Half-metallic ferromagnetic nature of the double perovskite Pb2FeMoO6 from first-principle calculations

Journal of Physics and Chemistry of Solids 73 (2012) 1116–1121

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Half-metallic ferromagnetic nature of the double perovskite Pb2FeMoO6 from first-principle calculations Yan Zhang n, Vincent Ji ICMMO/LEMHE UMR CNRS 8182, Universite´ Paris-Sud, 91405 Orsay Cedex, France

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 November 2011 Received in revised form 7 May 2012 Accepted 15 May 2012 Available online 23 May 2012

The structural, electronic and magnetic properties of the double perovskite Pb2FeMoO6 have been studied by using the first-principle projector augmented wave (PAW) potential within the generalized gradient approximation (GGA) as well as taking into account the on-site Coulomb repulsive interaction (GGA þU). Similar to Sr2FeMoO6 and Pb2FeReO6, the optimized crystal structure of Pb2FeMoO6 is a ˚ The two axial body-centered tetragonal (BCT) with the lattice constants a ¼b ¼5.60 A˚ and c ¼ 7.94 A. TM  O distances are slightly larger than the four equatorial TM  O distances, which shows that the Jahn–Teller structural distortion exists in FeO6 and MoO6 octahedra. The half-metallic ferromagnetic nature implies a potential application of this new compound in spintronics devices. The Fe3 þ and Mo5 þ ions are in the states (3d5, S ¼5/2) and (4d1, S ¼1/2) with magnetic moments 3.87 and  0.38mB respectively and thus there exists an antiferromagnetic coupling via oxygen between them. & 2012 Elsevier Ltd. All rights reserved.

Keywords: A. Ceramics A. Magnetic materials C. Ab initio calculations D. Electronic structures D. Magnetic properties

1. Introduction Based on the band structure calculations for magnetic semiHeusler compounds NiMnSb and PtMnSb, the concept of halfmetallic (HM) ferromagnets (FM) was first discovered by de Groot et al. [1] in 1983. After this important discovery, half-metallic ferromagnets (HMFMs) immediately attracted much research in theory [2–10] and experiment [11–15] for their potential applications in magnetoelectronic [16] and spintronic [17] devices. Typical examples of the HM magnetic materials include spinel Fe3O4 [18,19] and FeCr2S4 [20], rutile CrO2 [21–23], Mn doped GaAs [24,25], and Ca doped single perovskites La1  xCaxMnO3 [26], as well as double perovskites Sr2FeMoO6 [27] and Sr2FeReO6 [28]. The HM materials are characterized by the coexistence of metallic behavior in one electron spin channel and insulating behavior in the other channel. Their electronic density of states (DOS) is completely spin polarized at the Fermi level, and conductivity is dominated by these metallic single-spin charge carriers. Therefore, the HM materials offer potential technological applications in the realm of single-spin electron source and highefficiency magnetic sensors [16,17]. The finding of the HM ferromagnetism, large tunneling magnetoresistance (TMR) and high Curie temperature (Tc) in ordered Sr2FeMoO6 [27] and Sr2FeReO6 [28] by Kobayashi et al. in 1998 and 1999 revives the extensive study of the double perovskites

n

Corresponding author. Tel.: þ33 762581599. E-mail address: [email protected] (Y. Zhang).

0022-3697/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jpcs.2012.05.012

A2BB’O6. Most of the double perovskites, which were discovered by Ward et al. in 1961 [29,30], have been found to take a rock-salt crystal structure with alternate perovskite units ABO3 and AB’O3 along three crystallographical axes. The corners of each perovskite unit are in turn occupied by the transition-metal (TM) atoms B and B’ with oxygen atoms located in between, forming alternate BO6 and B’O6 octahedra. The large alkaline-earth-metal atom A occupies the body-centered site with a 12-fold oxygen coordination in each unit. The choice of suitable elements A, B and B’ can achieve various applications such as in the fields of spintronics (Sr2FeMoO6 [27] and Sr2FeReO6 [28]), multiferroicity (Ba2NiMnO6 [31]), magnetodielectric materials (La2NiMnO6 [32,33]) and magneto-optic devices (Sr2CrReO6 and Sr2CrOsO6 [34]). Compared with spinel Fe3O4 [18,19], rutile CrO2 [21–23] and Ca doping single perovskite La1  xCaxMnO3 [26], containing a single TM atom, the presence of two TM atoms B and B’ in double perovskites A2BB’O6 is expected to give rise to far more tunability and richness of the electronic and magnetic properties. The choice of a suitable combination of the atoms A, B and B’ is a key issue to obtain the required electronic and magnetic properties and ultimately industrial applications. In 2009, an ordered double perovskite Pb2FeReO6 was prepared at 6 GPa and 1000 1C by Nishimura et al. [35]. Despite the presence of Pb2 þ ion at the A site, its crystal structure was determined to be a body-centered tetragonal (BCT) with a space group of I4/m and the lattice ˚ No structural transition constants of a¼b ¼5.62 A˚ and c¼7.95 A. to the lower symmetry was observed at temperatures down to 23 K and its ferrimagnetic transition temperature (Tc) of 420 K is slightly higher than that of 401 K for Sr2FeReO6 [28]. In this

Y. Zhang, V. Ji / Journal of Physics and Chemistry of Solids 73 (2012) 1116–1121

context, it is natural for one to substitute Sr2 þ ion with Pb2 þ ion in Sr2FeMoO6 and expect the Pb2FeMoO6 compound to have a comparable magnetic transition temperature (Tc) to Sr2FeMoO6. However, from an extensive literature survey it is found that no work has been done on Pb2FeMoO6. In this paper, the structural, electronic and magnetic properties of the double perovskite Pb2FeMoO6 have been studied by using the first-principle projector augmented wave (PAW) potential within the generalized gradient approximation (GGA) as well as taking into account the on-site Coulomb repulsive interaction (GGAþ U). The HM ferromagnetic nature implies the potential applications of the new double perovskite Pb2FeMoO6 in magnetoelectronic [16] and spintronic [17] devices.

2. Calculation method and model

occupy the hollow formed by the corners of FeO6 and MoO6 octahedra at the body-centered positions with a 12-fold oxygen coordination. According to Ref. [46], the structure of a double perovskite may be related to its tolerance factor f ¼ ðr A þ pffiffiffi r O Þ= 2ðr B þ r O Þ. For f41.05 a hexagonal structure is adopted; for 1.054f41.00 the compound becomes cubic within the Fm3m space group; for 1.004f40.97 the most likely structure corresponds to the I4m tetragonal space group, and finally, if 0.97 4f the compound becomes either monoclinic (P21/n) or orthorhombic. The tolerance pffiffiffi factor of this new compound is calculated to be f ¼ ðr A þ r O Þ= 2ðr B þ r O Þ ¼ 1:032, where rA ¼1.49 A˚ is the ionic radius of Pb2 þ , rO ¼1.40 A˚ is the ionic radius of O2  , and ˚ and r B ¼ 0:58 A˚ is the average ionic radius of Fe3 þ (0.55 A) ˚ tabulated by Shannon [47]. So the crystal structure Mo5 þ (0.61 A) of Pb2FeMoO6 seems to be a cubic structure within the Fm3m space group. However, after calculating and comparing the total energies of various possible structures (monoclinic, orthorhombic, tetragonal and cubic) and allowing all degrees of freedom (internal coordinates of all ions, cell volume, cell shape and symmetry) to change during structure optimization, we found that the optimized crystalloid structure of Pb2FeMoO6 is body-centered tetragonal (BCT) with the lattice constants ˚ Furthermore, the optimized bond of a ¼b¼5.60 A˚ and c ¼7.94 A. lengths are 2.011 A˚ (ab plane) and 2.016 A˚ (c axis) for Fe–O bonds and 1.950 A˚ (ab plane) and 1.954 A˚ (c axis) for Mo–O bonds. The two axial TM  O distances are slightly larger than the four equatorial TM O distances which shows that the Jahn–Teller structural distortion exists in FeO6 and MoO6 octahedra. Such a tetragonal structure was also obtained for Sr2FeMoO6 [27,48,49] and Pb2FeReO6 [35], which is also inconsistent with the predicted cubic structure from the tolerance factors of Serrate et al. [46]. Their tolerance factors are calculated to be 1.014 and 1.040, respectively, by using the rA ¼1.44 A˚ for the ionic radius of Sr2 þ and rB0 ¼0.58 A˚ for the ionic radius of Re5 þ tabulated by Shannon [47].

3. Results and discussions The calculated total and partial density of states (DOS) projected onto O2p, Fe3d, Mo4d and Pb6p orbitals are shown in Fig. 2 for the ordered double perovskite Pb2FeMoO6 from GGA þU spinpolarized calculations. The positive and negative values of the EF

50 40

DOS (states/eV)

The calculations are performed using the Vienna ab-initio simulation package (VASP) based on the density function theory (DFT) [36–39] at College of Physics and Information Technology, Shaanxi Normal University. The electron–ionic core interaction is represented by the projector augmented wave (PAW) potentials [40] which are more accurate than the ultra-soft pseudopotentials. To treat electron exchange and correlation, we chose the Perdew–Burke–Ernzerhof (PBE) [41] formulation of the generalized gradient approximation (GGA) taking into account the onsite Coulomb repulsive (U¼ 2.0 eV for Fe and 1.0 eV for Mo) [42,43] as well as exchange coupling interaction (J¼0.89 eV for Fe and 0.95 eV for Mo) [44]. The common feature is the enhancement in both the exchange splitting and the band gap of the compounds after taking into account the on-site Coulomb repulsive as well as exchange coupling interactions, especially for larger U value [45]. A conjugate-gradient algorithm is used to relax the ions into their ground states, and the energies and the forces on each ion are converged within 1.0  10  4 eV/atom and ˚ respectively. The cutoff energy for the plane-waves is 0.02 eV/A, chosen to be 450 eV. The Pb 6s26p2, Fe 3d64s2, Mo 4d55s1 and O 2s22p4 electrons are treated as valence electrons. The k-points are sampled according to the Monkhorst–Pack automatic generation scheme with their origin at G point, together with a tetrahedron ¨ algorithm with Blochl corrections and broadening of 0.1 eV. The optimized structure of the double perovskite Pb2FeMoO6 is shown in Fig. 1 with four-formula-unit supercell (Pb: 8, Fe: 4, Mo: 4 and O: 24). The six oxygen atoms surrounding the Fe and Mo sites provide an octahedral environment. The FeO6 and MoO6 octahedra alternate along the three cubic axes, while Pb atoms

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Total O2p

up-spin

Fe3d

30

Mo4d

20

Pb6p

10 0 -10

2.016Å 1.954Å

-20 -30 -40 -50 -10

2.011Å 1.950Å Fig. 1. Optimized structure of the ordered double perovskite Pb2FeMoO6.

down-spin -8

-6

-4

-2 0 Energy (eV)

2

4

6

Fig. 2. Total and partial densities of states (DOS) projected onto O2p, Fe3d, Mo4d and Pb6p orbitals of the ordered double perovskite Pb2FeMoO6. The positive and negative values of the DOS represent up-spin and down-spin channels, respectively; the Fermi level is set at zero energy and is indicated by the vertical black dashed line.

Y. Zhang, V. Ji / Journal of Physics and Chemistry of Solids 73 (2012) 1116–1121

EF 3 2

up-spin

t2g

Fe4p

1

t2g

up-spin

Mo total Mo5s

3

Mo5p

2

Mo4 d

1

eg

0 eg -1 -2

t2g

down-spin -3 -10

-8

-6

-4

-2 0 Energy (eV)

2

4

6

Fig. 4. Total and partial densities of states (DOS) projected onto Mo4d, Mo5s and Mo5p orbitals. The positive and negative values of the DOS represent up-spin and down-spin channels, respectively; the Fermi level is set at zero energy and is indicated by the vertical black dashed line.

EF 1.0 0.8

up-spin

O total O2s

0.6

O2p

0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -10

down-spin -8

-6

-4

-2 0 Energy (eV)

2

4

6

Fig. 5. Total and partial densities of states (DOS) projected onto O2s and O2p orbitals. The positive and negative values of the DOS represent up-spin and downspin channels, respectively; the Fermi level is set at zero energy and is indicated by the vertical black dashed line.

Fe total Fe4s

eg

EF 4

DOS (states/eV)

DOS represent up-spin and down-spin channels, respectively; the Fermi level is set at zero energy and indicated by vertical black dashed line. It is interesting to note that the ground state of the Pb2FeMoO6 has a HM nature, because the total DOS (black lines) of the down-spin channel crosses the Fermi level, while the upspin channel forms a gap of about 1.37 eV around the Fermi level, resulting in a complete (100%) spin polarization of the charge carriers, usable in magnetoelectronic [16] and spintronic [17] devices. From various partial DOS we can see that the occupied up-spin band, lying below the Fermi level, is mainly composed of O2p state hybridized with dominant Fe3d electrons and much less number of the Mo4d and Pb6p electrons. The occupied up-spin band spanning from 2.0 to  0.91 eV just below the Fermi level is mostly due to the Fe3d eg and the O2p states without appreciable Mo4d and Pb6p contributions, while the unoccupied up-spin band spanning from 0.46 to 1.46 eV just above the Fermi level is mostly of the Mo4d t2g state origin. By contrast, the down-spin band is mainly occupied by O2p state and around the Fermi level by both the Mo4d t2g and Fe3d t2g states hybridized strongly with O2p electrons. To gain deep insight into the crystal-field-splitting and spinsplitting, the total and partial DOS projected onto various orbitals of the Fe, Mo, O and Pb atoms are shown in Figs. 3–6, respectively. From Fig. 3 we can see that, for both up-spin and down-spin channels the total DOS of the Fe atom is mainly composed of Fe3d state and much less of the Fe4s and excitated Fe4p electrons so we pay more attention on the Fe3d state. Considering the higher peaks near the Fermi level, we find that the presence of a octahedral crystal field of the six oxygen atoms around Fe site results in a splitting of the five-fold degenerate Fe3d states of a free Fe atom into triply degenerate t2g (dxy, dyz and dzx) states with lower energy and doubly degenerate eg (dz2 and dx2 y2 ) states with higher energy for either up-spin or down-spin channels. But the larger positive spin-splitting of about 3.3 eV (about 3.5 eV) makes the down-spin states of the triply degenerate t2g cross the Fermi level (the down-spin states of doubly degenerate eg locate above the Fermi level). Both the five Fe3d states in up-spin channel are completely occupied and most of the Fe3d states in down-spin channel are unoccupied, reflecting the Fe3 þ ion being in the highspin state (3d5, S ¼5/2) and having a positive magnetic moment (Table 1).

DOS (states/eV)

1118

DOS (states/eV)

Fe3d

0 -1 -2 -3 -4 -5 -10

down-spin -8

t2g -6

-4

-2 0 Energy (eV)

eg 2

4

6

Fig. 3. Total and partial densities of states (DOS) projected onto Fe3d, Fe4s and Fe4p orbitals. The positive and negative values of the DOS represent up-spin and downspin channels, respectively; the Fermi level is set at zero energy and indicated by the vertical black dashed line.

From Fig. 4 we can see that, for both up-spin and down-spin channels, the total DOS of the Mo atom is mainly composed of Mo4d state and much less of the Mo5s electrons and their partial excitated Mo5p electrons so we pay more attention to the Mo4d state. Similar to the cases of the Fe atom, the crystal-fieldsplitting also exists for Mo4d states in up-spin and down-spin channels. But two obvious differences can be seen for these Mo4d states compared with the Fe3d states shown in Fig. 3. The first one is that the most Mo4d states in up-spin channel lying above the Fermi level are not filled. This shows that the Mo5 þ ion is in the state (4d1, S¼1/2). The second one is that a negative spin-splitting makes the down-spin states of the triply degenerate t2g cross the Fermi level while the corresponding up-spin states are located above the Fermi level, reflecting the Mo5 þ ion having antiferromagnetic coupling with Fe3 þ ion via O2p states (see Fig. 2) and thus having a negative magnetic moment (Table 1).

Y. Zhang, V. Ji / Journal of Physics and Chemistry of Solids 73 (2012) 1116–1121

Similar crystal-field-splitting of the five-fold degenerate d states of a free Fe, Mo or Re atom into triply degenerate t2g states and doubly degenerate eg states, positive (negative) spin-splitting for t2g states of Fe (Mo, Re) atom and the hybridization between t2g states of Fe3d, Mo4d or Re5d with O2p electrons in down-spin states at the Fermi level were also observed in Sr2FeMoO6 [27,42–45,48,50] and Sr2FeReO6 [28,45,48,50]. Since the valence electrons of oxygen and Pb atoms are 2s22p4 and 6s26p2, respectively, and almost zero partial DOSs are obtained for their d orbitals, only the partial DOSs projected onto the s and p orbitals are given in Figs. 5 and 6. It can be seen that

EF 2.0 1.6

Pb total Pb6s

up-spin

Pb6p

DOS (states/eV)

1.2 0.8 0.4 0.0 -0.4 -0.8 -1.2

down-spin

-1.6 -10

-8

-6

-4

-2 0 Energy (eV)

2

4

6

Fig. 6. Total and partial densities of states (DOS) projected onto Pb6s and Pb6p orbitals. The positive and negative values of the DOS represent up-spin and downspin channels, respectively; the Fermi level is set at zero energy and is indicated by the vertical black dashed line.

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from Fig. 5, for both up-spin and down-spin channels in a broad energy region from  9.5 to 5 eV, the total DOS of the oxygen atom is primarily contributed by O2p state and much less by the O2s state. In fact, most of the O2s states are located in deeper energy region from  20 to  18 eV, because the smaller 2s subshell is completely filled by two electrons. Since there are four 2p electrons together with some transferred charges from the adjacent Fe and Mo atoms with smaller electronegativity, most of the O2p states are occupied, lying below the Fermi level. However, near the Fermi level, a positive spin-splitting of about 1.0 eV makes the down-spin states of the O2p cross the Fermi level while the up-spin states of the O2p locate below the Fermi level and thus a small positive magnetic moment is obtained (Table 1). By contrast, in Fig. 6, the deep occupied (from  9.5 to  8 eV) and unoccupied total DOSs of the Pb atom are dominated by Pb6s and Pb6p states, respectively. Since there are only two 6p electrons, most of the Pb6p states lying above the Fermi level are not occupied. However, near the Fermi level, a negative spin-splitting of about 0.64 eV makes the down-spin states of the Pb6p cross the Fermi level while the up-spin states of the Pb6p locate above the Fermi level and thus a negligibly negative magnetic moment is obtained (Table 1). Fig. 7 shows the total (left panel) and difference or spin (right panel) charge density of Pb2FeMoO6 with four-formula-unit supercell. It can be seen from the total charge density (left panel), more charges are accumulated around oxygen atoms, reflecting a substantial charge transfer from adjacent Fe and Mo atoms to oxygen atoms. This is because the electronegativity of 3.44 for oxygen atom is larger than 1.83 for Fe atom and 2.16 for Mo atom [51]. The charge distributions around Fe atoms are nearly spherical because of nearly half-filled Fe3d orbitals, i.e. Fe3 þ (3d5). Those Fe3d electrons of more than half-filled states have moved to oxygen atoms for stabilizing the ground state. Although the electronegativity of 2.16 for Mo atom is slightly larger than that of 1.83 for Fe atom, the loosely bounded Mo4d electrons with larger orbitals lead to more Mo4d electrons and they not only

Table 1 Partial (ms, mp and md) and total (mtot) magnetic moments (mB/atom) of Fe, Mo, O and Pb atoms in double perovskite Pb2FeMoO6. The total magnetic moments of Fe and Mo atoms in Sr2FeMoO6 from previous GGA þU calculations [44,45,48,50] are also listed for comparison. Atoms

ms

mp

md

mtot

Fe Mo O Pb

0.02 0.01 0.01 0.00

0.02 0.01 0.08  0.01

3.83  0.40 0.00 0.00

3.87, 3.94[44], 3.97[45], 3.96[48], 4.23[50],  0.38,  0.47[44],  0.39[45],  0.43[48],  0.60[50], 0.09  0.01

Fig. 7. The total (left panel) and difference or spin (right panel) charge density of double perovskite Pb2FeMoO6. In the total charge density (left panel), the yellow isosurfaces represent charge density of 0.021/A˚ 3, while in difference charge density (right panel), the yellow (turquoise) isosurfaces represent positive (negative) charge density of 0.005/A˚ 3. In both panels, the surfaces of the four-formula-unit supercell represent cross sections of the total (left panel) and difference (right panel) charge density of Pb2FeMoO6, and the colors blue, turquoise, green and yellow represent the values of charge densities in increasing order. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Y. Zhang, V. Ji / Journal of Physics and Chemistry of Solids 73 (2012) 1116–1121

spread out but also transfer to oxygen atoms compared to the Fe3d electrons with smaller orbitals, leaving the Mo atoms highly ionized, i.e. Mo5 þ (4d1). The oxygen atoms with large electron affinities or electronegativities therefore attract these d electrons as well as the itinerant Fe4s and Mo5s electrons to form a nearly closed O2p subshell with spherically distributed charge densities as well. No charge distributions between the nearest Fe–Fe or Mo–Mo pairs shows that no direct interaction exists between the nearest Fe–Fe or Mo–Mo pairs, whereas along Fe–O–Mo–O–Fe or Mo–O–Fe–O–Mo chain, the interactions between magnetic Fe and Mo cations are mediated by oxygen anions. With a large electronegativity of 2.33, the Pb atoms also attract those more than halffilled Fe3d electrons as well as the itinerant Fe4s and Mo5s electrons to form the largest Pb6s and Pb6p subshells, so the largest yellow spherical isosurfaces are formed around Pb atoms at the body-center sites. On the other hand, the distributions of the difference or spin charge density of Pb2FeMoO6 (right panel of Fig. 7) show that the spin moments of Fe and Mo are coupled antiferromagnetically (the yellow and turquoise isosurfaces represent positive and negative charge density, respectively of 0.005/A˚ 3). Both the five Fe3d states in up-spin channel are completely occupied and most of the Fe3d states in down-spin channel are unoccupied (Fig. 3), leading to a roughly spherical distribution of the positive spin densities at Fe sites, while the turquoise isosurfaces with eight rounded protuberance corners along o111 4 directions and six depressions at the centers of the {100} faces show that the occupied Mo4d orbital is mainly composed of down-spin t2g electrons. The small yellow egg-shaped isosurfaces protruded toward the adjacent Mo atoms slightly show that the occupied O2s and O2p orbitals are mainly composed of up-spin electrons. The absence of the spin density distribution at the body-center Pb sites indicates that the contributions to the magnetic moment from the Pb atoms are neglectable (Table 1). In order to find the ground-state magnetic structure, we perform the total-energy calculations of different magnetic configurations, ferromagnetic (FM) and anti-ferromagnetic (AFM) [52]. After comparing the total energies, we find that the AFM configuration is more stable than the FM configuration. The partial and total magnetic moments (mB/atom) of the Fe, Mo, O and Pb atoms in Pb2FeMoO6 are summarized in Table 1 together with the total magnetic moments of Fe and Mo atoms in Sr2FeMoO6 from GGA þU calculations [44,45,48,50] for comparison. The total magnetic moments are 3.87 and  0.38mB/atom for Fe and Mo atoms in Pb2FeMoO6, respectively, close to the values of the Fe and Mo atoms in Sr2FeMoO6 [44,45,48,50]. Also they are consistent with the measured spin moments of Sr2FeMoO6 ranging from 3.1 to 4.5mB for Fe atom and from 0 to  0.5mB for Mo atom [53–58]. Because of more itinerant nature of the Pb6s and Pb6p electrons with larger orbitals, the local moment of Pb atom is negligibly small. The spin moment of the oxygen atom is also small due to the nearly closed O2s and O2p subshells.

4. Conclusions The structural, electronic and magnetic properties of the double perovskite Pb2FeMoO6 have been studied by using the first-principle projector augmented wave (PAW) potential within the generalized gradient approximation (GGA) as well as taking into account the on-site Coulomb repulsive interaction (GGA þU). Following conclusions are obtained: (1) Similar to Sr2FeMoO6 and Pb2FeReO6, the optimized crystal structure of the Pb2FeMoO6 is a body-centered tetragonal ˚ (BCT) with the lattice constants a ¼b¼5.60 A˚ and c¼7.94A.

(2) The two axial TM O distances are slightly larger than the four equatorial TM  O distances, which shows that the Jahn–Teller structural distortion exists in FeO6 and MoO6 octahedra. (3) The half-metallic nature and complete (100%) spin polarization show that the new compound has a potential application in spintronics devices. (4) The Fe3 þ and Mo5 þ ions are in the states (3d5, S ¼5/2) and (4d1, S¼ 1/2) with magnetic moments 3.87 and  0.38mB respectively and thus an antiferromagnetic coupling exists via oxygen between them.

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