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Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation
Computational Condensed Matter xxx (2017) 1e5
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Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation O. El rhazouani*, A. Slassi LMPHE, Department of Physics, Facult e des Sciences, Universit e Mohammed V, Rabat, Morocco
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 March 2017 Received in revised form 13 May 2017 Accepted 14 May 2017 Available online xxx
Magnetocaloric effect (MCE) in double perovskite (DP) Sr2CrMoO6 has been investigated for low magnetic field change by using a Monte Carlo Simulation (MCS) in the framework of Ising model. Total magnetization and thermal derivative of the magnetization have been investigated. Magnetic entropy change has shown a significant extension around the transition temperature which is primordial for magnetic refrigeration. At transition temperature (TC) equal to 458K, the maximum of magnetic entropy change, the adiabatic temperature change and the Relative Cooling Power (RCP) have shown an increase from 1:427 to 2:582J$Kg 1 K 1 , from 5:43 to 8:71K, and from 18:33 to 28:62J$kg 1 , respectively, for magnetic field changes 100Oe and 700Oe, which is large for low magnetic field compared to other magnetocaloric materials. The Large MCE at low-field makes Sr2CrMoO6 a very promising candidate for magnetic refrigeration above room temperature. © 2017 Elsevier B.V. All rights reserved.
Keywords: Double perovskite Monte Carlo simulation Magnetocaloric effect Relative cooling power
Contents 1. 2. 3. 4. 5.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monte Carlo simulation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction Magnetic refrigeration is a cooling technology based on the use of a magnetic material in which a changing magnetic field can induce a Magnetocaloric effect (MCE) [1]. MCE is a physical concept that measures the capacity of a magnetic material to change its thermal behavior under application or removal of an external magnetic field. Classical refrigeration systems are mainly based on a compression/expansion vapor cycle [2], which is harmful to the environment and requires a large amount of
* Corresponding author. E-mail address: [email protected] (O. El rhazouani).
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energy. On the other hand, MCE refrigeration technology appears to be more beneficial, in term of environmental protection and energy costs reduction. Designing efficient magnetic refrigerators working on a broader thermal range depends basically on the use of refrigerants that show a large magnetic entropy change ðjDSM jÞ. In this respect, a great theoretical and experimental deal effort has been made to search for magnetic materials that obey the large DSM criterion. After the discovery of a large MCE in gadolinium element “Gd” [3], the latter has been considered for a long time to be the most suitable refrigerant for magnetic refrigeration in room temperature. However, problems encountered with Gd are its high cost and its transition temperature ðTC Þ cannot be
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Please cite this article in press as: O. El rhazouani, A. Slassi, Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation, Computational Condensed Matter (2017), http://dx.doi.org/10.1016/j.cocom.2017.05.002
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O. El rhazouani, A. Slassi / Computational Condensed Matter xxx (2017) 1e5
adjusted readily [4]. In recent years, significant progress has been made in searching alternative materials, especially compounds without rare-earth elements and showing a large MCE near room temperatures. Magnetic perovskite oxides, compared to rare-earth metals, exalt promising and exciting properties going from smaller magnetic hysteresis to higher chemical stability and higher electrical resistivity, which makes them more suitable candidates for magnetic refrigeration at high thermal conditions, especially near room temperatures. Double Perovskite (DP) materials belong to the class of perovskite oxides that show the higher Curie temperatures measured until now in magnetic oxides. Recently, these materials have attracted a considerable amount of investigation due to the colossal magnetoresistance [5e10] and large MCE near the second order transition temperature [11,12]. It has been reported that the DP Br2CrMo1-xWxO6 (x ¼ 0, 0.2 and 0.5) shows, near TC , a large MCE which decreases with the increasing of the substitution of Mo by W [13]. A large magnetic entropy change ð1:6J$g 1 K 1 Þ has been reported at TC ¼ 285K in the sample Br2CRMo0.5W0.5O6 under a large applied magnetic field of 10kOe. Other authors have reported a large MCE (with a magnetic entropy change of 1:32J$Kg 1 K 1 ) at TC ¼ 381K in the sample Sr2FeMo1-xWxO6 (x ¼ 0.35) [14]. The DP Sr2CrMoO6 has been reported to crystallize in a cubic cell (space group symmetry: Fm3m) with a ¼ 7:840 A. Its calculated magnetic structure indicates that it’s a half-metallic ferrimagnet with a Curie temperature TCexp ¼ 450K [15]. Thanks to its TC above room temperature, this compound could find an application in magnetic refrigeration (in aerospace technology, metallurgy industry or automotive) or in domestic refrigeration and airconditioning systems after special treatment (doping for instance) to bring its transition temperature very close to the room temperature. In this connection, this study has been conducted to predict the MCE at low fields in this DP by using a numerical simulation in the framework of Monte Carlo Simulation (MCS). The system has been taken as an Ising model involving super exchange and double exchange interactions and the interaction with an external magnetic field. In the following section, a presentation of interactions taken into account in the adopted model is given. In section three, Monte Carlo simulation process and different physical quantities calculated through simulation are described. Section four is devoted to the presentation and the discussion of results. Conclusions are summarized in section five. 2. Simulated model Sr2CrMoO6 DP belongs to the family of Cr-based DPs. Like the majority of compounds inside this class of materials [16e24], the DP Sr2CrMoO6 has a face centered cubic (fcc) crystal lattice of the rock salt structure containing two transition metal elements (Cr and Mo). Each transition metal ion is surrounded by an oxygenoctahedra. Accordingly, the main structure is composed of two sublattices having the same size and the same number of ions. Cr3þ ions interact with each other in the first sublattice via the double exchange (DE) coupling JCrCr , which is a next nearest neighbor (NNN) interaction coupling involving 12 NNN Cr3þ ions. Mo5þ ions interact with each other in the second sublattice via the DE coupling JMoMo , which is also a NNN interaction coupling involving 12 NNN Mo5þ ions. Ions of Cr3þ sublattice interact with ions of Mo5þ sublattice through the super exchange (SE) coupling JCrMo , which is a nearest neighbor (NN) interaction coupling involving 6 NN ions. The Hamiltonian hence, according to the Ising model, includes NN and NNN interactions terms and the
term of energy related to the interaction with the external magnetic field: N
H ¼ JCrMo
2 X
N
Si sj JCrCr
< i;j >
2 X
N
Si Sj JMoMo
< i;j >
2 X
< i;j >
N
h
2 X
si sj (1)
ðSi þ si Þ
i
< i; j > denotes the NN and NNN spins at i and j sites. Si ¼ ±32; ±12 and
si ¼ ±12 are the respective spins of (Cr3þ, 3d3) and (Mo5þ, 4d1). N is the total number of ions in the whole system.
3. Monte Carlo simulation method A MCS combined with a Metropolis algorithm has been performed in the framework of the Ising model above to predict the MCE in the DP Sr2CrMoO6. The system has been simulated as a cubic bulk with the size L ¼ 64, which is larger than the thermodynamic limit determined previously at LThL ¼ 28 for this class of materials [16e21]. Standard sampling method has been adopted to simulate the Hamiltonian given by Eq. (1). Cyclic boundary conditions have been imposed on the whole lattice and initial configurations has been randomly generated in a way Cr-spins ±32; ±12 are located randomly in i sites of the first sublattice, and Mo-spins±12 are located randomly in i sites of the second sublattice During the simulation, all sites in whole lattice are sequentially traversed at each MCS step and single-spin flips are attempted. A Metropolis algorithm enables to decide the acceptance or rejection of single spin flips. Data has been collected above an interval of MCS steps going from 1 to 3*106 steps. The equilibrium has been reached after 1.8105 steps, where averages of physical quantities have been computed. MCE is well known to be defined by the following physical quantities [25]: Total magnetization per site is given by:
1 M¼ N
*
X i
Si þ
X
+
si
(2)
i
Magnetic specific heat of Cr3þ and Mo5þ ions are given respectively by:
CCr ¼
o 1 nD 2 E ECr hECr i2 KB T
CMo ¼
o 1 nD 2 E EMo hEMo i2 KB T
(3)
(4)
where, KB is the Boltzmann's constant, T is the absolute temperature of the system and E is the internal energy per site defined as:
E¼
1 〈H〉 N
(5)
Thus, total Magnetic specific heat is given by:
CM ¼
CCr þ CMo 2
(6)
According to Debye model and Debye þ Einstein model [26,27], total specific heat Cp;h is composed of three terms; the first one is the electronic term, the second is the lattice term and the last one is the magnetic term. Thus, Cp;h is given by:
Please cite this article in press as: O. El rhazouani, A. Slassi, Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation, Computational Condensed Matter (2017), http://dx.doi.org/10.1016/j.cocom.2017.05.002
O. El rhazouani, A. Slassi / Computational Condensed Matter xxx (2017) 1e5
Cp;h ¼ 7:378T þ 0:115T 3 þ CM
3
(7)
Which leads to the magnetic entropy formula:
ZT SM ðT; hÞ ¼
Cp;h 0 0 dT dT
(8)
0
Variation of the magnetic entropy is given by:
DSM ðT; hÞ ¼
Zh vM dh vT hi i
(9)
0
vM
vT h i
is the thermal magnetization for a given magnetic field hi .
The adiabatic temperature change is given by:
DTad ¼ T
DSM Cp;h
(10)
Relative Cooling Power (RCP) is defined as an area under the dependence of DSM ðTÞ on temperature. This physical quantity is usually known to be a compromise between the magnitude of the magnetic entropy change and the width of the peak. Therefore, its expression can be given by:
ZT2 RCP ¼
DSM ðTÞdT
(11)
T1
where T1 and T2 are the low and the high temperatures at the extreme limits of the half maximum value of DSMAX M . 4. Results and discussion The basis of the MCE phenomenon relies on exposing the material to a changed external magnetic field to create a thermal change. The usual indicators to describe this phenomenon are magnetic entropy change DSm , adiabatic temperature change DTad and the RCP. Exchange couplings used for simulation have been approximated as in a previous work [28] for TCexp ¼ 450K and for zero magnetic field (JCrMo ¼ 7:488meV, JCrCr ¼ 17:473meV and JMoMo ¼ 5:611meV).
Fig. 1. Thermal dependence of total magnetization for different values of external magnetic field h ranging from 100 to 700Oe.
Fig. 2. Thermal dependence of dM/dT for different values of external magnetic field h ranging from 100 to 700Oe.
Fig. 1 shows the thermal dependence of the total magnetization of Sr2CrMoO6 obtained within a MCS for different values of an external magnetic field h ranging from 100 to 700 Oe. Magnetization curves, as expected, show a decrease by increasing the thermal-perturbation to reach the para-magnetism in the system. Rising the external magnetic field strength, staying within the interval of small fields, causes a small increase of TC and a small rise of the magnetization amplitude near the transition. Similar behavior has been reported in DP Sr2FeMoO6 [29] and in perovskite La0.67Sr0.33MnO3 [30] at low field measurements. Fig. 2 shows the plot of dM=dT versus temperature for external magnetic field h ranging from 100 to 700Oe. Minimums of dM=dT curves show a little increase of TC going from 454K for 100Oe magnetic field to 460K for 700Oe magnetic field. Thermal dependence of magnetic entropy change DSm calculated from equation (9) is shown in Fig. 3 for different values of external magnetic field change Dh ranging from 100 to 700Oe. Symmetric peak is noticed in DSm curves at TC indicating a second order phase transition from the ferromagnetic to the paramagnetic phase. Qualitatively, a same kind of DSm behavior was reported recently in the DP PrSrMnCoO6 by rising the magnetic field change [31]. Authors in the last refershows a moderate value comence have predicted that DSMAX M parable to those observed in contemporary DP oxides [32].
Fig. 3. Thermal dependence of magnetic entropy change DSm for different values of external magnetic field h ranging from 100 to 700Oe.
Please cite this article in press as: O. El rhazouani, A. Slassi, Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation, Computational Condensed Matter (2017), http://dx.doi.org/10.1016/j.cocom.2017.05.002
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O. El rhazouani, A. Slassi / Computational Condensed Matter xxx (2017) 1e5
compared to 2:5K reported recently in Pr0.73Pb0.27MnO3 for higher magnetic field change ð3kOeÞ [39] and 3.11 K reported more recently in LaPr0.85K0.15MnO3 for higher magnetic field change ð2kOeÞ [40]. Magnetic field dependence of RCP is plotted in Fig. 5. RCP plays an important role in characterizing magnetic materials for magnetic refrigeration and determining the efficiency of magnetic cooling [37]. RCP curve shows an increase from 18:33 to 28:62J$kg1 by increasing the magnetic field change from 100 to 700Oe. These RCP values are considerably large for low magnetic field, as such range of values can be found only in high magnetic field measurements like in La0.7Ca0.3MnCuO3 where RCP ¼ 39J$kg 1 for a very high magnetic field change ð10kOeÞ [41]. 5. Conclusion
Fig. 4. Thermal dependence of adiabatic temperature change DTad for different values of external magnetic field h ranging from 100 to 700Oe.
DSM is negative over the temperature domain and has a significant extension around the transition temperature which is a beneficial characteristic for magnetic refrigeration above room temperature. At TC around 458 K DSMAX denoted by the peaks of M
DSm curves increased from 1:427 to 2:582J$Kg1 K 1 for field changes 100Oe and 700Oe respectively. These magnetic entropy changes at low field changes are significantly large compared with other magnetocaloric materials, as instance DSMAX increases from M
0:51 to 2:1J$Kg 1 K 1 for higher field changes 1KOe and 5KOe respectively in quenched FeNiB nanoparticles [33], and in La1.6Ca1.4Mn2O7, which is a strong candidate for magnetic refrigeration application, where DSMAX reaches 3:8J$Kg 1 K 1 only at M higher field change ð1:5KOeÞ [34]. Furthermore, the large magnetic entropy change in perovskites has been reported to result mainly from the considerable variation of magnetization near TC [35,36]. Thermal dependence of adiabatic temperature change DTad is shown in Fig. 4 for different values of external magnetic field h ranging from 100 to 700Oe. Aspect of adiabatic temperature change curves is just as expected because it reflects a broadening of DTad by rising the magnetic field strength which is in agreement with the behavior reported recently in BaTiO3 and PbTiO3 [37] and in EuTiO3 [38]. DTad increases from 5:43 to 8:71K for magnetic field changes 100Oe and 700Oe respectively which is significantly large
Fig. 5. Magnetic field dependence of Relative Cooling Power (RCP) of Sr2CrMoO6.
In summary, MCE has been investigated in DP Sr2CrMoO6 by using a MCS in the frame work of Ising model with approximated exchange couplings values. The system has been dealt with as an Ising model involving super exchange and double exchange interactions and the interaction with an external magnetic field. This study is based on a numerical simulation of the system to calculate three principal parameters describing the MCE, namely magnetic entropy change, adiabatic temperature change and RCP. Total magnetization and the thermal derivative of the magnetization dM/ dT have been investigated. Rising the external magnetic field strength, staying within the interval of small fields, causes a small increase of TC shown in the peaks of dM/dT. This behavior is similar to the one reported for the DP Sr2FeMoO6 [29] and the one reported for the perovskite La0.67Sr0.33MnO3 [30] at low field measurements. Large MCE has been noticed at TC around 458K for magnetic field changes 100Oe and 700Oe, respectively: the maximum of magnetic entropy change has shown an increase from 1:427 to 2:582J$Kg1 K 1 , the adiabatic temperature change has shown an increase from 5:43 to 8:71K, and the RCP has shown an increase from 18:33 to 28:62J$kg1 . These values reflect a large MCE compared to other Magnetocaloric materials for low magnetic field. The low-field large MCE makes Sr2CrMoO6 a very promising candidate for magnetic refrigeration above room temperature in aerospace technology, metallurgy industry or automotive. References [1] R.N. Mahato, K.K. Bharathi, K. Sethupathi, V. Sankaranarayanan, R. Nirmala, et al., J. Appl. Phys. 105 (07A908) (2009). [2] O. Tegus, E. Brück, K.H. Buschow, F.R. de Boer, Transition-metal-based magnetic refrigerants for room-temperature applications, Nature 415 (6868) (2002) 150e152. [3] G.V. Brown, Magnetic heat pumping near room temperature, J. Appl. Phys. 47 (8) (1976) 3673e3680. [4] Z. Wei, A.C. Tong, D.Y. Wei, Chin. Phys. B 22 (No. 5) (2013) 057501. [5] J.P. Zhou, R. Dass, H.Q. Yin, J.S. Zhou, L. Rabenberg, J.B. Goodenough, J. Appl. Phys. 87 (9) (2000) 5037. € der, Jun Zang, A.R. Bishop, Lattice effects in the colossal[6] H. Ro magnetoresistance manganites, Phys. Rev. Lett. 76 (8) (1996) 1356e1359. [7] B. Vertruyen, R. Cloots, A. Rulmont, G. Dhalenne, M. Ausloos, Ph. Vanderbemden, Magnetotransport properties of a single grain boundary in a bulk LaeCaeMneO material, J. Appl. Phys. 90 (11) (2001) 5692e5697. [8] P.G. Radaelli, G. Iannone, M. Marezio, H.Y. Hwang, S.-W. Cheong, J.D. Jorgensen, D.N. Argyriou, Structural effects on the magnetic and transport properties of perovskiteA1xAx'MnO3(x¼0.25,0.30), Phys. Rev. B 56 (13) (1997) 8265e8276. [9] K. Cherif, J. Dhahri, E. Dhahri, M. Omezine, H. Vincent, J. Solid State Chem. 163 (2001) 466. [10] S. Zemni, Ja. Dhahri, K. Cherif, J. Dhahri, M. Oumezzine, M. Ghedira, H. Vincent, Structure, magnetic and electrical properties of La0.6Sr0.4xKxMnO3 perovskites, J. Alloys Compd. 392 (1e2) (2005) 55e61. [11] W. Zhong, W. Liu, X.L. Wu, N.J. Tang, W. Chen, C.T. Au, Y.W. Du, Magnetocaloric effect in the ordered double perovskite Sr2FeMo1xWxO6, Solid State Commun. 132 (3e4) (2004) 157e162. [12] K. Cherif, S. Zemni, Ja. Dhahri, Je. Dhahri, M. Oumezzine, M. Ghedira,
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Please cite this article in press as: O. El rhazouani, A. Slassi, Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation, Computational Condensed Matter (2017), http://dx.doi.org/10.1016/j.cocom.2017.05.002
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Computational Condensed Matter journal homepage: http://ees.elsevier.com/cocom/default.asp
Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation O. El rhazouani*, A. Slassi LMPHE, Department of Physics, Facult e des Sciences, Universit e Mohammed V, Rabat, Morocco
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 March 2017 Received in revised form 13 May 2017 Accepted 14 May 2017 Available online xxx
Magnetocaloric effect (MCE) in double perovskite (DP) Sr2CrMoO6 has been investigated for low magnetic field change by using a Monte Carlo Simulation (MCS) in the framework of Ising model. Total magnetization and thermal derivative of the magnetization have been investigated. Magnetic entropy change has shown a significant extension around the transition temperature which is primordial for magnetic refrigeration. At transition temperature (TC) equal to 458K, the maximum of magnetic entropy change, the adiabatic temperature change and the Relative Cooling Power (RCP) have shown an increase from 1:427 to 2:582J$Kg 1 K 1 , from 5:43 to 8:71K, and from 18:33 to 28:62J$kg 1 , respectively, for magnetic field changes 100Oe and 700Oe, which is large for low magnetic field compared to other magnetocaloric materials. The Large MCE at low-field makes Sr2CrMoO6 a very promising candidate for magnetic refrigeration above room temperature. © 2017 Elsevier B.V. All rights reserved.
Keywords: Double perovskite Monte Carlo simulation Magnetocaloric effect Relative cooling power
Contents 1. 2. 3. 4. 5.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monte Carlo simulation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction Magnetic refrigeration is a cooling technology based on the use of a magnetic material in which a changing magnetic field can induce a Magnetocaloric effect (MCE) [1]. MCE is a physical concept that measures the capacity of a magnetic material to change its thermal behavior under application or removal of an external magnetic field. Classical refrigeration systems are mainly based on a compression/expansion vapor cycle [2], which is harmful to the environment and requires a large amount of
* Corresponding author. E-mail address: [email protected] (O. El rhazouani).
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energy. On the other hand, MCE refrigeration technology appears to be more beneficial, in term of environmental protection and energy costs reduction. Designing efficient magnetic refrigerators working on a broader thermal range depends basically on the use of refrigerants that show a large magnetic entropy change ðjDSM jÞ. In this respect, a great theoretical and experimental deal effort has been made to search for magnetic materials that obey the large DSM criterion. After the discovery of a large MCE in gadolinium element “Gd” [3], the latter has been considered for a long time to be the most suitable refrigerant for magnetic refrigeration in room temperature. However, problems encountered with Gd are its high cost and its transition temperature ðTC Þ cannot be
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Please cite this article in press as: O. El rhazouani, A. Slassi, Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation, Computational Condensed Matter (2017), http://dx.doi.org/10.1016/j.cocom.2017.05.002
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adjusted readily [4]. In recent years, significant progress has been made in searching alternative materials, especially compounds without rare-earth elements and showing a large MCE near room temperatures. Magnetic perovskite oxides, compared to rare-earth metals, exalt promising and exciting properties going from smaller magnetic hysteresis to higher chemical stability and higher electrical resistivity, which makes them more suitable candidates for magnetic refrigeration at high thermal conditions, especially near room temperatures. Double Perovskite (DP) materials belong to the class of perovskite oxides that show the higher Curie temperatures measured until now in magnetic oxides. Recently, these materials have attracted a considerable amount of investigation due to the colossal magnetoresistance [5e10] and large MCE near the second order transition temperature [11,12]. It has been reported that the DP Br2CrMo1-xWxO6 (x ¼ 0, 0.2 and 0.5) shows, near TC , a large MCE which decreases with the increasing of the substitution of Mo by W [13]. A large magnetic entropy change ð1:6J$g 1 K 1 Þ has been reported at TC ¼ 285K in the sample Br2CRMo0.5W0.5O6 under a large applied magnetic field of 10kOe. Other authors have reported a large MCE (with a magnetic entropy change of 1:32J$Kg 1 K 1 ) at TC ¼ 381K in the sample Sr2FeMo1-xWxO6 (x ¼ 0.35) [14]. The DP Sr2CrMoO6 has been reported to crystallize in a cubic cell (space group symmetry: Fm3m) with a ¼ 7:840 A. Its calculated magnetic structure indicates that it’s a half-metallic ferrimagnet with a Curie temperature TCexp ¼ 450K [15]. Thanks to its TC above room temperature, this compound could find an application in magnetic refrigeration (in aerospace technology, metallurgy industry or automotive) or in domestic refrigeration and airconditioning systems after special treatment (doping for instance) to bring its transition temperature very close to the room temperature. In this connection, this study has been conducted to predict the MCE at low fields in this DP by using a numerical simulation in the framework of Monte Carlo Simulation (MCS). The system has been taken as an Ising model involving super exchange and double exchange interactions and the interaction with an external magnetic field. In the following section, a presentation of interactions taken into account in the adopted model is given. In section three, Monte Carlo simulation process and different physical quantities calculated through simulation are described. Section four is devoted to the presentation and the discussion of results. Conclusions are summarized in section five. 2. Simulated model Sr2CrMoO6 DP belongs to the family of Cr-based DPs. Like the majority of compounds inside this class of materials [16e24], the DP Sr2CrMoO6 has a face centered cubic (fcc) crystal lattice of the rock salt structure containing two transition metal elements (Cr and Mo). Each transition metal ion is surrounded by an oxygenoctahedra. Accordingly, the main structure is composed of two sublattices having the same size and the same number of ions. Cr3þ ions interact with each other in the first sublattice via the double exchange (DE) coupling JCrCr , which is a next nearest neighbor (NNN) interaction coupling involving 12 NNN Cr3þ ions. Mo5þ ions interact with each other in the second sublattice via the DE coupling JMoMo , which is also a NNN interaction coupling involving 12 NNN Mo5þ ions. Ions of Cr3þ sublattice interact with ions of Mo5þ sublattice through the super exchange (SE) coupling JCrMo , which is a nearest neighbor (NN) interaction coupling involving 6 NN ions. The Hamiltonian hence, according to the Ising model, includes NN and NNN interactions terms and the
term of energy related to the interaction with the external magnetic field: N
H ¼ JCrMo
2 X
N
Si sj JCrCr
< i;j >
2 X
N
Si Sj JMoMo
< i;j >
2 X
< i;j >
N
h
2 X
si sj (1)
ðSi þ si Þ
i
< i; j > denotes the NN and NNN spins at i and j sites. Si ¼ ±32; ±12 and
si ¼ ±12 are the respective spins of (Cr3þ, 3d3) and (Mo5þ, 4d1). N is the total number of ions in the whole system.
3. Monte Carlo simulation method A MCS combined with a Metropolis algorithm has been performed in the framework of the Ising model above to predict the MCE in the DP Sr2CrMoO6. The system has been simulated as a cubic bulk with the size L ¼ 64, which is larger than the thermodynamic limit determined previously at LThL ¼ 28 for this class of materials [16e21]. Standard sampling method has been adopted to simulate the Hamiltonian given by Eq. (1). Cyclic boundary conditions have been imposed on the whole lattice and initial configurations has been randomly generated in a way Cr-spins ±32; ±12 are located randomly in i sites of the first sublattice, and Mo-spins±12 are located randomly in i sites of the second sublattice During the simulation, all sites in whole lattice are sequentially traversed at each MCS step and single-spin flips are attempted. A Metropolis algorithm enables to decide the acceptance or rejection of single spin flips. Data has been collected above an interval of MCS steps going from 1 to 3*106 steps. The equilibrium has been reached after 1.8105 steps, where averages of physical quantities have been computed. MCE is well known to be defined by the following physical quantities [25]: Total magnetization per site is given by:
1 M¼ N
*
X i
Si þ
X
+
si
(2)
i
Magnetic specific heat of Cr3þ and Mo5þ ions are given respectively by:
CCr ¼
o 1 nD 2 E ECr hECr i2 KB T
CMo ¼
o 1 nD 2 E EMo hEMo i2 KB T
(3)
(4)
where, KB is the Boltzmann's constant, T is the absolute temperature of the system and E is the internal energy per site defined as:
E¼
1 〈H〉 N
(5)
Thus, total Magnetic specific heat is given by:
CM ¼
CCr þ CMo 2
(6)
According to Debye model and Debye þ Einstein model [26,27], total specific heat Cp;h is composed of three terms; the first one is the electronic term, the second is the lattice term and the last one is the magnetic term. Thus, Cp;h is given by:
Please cite this article in press as: O. El rhazouani, A. Slassi, Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation, Computational Condensed Matter (2017), http://dx.doi.org/10.1016/j.cocom.2017.05.002
O. El rhazouani, A. Slassi / Computational Condensed Matter xxx (2017) 1e5
Cp;h ¼ 7:378T þ 0:115T 3 þ CM
3
(7)
Which leads to the magnetic entropy formula:
ZT SM ðT; hÞ ¼
Cp;h 0 0 dT dT
(8)
0
Variation of the magnetic entropy is given by:
DSM ðT; hÞ ¼
Zh vM dh vT hi i
(9)
0
vM
vT h i
is the thermal magnetization for a given magnetic field hi .
The adiabatic temperature change is given by:
DTad ¼ T
DSM Cp;h
(10)
Relative Cooling Power (RCP) is defined as an area under the dependence of DSM ðTÞ on temperature. This physical quantity is usually known to be a compromise between the magnitude of the magnetic entropy change and the width of the peak. Therefore, its expression can be given by:
ZT2 RCP ¼
DSM ðTÞdT
(11)
T1
where T1 and T2 are the low and the high temperatures at the extreme limits of the half maximum value of DSMAX M . 4. Results and discussion The basis of the MCE phenomenon relies on exposing the material to a changed external magnetic field to create a thermal change. The usual indicators to describe this phenomenon are magnetic entropy change DSm , adiabatic temperature change DTad and the RCP. Exchange couplings used for simulation have been approximated as in a previous work [28] for TCexp ¼ 450K and for zero magnetic field (JCrMo ¼ 7:488meV, JCrCr ¼ 17:473meV and JMoMo ¼ 5:611meV).
Fig. 1. Thermal dependence of total magnetization for different values of external magnetic field h ranging from 100 to 700Oe.
Fig. 2. Thermal dependence of dM/dT for different values of external magnetic field h ranging from 100 to 700Oe.
Fig. 1 shows the thermal dependence of the total magnetization of Sr2CrMoO6 obtained within a MCS for different values of an external magnetic field h ranging from 100 to 700 Oe. Magnetization curves, as expected, show a decrease by increasing the thermal-perturbation to reach the para-magnetism in the system. Rising the external magnetic field strength, staying within the interval of small fields, causes a small increase of TC and a small rise of the magnetization amplitude near the transition. Similar behavior has been reported in DP Sr2FeMoO6 [29] and in perovskite La0.67Sr0.33MnO3 [30] at low field measurements. Fig. 2 shows the plot of dM=dT versus temperature for external magnetic field h ranging from 100 to 700Oe. Minimums of dM=dT curves show a little increase of TC going from 454K for 100Oe magnetic field to 460K for 700Oe magnetic field. Thermal dependence of magnetic entropy change DSm calculated from equation (9) is shown in Fig. 3 for different values of external magnetic field change Dh ranging from 100 to 700Oe. Symmetric peak is noticed in DSm curves at TC indicating a second order phase transition from the ferromagnetic to the paramagnetic phase. Qualitatively, a same kind of DSm behavior was reported recently in the DP PrSrMnCoO6 by rising the magnetic field change [31]. Authors in the last refershows a moderate value comence have predicted that DSMAX M parable to those observed in contemporary DP oxides [32].
Fig. 3. Thermal dependence of magnetic entropy change DSm for different values of external magnetic field h ranging from 100 to 700Oe.
Please cite this article in press as: O. El rhazouani, A. Slassi, Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation, Computational Condensed Matter (2017), http://dx.doi.org/10.1016/j.cocom.2017.05.002
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O. El rhazouani, A. Slassi / Computational Condensed Matter xxx (2017) 1e5
compared to 2:5K reported recently in Pr0.73Pb0.27MnO3 for higher magnetic field change ð3kOeÞ [39] and 3.11 K reported more recently in LaPr0.85K0.15MnO3 for higher magnetic field change ð2kOeÞ [40]. Magnetic field dependence of RCP is plotted in Fig. 5. RCP plays an important role in characterizing magnetic materials for magnetic refrigeration and determining the efficiency of magnetic cooling [37]. RCP curve shows an increase from 18:33 to 28:62J$kg1 by increasing the magnetic field change from 100 to 700Oe. These RCP values are considerably large for low magnetic field, as such range of values can be found only in high magnetic field measurements like in La0.7Ca0.3MnCuO3 where RCP ¼ 39J$kg 1 for a very high magnetic field change ð10kOeÞ [41]. 5. Conclusion
Fig. 4. Thermal dependence of adiabatic temperature change DTad for different values of external magnetic field h ranging from 100 to 700Oe.
DSM is negative over the temperature domain and has a significant extension around the transition temperature which is a beneficial characteristic for magnetic refrigeration above room temperature. At TC around 458 K DSMAX denoted by the peaks of M
DSm curves increased from 1:427 to 2:582J$Kg1 K 1 for field changes 100Oe and 700Oe respectively. These magnetic entropy changes at low field changes are significantly large compared with other magnetocaloric materials, as instance DSMAX increases from M
0:51 to 2:1J$Kg 1 K 1 for higher field changes 1KOe and 5KOe respectively in quenched FeNiB nanoparticles [33], and in La1.6Ca1.4Mn2O7, which is a strong candidate for magnetic refrigeration application, where DSMAX reaches 3:8J$Kg 1 K 1 only at M higher field change ð1:5KOeÞ [34]. Furthermore, the large magnetic entropy change in perovskites has been reported to result mainly from the considerable variation of magnetization near TC [35,36]. Thermal dependence of adiabatic temperature change DTad is shown in Fig. 4 for different values of external magnetic field h ranging from 100 to 700Oe. Aspect of adiabatic temperature change curves is just as expected because it reflects a broadening of DTad by rising the magnetic field strength which is in agreement with the behavior reported recently in BaTiO3 and PbTiO3 [37] and in EuTiO3 [38]. DTad increases from 5:43 to 8:71K for magnetic field changes 100Oe and 700Oe respectively which is significantly large
Fig. 5. Magnetic field dependence of Relative Cooling Power (RCP) of Sr2CrMoO6.
In summary, MCE has been investigated in DP Sr2CrMoO6 by using a MCS in the frame work of Ising model with approximated exchange couplings values. The system has been dealt with as an Ising model involving super exchange and double exchange interactions and the interaction with an external magnetic field. This study is based on a numerical simulation of the system to calculate three principal parameters describing the MCE, namely magnetic entropy change, adiabatic temperature change and RCP. Total magnetization and the thermal derivative of the magnetization dM/ dT have been investigated. Rising the external magnetic field strength, staying within the interval of small fields, causes a small increase of TC shown in the peaks of dM/dT. This behavior is similar to the one reported for the DP Sr2FeMoO6 [29] and the one reported for the perovskite La0.67Sr0.33MnO3 [30] at low field measurements. Large MCE has been noticed at TC around 458K for magnetic field changes 100Oe and 700Oe, respectively: the maximum of magnetic entropy change has shown an increase from 1:427 to 2:582J$Kg1 K 1 , the adiabatic temperature change has shown an increase from 5:43 to 8:71K, and the RCP has shown an increase from 18:33 to 28:62J$kg1 . These values reflect a large MCE compared to other Magnetocaloric materials for low magnetic field. The low-field large MCE makes Sr2CrMoO6 a very promising candidate for magnetic refrigeration above room temperature in aerospace technology, metallurgy industry or automotive. References [1] R.N. Mahato, K.K. Bharathi, K. Sethupathi, V. Sankaranarayanan, R. Nirmala, et al., J. Appl. Phys. 105 (07A908) (2009). [2] O. Tegus, E. Brück, K.H. Buschow, F.R. de Boer, Transition-metal-based magnetic refrigerants for room-temperature applications, Nature 415 (6868) (2002) 150e152. [3] G.V. Brown, Magnetic heat pumping near room temperature, J. Appl. Phys. 47 (8) (1976) 3673e3680. [4] Z. Wei, A.C. Tong, D.Y. Wei, Chin. Phys. B 22 (No. 5) (2013) 057501. [5] J.P. Zhou, R. Dass, H.Q. Yin, J.S. Zhou, L. Rabenberg, J.B. Goodenough, J. Appl. Phys. 87 (9) (2000) 5037. € der, Jun Zang, A.R. Bishop, Lattice effects in the colossal[6] H. Ro magnetoresistance manganites, Phys. Rev. Lett. 76 (8) (1996) 1356e1359. [7] B. Vertruyen, R. Cloots, A. Rulmont, G. Dhalenne, M. Ausloos, Ph. Vanderbemden, Magnetotransport properties of a single grain boundary in a bulk LaeCaeMneO material, J. Appl. Phys. 90 (11) (2001) 5692e5697. [8] P.G. Radaelli, G. Iannone, M. Marezio, H.Y. Hwang, S.-W. Cheong, J.D. Jorgensen, D.N. Argyriou, Structural effects on the magnetic and transport properties of perovskiteA1xAx'MnO3(x¼0.25,0.30), Phys. Rev. B 56 (13) (1997) 8265e8276. [9] K. Cherif, J. Dhahri, E. Dhahri, M. Omezine, H. Vincent, J. Solid State Chem. 163 (2001) 466. [10] S. Zemni, Ja. Dhahri, K. Cherif, J. Dhahri, M. Oumezzine, M. Ghedira, H. Vincent, Structure, magnetic and electrical properties of La0.6Sr0.4xKxMnO3 perovskites, J. Alloys Compd. 392 (1e2) (2005) 55e61. [11] W. Zhong, W. Liu, X.L. Wu, N.J. Tang, W. Chen, C.T. Au, Y.W. Du, Magnetocaloric effect in the ordered double perovskite Sr2FeMo1xWxO6, Solid State Commun. 132 (3e4) (2004) 157e162. [12] K. Cherif, S. Zemni, Ja. Dhahri, Je. Dhahri, M. Oumezzine, M. Ghedira,
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Please cite this article in press as: O. El rhazouani, A. Slassi, Low field magnetocaloric effect in the double perovskite Sr2CrMoO6: Monte Carlo simulation, Computational Condensed Matter (2017), http://dx.doi.org/10.1016/j.cocom.2017.05.002