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Magnetism, hysteresis cycle, and Ir-substitution doping of Sr2CrIrO6 double perovskite: A Monte Carlo simulation
Accepted Manuscript Magnetism, hysteresis cycle, and Ir-substitution doping of Sr2 CrIrO6 double perovskite: a Monte Carlo simulation
O. El rhazouani, M. El khatabi, Z. Zarhri, A. slassi, A. Benyoussef, A. El Kenz
PII: DOI: Reference:
S0375-9601(16)31285-3 http://dx.doi.org/10.1016/j.physleta.2016.10.015 PLA 24124
To appear in:
Physics Letters A
Received date: Revised date: Accepted date:
13 July 2016 10 October 2016 12 October 2016
Please cite this article in press as: O. El rhazouani et al., Magnetism, hysteresis cycle, and Ir-substitution doping of Sr2 CrIrO6 double perovskite: a Monte Carlo simulation, Phys. Lett. A (2016), http://dx.doi.org/10.1016/j.physleta.2016.10.015
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Highlights • • • •
Monte Carlo simulation has been performed to study Sr2 CrIrO6 double perovskite. Effect of crystal field of Ir on the magnetic properties has been explored. Magnetic hysteresis cycle has been studied regarding the exchange coupling values. Effects of Ir-substitution doping by Os and by Re have been investigated.
Magnetism, hysteresis cycle, and Ir-substitution doping of Sr2CrIrO6 double perovskite: a Monte Carlo simulation O. El rhazouani1,*, M. El khatabi1, Z. Zarhri1 , A. slassi1, A. Benyoussef 1, 2, 3 and A. El Kenz 1 1 LMPHE, Faculté des Sciences, Université Mohammed V - Agdal, Rabat, Morocco 2 Institute of Nanomaterials and Nanotechnology, MAScIR, Rabat, Morocco 3 Hassan II Academy of Science and Technology, Rabat, Morocco. *[email protected]
Abstract: Iridium-based double perovskite (DP) Sr2CrIrO6 is expected to have the highest Curie temperatures (TC) among all DPs and a high spin-polarization at room temperature, thanks to the more extended 5d orbitals of Ir, which makes it potential candidate in spintronic applications. Several publications have appeared in recent years documenting Ir-based double perovskites, but very few have explored the promising compound Sr2CrIrO6. In this paper, a Monte Carlo simulation has been carried out in the framework of Ising model to make an exploratory study of Sr2CrIrO6. Thermal magnetization, magnetic susceptibility, internal energy and specific heat have been studied. Effect of crystal field of Ir on the magnetic properties has been explored. Magnetic hysteresis cycle has been studied in relation to the exchange coupling values. Effects of Ir-substitution doping by Os “Sr2CrIrxOs1-xO6” and by Re “Sr2CrIrxRe1-xO6” (0.1x 0.5) on the magnetic behavior have been investigated.
Keywords: Ir-based Double Perovskite; Monte Carlo Simulation; magnetic properties; magnetic hysteresis; substitution doping;
1- Introduction: In the last few years there has been a growing interest in mixed oxides containing 5d transition-metal cations, as they show interesting physical properties and a great ability to use in spintronic applications [1]. Perovskites are transition-metal oxides that present a wide variety of interesting behaviors: giant magnetoresistance “GMR” [2, 3], half-metallicity [4], metal-insulator transition [5, 6], multiferroicity [7], high ordering temperature [8]. This list of phenomena has been recently expanded with other behaviors observed in Ir-oxides: non-Fermi-liquid behavior in SrIrO3 [9], spin-liquid ground state in Na4Ir3O8 [10], localized-like transport in Sr2IrO4 [11, 12] and magnetism in BaIrO3 [13]. Iridium-based double perovskites (DPs) are expected to have the highest Curie temperatures (TC) among all DPs and a high spin-polarization at room temperature, thanks to the more extended 5d orbitals of Ir, which makes
them potential candidates in spintronic applications. However, they are considerably less explored experimentally or theoretically. Ir has a great ability to exist in different oxidation states, such as, Ir3+ described in the octahedral site of Sr2TaIrO6 and Sr2NbIrO6 [14], or Ir5+ and Ir6+ which can be obtained under high oxygen conditions [15]. Having a stable oxidation state of Ir5+ and Ir6+ could be promising, because the bonds (Ir5+-O) and (Ir6+-O) should be among the strongest bonds in oxygen solidsolutions. Strong correlation between the covalence of such bonding and the magnetic-ordering temperature has been predicated [8, 14]. Ir5+ is the oxidation state hosted by the here described compound Sr2CrIrO6, giving it the ability to show the highest Tc calculated since now (Tc = 881K) [8]. A comparison of Tc of the compounds {Sr2CrWO6 with W(5d1) (Tc = 500k [4, 18]), Sr2CrReO6 with Re(5d2) (Tc = 635K [19]) and Sr2CrOsO6 with Os(5d3) (Tc = 725k [20]) Sr2CrIrO6 with Ir(5d4) (Tc = 881k [8])} shows clearly that Tc is increased by more than 100k each time an electron is added in the 5d orbitals, which reveals the essential role of 5d band filling in the magnetic properties of DPs [23]. This last observation has put the 5d-based DPs at the focal point of researches on this class of spintronic materials. Few authors have studied the hysteresis of Cr-based DPs, such as Asano et al. [26] that notice a large coercivity measured at 77K for a film of Sr2CrReO6, and suggest it can be due to the anisotropic nature of that magnetic material. For Ir-based DPs, recently, the hysteresis of Sr2MIrO6 (M= Ca, Mg, Zn, Sc, In, Ti, Fe, Ni) has been investigated and has shown only Sr2FeIrO6 exhibit a hysteresis loop at 5K. To our knowledge, the hysteresis cycle of Sr2CrIrO6 studied here, has never been dealt with by a Monte Carlo simulation (MCS) or by other computational method. Recent research has shown a highly tunable ground state of iridium oxides due to the competing electron-electron interactions; in addition, the electronic structure and magnetic-transport properties are found largely sensitive to changes in dimensionality, symmetry, or local environment [15,16,17]. Authors of these recent researches predict that, as result, iridium oxides become an interesting playground for the development of improved functional electronic and magnetic materials, because, the magnetic and transport properties can be tailored by slight alterations in the crystal structure, which can be driven by chemical pressure caused by elemental doping. Electronic doping process by substitution, in this class of oxides, is focused mainly on the rare-earth element, and shows in most studies a significant increase of Tc. For instance, in Sr2FeMoO6 the Sr2+ was substituted by other rare-earth ions such as Ba, Ca [21, 22] or diluted by the trivalent La3+ [23]. Recently in Sr2CrReO6, Sr2+ ions were diluted by La, Nd and Sm [24]. Results offered by this study show the absence of the expected increase of Tc by the electronic doping as predicted for Sr2FeMoO6. This indicates a total difference in the behavior of each DP regarding the electronic doping. Substitution doping of the 5d-transition metal has been reported in several studies, where the relevant effect observed is the structural change of the compound, for instance, in Sr2FeRe1-xFexO6 (0x0.5) a structural transition has
been reported from the ordered phase “x = 0” to various disordered phases when Increasing the degree of dilution [25]. There have been very few studies of substitution doping in the class of Ir-based DPs, and the available ones have been recently undertaken by Qasim et al. [12] Bremholm et al. [13] that report on the Sr2Ir2–xMxO6 solid solutions; in particular, SrIr1–xMgxO3 (x = 0.20 and 0.33) that show ferromagnetic properties and crystallize in the orthorhombic Pbnm space group. In this study, a MCS has been performed in the framework of Ising model to study the magnetism, the hysteresis, and the effect of substitution doping of the promising Sr2CrIrO6 DP, which so far has never been synthesized. Magnetization and internal energy have been studied versus different exchange coupling values. Effect of iridium crystal field on the magnetization and the magnetic susceptibility has been investigated. Magnetic hysteresis has been examined in relation to the exchange coupling values at different temperatures. Effect of Ir(5d4) substitution doping on the magnetic behavior has been explored for two cases: doping by Os(5d3) “Sr2CrIrxOs12 xO6” and by Re(5d ) “Sr2CrIrxRe1-xO6” (0.1x 0.5). 2- Ising Model: Sr2CrIrO6 is a transition metal oxide with the perovskite structure. It contains two ଷ
ଵ
ଶ
ଶ
transition metals Cr(3d3) and Ir(5d4) with the spins respectively ൌ േ ǡ േ ɐ ൌ േʹǡ േͳǡ Ͳ. As can be seen in figure 1, this magnetic oxide crystalizes in a structure known as rock-salt structure, where each transition metal (Cr and Ir) is housed in a face centered cubic (FCC) structure and surrounded by an oxygen-octahedra. Thus, the system is composed of two sublattices that have the same size and the same number of atoms. Cr atoms interact with each other in the first sublattice via the double exchange (DE) coupling J2, which is a next nearest neighbor (NNN) interaction coupling. Ir atoms interact with each other in the second sublattice via the DE coupling J2, which is also a NNN interaction coupling. Atoms of each sublattice interact with atoms of the other sublattice via the super exchange (SE) coupling J1, which is a nearest neighbor (NN) interaction coupling. Spin-orbit coupling of Ir has not been taken into account in our simulation, but we have considered the effect of its direct resultant (crystal field: ¨Ir). Consequently, the Hamiltonian of Sr2CrIrO6 includes NN and NNN interactions, the terms of energy related to the crystal fields of Cr and Ir, and the term of energy related to external magnetic field: ొ
ొ
ొ
ొ
ొ
మ మ మ ܪൌ െܬଵ σழǡவ ܵ ߪ୨ െ ܬଶ σழǡவ ܵ ܵ െ ܬଷ σழǡவ ߪ ߪ୨ െ ߂ σ୧మ ሺܵ ሻଶ െ οூ σ୧మ ሺߪ ሻଶ െ ొ మ
σ ሺܵ ߪ୧ ሻ
ଷ
ଵ
ଶ
ଶ
(1)
denotes the NN and NNN spins at i and j sites. ܵ ൌ േ ǡ േ and ߪ ൌ േʹǡ േͳǡ Ͳ are the respective spins of Cr and Ir. N is the total number of atoms in the lattice.
߂ and οூ are the respective crystal fields of Cr and Ir atoms. Crystal field ǻ of a transition metal is the splitting of d-orbitals in the field generated by the set of oxygenbonds surrounding the transition metal ion [27].
Figure 1: Qualitative sketch of interaction couplings prevailing in the Ising model. We illustrate only atoms of sites B and B’ present in the Ising model. To study the effect of substitution doping, a modification of that Hamiltonian is required. Thus, for the first case, when doping by Os “Sr2CrIrxOs1-xO6”, the Hamiltonian is given by: ొ
ొ
ొ
ొ
మ మ మ ܪൌ െܬଵ σழǡவ ܵ ሺߪ୨ ɀ୨ ሻ െ ܬଶ σழǡவ ܵ ܵ െ ܬଷ σழǡவ ሺߪ ߪ୨ ߪ ɀ୨ ɀ୧ ɀ୨ ሻ െ ߂ σ୧మ ሺܵ ሻଶ െ ౮ొ
ሺଵି୶ሻȀଶ
οூ σ୧మ ሺߪ ሻଶ െ οை௦ σ୧ ଷ
ଵ
ଶ
ଶ
ొ
ሺɀ୧ ሻଶ െ σమ ሺܵ ߪ୧ ɀ୧ ሻ
(2)
Where, ɀ୧ ൌ േ ǡ േ is the spin of Os, οை௦ is the crystal field of Os atoms, and x is the doping rate. For the second case, when doping by Re “Sr2CrIrxRe1-xO6”, the Hamiltonian is given by: ొ
ొ
ొ
ొ
మ మ మ ܪൌ െܬଵ σழǡவ ܵ ሺߪ୨ Ɂ୨ ሻ െ ܬଶ σழǡவ ܵ ܵ െ ܬଷ σழǡவ ሺߪ ߪ୨ ߪ Ɂ୨ Ɂ୧ Ɂ୨ ሻ െ ߂ σ୧మ ሺܵ ሻଶ െ ౮ొ
ሺଵି୶ሻȀଶ
οூ σ୧మ ሺߪ ሻଶ െ οோ σ୧
ొ
ሺɁ୧ ሻଶ െ σమ ሺܵ ߪ୧ Ɂ୧ ሻ
Where, Ɂ୧ ൌ േͳǡ Ͳ is the spin of Re and οோ is the crystal field of Re atoms.
(3)
3- Monte Carlo simulations MCS combined with the Metropolis algorithm has been performed to carry out this study. The simulated system is a cubic bulk with the size L=32, which is larger than the thermodynamic limit determined at LThL=28 in several studies for this class of compounds [28, 29, 30]. Therefore, the lattice contains an equal number of Cr-spins and Ir-spins (NCr=NIr=(L3)/2). Standard sampling method has been adopted to simulate the Hamiltonian given by eqs. (1), (2) and (3). Cyclic boundary conditions have been imposed on the lattice and initial configurations has been randomly generated, in the way the sites of the first sublattice are occupied randomly by Crଷ
ଵ
ଶ
ଶ
spins േ ǡ േ , and the sites of the second sublattice are occupied randomly by Irspins േʹǡ േͳǡ ͲǤ At each MCS step, the lattice is sequentially traversed and singlespin flip attempts are made. According to a heat-bath algorithm under the Metropolis approximation, the flips are accepted or rejected. The data has been collected for 1.2*106 MCS steps. The first 6*105 steps have been devoted to reach the equilibrium, after which the average of physical quantities has been computed. Total magnetizations, magnetic susceptibility, internal energy per site and specific heat of Sr2CrIrO6 have been respectively calculated by the eqs. (4), (5), (6) and (7):
݉ ൌ
σ ௌା σ ఙ ಿೝ ಿೝ
߯ ൌ ߚ ܰ כሺ݉ۃଶ ۄെ ۄ݉ۃଶ ሻ Whereߚ ൌ
(4) (5)
: T denotes the absolute temperature and KB is the Boltzmann’s
ࡷ ࢀ
constant. N is the total number of spins in the system.
ܧൌ
ேೝ כேೝ
൫െ ͳܬσ൏݅ǡ݆ ܵ݅ ߪ െ ʹܬσ൏݅ǡ݆ ܵ݅ ݆ܵ െ ͵ܬσ൏݅ǡ݆ ߪ݅ ߪ െ ߂ ݎܥσሺܵ݅ ሻʹ െ ο ݎܫσሺߪ݅ ሻʹ െ σሺܵ݅ ߪ ሻ൯
(6)
ܥ௩ ൌ ߚ ܰ כሺ ܧۃଶ ۄെ ۄ ܧۃଶ ሻ
(7)
Magnetization of the doped compound has been calculated, in the case of Irsubstitution by Os-doping “Sr2CrIrxOs1-xO6”, by eq. (8), and in the case of Irsubstitution by Re-doping “Sr2CrIrxRe1-xO6”, by eq. (9):
݉ ்ሺூିை௦ሻ ൌ
σ ௌା σ ఙା σ ஓ ಿೝ ሺభషೣሻಿೝ ೣכಿೝ
݉ ்ሺூିோሻ ൌ
σ ௌା σ ఙା σ ஔ ಿೝ ሺభషೣሻಿೝ ೣכಿೝ
(8)
(9)
4- Results and discussion In the class of DP oxides, the two transition metals are coupled antiferromagnetically, which entails the NN interaction coupling J1 to be negatif. Each type of transition metal atoms is coupled ferromagnetically, which means that the NNN interaction couplings J2 and J3 should be positive. Thus, the first coupling has been taken J1= -1, and all the other parameters has been reduced to its absolute value.
Figure 2: a) Magnetization and magnetic susceptibility vs. the reduced temperature T/|J1| for the reduced exchange couplings: J2 /|J1| = J3 /|J1| =1. b) Magnetization vs. the reduced temperature T /|J1| for the reduced exchange couplings: J2 /|J1| fixed at 1 and J3 /|J1| ranging from 1 to 1.6. Reduced crystal fields (ᇞCr/|J1|, ᇞIr/|J1|) and the reduced external field h/|J1| are taken null. Magnetization and magnetic susceptibility versus the reduced temperature T/|J1| have been computed for a uniform value of the reduced couplings (J2 /|J1|= J3 /|J1| =1) (figure 2-a), zero crystal field and zero external magnetic field. Magnetization has been drown for the reduced coupling J3 /|J1| ranging from 1 to 1.6 and for J2 /|J1|=1 (figure 2-b), zero crystal field and zero external magnetic field. Internal energy and specific heat versus the reduced temperature T/|J1| have been computed for a uniform value of the reduced couplings (J2 /|J1|= J3 /|J1| =1) (figure 3-a), zero crystal field and zero external magnetic field. Internal energy has been drown for the reduced coupling J3 /|J1| ranging from 1 to 1.6 and for J2 /|J1|=1 (figure 3-b), zero crystal field and zero external magnetic field. Peaks of the susceptibility and the specific heat coincide with the critical temperature where the system transit from the magnetic phase to the paramagnetic phase. The magnetization show a nonmonotonic behavior similar to the one reported by Krockenberger et al. [20] for Sr2CrOsO6. Where, the authors predict that such a behavior is a consequence of the different temperature evolution of the Cr magnetic moments and the induced moments at the Os site, and suppose that this unusual behavior can be coupled with the distortion of the lattice. Moreover, this behavior is observed only in Cr-based DPs with high valence electron number of the (5d) transition metal, because it was only observed in {Sr2CrOsO6 with Os(5d3)} and {Sr2CrIrO6 with Ir(5d4)} and not in
{Sr2CrReO6 with Re(5d2)} and {Sr2CrWO6 with Os(5d1)}, which means that it is correlated with the filling of the 5d band, just like the critical temperature. Raising the value of the exchange coupling J3 amplify the non-monotonic behavior of the magnetization (figure 2-b), making the interaction strength between the 5d-element atoms another important factor behind the unusual behavior of the magnetization. However, raising the value of the exchange coupling J3 enhance the stability of the material that can be seen in figure (2-b) by the decrease of the energy.
Figure 3: a) Internal energy and specific heat vs. the reduced temperature T /|J1| for the reduced exchange couplings: J2 /|J1| = J3 /|J1| =1. b) Internal energy vs. the reduced temperature T /|J1| for the reduced exchange couplings: J2 /|J1| fixed at 1 and J3 /|J1| ranging from 1 to 1.6. Reduced crystal fields (ᇞCr/|J1|, ᇞIr/|J1|) and the reduced external field h/|J1| are taken null.
Figure 4: a) Magnetization vs. the reduced temperature T/|J1|, b) magnetic susceptibility vs. the reduced temperature T/|J1|, for reduced crystal field ᇞIr /|J1| ranging from 0.25 to 2.25. Reduced crystal field ᇞCr/|J1| is fixed at 0.25. Reduced exchange couplings are taken: J2 /|J1| = J3 /|J1| =1. Reduced external field h/|J1| is taken null.
Figure 5: Magnetization vs. magnetic field loops for Sr2CrIrO6 DP for the reduced exchange couplings: J2 /|J1| =5, J3 /|J1| =1. Reduced crystal fields (ᇞCr/|J1|, ᇞIr/|J1|) are taken null. Data are calculated at the reduced temperatures: T/|J1| =10 (a), T/|J1| =20 (b), T/|J1| =30 (c), T/|J1| =40 (d).
As 5d orbitals of Ir are more extended than the 3d orbitals of Cr, the effect of the crystal field of Ir should be stronger that the Cr one, and exploring that effect could give interesting results. Therefore, the magnetization and the magnetic susceptibility versus the reduced temperature T/|J1| have been computed for the reduced crystal field of Ir ᇞIr/|J1| ranging from 0.25 to 2.25, fixed crystal field of Cr ᇞIr/|J1|=0.25, uniform value of the reduced couplings (J2 /|J1|= J3 /|J1| =1) (figure 2-a) and zero external magnetic field (figure 4). The results are just as expected, because they show an increase of Tc by the increase of ᇞIr/|J1|, and are in good agreement with those found for Sr2CrReO6 [29]. The unexpected result is the amplification of the nonmonotonic behavior, which make the crystal field strength of the 5d-element another factor behind the unusual behavior of the magnetization.
Figure 6: Magnetization vs. magnetic field loops for Sr2CrIrO6 DP for the reduced exchange couplings: J2 /|J1| =1, J3 /|J1| =5. Reduced crystal fields (ᇞCr/|J1|, ᇞIr/|J1|) are taken null. Data are calculated at the reduced temperatures: T/|J1| =10 (a), T/|J1| =20 (b), T/|J1| =30 (c), T/|J1| =40 (d).
Figure 7: Magnetic field dependence of the magnetization of Sr 2CrIrO6 DP, a) at the reduced temperature T/|J1| =20 for the reduced exchange couplings ( J2 /|J1| =5, J3 /|J1| =1) and ( J2 /|J1| =1, J3 /|J1| =5), and b) at the reduced temperature T/|J1| =60 for the reduced exchange couplings ( J2 /|J1| = J3 /|J1| =1), ( J2 /|J1| =5, J3 /|J1| =1) and ( J2 /|J1| =1, J3 /|J1| =5). Reduced crystal fields (ᇞCr/|J1|, ᇞIr/|J1|) are taken null.
Since future applications of the here studied compound to tunnel junctions require a proper coercive field hc, we have examined the magnetization versus the magnetic field loops at reduced temperatures T/|J1| ranging from 10 to 40, for the reduced couplings (J2 /|J1|=5, J3 /|J1| =1) (figure 5) and for (J2 /|J1|=1, J3 /|J1| =5) (figure 6), zero crystal fields. A comparison between the hysteresis loops at T/|J1|=20 is plotted in (figure 7-a), and at T/|J1|=60 in (figure 7-b). The data show the high exchange coupling J2 is in favor of high coercive fields’ hc, while high exchange coupling J3 gives smaller coercive fields’ hc. Hysteresis loops are displayed for high J2 even at T/|J1|=40, while they disappear at T/|J1|=30. Magnetic saturation MS is smaller in the case of high J3 than in the case of high J2. That means that, the exchange interactions between 3d-element atoms (Cr-atoms) affect the magnetic performance less than those between 5d-element atoms (Ir-atoms). At T=60, S-shaped magnetization curves of both cases {(J2 /|J1|=J3 /|J1| =1) and (J2 /|J1|=5, J3 /|J1| =1)} may be indicative of major paramagnetic contribution. Curve of the case (J 2 /|J1|=1, J3 /|J1| =5) is a linear characteristic of the antiferromagnetic behavior, which result from the complexity of this strongly correlated electron system.
Figure 8: Magnetization (a-a’) and magnetic susceptibility (b-b’) vs. the reduced temperature T/|J1| of Sr2CrIrxOs1-xO6 (a-b) and Sr2CrIrxRe1-xO6 (a’-b’) for x ranging from 0.1 to 0.5. Reduced exchange couplings are taken uniform: J2 /|J1| = J3 /|J1| =1. Reduced crystal fields (ᇞCr/|J1|, ᇞ/|J1|, ᇞRe/|J1|, ᇞIr/|J1|) and the reduced external field h/|J1| are taken null.
To modifying the magnetic properties of Ir-based DPs, not varying the occupation of the 5d orbitals by control of Ir valence state is the only route less explored [16], but doping by substitution of Ir is also a route less explored. Simplifications on the exchange interactions, has been used to reduce the computational complexity of the doped compound: - in the first case of doping “Sr2CrIrxOs1-xO6”, the NN interaction coupling J1, which acts between Cr and Ir atoms and between Cr and Os atoms, is taken of the same value. Ir and Os atoms are localized in the second sublattice and interact with each other (Ir—Ir, Ir—Os and Os—OS) by the same NNN coupling J3. in the second case of doping “Sr2CrIrxRe1-xO6”, the NN interaction coupling J1, which acts between Cr and Ir atoms and between Cr and Re atoms, is taken of the same value. Ir and Re atoms are localized in the second sublattice and interact with each other (Ir—Ir, Ir—Re and Re—Re) by the same NNN coupling J3. Magnetization and magnetic susceptibility are computed versus the reduced temperature T/|J1| of Sr2CrIrxOs1-xO6 (figure 8-a,b) and Sr2CrIrxRe1-xO6 (figure 8-a’,b’) for x ranging from 0.1 to 0.5, the reduced exchange couplings are taken uniform (J2 /|J1| = J3 /|J1| =1), the reduced crystal fields (ᇞCr/|J1|, ᇞ/|J1|, ᇞRe/|J1|, ᇞIr/|J1|) and the reduced external
magnetic field h/|J1| are taken null. Sr2CrIrO6 behave quite differently depending on the type of atom that substitutes Ir(5d4). When Ir(5d4) is substituted by Os(5d3), the transition temperature and the magnetization amplitude decrease gradually by the increase of the substitution rate x. this result is in good agreement with the result reported by Krockenberger et al. [20] that shows a strong correlation between the transition temperature and the number of 5d electrons. Subsequently, the result found when Ir(5d4) is substituted by Re(5d2) is unexpected. In this case, the only Tc displayed is equal to 32, which is largely smaller than Tc = 54 calculated without doping (see figure 2-a). In addition, there is no gradual change in the transition temperature either, nor in the magnetization amplitude. This result can be explained by the fact that the spins of Re atoms (േͳǡ Ͳ) have the same values as the small spins of Ir atoms (േʹǡ േͳǡ Ͳ), thus, when doping by Re, the system will be occupied mostly by the small values of spin (േͳǡ Ͳ). Consequently, the spin polarization of the system is reduced, which affect the transition temperature and the magnetic behavior.
5- Conclusion The findings of our investigation allow better understanding of the complexity of correlated interactions characterizing the promising compound Sr2CrIrO6. The magnetization has shown a non-monotonic behavior similar to the one reported by Krockenberger et al. [20] for Sr2CrOsO6. Where, the authors predict that such a behavior is a consequence of the different temperature evolution of atom moments, and suppose that this unusual behavior can be coupled with the distortion of the lattice. Moreover, this behavior is observed only in Cr-based DPs with high valence electron number of the (5d) transition metal, which means that it is correlated with the filling of the 5d band, just like the critical temperature. Raising the value of the exchange coupling J3 amplify the non-monotonic behavior of the magnetization, making the interaction strength between 5d-element atoms another important factor behind the unusual behavior of the magnetization. However, raising this interaction strength enhance the stability of the material that can be seen in the decrease of the energy. Effects of the crystal field of Ir are just as expected, because they show an increase of Tc by the increase of ᇞIr/|J1|, and are in good agreement with those found for Sr2CrReO6 [29]. The unexpected result is the amplification of the non-monotonic behavior, which make the crystal field strength of the 5d-element the second factor, found in this work, behind the unusual behavior of the magnetization. The data show the high exchange coupling J2 is in favor of high coercive fields’ hc, while high exchange coupling J3 gives smaller coercive fields’ hc. Hysteresis loops are displayed for high J2 even at T/|J1|=40, while they disappear at T/|J1|=30. Magnetic saturation MS is smaller in the case of high J3 than in the case of high J2. That means that, the exchange interactions between 3d-element atoms (Cr-atoms) affect the magnetic performance less than those between 5d-element atoms (Ir-atoms). Sr2CrIrO6 behave quite differently depending on the type of atom that substitutes Ir(5d4).
Substitution doping by Os(5d3) shows a gradual decrease of the magnetization and the transition temperature, which is in good agreement with the result reported by Krockenberger et al. [20] that shows a strong correlation between the transition temperature and the number of 5d electrons. This is not the case for the substitution doping by Re(5d2) where the two quantities remain unchanged . This result can be explained by the fact that the spins of Re atoms (േͳǡ Ͳ) have the same values as the small spins of Ir atoms (േʹǡ േͳǡ Ͳ), which reduced the spin polarization of the system, and so affects the transition temperature and the magnetic behavior.
References [1] A. V. Powell, J. G. Gore, P. D. Battle, J. Alloys Compd. 73 (1993) 201. [2] Y. Tokura and N. Nagaosa, Science 288 (2000) 462. [3] K.-I. Kobayashi, T. Kimura, H. Sawada, K. Terakura, and Y. Tokura, Nature (London) 395 (1998) 677. [4] J. B. Philipp, P. Majewski, L. Alff, A. Erb, R. Gross, T. Graf, M. S. Brandt, J. Simon, T. Walther, W. Mader et al., Phys. Rev. B 68 (2003) 144431. [5] A. A. Aligia, P. Petrone, J. O. Sofo, and B. Alascio, Phys. Rev. B 64 (2001) 092414. [6] A. Poddar and S. Das, Physica B (Amsterdam) 344 (2004) 325. [7] R. Ramesh and N. Spaldin, Nat. Mater. 6 (2007) 21. [8] T. K. Mandal, C. Felser, M. Greenblatt, J. Kübler, Phys. Rev. B 78 (2008)134431. [9] R. D. Shannon, Acta Crystallogr., Sect. A 32 (1976) 751. [10] P. M. Woodward, Acta Crystallogr., Sect. B 53 (1997) 32. [11] D.-Y. Jung, P. Gravereau, G. Demazeau, Eur. J. Solid State Inorg. Chem. 30 (1993) 1025. [12] I. Qasim, B. J. Kennedy, M. Avdeev, J. Mater. Chem. A 1 (2013) 3127. [13] M. Bremholm, C. K. Yim, D. Hirai, E. Climent-Pascual, Q. Xu, H. W. Zandbergen, M. N. Ali, R. J. Cava, J. Mater. Chem. 22 (2012) 16431. [14] D.-Y. Jung, G. Demazeau, J. H. Choy, J. Mater. Chem. 5 (1995) 517. [15] P. Kayser et al., Eur. J. Inorg. Chem. (2014) 178. [16] M. A. Laguna-Marco, G. Fabbris, N. M. Souza-Neto, S. Chikara, J. S. Schilling, G. Cao, and D. Haskel, Phys. Rev. B 90 (2014) 014419. [17] O. B. Korneta, S. Chikara, S. Parkin, L. E. Delong, P. Schlottmann, and G. Cao, Phys. Rev. B 81 (2010) 045101. [18] J. B. Philipp, D. Reisinger, M. Schonecke, A. Marx, A. Erb, L. Alff, R. Gross, and J. Klein, Appl. Phys. Lett. 79 (2002) 3654.
[19] H. Kato, T. Okuda, Y. Okimoto, Y. Tomioka, Y. Takenoya, A. Ohkubo, M. Kawasaki, and Y. Tokura, Appl. Phys. Lett. 81 (2002) 328. [20] Y. Krockenberger et al., Phys Rev B 75 (2007) 020404(R). [21] J. Navarro, C. Frontera, Ll. Balcells, B. Martínez, and J. Fontcuberta, Phys. Rev. B 64 (2001) 092411. [22] J. Navarro, J. Fontcuberta, M. Izquierdo, J. Avila, and M. C. Asensio, Phys. Rev. B 69 (2004) 115101. [23] E. K. Hemery, G. V. M. Williams and H. J. Trodahl, Phys. Rev. B 74 (2006) 054423. [24] J.M. Michalik, J.M. De Teresa, J. Blasco, C. Ritter, P.A. Algarabel, M.R. Ibarraa, and Cz. Kapusta, Solid State Sciences 12 (2010) 1121-1130. [25] C. Felser, G. H. Fecher, Spintronics from Materials to Devices , Springer Dordrecht Heidelberg New York, 2013, pp 64. [26] H. Asano,N. Kozuka, A. Tsuzuki, and M. Matsui, App. Phys. Lett. 85 (2004) 263. [27] V. Vleck, J. Physical Review 41 (1932) 208. [28] O. El Rhazouani, A. Benyoussef, A. El Kenz, J. M. M. M. 377 (2015) 319. [29] O. El Rhazouani, A. Benyoussef, S. Naji, A. El Kenz, Physica A 10 (2013) 1016. [30] S. Naji, A. Benyoussef, A. El Kenz , H. Ez-Zahraouy, M. Loulidi, Physica A 391 (2012) 3885.
O. El rhazouani, M. El khatabi, Z. Zarhri, A. slassi, A. Benyoussef, A. El Kenz
PII: DOI: Reference:
S0375-9601(16)31285-3 http://dx.doi.org/10.1016/j.physleta.2016.10.015 PLA 24124
To appear in:
Physics Letters A
Received date: Revised date: Accepted date:
13 July 2016 10 October 2016 12 October 2016
Please cite this article in press as: O. El rhazouani et al., Magnetism, hysteresis cycle, and Ir-substitution doping of Sr2 CrIrO6 double perovskite: a Monte Carlo simulation, Phys. Lett. A (2016), http://dx.doi.org/10.1016/j.physleta.2016.10.015
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Highlights • • • •
Monte Carlo simulation has been performed to study Sr2 CrIrO6 double perovskite. Effect of crystal field of Ir on the magnetic properties has been explored. Magnetic hysteresis cycle has been studied regarding the exchange coupling values. Effects of Ir-substitution doping by Os and by Re have been investigated.
Magnetism, hysteresis cycle, and Ir-substitution doping of Sr2CrIrO6 double perovskite: a Monte Carlo simulation O. El rhazouani1,*, M. El khatabi1, Z. Zarhri1 , A. slassi1, A. Benyoussef 1, 2, 3 and A. El Kenz 1 1 LMPHE, Faculté des Sciences, Université Mohammed V - Agdal, Rabat, Morocco 2 Institute of Nanomaterials and Nanotechnology, MAScIR, Rabat, Morocco 3 Hassan II Academy of Science and Technology, Rabat, Morocco. *[email protected]
Abstract: Iridium-based double perovskite (DP) Sr2CrIrO6 is expected to have the highest Curie temperatures (TC) among all DPs and a high spin-polarization at room temperature, thanks to the more extended 5d orbitals of Ir, which makes it potential candidate in spintronic applications. Several publications have appeared in recent years documenting Ir-based double perovskites, but very few have explored the promising compound Sr2CrIrO6. In this paper, a Monte Carlo simulation has been carried out in the framework of Ising model to make an exploratory study of Sr2CrIrO6. Thermal magnetization, magnetic susceptibility, internal energy and specific heat have been studied. Effect of crystal field of Ir on the magnetic properties has been explored. Magnetic hysteresis cycle has been studied in relation to the exchange coupling values. Effects of Ir-substitution doping by Os “Sr2CrIrxOs1-xO6” and by Re “Sr2CrIrxRe1-xO6” (0.1x 0.5) on the magnetic behavior have been investigated.
Keywords: Ir-based Double Perovskite; Monte Carlo Simulation; magnetic properties; magnetic hysteresis; substitution doping;
1- Introduction: In the last few years there has been a growing interest in mixed oxides containing 5d transition-metal cations, as they show interesting physical properties and a great ability to use in spintronic applications [1]. Perovskites are transition-metal oxides that present a wide variety of interesting behaviors: giant magnetoresistance “GMR” [2, 3], half-metallicity [4], metal-insulator transition [5, 6], multiferroicity [7], high ordering temperature [8]. This list of phenomena has been recently expanded with other behaviors observed in Ir-oxides: non-Fermi-liquid behavior in SrIrO3 [9], spin-liquid ground state in Na4Ir3O8 [10], localized-like transport in Sr2IrO4 [11, 12] and magnetism in BaIrO3 [13]. Iridium-based double perovskites (DPs) are expected to have the highest Curie temperatures (TC) among all DPs and a high spin-polarization at room temperature, thanks to the more extended 5d orbitals of Ir, which makes
them potential candidates in spintronic applications. However, they are considerably less explored experimentally or theoretically. Ir has a great ability to exist in different oxidation states, such as, Ir3+ described in the octahedral site of Sr2TaIrO6 and Sr2NbIrO6 [14], or Ir5+ and Ir6+ which can be obtained under high oxygen conditions [15]. Having a stable oxidation state of Ir5+ and Ir6+ could be promising, because the bonds (Ir5+-O) and (Ir6+-O) should be among the strongest bonds in oxygen solidsolutions. Strong correlation between the covalence of such bonding and the magnetic-ordering temperature has been predicated [8, 14]. Ir5+ is the oxidation state hosted by the here described compound Sr2CrIrO6, giving it the ability to show the highest Tc calculated since now (Tc = 881K) [8]. A comparison of Tc of the compounds {Sr2CrWO6 with W(5d1) (Tc = 500k [4, 18]), Sr2CrReO6 with Re(5d2) (Tc = 635K [19]) and Sr2CrOsO6 with Os(5d3) (Tc = 725k [20]) Sr2CrIrO6 with Ir(5d4) (Tc = 881k [8])} shows clearly that Tc is increased by more than 100k each time an electron is added in the 5d orbitals, which reveals the essential role of 5d band filling in the magnetic properties of DPs [23]. This last observation has put the 5d-based DPs at the focal point of researches on this class of spintronic materials. Few authors have studied the hysteresis of Cr-based DPs, such as Asano et al. [26] that notice a large coercivity measured at 77K for a film of Sr2CrReO6, and suggest it can be due to the anisotropic nature of that magnetic material. For Ir-based DPs, recently, the hysteresis of Sr2MIrO6 (M= Ca, Mg, Zn, Sc, In, Ti, Fe, Ni) has been investigated and has shown only Sr2FeIrO6 exhibit a hysteresis loop at 5K. To our knowledge, the hysteresis cycle of Sr2CrIrO6 studied here, has never been dealt with by a Monte Carlo simulation (MCS) or by other computational method. Recent research has shown a highly tunable ground state of iridium oxides due to the competing electron-electron interactions; in addition, the electronic structure and magnetic-transport properties are found largely sensitive to changes in dimensionality, symmetry, or local environment [15,16,17]. Authors of these recent researches predict that, as result, iridium oxides become an interesting playground for the development of improved functional electronic and magnetic materials, because, the magnetic and transport properties can be tailored by slight alterations in the crystal structure, which can be driven by chemical pressure caused by elemental doping. Electronic doping process by substitution, in this class of oxides, is focused mainly on the rare-earth element, and shows in most studies a significant increase of Tc. For instance, in Sr2FeMoO6 the Sr2+ was substituted by other rare-earth ions such as Ba, Ca [21, 22] or diluted by the trivalent La3+ [23]. Recently in Sr2CrReO6, Sr2+ ions were diluted by La, Nd and Sm [24]. Results offered by this study show the absence of the expected increase of Tc by the electronic doping as predicted for Sr2FeMoO6. This indicates a total difference in the behavior of each DP regarding the electronic doping. Substitution doping of the 5d-transition metal has been reported in several studies, where the relevant effect observed is the structural change of the compound, for instance, in Sr2FeRe1-xFexO6 (0x0.5) a structural transition has
been reported from the ordered phase “x = 0” to various disordered phases when Increasing the degree of dilution [25]. There have been very few studies of substitution doping in the class of Ir-based DPs, and the available ones have been recently undertaken by Qasim et al. [12] Bremholm et al. [13] that report on the Sr2Ir2–xMxO6 solid solutions; in particular, SrIr1–xMgxO3 (x = 0.20 and 0.33) that show ferromagnetic properties and crystallize in the orthorhombic Pbnm space group. In this study, a MCS has been performed in the framework of Ising model to study the magnetism, the hysteresis, and the effect of substitution doping of the promising Sr2CrIrO6 DP, which so far has never been synthesized. Magnetization and internal energy have been studied versus different exchange coupling values. Effect of iridium crystal field on the magnetization and the magnetic susceptibility has been investigated. Magnetic hysteresis has been examined in relation to the exchange coupling values at different temperatures. Effect of Ir(5d4) substitution doping on the magnetic behavior has been explored for two cases: doping by Os(5d3) “Sr2CrIrxOs12 xO6” and by Re(5d ) “Sr2CrIrxRe1-xO6” (0.1x 0.5). 2- Ising Model: Sr2CrIrO6 is a transition metal oxide with the perovskite structure. It contains two ଷ
ଵ
ଶ
ଶ
transition metals Cr(3d3) and Ir(5d4) with the spins respectively ൌ േ ǡ േ ɐ ൌ േʹǡ േͳǡ Ͳ. As can be seen in figure 1, this magnetic oxide crystalizes in a structure known as rock-salt structure, where each transition metal (Cr and Ir) is housed in a face centered cubic (FCC) structure and surrounded by an oxygen-octahedra. Thus, the system is composed of two sublattices that have the same size and the same number of atoms. Cr atoms interact with each other in the first sublattice via the double exchange (DE) coupling J2, which is a next nearest neighbor (NNN) interaction coupling. Ir atoms interact with each other in the second sublattice via the DE coupling J2, which is also a NNN interaction coupling. Atoms of each sublattice interact with atoms of the other sublattice via the super exchange (SE) coupling J1, which is a nearest neighbor (NN) interaction coupling. Spin-orbit coupling of Ir has not been taken into account in our simulation, but we have considered the effect of its direct resultant (crystal field: ¨Ir). Consequently, the Hamiltonian of Sr2CrIrO6 includes NN and NNN interactions, the terms of energy related to the crystal fields of Cr and Ir, and the term of energy related to external magnetic field: ొ
ొ
ొ
ొ
ొ
మ మ మ ܪൌ െܬଵ σழǡவ ܵ ߪ୨ െ ܬଶ σழǡவ ܵ ܵ െ ܬଷ σழǡவ ߪ ߪ୨ െ ߂ σ୧మ ሺܵ ሻଶ െ οூ σ୧మ ሺߪ ሻଶ െ ొ మ
σ ሺܵ ߪ୧ ሻ
ଷ
ଵ
ଶ
ଶ
(1)
߂ and οூ are the respective crystal fields of Cr and Ir atoms. Crystal field ǻ of a transition metal is the splitting of d-orbitals in the field generated by the set of oxygenbonds surrounding the transition metal ion [27].
Figure 1: Qualitative sketch of interaction couplings prevailing in the Ising model. We illustrate only atoms of sites B and B’ present in the Ising model. To study the effect of substitution doping, a modification of that Hamiltonian is required. Thus, for the first case, when doping by Os “Sr2CrIrxOs1-xO6”, the Hamiltonian is given by: ొ
ొ
ొ
ొ
మ మ మ ܪൌ െܬଵ σழǡவ ܵ ሺߪ୨ ɀ୨ ሻ െ ܬଶ σழǡவ ܵ ܵ െ ܬଷ σழǡவ ሺߪ ߪ୨ ߪ ɀ୨ ɀ୧ ɀ୨ ሻ െ ߂ σ୧మ ሺܵ ሻଶ െ ౮ొ
ሺଵି୶ሻȀଶ
οூ σ୧మ ሺߪ ሻଶ െ οை௦ σ୧ ଷ
ଵ
ଶ
ଶ
ొ
ሺɀ୧ ሻଶ െ σమ ሺܵ ߪ୧ ɀ୧ ሻ
(2)
Where, ɀ୧ ൌ േ ǡ േ is the spin of Os, οை௦ is the crystal field of Os atoms, and x is the doping rate. For the second case, when doping by Re “Sr2CrIrxRe1-xO6”, the Hamiltonian is given by: ొ
ొ
ొ
ొ
మ మ మ ܪൌ െܬଵ σழǡவ ܵ ሺߪ୨ Ɂ୨ ሻ െ ܬଶ σழǡவ ܵ ܵ െ ܬଷ σழǡவ ሺߪ ߪ୨ ߪ Ɂ୨ Ɂ୧ Ɂ୨ ሻ െ ߂ σ୧మ ሺܵ ሻଶ െ ౮ొ
ሺଵି୶ሻȀଶ
οூ σ୧మ ሺߪ ሻଶ െ οோ σ୧
ొ
ሺɁ୧ ሻଶ െ σమ ሺܵ ߪ୧ Ɂ୧ ሻ
Where, Ɂ୧ ൌ േͳǡ Ͳ is the spin of Re and οோ is the crystal field of Re atoms.
(3)
3- Monte Carlo simulations MCS combined with the Metropolis algorithm has been performed to carry out this study. The simulated system is a cubic bulk with the size L=32, which is larger than the thermodynamic limit determined at LThL=28 in several studies for this class of compounds [28, 29, 30]. Therefore, the lattice contains an equal number of Cr-spins and Ir-spins (NCr=NIr=(L3)/2). Standard sampling method has been adopted to simulate the Hamiltonian given by eqs. (1), (2) and (3). Cyclic boundary conditions have been imposed on the lattice and initial configurations has been randomly generated, in the way the sites of the first sublattice are occupied randomly by Crଷ
ଵ
ଶ
ଶ
spins േ ǡ േ , and the sites of the second sublattice are occupied randomly by Irspins േʹǡ േͳǡ ͲǤ At each MCS step, the lattice is sequentially traversed and singlespin flip attempts are made. According to a heat-bath algorithm under the Metropolis approximation, the flips are accepted or rejected. The data has been collected for 1.2*106 MCS steps. The first 6*105 steps have been devoted to reach the equilibrium, after which the average of physical quantities has been computed. Total magnetizations, magnetic susceptibility, internal energy per site and specific heat of Sr2CrIrO6 have been respectively calculated by the eqs. (4), (5), (6) and (7):
݉ ൌ
σ ௌା σ ఙ ಿೝ ಿೝ
߯ ൌ ߚ ܰ כሺ݉ۃଶ ۄെ ۄ݉ۃଶ ሻ Whereߚ ൌ
(4) (5)
: T denotes the absolute temperature and KB is the Boltzmann’s
ࡷ ࢀ
constant. N is the total number of spins in the system.
ܧൌ
ேೝ כேೝ
൫െ ͳܬσ൏݅ǡ݆ ܵ݅ ߪ െ ʹܬσ൏݅ǡ݆ ܵ݅ ݆ܵ െ ͵ܬσ൏݅ǡ݆ ߪ݅ ߪ െ ߂ ݎܥσሺܵ݅ ሻʹ െ ο ݎܫσሺߪ݅ ሻʹ െ σሺܵ݅ ߪ ሻ൯
(6)
ܥ௩ ൌ ߚ ܰ כሺ ܧۃଶ ۄെ ۄ ܧۃଶ ሻ
(7)
Magnetization of the doped compound has been calculated, in the case of Irsubstitution by Os-doping “Sr2CrIrxOs1-xO6”, by eq. (8), and in the case of Irsubstitution by Re-doping “Sr2CrIrxRe1-xO6”, by eq. (9):
݉ ்ሺூିை௦ሻ ൌ
σ ௌା σ ఙା σ ஓ ಿೝ ሺభషೣሻಿೝ ೣכಿೝ
݉ ்ሺூିோሻ ൌ
σ ௌା σ ఙା σ ஔ ಿೝ ሺభషೣሻಿೝ ೣכಿೝ
(8)
(9)
4- Results and discussion In the class of DP oxides, the two transition metals are coupled antiferromagnetically, which entails the NN interaction coupling J1 to be negatif. Each type of transition metal atoms is coupled ferromagnetically, which means that the NNN interaction couplings J2 and J3 should be positive. Thus, the first coupling has been taken J1= -1, and all the other parameters has been reduced to its absolute value.
Figure 2: a) Magnetization and magnetic susceptibility vs. the reduced temperature T/|J1| for the reduced exchange couplings: J2 /|J1| = J3 /|J1| =1. b) Magnetization vs. the reduced temperature T /|J1| for the reduced exchange couplings: J2 /|J1| fixed at 1 and J3 /|J1| ranging from 1 to 1.6. Reduced crystal fields (ᇞCr/|J1|, ᇞIr/|J1|) and the reduced external field h/|J1| are taken null. Magnetization and magnetic susceptibility versus the reduced temperature T/|J1| have been computed for a uniform value of the reduced couplings (J2 /|J1|= J3 /|J1| =1) (figure 2-a), zero crystal field and zero external magnetic field. Magnetization has been drown for the reduced coupling J3 /|J1| ranging from 1 to 1.6 and for J2 /|J1|=1 (figure 2-b), zero crystal field and zero external magnetic field. Internal energy and specific heat versus the reduced temperature T/|J1| have been computed for a uniform value of the reduced couplings (J2 /|J1|= J3 /|J1| =1) (figure 3-a), zero crystal field and zero external magnetic field. Internal energy has been drown for the reduced coupling J3 /|J1| ranging from 1 to 1.6 and for J2 /|J1|=1 (figure 3-b), zero crystal field and zero external magnetic field. Peaks of the susceptibility and the specific heat coincide with the critical temperature where the system transit from the magnetic phase to the paramagnetic phase. The magnetization show a nonmonotonic behavior similar to the one reported by Krockenberger et al. [20] for Sr2CrOsO6. Where, the authors predict that such a behavior is a consequence of the different temperature evolution of the Cr magnetic moments and the induced moments at the Os site, and suppose that this unusual behavior can be coupled with the distortion of the lattice. Moreover, this behavior is observed only in Cr-based DPs with high valence electron number of the (5d) transition metal, because it was only observed in {Sr2CrOsO6 with Os(5d3)} and {Sr2CrIrO6 with Ir(5d4)} and not in
{Sr2CrReO6 with Re(5d2)} and {Sr2CrWO6 with Os(5d1)}, which means that it is correlated with the filling of the 5d band, just like the critical temperature. Raising the value of the exchange coupling J3 amplify the non-monotonic behavior of the magnetization (figure 2-b), making the interaction strength between the 5d-element atoms another important factor behind the unusual behavior of the magnetization. However, raising the value of the exchange coupling J3 enhance the stability of the material that can be seen in figure (2-b) by the decrease of the energy.
Figure 3: a) Internal energy and specific heat vs. the reduced temperature T /|J1| for the reduced exchange couplings: J2 /|J1| = J3 /|J1| =1. b) Internal energy vs. the reduced temperature T /|J1| for the reduced exchange couplings: J2 /|J1| fixed at 1 and J3 /|J1| ranging from 1 to 1.6. Reduced crystal fields (ᇞCr/|J1|, ᇞIr/|J1|) and the reduced external field h/|J1| are taken null.
Figure 4: a) Magnetization vs. the reduced temperature T/|J1|, b) magnetic susceptibility vs. the reduced temperature T/|J1|, for reduced crystal field ᇞIr /|J1| ranging from 0.25 to 2.25. Reduced crystal field ᇞCr/|J1| is fixed at 0.25. Reduced exchange couplings are taken: J2 /|J1| = J3 /|J1| =1. Reduced external field h/|J1| is taken null.
Figure 5: Magnetization vs. magnetic field loops for Sr2CrIrO6 DP for the reduced exchange couplings: J2 /|J1| =5, J3 /|J1| =1. Reduced crystal fields (ᇞCr/|J1|, ᇞIr/|J1|) are taken null. Data are calculated at the reduced temperatures: T/|J1| =10 (a), T/|J1| =20 (b), T/|J1| =30 (c), T/|J1| =40 (d).
As 5d orbitals of Ir are more extended than the 3d orbitals of Cr, the effect of the crystal field of Ir should be stronger that the Cr one, and exploring that effect could give interesting results. Therefore, the magnetization and the magnetic susceptibility versus the reduced temperature T/|J1| have been computed for the reduced crystal field of Ir ᇞIr/|J1| ranging from 0.25 to 2.25, fixed crystal field of Cr ᇞIr/|J1|=0.25, uniform value of the reduced couplings (J2 /|J1|= J3 /|J1| =1) (figure 2-a) and zero external magnetic field (figure 4). The results are just as expected, because they show an increase of Tc by the increase of ᇞIr/|J1|, and are in good agreement with those found for Sr2CrReO6 [29]. The unexpected result is the amplification of the nonmonotonic behavior, which make the crystal field strength of the 5d-element another factor behind the unusual behavior of the magnetization.
Figure 6: Magnetization vs. magnetic field loops for Sr2CrIrO6 DP for the reduced exchange couplings: J2 /|J1| =1, J3 /|J1| =5. Reduced crystal fields (ᇞCr/|J1|, ᇞIr/|J1|) are taken null. Data are calculated at the reduced temperatures: T/|J1| =10 (a), T/|J1| =20 (b), T/|J1| =30 (c), T/|J1| =40 (d).
Figure 7: Magnetic field dependence of the magnetization of Sr 2CrIrO6 DP, a) at the reduced temperature T/|J1| =20 for the reduced exchange couplings ( J2 /|J1| =5, J3 /|J1| =1) and ( J2 /|J1| =1, J3 /|J1| =5), and b) at the reduced temperature T/|J1| =60 for the reduced exchange couplings ( J2 /|J1| = J3 /|J1| =1), ( J2 /|J1| =5, J3 /|J1| =1) and ( J2 /|J1| =1, J3 /|J1| =5). Reduced crystal fields (ᇞCr/|J1|, ᇞIr/|J1|) are taken null.
Since future applications of the here studied compound to tunnel junctions require a proper coercive field hc, we have examined the magnetization versus the magnetic field loops at reduced temperatures T/|J1| ranging from 10 to 40, for the reduced couplings (J2 /|J1|=5, J3 /|J1| =1) (figure 5) and for (J2 /|J1|=1, J3 /|J1| =5) (figure 6), zero crystal fields. A comparison between the hysteresis loops at T/|J1|=20 is plotted in (figure 7-a), and at T/|J1|=60 in (figure 7-b). The data show the high exchange coupling J2 is in favor of high coercive fields’ hc, while high exchange coupling J3 gives smaller coercive fields’ hc. Hysteresis loops are displayed for high J2 even at T/|J1|=40, while they disappear at T/|J1|=30. Magnetic saturation MS is smaller in the case of high J3 than in the case of high J2. That means that, the exchange interactions between 3d-element atoms (Cr-atoms) affect the magnetic performance less than those between 5d-element atoms (Ir-atoms). At T=60, S-shaped magnetization curves of both cases {(J2 /|J1|=J3 /|J1| =1) and (J2 /|J1|=5, J3 /|J1| =1)} may be indicative of major paramagnetic contribution. Curve of the case (J 2 /|J1|=1, J3 /|J1| =5) is a linear characteristic of the antiferromagnetic behavior, which result from the complexity of this strongly correlated electron system.
Figure 8: Magnetization (a-a’) and magnetic susceptibility (b-b’) vs. the reduced temperature T/|J1| of Sr2CrIrxOs1-xO6 (a-b) and Sr2CrIrxRe1-xO6 (a’-b’) for x ranging from 0.1 to 0.5. Reduced exchange couplings are taken uniform: J2 /|J1| = J3 /|J1| =1. Reduced crystal fields (ᇞCr/|J1|, ᇞ/|J1|, ᇞRe/|J1|, ᇞIr/|J1|) and the reduced external field h/|J1| are taken null.
To modifying the magnetic properties of Ir-based DPs, not varying the occupation of the 5d orbitals by control of Ir valence state is the only route less explored [16], but doping by substitution of Ir is also a route less explored. Simplifications on the exchange interactions, has been used to reduce the computational complexity of the doped compound: - in the first case of doping “Sr2CrIrxOs1-xO6”, the NN interaction coupling J1, which acts between Cr and Ir atoms and between Cr and Os atoms, is taken of the same value. Ir and Os atoms are localized in the second sublattice and interact with each other (Ir—Ir, Ir—Os and Os—OS) by the same NNN coupling J3. in the second case of doping “Sr2CrIrxRe1-xO6”, the NN interaction coupling J1, which acts between Cr and Ir atoms and between Cr and Re atoms, is taken of the same value. Ir and Re atoms are localized in the second sublattice and interact with each other (Ir—Ir, Ir—Re and Re—Re) by the same NNN coupling J3. Magnetization and magnetic susceptibility are computed versus the reduced temperature T/|J1| of Sr2CrIrxOs1-xO6 (figure 8-a,b) and Sr2CrIrxRe1-xO6 (figure 8-a’,b’) for x ranging from 0.1 to 0.5, the reduced exchange couplings are taken uniform (J2 /|J1| = J3 /|J1| =1), the reduced crystal fields (ᇞCr/|J1|, ᇞ/|J1|, ᇞRe/|J1|, ᇞIr/|J1|) and the reduced external
magnetic field h/|J1| are taken null. Sr2CrIrO6 behave quite differently depending on the type of atom that substitutes Ir(5d4). When Ir(5d4) is substituted by Os(5d3), the transition temperature and the magnetization amplitude decrease gradually by the increase of the substitution rate x. this result is in good agreement with the result reported by Krockenberger et al. [20] that shows a strong correlation between the transition temperature and the number of 5d electrons. Subsequently, the result found when Ir(5d4) is substituted by Re(5d2) is unexpected. In this case, the only Tc displayed is equal to 32, which is largely smaller than Tc = 54 calculated without doping (see figure 2-a). In addition, there is no gradual change in the transition temperature either, nor in the magnetization amplitude. This result can be explained by the fact that the spins of Re atoms (േͳǡ Ͳ) have the same values as the small spins of Ir atoms (േʹǡ േͳǡ Ͳ), thus, when doping by Re, the system will be occupied mostly by the small values of spin (േͳǡ Ͳ). Consequently, the spin polarization of the system is reduced, which affect the transition temperature and the magnetic behavior.
5- Conclusion The findings of our investigation allow better understanding of the complexity of correlated interactions characterizing the promising compound Sr2CrIrO6. The magnetization has shown a non-monotonic behavior similar to the one reported by Krockenberger et al. [20] for Sr2CrOsO6. Where, the authors predict that such a behavior is a consequence of the different temperature evolution of atom moments, and suppose that this unusual behavior can be coupled with the distortion of the lattice. Moreover, this behavior is observed only in Cr-based DPs with high valence electron number of the (5d) transition metal, which means that it is correlated with the filling of the 5d band, just like the critical temperature. Raising the value of the exchange coupling J3 amplify the non-monotonic behavior of the magnetization, making the interaction strength between 5d-element atoms another important factor behind the unusual behavior of the magnetization. However, raising this interaction strength enhance the stability of the material that can be seen in the decrease of the energy. Effects of the crystal field of Ir are just as expected, because they show an increase of Tc by the increase of ᇞIr/|J1|, and are in good agreement with those found for Sr2CrReO6 [29]. The unexpected result is the amplification of the non-monotonic behavior, which make the crystal field strength of the 5d-element the second factor, found in this work, behind the unusual behavior of the magnetization. The data show the high exchange coupling J2 is in favor of high coercive fields’ hc, while high exchange coupling J3 gives smaller coercive fields’ hc. Hysteresis loops are displayed for high J2 even at T/|J1|=40, while they disappear at T/|J1|=30. Magnetic saturation MS is smaller in the case of high J3 than in the case of high J2. That means that, the exchange interactions between 3d-element atoms (Cr-atoms) affect the magnetic performance less than those between 5d-element atoms (Ir-atoms). Sr2CrIrO6 behave quite differently depending on the type of atom that substitutes Ir(5d4).
Substitution doping by Os(5d3) shows a gradual decrease of the magnetization and the transition temperature, which is in good agreement with the result reported by Krockenberger et al. [20] that shows a strong correlation between the transition temperature and the number of 5d electrons. This is not the case for the substitution doping by Re(5d2) where the two quantities remain unchanged . This result can be explained by the fact that the spins of Re atoms (േͳǡ Ͳ) have the same values as the small spins of Ir atoms (േʹǡ േͳǡ Ͳ), which reduced the spin polarization of the system, and so affects the transition temperature and the magnetic behavior.
References [1] A. V. Powell, J. G. Gore, P. D. Battle, J. Alloys Compd. 73 (1993) 201. [2] Y. Tokura and N. Nagaosa, Science 288 (2000) 462. [3] K.-I. Kobayashi, T. Kimura, H. Sawada, K. Terakura, and Y. Tokura, Nature (London) 395 (1998) 677. [4] J. B. Philipp, P. Majewski, L. Alff, A. Erb, R. Gross, T. Graf, M. S. Brandt, J. Simon, T. Walther, W. Mader et al., Phys. Rev. B 68 (2003) 144431. [5] A. A. Aligia, P. Petrone, J. O. Sofo, and B. Alascio, Phys. Rev. B 64 (2001) 092414. [6] A. Poddar and S. Das, Physica B (Amsterdam) 344 (2004) 325. [7] R. Ramesh and N. Spaldin, Nat. Mater. 6 (2007) 21. [8] T. K. Mandal, C. Felser, M. Greenblatt, J. Kübler, Phys. Rev. B 78 (2008)134431. [9] R. D. Shannon, Acta Crystallogr., Sect. A 32 (1976) 751. [10] P. M. Woodward, Acta Crystallogr., Sect. B 53 (1997) 32. [11] D.-Y. Jung, P. Gravereau, G. Demazeau, Eur. J. Solid State Inorg. Chem. 30 (1993) 1025. [12] I. Qasim, B. J. Kennedy, M. Avdeev, J. Mater. Chem. A 1 (2013) 3127. [13] M. Bremholm, C. K. Yim, D. Hirai, E. Climent-Pascual, Q. Xu, H. W. Zandbergen, M. N. Ali, R. J. Cava, J. Mater. Chem. 22 (2012) 16431. [14] D.-Y. Jung, G. Demazeau, J. H. Choy, J. Mater. Chem. 5 (1995) 517. [15] P. Kayser et al., Eur. J. Inorg. Chem. (2014) 178. [16] M. A. Laguna-Marco, G. Fabbris, N. M. Souza-Neto, S. Chikara, J. S. Schilling, G. Cao, and D. Haskel, Phys. Rev. B 90 (2014) 014419. [17] O. B. Korneta, S. Chikara, S. Parkin, L. E. Delong, P. Schlottmann, and G. Cao, Phys. Rev. B 81 (2010) 045101. [18] J. B. Philipp, D. Reisinger, M. Schonecke, A. Marx, A. Erb, L. Alff, R. Gross, and J. Klein, Appl. Phys. Lett. 79 (2002) 3654.
[19] H. Kato, T. Okuda, Y. Okimoto, Y. Tomioka, Y. Takenoya, A. Ohkubo, M. Kawasaki, and Y. Tokura, Appl. Phys. Lett. 81 (2002) 328. [20] Y. Krockenberger et al., Phys Rev B 75 (2007) 020404(R). [21] J. Navarro, C. Frontera, Ll. Balcells, B. Martínez, and J. Fontcuberta, Phys. Rev. B 64 (2001) 092411. [22] J. Navarro, J. Fontcuberta, M. Izquierdo, J. Avila, and M. C. Asensio, Phys. Rev. B 69 (2004) 115101. [23] E. K. Hemery, G. V. M. Williams and H. J. Trodahl, Phys. Rev. B 74 (2006) 054423. [24] J.M. Michalik, J.M. De Teresa, J. Blasco, C. Ritter, P.A. Algarabel, M.R. Ibarraa, and Cz. Kapusta, Solid State Sciences 12 (2010) 1121-1130. [25] C. Felser, G. H. Fecher, Spintronics from Materials to Devices , Springer Dordrecht Heidelberg New York, 2013, pp 64. [26] H. Asano,N. Kozuka, A. Tsuzuki, and M. Matsui, App. Phys. Lett. 85 (2004) 263. [27] V. Vleck, J. Physical Review 41 (1932) 208. [28] O. El Rhazouani, A. Benyoussef, A. El Kenz, J. M. M. M. 377 (2015) 319. [29] O. El Rhazouani, A. Benyoussef, S. Naji, A. El Kenz, Physica A 10 (2013) 1016. [30] S. Naji, A. Benyoussef, A. El Kenz , H. Ez-Zahraouy, M. Loulidi, Physica A 391 (2012) 3885.