.3MnO3 La0.5Ca0.5MnO3

327 296 282 294 302 481 272 265 245

2 2 2 2 2.5 2.5 3 2 2

0.67 0.64 0.62 5.5 0.86 1.15 0.91 0.86 0.75

168 184 200 e e e e e

112 117 124 164 120 161 36.50 80 93

This work This work This work [8] [12] [12] [13] [30] [31]


241

Fig. 5. Isothermal magnetization for Zn0.7Ni0.3-xCuxFe2O4 (x ¼ 0, 0.1 and 0.20) measured at different temperatures.

Fig. 6. Arrott plots (m0H/M vs.M2) of Zn0.7Ni0.3-xCuxFe2O4 (x ¼ 0, 0.1 and 0.20) compounds at different temperatures.

be linear when the samples enter into the paramagnetic region, due to the thermal agitation which disrupts the arrangement of the magnetic moments. To identify the nature of the magnetic phase transition (first or second order) for our samples, we derived the Arrott's plots (m0H/M vs. M2) from isothermal

magnetization curves, are shown in Fig. 6. These plots exhibited a positive slope around TC which confirms that our samples exhibit of second order magnetic phase transition, according to Banerjee's criterion [26].

242


3.3. Magnetocaloric properties Near room temperature, magnetocaloric effect (MCE) has a tremendous importance for the cooling technology. The MCE is defined as the heating or cooling of a magnetic material due to the application of an external magnetic field [27]. So, to examine this effect, the temperature and field dependence of the magnetization M (T, H) was used to plot the magnetic entropy change DSM. According to classical thermodynamic theory, the magnetic entropy change can be evaluated using the standard Maxwell relation [28]:

DSM ðT; HÞ ¼ SM ðT; HÞ SM ðT; 0Þ ZH ¼ 0

ZH vS vM dH ¼ dH vM T vT H

(4)

0

In case of discrete change of applied fields and temperature intervals, this relation can be approximated as [29]:

jDSM j ¼

XM i

iþ1 Mi DH Tiþ1 Ti

(5)

were Mi and Miþ1 are the experimental values of the magnetization obtained at the temperatures Ti and Tiþ1 , respectively. The obtained jDSM j for Zn0.7Ni0.3-xCuxFe2O4 (x ¼ 0, 0.1 and 0.2) has been plotted as a function of temperature at different magnetic fields from 0.5 to 2 T (Fig. 7). The sign of the magnetic entropy change is negative, meaning that heat is released when the magnetic field is adiabatically applied which confirms the ferromagnetic character. Clearly, the DSM reach its maximum around TC and increase with the magnetic field change. The peak values of the DSM curves under a m0H ¼ 2T are 0.67, 0.64 and 0.62 J/kgK for x ¼ 0, 0.1 and x ¼ 0.2 samples, respectively. Thus, introducing Cu into octahedral site is not favorable to enhance DSmax . This result could be M attributed to the decrease of magnetization of B sublattice with the substitution of Ni2þ by Cu2þ in octahedral B-sites. It should be noted also that the maximum of the magnetic entropy change ðD Smax M Þ is not the only deciding parameter about the applicability of a magnetic material in the MR. The relative cooling power (RCP) is another important parameter used to evaluate the cooling efficiency of a magnetic refrigerants. This quantity depends on both the maximum value of the magnetic entropy change ðDSmax M Þ and the full-width at half-maximum ðdTFWHM Þ , of the peak profile in accordance with the relation:

dTFWHM RCP ¼ DSmax M

(6)

The DSmax M , dTFWHM and RCP values corresponding to a magnetic field of 2 T obtained for all the samples are summarized in Table 3. The RCP values observed for x ¼ 0, 0.1 and 0.2 are found to be 112, 117 and 124 J/kg, respectively, under an applied magnetic field of 2 T. It should be noted that the increase in dTFWHM is greater than the decrease in DSmax , thus resulting in a larger RCP values. M We can deduce that the Cu2þ doping favors the enhancement of the RCP in this series. Moreover, Fig. 8 shows the variations in DSmax M , dTFWHM and RCP under m0H ¼ 2 T as functions of the Cu amount. Our values are in the order of 68%, 71% and 75% compared with the prototype magnetic refrigerant material Gd [8], while they are comparable in other doped ferrite spinel based on the Zn-Ni ferrite [12], much larger than Zn-Cu ferrite composition [13] and larger than those found in other doped manganites perovskite [30,31]. Our materials can be considered as possible candidates for use in magnetic cooling applications at around room temperature, thanks to their high RCP values compared with those of refrigerant materials working at low-field.

Fig. 7. DSM (T) curves with applied field intervals ranging from 0.5T to 2T for Zn0.7Ni0.3(x ¼ 0, 0.1 and 0.20) compounds.

xCuxFe2O4

3.4. Landau theory In order to further understand the nature of magnetic phase transition around the Curie temperature, we analyzed it using the Landau theory. The Gibbs free energy is written by following equations [32]:


DSM ðT; m0 HÞ ¼

243

vG m H vT 0

1 1 1 ¼ A0 ðTÞM2 þ B0 ðTÞM4 þ C0 ðTÞM6 2 4 6

(9)

where A0 ðTÞ; B0 ðTÞ and C0 ðTÞ are the temperature derivatives of the expansion coefficients. Fig. 9b shows the evolution of the magnetic entropy change versus temperature under 2 T for Zn0.7Ni0.3xCuxFe2O4. While circles represent experimental data and red lines show the calculated by Landau theory. It is seen that the theoretical and experimental values are not in accord with each other for all samples. This express that the magnetoelastic coupling and electron interaction do not contribute directly to the magnetic entropy and it is temperature dependence [32]. 3.5. Universal curves For magnetocaloric materials which present second order transition, Franco et al. [35] has been offered universal curves method. The universal curve have many practical applications in the characterization of new magnetic materials. It is a method for making extrapolations of magnetic measurements to temperatures or fields not available in the laboratory and it is a simple screening procedure of the performance of materials … etc [36]. The phenomenological universal curve consists in the collapse of the entropy change plots after a scaling process, regardless the magnetic applied field. Hence, the major assumption is based on the fact that if a universal curve exists, the equivalent points of the DSM ðTÞ plots measured at different magnetic applied fields must collapse onto one universal curve. The universal curve can be formed by normalizing all the DSM ðTÞ curves by using their respective maximum value DSmax and then rescale the temperature axis M defined a new variable Q [37]:

Fig. 8. Variation of DSmax M , dTFWHM and RCP with Cu content for m0H ¼ 2T.

1 1 1 GðT; MÞ ¼ G0 þ AðTÞM2 þ BðTÞM4 þ CðTÞM6  m0 HM 2 4 6 By minimizing GðT; MÞ , i.e., computing equation of state can be written:

m0 H ¼ AðTÞM þ BðTÞM3 þ CðTÞM5

vG vM

(7)

¼ 0 , a magnetic

(8)

where the Landau coefficients AðTÞ, BðTÞ and CðTÞ are temperature dependent parameters representing the magnetoelastic coupling and electron condensation energy [33]. According to Eq. (8), these coefficients can be determined by fitting experimental isothermal magnetization curves at different temperatures. Examination of the Gibbs free demonstrates that the parameter A (T) is always positive and should get a minimum value at the Curie temperature corresponding to a maximum of the susceptibility. On the other hand, the sign of the coefficients B (T) and C (T) determines the order of the phase transition, which can be negative or positive. If B (TC) < 0, this indicates the first-order transition. If B (TC) > 0, this is a sign of a second-order transition. Otherwise, C (T) is positive at TC while in the other temperature regions it can be negative or positive. The dependence of A, B and C parameters as a function of temperature for Zn0.7Ni0.3-xCuxFe2O4 (x ¼ 0, 0.1 and 0.2) are shown in Fig. 9a. It may be noted from Fig. 9a that for all samples the A (T) is positive with a minimum at TC. Besides, B (TC) is positive, at this point which worth noting the transition is of a second order. This is in good agreement with the model of Landau. Further, if we differentiate only the magnetic part of Gibb's free energy [Eq. (7)] with temperature, we can obtain the change in magnetic entropy as [34]:

Q¼

ðT TC Þ=ðTr1 TC Þ; T TC ðT TC Þ=ðTr2 TC Þ; T > TC

(10)

where Tr1 and Tr2 are the temperatures of two reference points which have been selected in such way that DSM ðTr1;2 Þ ¼ DSmax M =2: The universal curves for all samples are shown in Fig. 10. It is seen that the normalized entropy change curves in a different applied magnetic field (m0H ¼ 0.5e2T) collapse into a single curve for all samples. Furthermore, the result indicated that the paramagneticeferromagnetic phase transitions of the samples are second order. This is in good agreement with the Banerjee criterion and landau's theory as analyzed in previous sections. 4. Conclusion In the present paper, we have studied in detail the structural, magnetic and magnetocaloric properties of polycrystalline Zn0.7Ni0.3-xCuxFe2O4 spinel ferrites with doping level x ¼ 0, 0.1 and 0.2. Our synthesized samples crystallize in the cubic structure with Fd-3m space group. An increase of the unit cell volume with the increase of Cu content was observed. It is clearly shown that the ferromagnetic e paramagnetic transition temperature (TC) decreases with Cu content, pointing to the weakening of magnetization of B sublattice due to the decreasing of the number of Ni2þeO2eNi2þ linkages at octahedral B-sites. Based on the Banerjee criterion, Landau theory and the construction of universal curves, it has been successfully confirm that the nature of transition is of second order for all samples. When increasing Cu concentration, the maximum values of the magnetic entropy change ðDSmax M Þ decreases while the

244


Fig. 9. (a): Landau parameters (A, B and C) evolution versus temperature for Zn0.7Ni0.3-xCuxFe2O4 (x ¼ 0, 0.1 and 0.20) compounds. (b): Temperature dependence of the magneticentropy change (-DSM (T)) for m0H ¼ 2 T according to the Landau theory for Zn0.7Ni0.3-xCuxFe2O4 (x ¼ 0, 0.1 and 0.20) compounds.


245

Acknowledgements The Tunisian Ministry of Higher Education and Scientific Research supported this work. References

Fig. 10. Universal master curves, DSM =DSmax versus Q, for Zn0.7Ni0.3-xCuxFe2O4 (x ¼ 0, M 0.1 and 0.20) compounds measured under different applied magnetic field changes.

values of the relative cooling power (RCP) increases. This enhancement of RCP values is attributed to the increase in the full width at half maximum ðdTFWHM Þ witch is greater than the decrease in DSmax for ours samples. Thus based on the above M observations, it can be said that the samples show good magnetocaloric properties at around room temperature.

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