Journal of Superconductivity and Novel Magnetism https://doi.org/10.1007/s10948-018-4798-1
ORIGINAL PAPER
Prediction of Magnetocaloric Effect in La0.67 Pb0.33 (Mn1−x Cox )O3 Compounds (x = 0.01, 0.06, 0.1 and 0.15) Mohamed Hsini1 · Sobhi Hcini2 · Sadok Zemni1 Received: 3 June 2018 / Accepted: 4 July 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018
Abstract The magnetocaloric properties for the Co-doped La0.67 Pb0.33 (Mn1−x Cox )O3 samples with x= 0.01, 0.06, 0.1 and 0.15 under a 0.005 T magnetic field have been theoretically investigated and compared with experimental results. It has been found that the Co doping in this system decreases lightly the magnetocaloric properties. Moreover, the results of Co doping indicate that the magnetocaloric effect in this system is tunable, which is beneficial for manipulating magnetocaloric refrigeration that occurs in various temperature ranges. This makes the La0.67 Pb0.33 (Mn1−x Cox )O3 samples potential candidates for practical applications. Keywords Magnetocaloric effect · Phenomenological model · Magnetization · Magnetic entropy change
1 Introduction In recent years, the concerns on the global warming and everincreasing cost of energy require developing alternative refrigeration technologies to gas compression expansion cycle technology [1]. The magnetic refrigeration (MR) technology based on magnetocaloric effect (MCE) of materials is more energy efficient and more environmentally friendly compared to the conventional vapor-compression-based refrigeration [2]. MR technology has been extensively studied, and it is continuously being developed. Therefore, several materials having excellent MCE have been developed in the last two decades for use as working materials in MR technology [3–6]. At present, the development of materials exhibiting MCE around room temperature at fairly low fields is an important challenge to apply MCE to magnetic energy conversion machines or magnetic refrigerators [7–10]. Currently, a large number of experiments are going on to search the perfect composition for Heusler alloys that shows the giant MCE and
other magnetoresponsive properties [11–14]. The key point of performing MR looks for the proper material, which its Curie temperature is near to the room temperature, and which has a large magnetic entropy change, high adiabatic temperature change and excellent refrigerant capacity. In their work, Gritzner et al. [15] have reported the investigation of synthesis, structure and magnetic and electrical properties of La0.67 Pb0.33 (Mn1−x Cox )O3 manganites. The object of the present study is the development of theoretical investigation of MCE in La0.67 Pb0.33 (Mn1−x Cox )O3 samples, based on the M(T ) data measured under low magnetic field (H = 0.005 T), extracted from the work of Gritzner et al. [15]. To do this, we have used a phenomenological model [16] to simulate respectively the dependence of the magnetization (M), the magnetic entropy change (−SM ) and the specific heat change (CP,H ) on the temperature variation. Such simulated M (T ), −SM (T ) and C P,H (T ) curves are compared to the experimental ones.
Mohamed Hsini
[email protected]
2 Theoretical Considerations
1
Laboratory of Physical Chemistry of Materials, Faculty of Science of Monastir, Department of Physics, University of Monastir, 5019 Monastir, Tunisia
2
Research Unit of Valorization and Optimization of Exploitation of Resources, Faculty of Science and Technology of Sidi Bouzid, University Campus Agricultural City, University of Kairouan, 9100 Sidi Bouzid, Tunisia
According to the phenomenological model [16–20], the dependence of magnetization (M) on temperature (T ) is presented by M(T ) =
Mf − Mi tanh(A(TC − T )) + BT + C 2
(1)
J Supercond Nov Magn
where Mi and Mf are respectively the initial and the final values of magnetization at ferromagnetic–paramagnetic c) transition, TC is the Curie temperature, A = 2(B−S Mi −Mf , B
The foundation of large magnetic entropy change is attributed to high magnetic moment and rapid change of magnetization at TC . Consequently, a maximum magnetic max ) (at T = T ) can be evaluated entropy change (−SM C from (2) as Mi − Mf max = A (3) − B Hmax . −SM 2 In fact, (3) is crucial in taking into consideration the value of the magnetic entropy change to evaluate the magnetic cooling efficiency with its full width at half maximum (δTFWHM ), which may be carried out as 2A(Mi − Mf ) 2 δTFWHM = cosh−1 B. (4) A A(Mi − Mf ) + 2 Moreover, the refrigerant capacity (RC), which is also an essential parameter in evaluating the magnetocaloric materials, is given by TC +
TC −
δTFWHM 2
δTFWHM 2
200 220 240 260 280 300 320 340 360 380 400
T (K) Fig. 1 M vs. T under a 0.005 T applied field for the La0.67 Pb0.33 (Mn1−x Cox )O3 compounds
3 Results and Discussion Figure 1 presents the dependence of magnetization (M) on temperature (T ) in a range close to values of transition temperature between 210 and 380 K, under a 0.005 T applied field for La0.67 Pb0.33 (Mn1−x Cox )O3 samples. However, Fig. 2 shows the derivative of the magnetization with respect to the temperature, dM dT versus T . These two figures have been treated in order to determine Mi and Mf (from Fig. 1) and TC , B and SC (from Fig. 2). Such determined parameters useful for the simulation of magnetic properties have been recapitulated in Table 1. Simulated
0.0
(5)
The relative cooling power (RCP) which is the product of max and δT −SM FWHM is given as follows: max RCP = −δTFWHM .SM 2A(Mi −Mf ) 2B = Mi −Mf − . cosh−1 B. A A(Mi −Mf )+2
4
0
SM (T )dT
δTFWHM = Hmax (Mi − Mf ). tanh A +B.δTFWHM . 2
6
2
(6)
Moreover, the dependence of the specific heat change on T is given by
dM/dT (emu.g-1.T-1)
RC =
8
M (emu.g-1)
is the magnetization sensitivity ( dM dT ) at ferromagnetic state before transition, Sc is the magnetization sensitivity ( dM dT ) at f TC and C = Mi +M − BT . C 2 The dependence of magnetic entropy change on T under varied magnetic field from 0 to final value (Hmax ) is given as Mi −Mf sech2 (A(TC −T ))−B Hmax . −SM (T ) = A 2 (2)
x=0.01 x=0.06 x=0.1 x=0.15
10
-0.1 -0.2
x=0.01 x=0.06 x=0.1 x=0.15
-0.3 -0.4 -0.5 -0.6
200 220 240 260 280 300 320 340 360 380 400
T (K) CP,H (T ) = −T A2 (Mi −Mf ).sech2 (A(TC −T )). tanh(A(TC −T ))Hmax . (7)
Fig. 2 dM dT vs. T under a 0.005 T applied magnetic field for the La0.67 Pb0.33 (Mn1−x Cox )O3 samples
J Supercond Nov Magn Table 1 Experimental parameters under a 0.005 T magnetic field served for the application of the phenomenological model
Mi (emu g−1 ) Mf (emu g−1 ) TC (K) B (emu g−1 K−1 ) SC (emu g−1 K−1 )
x = 0.01
x = 0.06
x = 0.1
x = 0.15
8.94 0.3 330 −0.01096 0.448
5.78 0.17 288.1 −0.004261 0.321
3.2 0.12 260.7 −0.001171 0.2228
2.24 0.01 231.2 −0.001021 0.1519
curves (red lines) of M versus T , obtained using (1), are in good agreement with the experimental ones (black symbols) as shown in Fig. 3. Using (2), −SM values can be estimated and −SM versus T curves (red lines), in Fig. 4, are compared to the experimental ones (black symbols) determined from Fig. 1 using the Maxwell relation [21] SM =
Hmax
0
∂M ∂T
dH .
(8)
H
Figure 4 shows an acceptable agreement between simulated (red lines) and experimental (black symbols) −SM versus T curves. Generally, the magnetic entropy change in manganites has been investigated to be linked to the considerable variation of magnetization near TC [22]. The spin–lattice coupling in the magnetic ordering process can play an efficient role in additional magnetic entropy change [23]. Because of the strong coupling between spin and lattice, significant lattice change following magnetic transition in perovskite manganites has been observed [24, 25]. The lattice structural change in the Mn–O bond
distance as well as the Mn–O–Mn bond angle would, in turn, favor the spin ordering. Thus, a more abrupt reduction of magnetization near TC occurs and results in a significant magnetic entropy change [26–30]. In this way, a conclusion might be establish that a strong spin–lattice coupling in the magnetic transition process would lead to an additional magnetic entropy change near TC and, consequently, enhances the MCE. Therefore, the specific heat change deduced using the M Maxwell relation, C P,H = T δS δT , can be estimated from experimental −SM values in Fig. 4. Thus, simulated C P,H versus T curves (red lines), using (7), agree well with the experimental ones (black symbols) using the Maxwell relation as depicted in Fig. 5. The agreement between simulated and experimental results proves the validity of the phenomenological model in describing magnetic properties under low applied field. As a result, it can be easy to assess the values max , RC and RCP, using Eqs. (3– of δTFWHM , −SM max and C min 6), and we can graphically get CP,H P,H for La0.67 Pb0.33 (Mn1−x Cox )O3 samples under a 0.005 T applied field. Our results have been compared to some magnetic properties of other compounds but under a 0.05
12 x=0.01
Experimental data Phenomenological simulation
- SM (J.Kg-1.K-1)
M (emu.g-1)
0.0028
8 x=0.06
4
x=0.1
Maxwell relation Phenomenological simulation x=0.01
0.0021 x=0.06 0.0014 x=0.1 x=0.15 0.0007
x=0.15 0
0.0000
200 220 240 260 280 300 320 340 360 380 400
T (K) Fig. 3 Comparison between simulated (red lines) and experimental (black symbols) M vs. T under a 0.005 T applied field for the La0.67 Pb0.33 (Mn1−x Cox )O3 perovskites
200 220 240 260 280 300 320 340 360 380 400
T (K) Fig. 4 Comparison between simulated (red lines) and experimental (black symbols) −SM vs. T under a 0.005 T applied field for the La0.67 Pb0.33 (Mn1−x Cox )O3 compounds
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CP,H (J.Kg-1.K-1)
0.08
4 Conclusion
Maxwell relation Phenomenological simulation
0.04
0.00
x=0.15 x=0.1
-0.04
x=0.06 x=0,01
-0.08 210
240
270
300
330
360
390
The magnetocaloric properties for the Co-doped La0.67 Pb0.33 (Mn1−x Cox )O3 samples with x = 0.01, 0.06, 0.1 and 0.15 upon a 0.005 T magnetic field variation have been investigated and discussed. It is found that the Co doping in this system decreases the magnetocaloric properties lightly. The results of Co doping indicate clearly that the MCE in this system is tunable. This makes the La0.67 Pb0.33 (Mn1−x Cox )O3 samples potential candidates for practical applications. A complete characterization of the magnetic properties of these materials aids to the understanding required for the technological exploitation of such materials in the new refrigeration.
T (K) Fig. 5 Comparison between simulated (red lines) and experimental (black symbols) CP,H vs. T under a 0.005 T applied field for the La0.67 Pb0.33 (Mn1−x Cox )O3 samples
T applied magnetic field in Table 2. They are in the order of ten less than others because our applied magnetic field is ten times less than those taken in [29, 30]. In addition, the Co in La0.67 Pb0.33 (Mn1−x Cox )O3 samples decreases the magnetocaloric properties. However, for an increase of the Co-doped portion from 0.01 to 0.15, there max and RCP, respectively, from is a decrease of TC , −SM −1 K−1 and 0.03646 J kg−1 to 330 K, 0.00224 J kg 231.2 K, 0.00076 J kg−1 K−1 and 0.00971 J kg−1 . In general, we can predict the performance of Co doping for La0.67 Pb0.33 (Mn1−x Cox )O3 in having an important RCP under low applied magnetic field and near to the ambient temperature.
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Table 2 Comparison of reported values of magnetic proprieties for various samples Samples
x
δTFWHM (K)
max (J −SM kg−1 K−1 )
|RC| (J kg−1 )
RCP (J kg−1 )
max (J CP,H −1 −1 kg K )
min (J CP,H −1 −1 kg K )
La0.67 Pb0.33 (Mn1−x Cox )O3 H = 0.005 T (this work)
0.01
16.2760
0.00224
0.03107
0.03646
0.03646
−0.0619
0.06 0.1 0.15 0.05 0.1 0.15 0.05 0.15 0.2 0.3
15.0424 10.8941 12.7841 17.192 19.778 9.4656 18.61 19.09 23.66 25.21
0.00161 0.00111 0.00076 0.027600 0.029299 0.062852 0.07 0.07 0.06 0.06
0.02002 0.00987 0.00792 0.43936 0.53861 0.59493 0.99 1.01 1.05 1.12
0.02414 0.01214 0.00971 0.47450 0.57947 0.55289 1.24 1.26 1.31 1.4
0.02414 0.01214 0.00971 0.28833 0.31536 1.4602 1.71 1.54 0.98 0.24
−0.041 −0.031 −0.019 −0.26592 −0.28576 −1.3968 −1.65 −1.48 −0.93 −0.69
La0.8 Srx Ca0.2−x MnO3 H = 0.05 T [25]
La0.65−x Eux Sr0.35 MnO3 H = 0.05 T [26]
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