First-principles study of structural, electronic and magnetic properties of double perovskite oxides Ba2CoMO6 (M=Mo and W)

Materials Science in Semiconductor Processing 34 (2015) 281–290

Contents lists available at ScienceDirect

Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp

First-principles study of structural, electronic and magnetic properties of double perovskite oxides Ba2CoMO6 (M¼ Mo and W) M. Musa Saad H.-E. a,n, Mohamed Anwar K. Abdelhalim b, A. El-Taher a a b

Department of Physics, College of Science, Qassim University, Buraidah 51452, Saudi Arabia Department of Physics and Astronomy, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

a r t i c l e i n f o

abstract

Available online 11 March 2015

Ba2CoMO6 (M ¼ Mo and W) ordered double perovskite oxides have been investigated by using the first-principles of full potential linearized muffin-tin orbital (FP-LMTO) computational method. The structural, electronic and magnetic properties of Ba2CoMO6 were calculated using both the local spin density approximation (LSDA) and generalized gradient approximation (GGA) methods. The room temperature crystal structures of Ba2CoMO6 are face-centered cubic (space group Fm3m and tilt system a0a0a0) with lattice constants of (a ¼8.011 Å) and (a ¼8.031 Å) for (M ¼ Mo) and (M ¼ W), respectively. The crystals of Ba2CoMO6 contain alternating CoO6 and MO6 octahedra, almost fully ordered in the basal ab planes. It was shown that the obtained lattice constants agree well with the experimental data. The influence of M-cation on structural, electronic and magnetic properties of Ba2CoMO6 compounds is analyzed. The total and partial densities of states (DOSs) and partial and total spin magnetic moments are calculated, and the valence states of Co and M ions are examined. The magnetic and electronic properties and bond valence sums are consistent with the electronic configuration Co2 þ (3d7)–M6 þ (4d/5d)0 with Co2 þ in high spin states. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Double perovskite oxides Crystal structure Magnetic properties

1. Introduction Theoretical and experimental research activities on crystalline magnetic materials have been increased over the past half-century mainly due to their unique and interesting structural, electronic and magnetic properties. Transitionmetal oxides with ordered double perovskite structures class belong to the large family of crystalline magnetic materials. Double perovskite oxide materials have attracted special attention in many applied and fundamental area of solid state physics and advanced materials science due to exotic electronic and magnetic properties. For example, colossal n Corresponding author. Mobile: þ966 509353808; fax: þ966 163800911. E-mail address: [email protected] (M. Musa Saad H.-E.).

http://dx.doi.org/10.1016/j.mssp.2015.02.038 1369-8001/& 2015 Elsevier Ltd. All rights reserved.

magnetoresistance (CMR) in Sr2MMoO6 (M¼Cr and Fe) [1–4], tunnel magnetoresistance (TMR) in Sr2FeMoO6 [5], half-metallicity (HM) in Ca2FeReO6 and Ba2FeMoO6 [6], magnetoelectricity in Sr2CoMoO6 [7] etc. Double perovskite oxides with the general chemical formula unit of A2MBO6 result from the ordering of M and B on the octahedral site of primitive perovskite AMO3 in rock-salt (Na þ Cl  ) arrangement. By varying different cations with other alkaline ions at A-site or transition-metals at (M–B)-sites very rich structural, electronic and magnetic properties can be obtained. However, the understanding of the relations between structural, electronic and magnetic properties is actually a hot field of study. Magnetic double perovskite oxides A2MBO6 were first proposed by Longo and Ward in 1960s [8]. According to those authors, A-site is an alkaline earth metal and (M–B)sites were occupied by magnetic and nonmagnetic

282

M. Musa Saad H.-E. et al. / Materials Science in Semiconductor Processing 34 (2015) 281–290

Fig. 1. 3D view of the cubic crystal structure of double perovskite oxide Ba2CoMO6 with 1:1 ordering of two different cations (space group Fm3m), the black and red spheres represent the Ba2 þ and O2  ions, respectively. The view showing the corner-sharing CoO6 (blue octahedral) and MO6 (green octahedral) in straight angle ( oCo–O–M 4 ¼ 1801) with Ba2 þ cations residing in the cavities formed by the octahedral network. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 1 Calculated (Cal.) and experimental (Exp.) crystallographic data for Ba2CoMO6 (M ¼Mo and W); the tolerance factors t, formula unit volumes V, lattice constants a, oxygen positions O (x, 0, 0) and average bondlengths. M6 þ (4d/5d)

Mo

Method

Cal.

Exp.

t V (Å3) a (Å) O (x) 6  oCo–O 4 (Å) 6  o M–O4 (Å)

1.0408 514.11 8.0110 0.2620 2.0985 1.9070

1.0410 519.49 8.0388 0.2614 2.109 1.935

a b

2. Methods and computational details

W a

such as spin valves, sources for spin polarized electrons and magnetic information storages. Barium double perovskite oxides Ba2MBO6 have revealed a variety of crystal structures and electronic and magnetic properties. Antiferromagnetic ordered Ba2MBO6 with M¼magnetic ion and B¼ nonmagnetic ion characterizes by the superexchange interaction between the magnetic ions via an array of nonmagnetic ions. When Ba2MBO6 includes transition-metal ions within M or B sub-lattice, the magnetic properties are strongly influenced by the ordering of the cations within this sub-lattice. Like other known double perovskite oxides, ordered Ba2CoMO6 compounds not found enough attention; however, there are a few experimental studies focused on Co-based double perovskite oxides Ba2CoMO6. Martinez-Lope et al. analyzed and reported that Ba2CoMoO6 and Ba2CoWO6 were antiferromagnetic materials with low Neel temperatures of TN ¼27 K and TN ¼19 K, respectively [9]. Hirama et al. investigated the La-substitution effects on the antiferromagnetic insulator Ba2CoMoO6 [10]. Recently, Zhang et al. explored Ba2CoMoO6 as anode material for solid oxide fuel cells [11]. Also, Lopez et al. reported that A2CoWO6 crystallized in cubic structure with antiferromagnetic when A¼Ba [12]. In the present work, the structural, electronic and magnetic properties of ordered double perovskite oxides Ba2CoMO6 (M¼Mo and W) have been studied. Crystal structure information, ground states, band gaps, total and partial densities of states are calculated for the first time by using the self-consistent full potential linear muffin-tin orbital (FPLMTO) method within the von Barth–Hedin localized spin density approximation (LSDA) and Perdew et al. generalized gradient approximation (GGA). It is expected that the present work will help in understanding how the M-site substitution affects the structural, electronic and magnetic properties of Ba2CoMO6, and the paper will also cover the lack theoretical data on physical properties of double perovskite oxides Ba2CoMoO6 and Ba2CoWO6.

b

Cal.

Exp.

1.0382 517.97 8.0310 0.2613 2.0985 1.9170

1.0380 533.02 8.1080 0.2625 2.1291 1.9476

From Refs. [9,11]. From Ref. [22].

transition-metals, respectively. Nevertheless, the HM electronic feature of the well-known double perovskite oxide Sr2FeMoO6 was only established by Kobayashi et al. in 1998s [1]. HM property can be characterized by the difference between the conduction electrons. The density of states as a function of energy [DOS (E)] clearly evidences that the spin-up moment (DOS↑) shows an energy-gap (Eg) at the Fermi level (EF), as the insulating material, while the spindown moment (DOS↓) continuous at EF, due to the strong hybridization Fe (3d)–O (2p)–Mo (3d). The extensive HM studies on double perovskite oxides are relate with the probable technological applications in spintronic devices,

First-principles density functional theory (DFT) calculations within localized spin density approximation (LSDA) [13] and generalized gradient approximation (GGA) [14] for the exchange–correlation functional have been utilized to study the structural, electronic and magnetic properties of double perovskite oxides Ba2CoMO6 (M¼Mo and W). The computational method was considered as the full potential linearized muffin-tin orbital (FP-LMTO) [15] implemented in the fast and efficient LMTART software package [16,17]. The FP-LMTO method, for which the self-consistent version is yet to be available, relies on the self-consistent potential borrowed from the LMTO calculations. For self-consistent calculation with plane wave (PLW) basis the number of k points was chosen to be 120, and has checked for convergence. The commonly used criterion relating the PLW and angular momentum cutoff (Lmax ¼Rmax  Kmax) was taken to be 6.0, where Rmax and Kmax are the maximum muffin-tin (MT) sphere radius and the PLW cutoff for the basis. The valence electron configurations were taken as Ba (6s2), Co (3d7 4s2), Mo (4d5 5s1), W (5d4 6s2) and O (2s2 2p4). In the present study, the atomic MT spheres radii were chosen as R (Ba)¼3.83, R (Co)¼ 2.53, R (Mo)¼2.14, R (W)¼ 2.15 and R (O)¼1.51. Spin orbital coupling (SOC) has been including in

M. Musa Saad H.-E. et al. / Materials Science in Semiconductor Processing 34 (2015) 281–290

the calculations. For the self-consistent LMTO calculations within the atomic PLW approximation, no empty spheres were introduced, since the structures are closed packed. The self-consistency was achieved with (8  8  8) k-points in the Brillouin zone. Calculations have been carried out within LSDA (GGA) þU framework in PLW basis to take into account the missing correlation effect beyond LSDA and GGA [13,14]. In LSDA (GGA) þU calculations, the near-maximum values of the Coulomb U and exchange J parameters were selected from the reasonable range of U and J in the literature [18–20]. For example, the range of U for Co (3d) is 3.0–6.0 eV and for M (4d/5d) is 1.0–2.0 eV. In the present calculations, U (Co)¼5.0 eV and U (M)¼1.0 eV are used, while (J¼0.89 eV) for all 3d, 4d and 5d transition-metals. 3. Results and discussion 3.1. Room-temperature structural properties of Ba2CoMO6 Ba2CoMO6 (M¼Mo and W) ordered double perovskite oxides crystallize in face-centered cubic (FCC) structure with space-group of (Fm3m; No. 225) (Fig. 1). At room temperature, the lattice constants of compounds are almost equal to aE8.0 Å. Table 1 displays the ionic radii of M ions, tolerance factors, formula unit volumes, lattice constants (a, b, c), oxygen positions in O (x, 0, 0) and the average bondTable 2 Ions, sites, positions (x, y, z), ionic valence states and occupancy in ordered double perovskite oxides Ba2CoMO6 (M¼ Mo and W) with Fm3m crystal structure. Ion

Site

x

y

z

Valence

Occupancy

Ba Co M O

8c 4a 4b 24e

0.25 0.0 0.5 x

0.25 0.0 0.5 0.0

0.25 0.0 0.5 0.0

2þ 2þ 6þ 2

1 1 1 1

283

lengths of oCo–O4 and oM–O4. It is seen that the values of lattice constant are around the ideal value (a¼2a0; a0 ¼4 Å) and depends mainly on the ionic radii in Ba2CoMO6; Ba2 þ (r¼1.61 Å), Co2 þ (r¼ 0.65 Å in HS and r¼0.545 Å in LS), Mo6 þ (r¼0.59 Å), W6 þ (r¼0.60 Å) and O2 (r¼1.41 Å). As shown in Table 1, the oxygen coordinate x varies in small amount (Δx¼ 70.1) and depends on the M-site in Ba2CoMO6. The calculated crystallographic data of Ba2CoMO6 were compared with the previous experimental data. The common atomic sites and positions (x, y, z), and valence states in FCC crystal structure of Ba2CoMO6 formula units are revealed in Table 2. The structural results obtained in this work are in close agreement with those obtained experimentally [9,12,22,23]. It can be seen that the lattice constant a and formula unit volume V increase linearly when M¼Mo to M¼W in Ba2CoMO6. As seen in Fig. 1, from Ref. [21], 3D geometric crystal structure of cubic formula unit of double perovskite Ba2CoMO6 in Fm3m symmetry can be described by the FCC arrangement of Co and M ions in rock-salt order. In this crystal structure, both Co2 þ (0, 0, 0) and M6 þ (0.5, 0.5, 0.5) ions form an FCC lattice with the displacement of half of the lattice constant. The Oxygen ions O2 (0, 0, x) are located near the center of each nearest-neighboring Co–M pair and the bond-length of oCo2 þ –O2 4 and oM6 þ –O2 4 is approximately equal to 2.0 Å (Table 1). Only six O2 ions around the center Co2 þ and M6 þ ions formulate the CoO6 and MO6 octahedra, in a tilt system of (a0a0a0), whereas the Ba2 þ ions are located in the cavities between CoO6 and MO6 octahedra. Moreover, to verify whether the crystal structure of double perovskite oxide is distorted from the ideal structure the Goldschmidt tolerance factor t is used pto ffiffiffi evaluate the symmetry deviations, as: t ¼ ðr Ba þ r O Þ= 2   ðr Co þ r M Þ=2 þr O . Where rBa, rCo, rM, and rO are the radii of cations and oxygen in Ba2CoMO6. This factor describes the stability of double perovskite oxide structure; (t¼1.0) represents the ideal cubic structure. The structure of Ba2CoMO6

Fig. 2. Calculated total energy as a function of volume for Ba2CoMO6 (a) M ¼Mo and (b) M¼ W; the stars and lines show the calculated and fitted curves, respectively.

284

M. Musa Saad H.-E. et al. / Materials Science in Semiconductor Processing 34 (2015) 281–290

compounds are stable from room temperature and adopt a cubic symmetry (Fm3m); their tolerance factors are closed to 1.0, see Table 1. As a result, the CoO6 and MO6 octahedra did not deviate (Tilt¼01) in order to fill the space, see Fig. 1. The ordered double perovskites Ba2CoMO6 adopt the Na þ Cl  structure arrangement, and can be viewed as a network of regular arrangement of corner-sharing CoO6 and MO6 octahedra with Ba-cations occupy the voids formed by these octahedral. CoO6 and MO6 alternate along the three crystallographic directions (a, b, c). As known, 2þ Ba2 þ -cations have a large size (rBa ¼1.61 Å), so, the octahedral network is not tilted (Tilt ¼01) keeping oCo–O–M4 angle at 1801. In addition, there is a perfect 1:1 M-site ordering of Co and M, due to the large difference in size and charge existing between Co2 þ and M6 þ cations. As shown in Table 1, it is seen that the CoO6 octahedra ( oCo–O 4 ¼2.0985 Å) are larger than the MO6 ( oM–O4 ¼1.9107 Å), and this is in accordance with the 2þ larger ionic radius of Co2 þ (rCo ¼0.65 Å) compared to M6 þ 6þ 6þ (rMo ¼0.60 Å and rW ¼0.60 Å) [24]. The bond valence calculations from the observed bond-lengths can give some insight into the actual oxidation states of the different cations present in the crystal structure of Ba2CoMO6. The calculated valence for Ba, Co and M is 2.24, 2.23 and 5.79, respectively. The Ba-cation seems to

be significantly over-bonded, exhibited a valence much higher than the expected value 2 þ. In fact, the observed oBa–O 4 bond-length is much shorter than expec ted from the sum of the ionic radii of Ba2 þ and O2  ions, (1.61þ1.41 ¼3.02 Å), in closed packing structure. It seems that the much more covalent network determined by the CoO6 and MO6 octahedra chiefly determines the volume of the formula unit; the low degree of freedom of cubic crystal structure of Ba2CoMO6 constrains the oBa–O4 bond-length outside of the optimal values. Beside, the valence states of Co and M suggest the oxidation states of 2 þ and 6 þ, respectively. From these results, the antiferromagnetic electronic configurations in Ba2CoMO6 at room temperature are Co2 þ (3d7)–O (2p)–M6 þ (4d0/5d0), and this similar of that explored in Sr2Co2 þ M6 þ O6 (M ¼Mo and W) compounds [3,7]. The ground state structures of double perovskite oxides Ba2CoMO6 (M¼Mo and W) are calculated by using the optimum values of the lattice parameters (a¼8.0110 Å) for M¼Mo and (a¼8.0310 Å) for M¼W. To obtain the optimum values of the lattice parameters, the ground state total energies for different volumes are calculated starting with the experimental lattice parameters, Table 1; (a¼8.0338 Å) for M¼Mo and (a¼ 8.1080 Å) for M¼W. In the whole calculations the internal parameters of atoms are fixed at

Fig. 3. TDOS of Ba2CoMoO6 from LSDA (GGA) and LSDA (GGA) þ U (U¼ 5.0 eV).

M. Musa Saad H.-E. et al. / Materials Science in Semiconductor Processing 34 (2015) 281–290

the experimental values. Then the calculated results are fitted to the third-order Birch Murnaghan equation of state [25], which can be defined as: " # B0 VB0 V 0 =V 0 V B  0  þ1  0 0 0  EðV Þ ¼ E0 þ 0 B0 B 1 B0 1 where V0 is the equilibrium volume, B0 is the bulk modulus, evaluated  at volume V0, which can be given by B0 ¼ V ∂P=∂V T [26], and B00 is the pressure derivative of B0, also evaluated at volume V0. Fig. 2 shows the optimization of total energy as a function of volume for double perovskite oxides Ba2CoMO6 (M¼ Mo and W). The minimum energy values are obtained (E0 ¼ 602867.620 eV) for M¼Mo and (E0 ¼  932318.296 eV) for M¼W. Thus, the equilibri um volumes are (V0 ¼514.11 Å3) and (V0 ¼517.97 Å3), which correspond with lattices parameters (a¼8.0110 Å) and (a¼8.0310 Å) for M¼ Mo and M¼W, respectively. Therefore, the lattice parameters obtained from the calculations are 99.5% in agreement with the experimental results, see Table 1. 3.2. Ground state electronic properties of Ba2CoMO6 The total energy and electronic properties of the Ba2CoMO6 (M¼Mo and W) have been calculated by using the LSDA

285

(GGA) (U¼0.0 eV) and LSDA (GGA) þ U methods. First, In order to find the stable magnetic structure in Ba2CoMO6 formula unit, the total energies were calculated. There are four magnetic phases in the crystal structure of ordered double perovskite oxides Ba2CoMO6 denoted as ferromagnetic (FM), ferrimagnetic (FIM), antiferromagnetic (AFM) and nonmagnetic (NM) states. Only the spin state, of Co2þ and M6þ ions, dominates the magnetic phase of Ba2CoMO6. The transition-metal ions Co2þ and M6þ have their own spin state, that is, (Co2þ ↑–Co2þ ↑–M6 þ ↑–M6 þ ↑)¼FM, (Co2 þ ↑– Co2þ ↑–M6þ ↓–M6þ ↓)¼ FiM, which can probably lead to assume of the HM electronic state in these cases with an integer spin magnetic moment (S¼ 7m). The AFM state occurs when the Co2þ and M6þ ions along the chain are ferromagnetically polarized but the neighbor chain is antiferromagnetic coupled, i.e., (Co2 þ ↑–Co2 þ ↓–M6 þ ↓–M6 þ ↑)¼ AFM. In AFM state, no HM state exists because the TDOS↑ and TDOS↓ are symmetrical, which results from the induced equivalent in the charge densities. For the NM state, no spin polarized and therefore, (Co2 þ –Co2 þ –M6 þ –M6 þ )¼NM; no magnetic properties exist. The results show that the spinpolarized calculations of total energies are always lower than that without spin-polarization. To guarantee the accuracy of the calculation results, full structural optimization with higher convergence criteria was also performed. The total energy of

Fig. 4. Calculated TDOS and PDOSs [Co (3d), Mo (4d) and O (2p)] of Ba2CoMoO6 (space group Fm3m) from LSDA (GGA) and LSDA (GGA) þ U (U ¼5.0 eV).

286

M. Musa Saad H.-E. et al. / Materials Science in Semiconductor Processing 34 (2015) 281–290

the prominent phases in double perovskite oxides, ferromagnetic (FM) and ferrimagnetic (FiM) magnetic phases was calculated in comparable approaches. It is found that the FiM phase lower in energy than the FM phase, in excellent harmony with the earlier DFT computational results for the parent magnetic double perovskites Sr2CoMO6 (M¼Mo and W) [3]. 3.2.1. Ba2CoMoO6 The total and partial densities of states of the ground states of Ba2CoMoO6 compound have been calculated using the LSDA (GGA) and LSDA (GGA) þU approaches. Fig. 2 illustrates the results of total density of states (TDOS) for Ba2CoMoO6 from LSDA (GGA) (U¼0.0 eV) and LSDA (GGA) þU; [U (Co)¼5.0 eV and U (Mo)¼1.0 eV] calculations. As shown in Fig. 3, from TDOS close to Fermi level (EF), it is observed that Ba2CoMoO6 evidences metallic feature in LSDA (GGA) results; there are two peaks crossing the EF in spin-up (TDOS↑) and spin-down (TDOS↓) channels, while in LSDA (GGA) þU, Ba2CoMoO6 obviously reveals half-metallic character with an energy-gap in the spin-up channel (TDOS↑) and a continuous band in the

spin-down channel (TDOS↓), in agreement with the experimental results. The energy-gaps are (Eg↑ ¼1.81 eV; from 0.60 eV to 1.21 eV) and (Eg↑ ¼2.04 eV; from  1.40 eV to 0.64 eV), from LSDA þU and GGA þU calculations, respectively. The extended Eg in TDOS reveal the effect of repulsion energy (U¼5.0 eV) in LSDA (GGA) þ U treatment, which opens the TDOS↑ bands. In addition, there are Co (3d) states in both spin-up [Co (3d)↑] and spin-down [Co (3d)↓] channel of the valence band (VB) (Fig. 4) and are responsible for the HM effect in Ba2CoMoO6. On the other hand, the contribution of Mo (4d) ion to the conduction band (CB) (Fig. 4) states close to the EF in CB, however; it has a dominant contribution from the Mo (4d) ion in the spin-up channel and Co (3d) ion in the spindown channel. While in the spin-up channel, there is strong hybridization between Co2 þ (3d7) and O2  (2p) ions in the VB and relatively weak bonding between Mo6 þ (4d0) and O2  (2p) ions in the CB. The bandwidths of CBs are (ΔW↓¼1.82 eV); from  0.31 eV to 1.51 eV and (ΔW↑¼ 1.59 eV); from  0.76 eV to 0.83 eV from LSDA, and (ΔW↓¼ 2.04 eV); from  0.87 eV to 0.49 eV from LSDA þU. From GGA and GGA þU, (ΔW↓ ¼1.70 eV); from

Fig. 5. Spin-up (↑) and spin-down (↓) band structures of Ba2CoMoO6 from LSDA (GGA) and LSDA (GGA) þU (U¼ 5.0 eV), the horizontal and vertical dashlines represent the Fermi energy and k-vectors, respectively.

M. Musa Saad H.-E. et al. / Materials Science in Semiconductor Processing 34 (2015) 281–290

0.05 eV to 1.65 eV and (ΔW↑ ¼1.69 eV); from  1.06 eV to 0.63 eV, and (ΔW↓ ¼1.70 eV); from  1.06 eV to 0.64 eV, respectively. Therefore, the more extended of ΔW in the LSDA (GGA) þU bands revealing, also, the effect of U on 3d and 4d states in [Co2 þ (3d7)–Mo6 þ (4d0)] ionic bond. The spin-up and spin-down band structures were computed based on the cubic structure of Ba2CoMoO6 and represented in Fig. 5. In general, LSDA and GGA calculations gave rise to a FiM metallic and fail to produce a FiM halfmetallic phase; there are few spin-up and spin-down bands between 1.0 eV and þ1.0 eV cross the EF. When LSDAþU and GGAþU methods, with U¼ 5.0 eV and J¼0.89 eV, were applied, band-gaps in spin-up (↑) were opened in original t2g degenerated bands, indicative of FiM-HM nature for Ba2CoMoO6, in agreement with the FiM-HM obtained in DOSs calculations, see Figs. 3 and 4. The band-gaps are (Eg↑¼1.87 eV) and (Eg↑¼2.14 eV) through EF, from LSDAþU and GGAþU, respectively. In spin-up bands, the band-gaps formed by Co (3d)-eg and Mo (4d)-t2g states. In spin-up channels, the bands between  8.0 eV and  2.0 eV are from the O (2p) states; the three bands between  1.0 eV and 0.0 eV originate mainly from Co (3d)-eg states; the three empty bands are almost Mo (4d)-t2g states; and the upper states are from Co (3d)-eg and Mo (4d)-eg. In spin-down channels, the filled bands are from O (2p) and Mo (4d)-t2g

287

states; and the three empty bands are from Co (3d)-eg states. Here, the Mo (4d)-t2g↓ states hybridize with O (2p) and Co (3d)-t2g↓ states interact strongly with the Ba (6s), in contrast to the spin-up bands. 3.2.2. Ba2CoWO6 Fig. 6 shows the results of TDOS for Ba2CoWO6 from LSDA (GGA) (U¼0.0 eV) and LSDA (GGA) þU; (U [Co) ¼ 5.0 eV and U (W) ¼1.0 eV]. Ba2CoWO6 clearly exhibits halfmetallic character with an energy-gap in the spin-up channel (TDOS↑) and a continuous band in the spindown channel (TDOS↓), in agreement with the experimental results [9,12,22]. The calculated energy-gaps are found to be (Eg↑¼1.37 eV; from  0.76 eV to 0.61 eV) and (Eg↑ ¼3.30 eV; from  2.48 eV to 0.82 eV), from the LSDA and LSDA þU, respectively. Also, GGA and GGA þU yield (Eg↑ ¼1.3 eV; from  0.78 eV to 0.58 eV) and (Eg↑¼2.73 eV; from  1.72 eV to 1.01 eV), respectively. This elongated energy-gap reflects the effect of repulsion energy (U¼5.0 eV) in LSDA (GGA) þ U treatment, which opens the TDOS↑ bands. Whereas, there are states of Co (3d) ion in both spin-up [Co (3d)↑] and spin-down [Co (3d)↓] channel of the VB (Fig. 7) and is responsible for the HM effect in Ba2CoWO6. Conversely, the W (5d) ion contribution to the CB, states close to the EF, however, it has a

Fig. 6. TDOS of Ba2CoWO6 from LSDA (GGA) and LSDA (GGA) þ U (U¼ 5.0 eV).

288

M. Musa Saad H.-E. et al. / Materials Science in Semiconductor Processing 34 (2015) 281–290

dominant contribution from the W (5d) ion in the spin-up channel and Co (3d) ion in the spin-down channel. While in the spin-up channel, there is strong hybridization between Co2 þ (3d7) and O2  (2p) ions in the VB and relatively weak bonding between W6 þ (5d0) and O2  (2p) ions in the CB. The bandwidths are (ΔW↓ ¼1.37 eV); from  1.10 eV to 0.27 eV, (ΔW↓¼1.70 eV); from  1.12 eV to 0.58 eV, (ΔW↓¼ 1.75 eV); from  1.16 eV to 0.59 eV, and (ΔW↓ ¼1.37 eV); from 1.04 eV to 0.33 eV, from LSDA, GGA, LSDA þU and GGA þU, respectively. Thus, the more extended of ΔW in the LSDA (GGA) þ U bands revealing, also, the effect of U on 3d and 5d states in [Co2 þ (3d7)– W6 þ (5d0)] ionic bond. The spin-up and spin-down band structures were computed based on the cubic structure of Ba2CoWO6 and represented in Fig. 8. Both calculations gave rise to a very similar band structure. In general, LSDA and GGA both gave rise to a FiM-HM phase; there are band-gaps in spin-up bands while few spin-down bands between 1.5 eV and þ1.5 eV cross the EF. After LSDAþU and GGAþU methods, with U¼5.0 eV and J¼0.89 eV, were applied, band-gaps in spin-up (↑) were opened more in original t2g degenerated bands, indicative of FiM-HM nature for Ba2CoWO6, in agreement with the FiM-HM obtained from DOSs results, see Figs. 6 and 7. The band-gaps are (Eg↑¼1.81 eV),

(Eg↑¼1.67 eV), (Eg↑¼2.04 eV) and (Eg↑¼2.24 eV) through EF, from LSDA, GGA LSDAþU and GGAþU, respectively. In spin-up bands, the band-gaps are formed by the Co (3d) eg and W (5d) t2g partial states. In spin-up channels, the bands between  8.5 eV and  1.5 eV are from the O (2p) states; the three bands between 1.5 eV and 0.0 eV originate mainly from Co (3d)-eg states; the three empty bands are almost W (5d)-t2g states; and the upper states are from Co (3d)-eg and W (5d)-eg. In spin-down channels, the filled bands are from O (2p) and W (5d)-t2g states; and the three empty bands are from Co (3d)-eg states. Here, the W (5d)t2g↓ states hybridize with O (2p) and Co (3d)-t2g↓ states interact strongly with the Ba (6 s), in contrast to the spinup bands. 3.3. Ground state magnetic properties of Ba2CoMO6 In this section, the magnetism in the ground state of Ba2CoMO6 was address in detail. The partial and total spin magnetic moments in double perovskite oxide Ba2CoMO6 (M¼Mo and W) compounds have been calculated using the LSDA (GGA) (U¼0.0 eV) and LSDA (GGA) þ U (U¼5.0 eV) methods. As shown in Table 3 the electronic configuration of atoms, the valence state, the ionic spin picture and ionic radius of the ground states of ordered double perovskite

Fig. 7. Calculated TDOS and PDOSs [Co (3d), W (5d) and O (2p)] of Ba2CoWO6 (space group Fm3m) from LSDA (GGA) and LSDA (GGA) þ U (U ¼5.0 eV).

M. Musa Saad H.-E. et al. / Materials Science in Semiconductor Processing 34 (2015) 281–290

289

Fig. 8. Spin-up (↑) and spin-down (↓) band structures of Ba2CoWO6 from LSDA (GGA) and LSDA (GGA) þ U (U¼ 5.0 eV), the horizontal and vertical dashlines represent the Fermi energy and k-vectors, respectively.

oxides Ba2CoMO6 (M¼ Mo and W). In addition to, the calculated total and partial spin magnetic moment contributions are shown in Table 4, for Ba2CoMoO6, the partial Co (3d) states have spin magnetic moments of (mCo ¼2.826 μB/f.u.) and (mCo ¼2.845 μB/f.u.), and for Mo (4d) states are (mMo ¼ 0.106 μB/f.u.) and (mMo ¼  0.156 μB/f.u.) in LSDA and LSDAþU, respectively, while from GGA and GGAþU, (mCo ¼2.875 μB/f.u.) and (mCo ¼2.876 μB/f.u.), and for Mo (4d) states are (mMo ¼  0.058 μB/f.u.) and (mMo ¼  0.175 μB/f.u.), respectively. At the same time as, for Ba2CoWO6, (mCo ¼2.821 μB/f.u.) and (mCo ¼2.816 μB/f.u.), and for W (5d) (mW ¼ 0.117 μB/f.u.) and (mW ¼  0.083 μB/f.u.) in LSDA and LSDAþU, respectively, even as from GGA and GGAþU, (mCo ¼2.839 μB/f.u.) and (mCo ¼2.874 μB/f.u.), and for W (5d) (mW ¼ 0.12 μB/f.u.) and (mW ¼  0.087 μB/f.u.), respectively. The total spin magnetic moments achieved from these magnetic calculations are: (mTot ¼ 2.925/2.928 μB/f.u.) from LSDA/GGA and (mTot ¼ 2.976/2.989 μB/f.u.) from LSDA/GGA þU, for Ba2CoMoO6, while (mTot ¼2.968/2.984 μB/f.u.) from LSDA/GGA and (mTot ¼ 2.979/2.993 μB/f.u.) from LSDA/GGA þU, for Ba2CoWO6. These results, also, suggest the high-spin

Table 3 The electronic configuration of atoms, valence state, ionic spin picture and ionic radius in the ground states of ordered Ba2CoMO6 (M¼Mo and W). Atom Electronic configuration

Valence state

Ionic configuration

Ionic spin S

Ionic radius r (Å)

Ba2 þ (6s0) Co2 þ (3d7; 3 2 2 t2g↑ t2g↓ eg↑) 6þ Mo (4d0; 0 0 t2g↑ eg↑) W6 þ (5d0; 0 0 t2g↑ eg↑) O2  (2s0 2p0)

0 3/2

1.61 0.65

0

0.59

0

0.60

0

1.41

Ba Co

[Xe] 6s2 [Ar] 3d7 4s2

2þ 2þ

Mo

[Kr] 4d5 5s1

6þ

W O

14

4

[Xe] 4f 5d 6s2 [He] 2s2 2p4

6þ 2

configuration of Co2 þ (3d7; t2g↑t2g↓eg, S¼3/2 μB/f.u.) and a 0 0 non-magnetic for M6 þ ion (d0; t2g eg, S¼0 μB/f.u.). The magnetic data are in agreement with the experimental results [9,12,22]. The small deviation of total magnetic moments with 3

2

2

290

M. Musa Saad H.-E. et al. / Materials Science in Semiconductor Processing 34 (2015) 281–290

Table 4 Partial and total magnetic moments (mB/f.u.) in Ba2CoMO6 (M ¼Mo and W). Compound

Ba2CoMoO6

Ba2CoWO6

Method

LSDA

GGA

LSDA þU

GGAþ U

LSDA

GGA

LSDA þ U

GGA þ U

Co (3d) M (4d/5d) Total

2.826  0.106 2.925

2.875  0.058 2.928

2.845  0.156 2.976

2.876  0.175 2.989

2.821  0.117 2.968

2.839  0.126 2.984

2.816  0.083 2.979

2.874  0.087 2.993

respect to the theoretical value (m¼ 3.0 μB/f.u.) is believed to be due to the bond-valences, on-site disorder of Co–M ions, and correlation energy effects.

University for its funding of this research through the research Group Project no. RGP-VPP-285. References

4. Conclusions Using the first-principles of full potential linearized muffin-tin orbital (FP-LMTO) computational method, a systematic structural, electronic, magnetic and properties study of ordered double perovskite oxides Ba2CoMO6 (M ¼Mo and W) has been performed by employing LSDA (GGA) (U¼0.0 eV) and LSDA (GGA)þ U (U¼5.0 eV) calculations. It is found that Ba2CoMO6 compounds have crystal structures of face-centered cubic (space group Fm3m and tilt system a0a0a0) with lattice constants of (a ¼8.011 Å) and (a ¼8.031 Å) for Ba2CoMoO6 and Ba2CoWO6, respectively. The crystals of Ba2CoMO6 contain alternating CoO6 and MO6 octahedra, almost fully ordered in the basal ab planes. Both, the LSDA (GGA) and LSDA (GGA) þU calculations depicted well the proper half-metallic (HM) ground state for Ba2CoWO6, while, for Ba2CoMoO6, only, LSDA (GGA) þU presented the HM nature. It is established that the HM character of Ba2CoMO6 is caused by the indirect Co2 þ (3d7)–O (2p)–M6 þ (4d0/5d0) ddpπ long range AFM couplings which are simultaneously responsible for the ferrimagnetic (FiM) character. The calculated level distributions and partial spin moments, of the 3d, 4d and 5d ions, indicate the (Co2 þ –M6 þ ) ionic state in Ba2CoMO6 compounds, with electronic configurations of Co2 þ (3d7; 3 2 2 0 0 t2g↑t2g↓eg, S¼3/2), Mo6 þ (4d0; t2g eg, S¼0) and W6 þ (5d0; 0 0 t2g eg, S¼0). The influence of M-cation analyses shows that Ba2CoMO6 has same valence state combinations due to strong intrinsic pd covalent bonds. Also, the DOSs and band structure analyses explain the major effects of Coulomb energy U and spin orbital coupling (SOC) on electronic and magnetic properties of Ba2CoMO6. Acknowledgments The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud

[1] K.-I. Kobayashi, T. Kimura, H. Sawada, K. Terakura, Y. Tokura, Nature 395 (1998) 677–680. [2] Horng-Tay Jeng, G.Y. Guo, Phys. Rev. B 67 (094438) (2003) 1–7. [3] T.S. Chan, R.S. Liu, G.Y. Guo, S.F. Hu, J.G. Lin, J.-F. Lee, L.-Y. Jang, C.-R. Chang, C.Y. Huang, Solid State Commun. 131 (2004) 531–535. [4] Yan Zhang, Vincent Ji, Xu Ke-Wei, Phys. B: Condens. Matter 407 (2012) 2617–2621. [5] M. Bibes, K. Bouzehouane, A. Barthélémy, M. Besse, S. Fusil, M. Bowen, P. Seneor, J. Carrey, V. Cros, A. Vauré s, J.-P. Contour, A. Fert, Appl. Phys. Lett. 83 (13) (2003) 2629–2631. [6] Z. Szotek, W.M. Temmerman, A. Svane b, L. Petit, G.M. Stocks, H. Winter, J. Magn. Magn. Mater. 272–276 (2004) 1816–1817. [7] S.A. Ivanov, S.-G. Eriksson, R. Tellgren, H. Rundlöf, M. Tseggai, Mater. Res. Bull. 40 (5) (2005) 840–849. [8] J. Longo, R. Ward, J. Am. Chem. Soc. 83 (1961) 2816. [9] María J. Martínez-Lope, José A. Alonso, María T. Casais, María T. Fernández, Eur. J. Inorg. Chem. 2002 (9) (2002) 2463–2469. [10] T. Hirama, N. Tsujii, H. Kitazaw, G. Kido, Phys. B: Condens. Matter 359–361 (2005) 1336–1338. [11] Qin Zhang, Tao Wei, Yun-Hui Huang, J. Power Sources 198 (2012) 59–65. [12] C.A. López, M.E. Saleta, J. Curiale, R.D. Sánchez, Mater. Res. Bull. 47 (5) (2012) 1158–1163. [13] Vladimir I. Anisimovy, F. Aryasetiawanz, A.I. Lichtenstein, J. Phys.: Condens. Matter 9 (1997) 767. [14] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jakson, M.R. Pederson, D.J. Singh, C. Fiolhais, Phys. Rev. B 46 (1992) 6671–6687. [15] S.Yu Savrasov, D.Yu Savrasov, Phys. Rev. B 46 (1992) 12181–12195. [16] S.Y. Savrasov May 2, Full-Potential Program Package Lmtart 6.50 user's Manual, New Jersey Institute of Technology, 2004. [17] S.Y. Savrasov, Program LMTART for electronic structure calculations, Los Almos National Laboratory, 2004. [18] S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Phys. Rev. B 57 (1998) 1505. [19] Antonis Andriotis, R. Michael Sheetz, Madhu Menon, Phys. Rev. B 81 (2010) 245103. [20] H. -E. Mohamed Musa Saad, Phys. B: Condens. Matter 407 (13) (2012) 2512–2518. [21] Jing Wang, Jian Meng, Zhijian Wu, Chem. Phys. Lett. 501 (4–6) (2011) 324–329. [22] D.E. Cox, G. Shirane, B.C. Frazer, J. Appl. Phys. 38 (1967) 1459. [23] N. Rammeh, H. Ehrenberg, H. Fuess, A. Cheikkh-Rouhou, Phys. Status Solidi C 3 (9) (2006) 3225–3228. [24] R.D. Shannon, Acta Cryst. A32 (1976) 751–767. [25] F.D. Murnaghan, Proc. Natl. Acad. Sci. USA 30 (9) (1944) 244–247. [26] Birch, Phys. Rev. 71 (11) (1947) 809–824.