Electronic structure of A2CrSbO6 [A=Sr, Ca]: Ab-initio study

Journal of Physics and Chemistry of Solids 74 (2013) 250–254

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Electronic structure of A2CrSbO6 [A ¼Sr, Ca]: Ab-initio study Alo Dutta n, T.P. Sinha Department of Physics, Bose Institute, 93/1 Acharya Prafulla Chandra Road, Kolkata-700009, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 April 2012 Received in revised form 17 September 2012 Accepted 26 September 2012 Available online 5 October 2012

First principles calculations have been performed to study the electronic structure and magnetic properties of Cr-based double perovskite oxides Sr2CrSbO6 and Ca2CrSbO6 using full potential linearized augmented plane wave method under generalized gradient approximation (GGA) scheme. In our calculation, we have applied onsite Coulomb potential U at Cr site. The density of states (DOS) of Sr2CrSbO6 has been studied in three different crystal structures. Due to the different crystal symmetry of Sr2CrSbO6 at different temperatures, the DOS spectra differ from one another near the Fermi level. The insulating ground states have been obtained from GGA þ U calculation for both the materials. It has been observed from DOS spectra that oxygen 2p-derived states hybridize strongly with Cr-d states and this hybridization plays an important role in the magnetic properties. The calculated magnetic moments for Cr are found to be 2.65, 2.60 and 2.72 mB for monoclinic, tetragonal, cubic phases of Sr2CrSbO6, respectively and 2.68 mB for Ca2CrSbO6. The obtained magnetic moments suggest the 3þ states of Cr (3d3) in these oxides. & 2012 Elsevier Ltd. All rights reserved.

Keywords: A. Ceramics C. Ab initio calculations D. Electronic structure

1. Introduction There are currently immense research interests in double perovskite oxides due to the flexibility of their structure, which permits in-corporation of a uniquely wide range of elements and oxidation states. These strongly correlated electronic systems show various responses to multiple external stimuli. These phenomena enable to use such oxides in novel device applications. These applications are a consequence of their low chemical reactivity, good dielectric, magnetic and optical properties. The electrical and magnetic properties of double perovskites having the general formula A2B0 B00 O6 are strongly dependent on the valence pairs B0 B00 [1–5]. Usually in A2B0 B00 O6 structure, the A-sites are occupied by ions of higher co-ordination number and the B-sites by ions of relatively low co-ordination number. Alkaline earth metal ions like Ba, Sr or Ca have higher co-ordination number in comparison to that of the rare earth or transition metal ions, and therefore occupy the A-site. As a result, the B-site is occupied either by the transition metal or rare earth metal ions. The potential use of double perovskite oxides having one or two magnetic cations into spintronic devices as electrode has stimulated theoretical investigations, in terms of magnetic ordering and spin dependent band structure, aiming to predict their capability to spin polarize a current [6,7]. The strong coupling between magnetic and electronic degrees of freedom provides

n

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both challenges for solid-state theory as well as novel phenomena for applications such as magnetoresistance [8], ionic mobility [9,10] and ferromagnetism [11,12]. In this work, our concern is to study the electronic structure and magnetic properties of two double perovskite oxides, strontium chromium antimony oxide, Sr2CrSbO6 (SCS) and calcium chromium antimony oxide, Ca2CrSbO6 (CCS). These oxides show some interesting magnetic properties. According to Retuerto et al. [13], CCS is a ferromagnetic material with Curie temperature at 16 K, whereas SCS shows the antiferro-magnetic properties with Neel temperature at 12 K. Another interesting point is that the B-sites of these oxides are occupied by one magnetic cation with a p-block element, whereas most of the works available on double perovskite oxides contain two transition metal cations at B-sites [14–17]. The most recent study by Faik et al. [18] shows that SCS follows two structural phase transitions with the variation of temperature, one from monoclinic structure at 310 K to tetragonal structure at 510 K and tetragonal to cubic structure at 700 K. Thus, the study of electronic structure of SCS is required to fully understand the physical properties at different phases and to compare the results with an analogous system CCS. Here we have used the density functional theory (DFT) to study the electronic structure and magnetic properties of these oxides.

2. Computational details In this work, full potential linearized augmented plane wave method (FLAPW) [19] has been applied to calculate the electronic

A. Dutta, T.P. Sinha / Journal of Physics and Chemistry of Solids 74 (2013) 250–254

structure of the materials. This method is based on density functional theory (DFT) [20,21] which is an universal quantum mechanical approach for many body problems. To take into account the exchange and correlation effects, generalized gradient approximation (GGA) as parametrized by Perdew et al. [22] has been applied. In this calculation we have used the optimum value of the lattice parameters obtained from the experimental value [13,18]. In the whole calculation the internal parameters of atoms are fixed at the experimental values. To obtain the optimum value of the lattice parameters we have calculated the ground-state total energies for different volumes starting with the experimental lattice parameter. Then, the calculated results are fitted to the Birch–Murnaghan equation of state defined as [23]: 8" 9 #3 "  #2 "    2=3 #= 9V 0 B0 < V 0 2=3 V 0 2=3 V0 0 EðV Þ ¼ E0 þ 1 B0 þ 1 64 ; 16 : V V V

ð1Þ where V0 is the equilibrium volume and B0 is the bulk modulus and is given by B0 ¼ V(dP/dV)T evaluated at volume V0. B00 is the pressure derivative of B0 also evaluated at volume V0. The fitting of calculated volume with Birch–Murnaghan equation is shown in Fig. 1. The values of calculated lattice parameters, B0 andB00 at V0 are given in Table 1. We have chosen the muffin-tin (MT) radii for Sr, Ca, Cr, Sb and O as 2.45, 2.20, 2.00, 1.90 and 1.75 au, respectively. Spin polarized calculation have been done. No shape

251

approximation corresponding to potential is taken into account. In the calculation we have used a parameter RMTKmax ¼7, which determines matrix size (convergence), where Kmax is the plane wave cut-off and RMT is the smallest of all atomic sphere radii. To perform k point integrations over the Brillouin zone (BZ) Monkhorst–Pack [24] is used. The iteration process was continued until calculated total energy and charge density of the crystal converged and becomes less than 0.01 mRy/unit cell and 0.001 e/ a.u.3, respectively. For the d-state of Cr we have applied the onsite Coulomb potential (U ¼4 eV) in GGA þU calculations.

3. Results and discussion The spin polarized total density of states (DOS) per unit cell of SCS is shown in Fig. 2 in I2/m (monoclinic), I4/m (tetragonal) and Fm3m (cubic) phases. Fig. 3 shows the spin-polarized DOS of CCS in monoclinic phase (P21/n) at 310 K. The total DOS of SCS and CCS at 310 K shows insulating nature with direct band gap at Fermi level in both up spin and down spin channels. It is observed from Fig. 2 that there are some states at Fermi level (marked by circle) in up spin channel for I4/m and Fm3m phases of SCS, which is not consistent with the insulating property of SCS. The crystal field produced by the oxygen octahedra lifts the five-fold degeneracy of Cr d-states and splits into two degenerate states, t2g (dxy, dyz, dzx) and eg (dz2 , dx2 þ y2 ) as observed from the PDOS (partial DOS) of

-57383.83

-57383.84

Energy (ev)

Energy (ev)

-37388.26

-57383.85

-37388.28

-57383.86 -37388.30 1620

1650

1680

1710

1740

1770

1500

1550

-28691.775

-28691.990

-28691.780 Energy (ev)

Energy (ev)

-28691.985

-28691.995

-28691.790

-28692.005

-28691.795 825

840

855

870

1700

1650

-28691.785

-28692.000

810

1600

Volume (a.u.3)

Volume (a.u.3)

885

900

820

830

Volume (a.u.3)

840

850

860

870

880

890

Volume (a.u.3)

Fig. 1. Energy versus volume curves for Sr2CrSbO6 at 310 K (a), Sr2CrSbO6 at 510 K (b), Sr2CrSbO6 at 700 K (c) and Ca2CrSbO6 at 310 K (d).

Table 1 Structural data and calculated band gap of Sr2CrSbO6 and Ca2CrSbO6. Materials

Temperature (K)

˚ Lattice constant (A)

B0 (GPa)

B00

Band gap (eV) up spin

(GGA þU) down spin

Sr2CrSbO6 Sr2CrSbO6 Sr2CrSbO6 Ca2CrSbO6

310 510 700 310

a¼ 5.652, b ¼5.630 c ¼7.961, b ¼ 89.9811 a¼ b¼ 5.657 c ¼8.018 a¼ b ¼c ¼8.012 a¼ 5.512, b ¼5.581 c ¼7.812, b ¼90.1011

151.51 136.62 279.40 171.31

14.91 10.88  3.27 3.023

1.88 1.97 1.86 2.26

2.85 2.37 3.32 3.05

DOS (states/eV/unit cell)

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18 12 6 0 7 14 21 10

I2/m

I4/m

5 0 4 8 8

Fm3m

4 0 4 8 12

-4

0

4

Energy (eV) Fig. 2. Spin-polarized total DOS of Sr2CrSbO6 at 310, 510 and 700 K (GGA).

get the correct information of the electronic structure of such strongly correlated systems which contain 3d transition metal. Hence, to obtain the full information of the electronic structures of SCS and CCS here we have used GGA þU approach in our calculations. The spin polarized total DOS along with PDOS of Cr-d states, Sb-p states and O-p states of SCS (in three phases) and CCS in monoclinic phase obtained from GGA þU calculations are shown in Figs. 4–7, respectively. All four DOS spectra reflect the insulating nature of the materials under study. In GGAþU calculation due to the application of on site Coulomb potential U, the t2g states of Cr-d are pushed to the lower energy side and hence the energy gap is opened up at the Fermi level in up spin channel for SCS in high temperatures and the bad gap values increase for SCS and CCS at 310 K. The direct band-gap values at Fermi level in up and down spin channels are listed in Table 1. It is observed from GGA þU calculation that the valence bands extended from 0 to  6 eV mainly consist of O-2p states. The p-states of Sb interact with O-2p states in the bottom region of valence band extended around 5 eV. Whereas at the top of valence band region (i.e., near the Fermi level) there is a strong hybridization between the O-2p states with Cr-dt2g states in up spin channel and hence the t2g states of Cr extends from 0 to  4 eV in that region. Our first principles studies have shown that the electronic structure of these oxides involves strong Cr-O covalency, and that O-2p derived states participate substantially in the DOS spectra near Fermi energy. This covalency also takes an important part in transport properties of these strongly correlated systems. The exchange splitting between t2g up and t2g down, and between eg up and eg down for Cr ion has been observed. In the up spin channel, t2g and eg states of Cr-d are in the valence and

25

16

20 15

2

10

5

20

0

Cr-d

3

5 10 15 20 25

6

0

10

-4

0

4

Energy (eV) Fig. 3. Spin-polarized total DOS of Ca2CrSbO6 at 310 K (GGA).

these materials. In the cubic (Fm3m) phase of SCS with the Cr in the centre of an octahedron, the dx2 þ y2 and dz2 orbitals point toward neighbouring oxygens, while the lobes of the dxy, dyz and dzx orbitals point between the O 2p orbitals. This results the higher energy of the eg states of Cr-3d orbitals in these materials. It is observed from DOS spectra that as the crystal structure of SCS goes to higher symmetry (i.e., from I2/m to Fm3m) with increasing temperature the band-width of Cr-t2g states increases which leads the pseudo-half metallicity in up-spin DOS spectra with a small contribution of Cr-t2g states at Fermi level. Due to the presence of strong electron-electron interaction strength (Coulomb repulsion term U) sometimes it is difficult to

DOS (states/eV/unit cell)

DOS (states/eV/unit cell)

Sr CrSbO

8

0 3 6 9 Sb-p

0.2 0.0 0.2 0.4 0.8

O-1 O-2 O-3

0.4

O-p

0.0 0.4 0.8 -8

-4

0 Energy (eV)

4

8

Fig. 4. Spin-polarized total DOS with angular momentum projected partial DOS of Sr2CrSbO6 at 310 K (GGA þU).

A. Dutta, T.P. Sinha / Journal of Physics and Chemistry of Solids 74 (2013) 250–254

8 0 4 8 12 4 2 0

Ca2CrSbO

6

10 0 10 20

Cr-d Cr-d

2 DOS (states/eV/unit cell)

DOS (states/eV/unit cell)

20

Sr2CrSbO6

4

253

2 4 0.4

Sb-p

0.2 0.0 0.3 0.6 1.0 0.5 0.0

O1 O2

O-p

0.5 1.0 -8

-4

0

4

8

Energy (eV)

0.2

Sb-p

0.0 0.2 0.4 1.0 0.5 0.0 0.5 1.0

O-1 O-2 O-3

-8

-4

0

12

0

Materials

Magnetic moments (mB)

Temperature (K)

DOS (states/eV/unit cell)

12

Cr-eg

Sb-p

310

Sr2CrSbO6

510

Sr2CrSbO6

700

Ca2CrSbO6

310

Total Cr O Interstitial Total Cr O Interstitial Total Cr O Interstitial Total Cr O Interstitial

GGA

GGA þ U

3.000 2.542 0.051 0.690 3.000 2.462 0.048 0.381 2.989 2.622 0.015 0.282 3.000 2.561 0.037 0.681

3.000 2.651 0.030 0.570 3.000 2.601 0.027 0.318 3.000 2.721 0.006 0.240 3.000 2.678 0.022 0.562

O-p

0.5 0.0 0.5 1.0 1.5

Sr2CrSbO6

Cr-eg

Cr-t2g

0.4 0.2 0.0 0.2 0.4 0.6 1.0

8

Fig. 7. Spin-polarized total DOS with angular momentum projected partial DOS of Ca2CrSbO6 at 310 K (GGAþ U).

6 Cr-t2g

4

Table 2 Magnetic moment data of Sr2CrSbO6 and Ca2CrSbO6 for GGA and GGAþ U calculations.

Sr2 CrSbO6

4 2 0 2 4 6 8

O-p

Energy (eV)

Fig. 5. Spin-polarized total DOS with angular momentum projected partial DOS of Sr2CrSbO6 at 510 K (GGAþ U).

6

0 3 6 0.4

-8

-4

0 Energy (eV)

4

8

Fig. 6. Spin-polarized total DOS with angular momentum projected partial DOS of Sr2CrSbO6 at 700 K (GGAþ U).

conduction band regions, respectively. This indicates that in up spin channel t2g states are completely filled and eg states are completely empty. Whereas in down spin channel both eg and t2g

states are in conduction band region and thus they are completely empty. The above nature of Cr-d states implies the high spin (d3; t32ge0g) configuration of Cr-d states in these oxides. It has been further verified from the magnetic moment data listed in Table 2. In DFT many assumptions have been taken to calculate the electronic structure of strongly correlated systems, which certainly affect the band gap and the electronic states near the Fermi level. Since, the magnetic moment is derived from the d-states of Cr, which lie near the Fermi level; the calculated magnetic moment for a unit cell as listed in Table 2 is smaller than the experimental value [25]. The experimental magnetic moment per unit cell are 3.35 and 3.53 mB for SCS and CCS, respectively as obtained from Curie-Weiss law in the temperature range from 110 to 370 K [25]. The magnetic

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properties in these oxides arise from the unfilled d-state of Cr. However, the magnetic moment of Cr atom is less than the net magnetic moment of the unit cell, because some of the moments are distributed in the oxygen site (due to hybridization between O-2p and Cr-d states) and interstitial regions. The calculated magnetic moment of Cr varies from 2.46 to 2.68 mB which is nearly equal to the magnetic moment for three unpaired electrons (3.3 mB) and indicates the t32ge0g spin configuration of Cr in these materials as we predicted form our DOS calculations. Since the electrons in 3d-state of transition metal are localized, the value of magnetic moment of Cr increases to 2.6–2.75 mB by the application of U. The calculated magnetic moments in GGAþU method are also listed in Table 2. There is a strong correlation between the magnetic properties and electronic structure of these systems. In I4/m symmetry of SCS the CrO6 octahedra is elongated along one axis, which may drag the t2g states of Cr near the Fermi level in down spin channel as observed from Fig. 2. Hence, the exchange splitting between the d-states of Cr becomes less, which leads to a lowest value of magnetic moment on Cr-site with respect to other two crystal structures. On the other hand for cubic structure there is no distortion of the octahedra, thus the interaction of doubly degenerate eg states with six oxygen ion is same and similar case for t2g states. This would increase the exchange splitting between eg or t2g states and hence increase the magnetic moment at Cr-site. Due to the tilting of octahedra in monoclinic (I2/m) structure, the width of the t2g and eg bands becomes narrower. Thus the exchange splitting becomes large and the magnetic moment at Cr-site increases than I4/m phase. It is observed from Table 1 that the band gap of CCS is large in both spin channels than SCS at 310 K though both have same monoclinic symmetry. The reason of this is the more titled CrO6 octahedra for CCS than SCS as the b value is large for CCS. Due to the more tilting of the octahedra the interaction between the d-states of Cr with 2p-states of O becomes less and results the increase of band gap value. Also due to the less interaction between Cr-d states and O-2p states, the magnetic moment shared by O ion is less for CCS than SCS. This in turn increases the magnetic moment at Cr-site for CCS than SCS though the total magnetic moment is same for both materials. The DOS spectra of CCS in Fig. 7 differ a lot from the previous study by Yuan et al. [26]. In their study, the PDOS of Cr-d states have the major contribution in the conduction band in both spin channels. This cannot be possible, because in such condition d-states of Cr should be completely vacant which is not in case of CCS. In recent years many works have been reported on Cr based double peroveskite oxides containing alkaline earth element at A-site [27–30]. All of these oxides show ferromagnetic nature with high Curie temperature. It is observed from literature survey that the decrease of ionic radii of A-site cation distorted the CrO6 octahedra, which in turn decreases the Curie temperature. In our systems, the ionic radii of A-site cations also influence the electronic band gap and magnetic moment at Cr-site.

4. Conclusions First principles calculations have been performed to study the electronic structure and magnetic properties of Cr-based double

perovskite oxides Sr2CrSbO6 and Ca2CrSbO6 using full potential linearized augmented plane wave method under generalized gradient approximation (GGA) scheme. On-site Coulomb repulsion term U is incorporated in the calculations for d-state of Cr atom. The density of states shows the insulating nature of the materials. The calculated magnetic moments are in good agreement with the experimental data. We have examined the valence state of Cr ion to be t32ge0g. Application of on-site Coulomb potential U in GGA þU calculation increases the magnetic moment in Cr-site.

Acknowledgement Alo Dutta thanks Department of Science and Technology of India for providing the financial support through DST Fast Track Project under grant No. SR/FTP/PS-032/2010 References [1] J. Gopalakrishnan, A. Chattopadhyay, S.B. Ogale, T. Venkatesan, R.L. Greene, A.J. Millis, K. Ramesha, B. Hannoyer, G. Marest, Phys. Rev. B 62 (2000) 9538. [2] P.S.R. Murthy, K.R. Priolkar, P.A. Bhobe, A. Das, P.R. Sarode, A.K. Nigam, J. Magn. Magn. Mater. 322 (2010) 3704. [3] M. Valldor, S. Esmaeilzadeh, M. Andersson, A. Morawski, J. Magn. Magn. Mater. 299 (2006) 161. [4] X. Luo, Y.P. Sun, B. Wang, X.B. Zhu, W.H. Song, Z.R. Yang, J.M. Dai, Solid State Commun. 149 (2009) 810. [5] A.B. Antunesa, O. Pena, C. Mourec, V. Gilc, G. Andred, J. Magn. Magn. Mater. 316 (2007) e652. [6] D.D. Sarma, Phys. Rev. Lett. 85 (2000) 2549. [7] D. Stoeffler, S. Colis, J. Phys. Condens. Matter 17 (2005) 6415. [8] S. Jin, T.H. Tiefel, M. McCormack, R.A. Fastacht, R. Ramesh, L.H. Chen, Science 264 (1994) 413. [9] M. Yashima, M. Itoh, Y. Inaguma, Y. Morii, J. Am. Chem. Soc. 127 (2005) 3491. [10] C.Y. Park, F.V. Azzarello, A.J. Jacobson, J. Mater. Chem. 16 (2006) 3624. [11] A.G. Floresa, M. Zazoa, J. Inigueza, V. Raposoa, C. de Franciscob, J.M. Munozb, W.J. Padillac, J. Magn. Magn. Mater. 254–255 (2003) 583. [12] B. Bakowski, P.D. Battle, E.J. Cussen, L.D. Noailles, M.J. Rosseinsky, A.I. Coldea, J. Singleton, Chem. Commun. (1999) 2209. [13] M. Retuerto, J.A. Alonso, M. Garcia-Hernandez, M.J. Martinez-Lope, Solid State Commun. 139 (2006) 19. [14] C.Q. Tang, Y. Zhang, J. Dai, Solid State Commun. 133 (2005) 219. [15] Y. Doi, Y. Hinatsu, J. Phys. Condens. Matter 11 (1999) 4813. [16] Y. Sasaki, Y. Doi, Y. Hinatsu, J. Mater. Chem. 12 (2002) 2361. [17] C.M. Bonillaa, D.A. Landinez Telleza, J. Arbey Rodriguezb, E. Vera Lopezc, J. Roa-Rojasa, Physica B 398 (2007) 208. [18] A. Faik, J.M. Igartua, M. Gateshki, G.J. Cuello, J. Solid State Chem. 182 (2009) 1717. [19] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Waveþ Local Orbitals Program for Calculating Crystal Properties Karlheinz Schwarz, Techn. Universit¨at Wien, Austria (2001) 9501031-1-2. [20] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864. [21] P. Blaha, K. Schwarz, P. Sorantin, S.B. Tricky, Comput. Phys. Commun. 59 (1990) 399. [22] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Sing, C. Fiolhais, Phys. Rev. B 46 (1992) 6671. [23] F. Birch, Phys. Rev. 71 (1947) 809. [24] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [25] M. Retuerto, M. Garcia-Hernandez,a, M.J. Martınez-Lope, M.T. FernandezDiaz, J.P. Attfieldc, J.A. Alonsoa, J. Mater. Chem. 17 (2007) 3555. [26] Z. Yuan, N.G. Xin, L.H. Ping, Y. Lin, Commun. Theor. Phys. 53 (2010) 180. [27] F.K. Patterson, C.W. Moeller, R. Ward, Inorg. Chem. 2 (1963) 196. [28] A. Arulraj, K. Ramesha, J. Gopalakrishnan, C.N.R. Rao, J. Solid State Chem. 155 (2000) 233. [29] H. Kato, T. Okuda, Y. Okimoto, Y. Tomioka, Y. Takenoya, A. Ohkubo, M. Kawasaki, Y. Tokura, Appl. Phys. Lett. 81 (2002) 328. [30] J.B. Philipp, P. Majewski, L. Alff, A. Erb, R. Gross, T. Graf, M.S. Brandt, J. Simon, T. Walther, W. Mader, D. Topwal, D.D. Sarma, Phys. Rev. B 68 (2003) 144431–144431.