- Email: [email protected]
The role of Co impurities and oxygen vacancies in the ferromagnetism of Co-doped SnO2: GGA and GGA+U studies
ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
The role of Co impurities and oxygen vacancies in the ferromagnetism of Codoped SnO2: GGA and GGA+U studies Hongxia Wang, Yu Yan , Y. Sh. Mohammed, Xiaobo Du, Kai Li, Hanmin Jin State Key Laboratory for Superhard Materials and Department of Physics, Jilin University, Changchun, 130021 PR China
a r t i c l e in f o
a b s t r a c t
Article history: Received 21 February 2009 Available online 15 May 2009
The electronic structure and ferromagnetic stability of Co-doped SnO2 are studied using the firstprinciple density functional method within the generalized gradient approximation (GGA) and GGA+U schemes. The addition of effective UCo transforms the ground state of Co-doped SnO2 to insulating from half-metallic and the coupling between the nearest neighbor Co spins to weak antimagnetic from strong ferromagnetic. GGA+UCo calculations show that the pure substitutional Co defects in SnO2 cannot induce the ferromagnetism. Oxygen vacancies tend to locate near Co atoms. Their presence increases the magnetic moment of Co and induces the ferromagnetic coupling between two Co spins with large Co–Co distance. The calculated density of state and spin density distribution calculated by GGA+UCo show that the long-range ferromagnetic coupling between two Co spins is mediated by spin-split impurity band induced by oxygen vacancies. More charge transfer from impurity to Co-3d states and larger spin split of Co-3d and impurity states induced by the addition of UCo enhance the ferromagnetic stability of the system with oxygen vacancies. By applying a Coulomb UO on O 2 s orbital, the band gap is corrected for all calculations and the conclusions derived from GGA+UCo calculations are not changed by the correction of band gap. & 2009 Elsevier B.V. All rights reserved.
PACS: 75.50.Pp 61.72.Ji 75.30.Hx Keywords: Co-doped SnO2 Ferromagnetism First-principle GGA+U
1. Introduction Diluted magnetic semiconductors (DMS), in which nonmagnetic semiconductors are doped with a few percent of magnetic atoms, have been received much attention due to their potential for applications in spintronics. Recently several types of transition-metal (TM)-doped oxide semiconductors, such as TM-doped TiO2 [1–3], ZnO [3–5], SnO2 [6–32] and In2O3 [33,34], have been reported to be room-temperature ferromagnets. SnO2 is an important oxide semiconductor with a wide band gap. The high-temperature ferromagnetism in TM-doped SnO2 films was first reported by Ogale et al. [6], who reported a high Curie temperature of 650 K and a giant magnetic moment of 7.5 mB/Co in a 5% Co-doped thin film sample. Room-temperature ferromagnetism was subsequently reported in SnO2 doped with V [14,15], Cr [7,16,17], Mn [7,18,30], Fe [7,17–22] and Ni [7,23–25]. Co-doped SnO2 system has been investigated most extensively and room-temperature ferromagnetism was found in Co-doped SnO2 films and nano-particles prepared by a variety of growth methods [7–13,20,26–29,31–32]. The reported magnetic moments in Co-doped SnO2 range from 0.04 mB/Co [31] to the value as high as 5.0 mB/Co [7], which are all less than 7.5 mB/Co [6]. It was
Corresponding author. Tel.: +86 043188499047; fax: +86 043188499073.
E-mail address: [email protected] (Y. Yan). 0304-8853/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2009.05.013
found that the ferromagnetic properties of TM-doped SnO2, such as the magnetic moment and Curie temperature, are sensitive to the sample preparation methods and conditions. The giant moment of 7.5 mB/Co [6] in Sn1xCoxO2d (x ¼ 0.05) film has not been reproduced even at the lab where it allegedly originated [35]. Therefore, besides the doping TM ions, other factors should be responsible for ferromagnetic properties in TM-doped SnO2. More and more experimental results suggest that oxygen vacancies play a crucial role in the ferromagnetism of TM-doped SnO2. Recently it is shown that depositing under different oxygen partial pressure [13,24] and annealing under different atmospheres [13,15] strongly influence the ferromagnetism of TM-doped SnO2 films. Hays et al. [11] found that substitution of Sn ions with Co ions result in the reduction in the oxygen content of ferromagnetic Co-doped SnO2 powders. Theoretically, several first-principle computational investigations based on local-spin density approximation (LSDA) and generalized gradient approximation (GGA) have been reported on the magnetic properties of TM-doped SnO2 [36–40]. It is known that LSDA or GGA often yield incorrect behavior for strongly correlated magnetic systems. As there exists strongly correlated interaction in the TM 3d shell, the calculations for TM-doped TiO2 [41] and ZnO [42–45] within LSDA and GGA scheme suffer from improper description of the electronic structure and the ferromagnetic behavior, and the incorporating of on-site Coulomb interaction between the TM 3d electrons into
ARTICLE IN PRESS H. Wang et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
LSDA and GGA can give improved results. Therefore, the inclusion of the Coulomb interaction between the electrons in the TM-3d shell is necessary for the TM 3d electrons. More recently, several reports for TM-doped ZnO and In2O3 suggest that band-gap correction of the host oxide is needed for the correct description of magnetism in transition-metal-doped wide-gap oxides [46–48]. A self-consistent band-gap correction can be achieved by applying a Coulomb U on s orbital to raise the conduction band minimum (CBM) level [48–50]. In this work, we perform first-principle calculations within GGA [51] and GGA+U [52–54] schemes for Co-doped SnO2 with and without oxygen vacancies and investigate the effect of Co dopants and oxygen vacancies on the electronic structure and the magnetic properties of Co-doped SnO2. Moreover, we correct the band gap of SnO2 for all calculations by applying a Coulomb U on O 2s orbital to study the impact of band-gap underestimation on the ferromagnetic mechanism.
3115
[52]as n 1 n n 1 n þ ; 3d" þ ; 1 2 2 2 2 2 2 n 1 n n 1 n F þ ; þ F þ ; 1 , 2 2 2 2 2 2
U ¼ 3d"
(3)
where e3dm is the spin-up 3d eigenvalue at the central atom, eF is the Fermi energy. Using Eq. (3) the parameter U for Co can be calculated by performing FLAPW calculations, where the exchange parameter for Co is set to the typical value of J ¼ 1 eV [53,54,57]. An effective interaction parameter Ueff ¼ UJ for Co, or simply UCo, was introduced. The Sn-4d level is at around 20 eV below the Fermi energy (EF), which indicates that the correlations on the Sn d states do not affect the magnetic properties, so the implement of Ueff for Sn d electrons is ignored.
3. Results and discussions 2. Computational details In this paper calculations are performed, using the FLAPW method as implemented in WIEN2k code [55]. The exchange and correlation effects are treated with GGA [51] and GGA+U [52–54]. The size of basis sets was controlled by the parameter RmtKmax, where Rmt is the smallest muffin tin radius in the unit cell and Kmax is the magnitude of the largest K vector in reciprocal space. In our calculations RmtKmax was taken to be seven. The number of kpoints in the whole Brillouin zone was increased until the total energy was well converged. SnO2 has a tetragonal rutile structure with a ¼ 4.737 A˚ and c ¼ 3.186 A˚ [56]. Each Sn atom is in the central site of an octahedron formed from four rectangular basal O atoms (O1) and two vertex O atoms (O2). Supercell built of 2 2 2 unit cells was used in the calculations for Co-doped system. In the supercell Sn atoms are replaced by Co atoms, since X-ray photoelectron diffraction (XPD) and XAS cobalt L edge spectra show that Co atoms occupy substitutional Sn sites in Co-doped SnO2 [8,12]. In all calculations we kept the lattice parameters fixed at experimental values [56] of undoped SnO2 and fully relax the internal coordinates until the forces on the ions are below 0.05 eV/A˚. The LSDA+U [53,54] total-energy functional can be written as ^ ¼ ELSDA ðrÞ þ Eee ðnÞ ^ Edc ðnÞ, ^ Etot ðr; nÞ
(1)
LSDA
where E (r) is the standard LSDA functional of the spin charge ˆ is the local orbital occupation number rÞ (s ¼ m,k), n density rs ð~ matrix, Eee is the intra-atomic electron–electron interaction energy for d (f) electrons, and Edc is the ‘double-counting’ term. In this work the double-counting term is taken to satisfy the fully localized limit [54], which approximately removes the selfinteraction of the electrons, hence it is often referred to as the self-interaction corrected (SIC) version. The potential which are added to the LSDA potential for the orbital m has the following expression [54]: 1 DV SIC m;s ¼ ðU JÞð2I nm;s Þ,
The case of isolated Co substitution in 2 2 2 supercell is first investigated. The corresponding Co concentration is 6.25%, which is close to the experimental concentration for thin films [6,7,9,13]. Applying the method of Anisimov and Gunnarsson to Sn15CoO32, the effective interaction for Co UCo ¼ 4.08 eV is obtained by performing FLAPW calculations. For a more straightforward comparison, we use the same value of UCo for all calculations in the paper. The calculated density of states (DOS) of Sn15CoO32 by GGA and GGA+UCo are presented in Fig. 1. Comparing with the GGA results, the addition of the effective UCo enlarges the splitting between the filled and empty states of Co3d, which causes the transition from half-metallic to insulating state. Fig. 1(b) shows that the occupied Co-3d states, which were localized in the gap by GGA, shift down in energy and hybridize with the valence band. The calculated magnetic moments by GGA and GGA+UCo are listed in Table 1. The magnetic moments of Co calculated by GGA is 0.76 mB, which is consistent with value of 0.78 mB calculated by Wang et al. [37]. After UCo correction the magnetic moments are more local at Co site. The 3d electrons located in the muffin tin sphere of Co calculated by GGA and GGA+UCo are all about 6.7, which suggests that the charge state of Co is close to +2, in agreement with the XPS and X-ray absorption spectroscopy (XAS) measurement results for Co-doped SnO2 [8,11–13]. To study the magnetic ordering in Co-doped SnO2, the cases with two Co ions substituting the near and far cation sites in the
(2)
where U and J are on-site Coulomb and exchange interactions for electrons with the given angular momentum l, nm,s is the corresponding occupation of m orbital. In a 3d electron system with n 3d electrons per atom, the parameter U is defined as the energy cost for moving a 3d electron between two atoms which both initially had n 3d electrons. To calculate parameter U, Anisimov and Gunnarsson [52] constructed a supercell and set the hopping integrals to the 3d shell of the central atom equal to zero. The number of 3d electrons on one of the atoms in the supercell is varied. According to Slater’s transition-state rule, U is expressed
Fig. 1. Total and Co-3d DOS for Co-doped SnO2 calculated by GGA (a) and GGA+UCo (b). The lines and shaded plots represent total and Co-3d DOS, respectively. The Fermi level EF is set to 0.0 eV.
ARTICLE IN PRESS 3116
H. Wang et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
Table 1 Magnetic moments of Co atoms (MCo) and its nearest neighbor O atoms (M O1 and M O2 ), and total magnetic moments of the supercell (MSC).
Table 2 The energies difference DE per Co atom for three configurations calculated by GGA and GGA+UCo.
System
MCo (mB)
M O1 ðmB Þ
M O2 ðmB Þ
MSC (mB)
Configuration
N-1
N-2
F
Sn15CoO32 (GGA) Sn15CoO32 (GGA+UCo)
0.76 1.05
0.02 0.02
0.06 0.02
1.00 1.00
DE (meV) (GGA) DE (meV) (GGA+UCo)
36.0 2.4
11.0 0.4
1.0 2.2
Table 3 The energies difference DE per Co atom and magnetic moments of two Co atoms and the supercell for FM/AFM alignment of two Co spins for F configuration with oxygen vacancies.
Fig. 2. (Color online) The schematic 48-atom supercell (2 2 2) of SnO2. Red and gray balls represent O and Sn atoms, respectively.
supercells are considered. For near configurations there are two spatial arrangements, in which two Co atoms are separated by a single O atom. As shown in Fig. 2, the first substitutional Co atom is fixed at 1 site and the second occupies 2 and 3 sites, respectively. For far configuration two Co atoms are separated by –O–Sn–O–, in which the second Co occupies the 4 site. The relaxed Co–Co distance for the three spatial arrangements is 3.186, 3.591 and 7.418 A˚, named N-1, N-2 and F configurations, respectively. The energy differences DE (EAFMEFM) between antiferromagnetic (AFM) and ferromagnetic (FM) alignments for three configurations were calculated by GGA and GGA+UCo. The calculated DE per Co atom for three configurations is listed in Table 2. The GGA results show that ground state for near configurations is FM state, which is in agreement with the result calculated by Wang et al. [37]. In contrast with the GGA calculations, the calculated results by GGA+UCo show that the ferromagnetic coupling between Co spins for near configurations is significantly weakened and the coupling for N-1 configuration is weak AFM. The values of DE calculated by GGA+UCo for three configurations in Table 2 suggest that the exchange interaction between the dopant Co spins alone, without taking into account other factors, cannot yield the ferromagnetism. Many experimental results suggest that oxygen vacancies play a crucial role for turning the ferromagnetism in DMS [11,13,15,24]. Moreover, Kılıc- and Zunger [58] predicted that the formation energy of oxygen vacancy (VO) in pure SnO2 is surprisingly low. Therefore the effect of VO on electronic and magnetic properties in Co-doped SnO2 is investigated. The formation energy of oxygen vacancy in undoped (Sn16O31) and doped (Sn15CoO31) system are first calculated. For Sn15CoO31 one oxygen atom is removed from Co contained octahedron and Sn contained octahedron in the supercell, respectively. The calculated formation energy of VO for Co-doped
Configuration
DE (meV)
MCo1 (mB)
MCo (mB)
MSC (mB)
F (GGA) F (GGA+UCo)
10.0 23.6
1.50/1.51 1.81/1.81
1.50/1.50 1.81/1.81
2.94/0.00 2.86/0.00
system with vacancy near Co is lower than that for undoped system and doped system with vacancy near Sn by 280 and 740 meV, respectively. This means that the doped systems will have more oxygen vacancies near Co. In this connection, the measurements of absorption and Raman spectra show that the oxygen vacancies tend to form a near-neighbor complex with the Co atoms in Co-doped SnO2 [32]. Because of the large Co–Co distance due to low Co concentration in Co-doped SnO2, the long-range FM exchange is prerequisite for room-temperature ferromagnetism in DMS. For that the role of oxygen vacancies in tuning exchange interaction between Co spins with large Co–Co distance is investigated. In far configuration an oxygen vacancy is introduced near each Co atom to compensate Sn4+ and Co2+ ion charge difference and vacancies near Co at 1 and 4 sites are located in the Co–VO–Sn–VO–Co chain. The energies difference DE per Co atom between AFM and FM alignments and magnetic moments are listed in Table 3. Both results calculated by GGA and GGA+UCo show that the presence of vacancies near Co strongly increases the magnetic moment of Co, in agreement with the calculated results by Wang et al. [37]. The calculated magnetic moments for F configuration with and without oxygen vacancies by GGA+UCo are 1.81 and 1.05 mB/Co, which is consistent qualitatively with experimental value of 2.37 and 0.91 mB/Co for vacuum and air annealed films [13]. The presence of vacancies also increase DE to a positive value, which indicates that vacancies can induce a FM coupling between two Co spins with large Co–Co distance. Moreover, the energy difference calculated by GGA+UCo is larger than that by GGA, meaning that UCo enhances the FM stability of the system with oxygen vacancies. This is explained in detail below. Fig. 3 is DOS of FM alignment for F configuration without and with oxygen vacancies calculated by GGA+UCo. Fig. 3 shows that the electrons offered by oxygen vacancies form a spin-polarized impurity band in the gap and the impurity band hybridize with Co-3d states near EF, which yields about 0.07 electrons transfer per Co atom from the impurity states to the Co-3d states. Fig. 4 is DOS of FM alignment for F configuration with oxygen vacancies calculated by GGA. Comparing Fig. 3(b) and 4 we see that the addition of UCo enlarge the split between filled and empty Co-3d states, which modifies the hybridization of the impurity and Co3d states in the gap and causes the larger spin split of Co-3d and impurity states near EF. As a result the impurity states are more localized near EF and its hybridization with Co-3d states yields more electrons transfer. The electrons of spin-split impurity band deduced by oxygen vacancies mediate long-range FM interaction between two separated Co atoms and Curie temperature can be boosted by increasing the donor electron density in the vicinity of
ARTICLE IN PRESS H. Wang et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
3117
Fig. 3. Total and Co-3d DOS of FM alignment for F configuration calculated by GGA+UCo. (a) Without oxygen vacancies and (b) with oxygen vacancies. The lines and shaded plots represent total and the sum of two Co-3d DOS, respectively. Arrows indicate impurity states induced by oxygen vacancies.
Fig. 5. (Color online) The spin density distribution of F configuration in (11 0) plane calculated by GGA+UCo. (a) Without O vacancies and (b) with O vacancies.
Fig. 4. Total and Co-3d DOS for F configuration with oxygen vacancies calculated by GGA. The lines and shaded plots represent total and the sum of two Co-3d DOS, respectively.
the magnetic impurity, as is proposed by Coey et al. [5,7,59]. Therefore, more charge transfer from the impurity to the Co-3d states and larger spin split of Co-3d and impurity states induced by the addition of UCo enhance FM coupling for F configuration with oxygen vacancies. Fig. 5 shows the spin density distribution in (11 0) plane passing Co impurity and its near VO for the F configuration without and with oxygen vacancies, respectively. The distribution show that polarized components mainly locate at atoms around VO and polarization of atoms around two near VO connect each other, which is absent in the case without oxygen vacancies. This spin density distribution also fit the polaron-pair picture of spin-split donor impurity-band model [59]. In order to study the impact of band-gap underestimation on the ferromagnetic ordering in Co-doped SnO2, the band gap for all calculations are corrected by applying a Coulomb U on O 2s orbital to raise the CBM level. With an additional Coulomb repulsive potential (UO ¼ 24 eV) on O-2s, the electronic structure description of valence band and conduction band is consistent with experiment [60,61] and the corrected band gap of pure SnO2 is
3.54 eV, which is close to the experimental value of 3.6 eV. Fig. 6 shows that the calculated DOS of SnO2 by GGA+UCo+UO is in agreement with the overall shape of the measured curves [60,61]. The results of F configuration without and with oxygen vacancies calculated by GGA+UCo+UO are listed in Table 4. The results listed in Table 4 show that the presence of vacancies increase DE to a positive value, which indicates that after band-gap correction vacancies can also induce a FM coupling between two Co spins with large Co–Co distance. Fig. 7 is the DOS of FM alignment for F configuration without and with oxygen vacancies calculated by GGA+UCo+UO. Figs. 3(a) and 7(a) show that the correction of the band gap just raises the conduction band and the unoccupied Co3d states are all in the gap or the bottom of conduction band, which means that the additional electrons will preferentially occupy the Co-3d states in the gap even when the band gap is not corrected. It is seen from Figs. 3(b) and 7(b) that whether the band gap is corrected or not, the electrons offered by oxygen vacancies form an spin-split impurity band in the gap, and the impurity states hybridize with the Co-3d states near EF. GGA+UCo+UO calculations show that the hybridization at EF also yields electrons transfer from the impurity to the Co-3d states. These results suggest that the conclusions derived from GGA+UCo+UO calculations are kept consistent with that derived from GGA+UCo calculations.
4. Conclusions The effective interaction UCo between the localized Co-3d electrons is calculated by performing FLAPW calculations. Incorporating of UCo caused the ground state of Co-doped SnO2 transition from half-metallic to insulating state and the magnetic coupling between the nearest neighbor Co spins transition from FM to weak AFM coupling. The exchange interaction between the doping Co spins alone cannot induce ferromagnetism in Co-doped SnO2. Oxygen vacancies near Co strongly increase the magnetic moment of Co and induce a long-range FM interaction between largely separated Co atoms. Moreover, the addition of UCo obviously enhances the FM stability for Co-doped SnO2 with
ARTICLE IN PRESS 3118
H. Wang et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
Fig. 6. The measured and calculated DOS of SnO2. (a) Valence band DOS measured by XPS [60]. (b) O 2p DOS measured by SXE (solid and dash–dotted lines) and SXA (solid line) [61]. Two SXE spectra are shown: hv ¼ 550.4 eV (solid line), above the absorption threshold, and hv ¼ 534.7 eV (dash–dotted line), at the first absorption peak. (c) Valence band DOS calculated by GGA+UCo+UO. (d) O 2p DOS calculated by GGA+UCo+UO.
Table 4 The energies difference DE per Co atom and magnetic moments of two Co atoms and the supercell for FM/AFM alignment for F configuration without and with oxygen vacancies calculated by GGA+UCo+UO. Configuration
DE (meV)
MCo1 (mB)
MCo (mB)
MSC (mB)
F (without VO) F (with VO)
0.9 15.2
1.02/1.03 1.77/1.77
1.02/1.03 1.77/1.77
2.00/0.00 1.99/0.00
Fig. 7. Total and Co-3d DOS of FM alignment for F configuration calculated by GGA+UCo+UO. (a) Without oxygen vacancies and (b) with oxygen vacancies. The lines and shaded plots represent total and the sum of two Co-3d DOS, respectively. Arrows indicate impurity states induced by oxygen vacancies.
oxygen vacancies. The calculations show that long-range FM interaction in Co-doped SnO2 with oxygen vacancies can be understood by the spin-split impurity-band model by Coey et al. [5,59]. The DFT band-gap underestimation of SnO2 is corrected for all calculations by applying a Coulomb UO on O 2s orbital and the obtained conclusions are consistent with that derived from GGA+UCo calculations.
Acknowledgments This work was supported by the Specialized Research fund for the Doctoral Program of Higher Education (No. 200801830010) and the National Found for Fostering Talents of Basic Science (Grant no. J0730311). References [1] Matsumoto, M. Murakami, T. Shono, T. Hasegawa, T. Fukumura, M. Kawasaki, P. Ahmet, T. Chikyow, S. Koshihara, H. Koinuma, Science 291 (2001) 854. [2] A. Chambers, S. Thevuthasan, R.F.C. Farrow, R.F. Marks, J.U. Thiele, L. Folks, M.G. Samant, A.J. Kellock, N. Ruzycki, D.L. Ederer, U. Diebold, Appl. Phys. Lett. 79 (2001) 3467. [3] A. Chambers, Surf. Sci. Rep. 61 (2006) 345. [4] K. Ueda, H. Tabata, T. Kawai, Appl. Phys. Lett. 79 (2001) 988. [5] M. Venkatesan, C.B. Fitzgerald, J.G. Lunney, J.M.D. Coey, Phys. Rev. Lett. 93 (2004) 177206. [6] S.B. Ogale, R.J. Choudhary, J.P. Buban, S.E. Lofland, S.R. Shinde, S.N. Kale, V.N. Kulkarni, J. Higgins, C. Lanci, J.R. Simpson, N.D. Browning, S. Das Sarma, H.D. Drew, R.L. Greene, T. Venkatesan, Phys. Rev. Lett. 91 (2003) 077205. [7] C.B. Fitzgerald, M. Venkatesan, L.S. Dorneles, R. Gunning, P. Stamenov, J.M.D. Coey, P.A. Stampe, R.J. Kennedy, E.C. Moreira, U.S. Sias, Phys. Rev. B 74 (2006) 115307. [8] A. Lussier, J. Dvorak, Y.U. Idzerda, S.B. Ogale, S.R. Shinde, R.J. Choudary, T. Venkatesan, J. Appl. Phys. 95 (2004) 7190. [9] K. Gopinadhan, D.K. Pandya, S.C. Kashyap, S. Chaudhary, J. Appl. Phys. 99 (2006) 126106. [10] A. Punnoose, J. Hays, V. Gopal, V. Shutthanandan, Appl. Phys. Lett. 85 (2004) 1559. [11] J. Hays, A. Punnoose, R. Baldner, M.H. Engelhard, J. Peloquin, K.M. Reddy, Phys. Rev. B 72 (2005) 075203. [12] M. Batzill, J.M. Burst, U. Diebold, Thin Solid Films 484 (2005) 132. [13] X.F. Liu, Y. Sun, R.H. Yu, J. Appl. Phys. 101 (2007) 123907. [14] Nguyen Hoa Hong, Joe Sakai, Physica B 358 (2005) 265. [15] Jun Zhang, R. Skomski, L.P. Yue, Y.F. Lu, D.J. Sellmyer, J. Phys. Condens. Matter 19 (2007) 256204. [16] Nguyen Hoa Hong, Joe Sakai, W. Prellier, Awatef Hassini, J. Phys. Condens. Matter 17 (2005) 1697. [17] Wendong Wang, Zhenjun Wang, Yuanjia Hong, Jinke Tang, Minghui Yu, J. Appl. Phys. 99 (2006) 08M115. [18] C.B. Fitzgerald, M. Venkatesan, A.P. Douvalis, S. Huber, J.M.D. Coey, T. Bakas, J. Appl. Phys. 95 (2004) 7390. [19] J.M.D. Coey, A.P. Douvalis, C.B. Fitzgerald, M. Venkatesan, Appl. Phys. Lett. 84 (2004) 1332. [20] A. Punnoosea, J. Hays, J. Appl. Phys. 97 (2005) 10D321. [21] A. Punnoose, J. Hays, A. Thurber, M.H. Engelhard, R.K. Kukkadapu, C. Wang, V. Shutthanandan, S. Thevuthasan, Phys. Rev. B 72 (2005) 054402.
ARTICLE IN PRESS H. Wang et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
[22] A. Punnoose, K.M. Reddy, J. Hays, A. Thurber, M.H. Engelhard, Appl. Phys. Lett. 89 (2006) 112509. [23] Nguyen Hoa Hong, Antoine Ruyter, W. Prellier, Joe Sakai, Ngo Thu Huong, J. Phys. Condens. Matter 17 (2005) 6533. [24] Nguyen Hoa Hong, Joe Sakai, Ngo Thu Huong, Nathalie Poirot, Antoine Ruyter, Phys. Rev. B 72 (2005) 045336. [25] P.I. Archer, D.R. Gamelin, J. Appl. Phys. 99 (2006) 08M107. [26] A. Punnoose, M.H. Engelhard, J. Hays, Solid State Commun. 139 (2006) 434. [27] S.K. Misra, S.I. Andronenko, K.M. Reddy, J. Hays, A. Punnoose, J. Appl. Phys. 99 (2006) 08M106. [28] X.F. Liu, R.H. Yu, J. Appl. Phys. 102 (2007) 083917. [29] A. Bouaine, N. Brihi, G. Schmerber, C. Ulhaq-Bouillet, S. Colis, A. Dinia, J. Phys. Chem. C. 111 (2007) 2924. [30] K. Gopinadhan, S.C. Kashyap, D.K. Pandya, S. Chaudhary, J. Appl. Phys. 102 (2007) 113513. [31] K. Gopinadhan, S.C. Kashyap, D.K. Pandya, S. Chaudhary, J. Phys. Condens. Matter 20 (2008) 125208. [32] V.G. Kravets, L.V. Poperenko, J. Appl. Phys. 103 (2008) 083904. [33] J. Philip, A. Punnoose, B.I. Kim, K.M. Reddy, S. Layne, J.O. Holmes, B. Satpati, P.R. Leclair, T.S. Santos, J.S. Moodera, Nat. Mater. 5 (2006) 298. [34] J. Philip, N. Theodoropoulou, G. Berera, J.S. Moodera, B. Satpati, Appl. Phys. Lett. 85 (2004) 777. [35] S.A. Chambers, Surf. Sci. Rep. 61 (2006) 345. [36] X.L. Wang, Z. Zeng, X.H. Zheng, H.Q. Lin, J. Appl. Phys. 101 (2007) 09H104. [37] X.L. Wang, Z.X. Dai, Z. Zeng, J. Phys. Condens. Matter 20 (2008) 045214. [38] S.J. Hu, S.S. Yan, X.X. Yao, Y.X. Chen, G.L. Liu, L.M. Mei, Phys. Rev. B 75 (2007) 094412. [39] C.E. Rodrı´guez Torres, L. Errico, F. Golmar, A.M. Mudarra Navarro, A.F. Cabrera, S. Duhalde, F.H. Sa´nchez, M. Weissmann, J. Magn. Magn. Mater. 316 (2007) e219.
3119
[40] Hongxia Wang, Yu Yan, Y.Sh. Mohammed, Xiaobo Du, Lei Lu, Hanmin Jin, J. Magn. Magn. Mater 321 (2009) 337. [41] X.S. Du, Q.X. Li, H.B. Su, J.L. Yang, Phys. Rev. B 74 (2006) 233201. [42] P. Gopal, N.A. Spaldin, Phys. Rev. B 74 (2006) 094418. [43] S.J. Hu, S.C. Yan, M.W. Zhao, L.M. Mei, Phys. Rev. B 73 (2006) 245205. [44] L.M. Huang, A.L. Rosa, R. Ahuja, Phys. Rev. B 74 (2006) 075206. [45] T. Chanier, M. Sargolzaei, I. Opahle, R. Hayn, K. Koepernik, Phys. Rev. B 73 (2006) 134418. [46] S. Lany, H. Raebiger, A. Zunger, Phys. Rev. B 77 (2008) 241201. [47] H. Raebiger, S. Lany, A. Zunger, Phys. Rev. Lett. 101 (2008) 027203. [48] A. Walsh, J.L.F.D. Silva, S.H. Wei, Phys. Rev. Lett. 100 (2008) 256401. [49] C. Persson, S. Mirbt, Brazilian J. Phys. 36 (2006) 286. [50] T.R. Paudel, W.R.L. Lambrecht, Phys. Rev. B 77 (2008) 205202. [51] J.P. Perdew, Y. Wang, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [52] V.I. Anisimov, O. Gunnarsson, Phys. Rev. B 43 (1991) 7570. [53] V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44 (1991) 943. [54] V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyzyk, G.A. Sawatzky, Phys. Rev. B 48 (1993) 16929. [55] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Liutz, in: K. Schwarz (Ed.), WIEN2k, An augmented plane wave plus local orbitals program for calculating crystal properties, Technical University, Wien, Austria, 2001. [56] R.W.G. Wyckoff, second ed., Crystal Structures, vol. I, Interscience, New York, 1963, p. 239. [57] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52 (1995) R5467. [58] C. Kılıc-, A. Zunger, Phys. Rev. Lett. 88 (2002) 095501. [59] J.M.D. Coey, M. Venkatesan, C.B. Fitzgerald, Nat. Mater. 4 (2005) 173. [60] L. Kover, G. Moretty, Z. Kovacs, R. Sanjines, I. Csemy, G. Margaritondo, J. Palinkas, H. Adachi, J. Vac. Sci. Technol. A 13 (1995) 1382. [61] C. McGuinness, C.B. Stagarescu, P.J. Ryan, J.E. Downes, D. Fu, K.E. Smith, Phys. Rev. B 68 (2003) 165104.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
The role of Co impurities and oxygen vacancies in the ferromagnetism of Codoped SnO2: GGA and GGA+U studies Hongxia Wang, Yu Yan , Y. Sh. Mohammed, Xiaobo Du, Kai Li, Hanmin Jin State Key Laboratory for Superhard Materials and Department of Physics, Jilin University, Changchun, 130021 PR China
a r t i c l e in f o
a b s t r a c t
Article history: Received 21 February 2009 Available online 15 May 2009
The electronic structure and ferromagnetic stability of Co-doped SnO2 are studied using the firstprinciple density functional method within the generalized gradient approximation (GGA) and GGA+U schemes. The addition of effective UCo transforms the ground state of Co-doped SnO2 to insulating from half-metallic and the coupling between the nearest neighbor Co spins to weak antimagnetic from strong ferromagnetic. GGA+UCo calculations show that the pure substitutional Co defects in SnO2 cannot induce the ferromagnetism. Oxygen vacancies tend to locate near Co atoms. Their presence increases the magnetic moment of Co and induces the ferromagnetic coupling between two Co spins with large Co–Co distance. The calculated density of state and spin density distribution calculated by GGA+UCo show that the long-range ferromagnetic coupling between two Co spins is mediated by spin-split impurity band induced by oxygen vacancies. More charge transfer from impurity to Co-3d states and larger spin split of Co-3d and impurity states induced by the addition of UCo enhance the ferromagnetic stability of the system with oxygen vacancies. By applying a Coulomb UO on O 2 s orbital, the band gap is corrected for all calculations and the conclusions derived from GGA+UCo calculations are not changed by the correction of band gap. & 2009 Elsevier B.V. All rights reserved.
PACS: 75.50.Pp 61.72.Ji 75.30.Hx Keywords: Co-doped SnO2 Ferromagnetism First-principle GGA+U
1. Introduction Diluted magnetic semiconductors (DMS), in which nonmagnetic semiconductors are doped with a few percent of magnetic atoms, have been received much attention due to their potential for applications in spintronics. Recently several types of transition-metal (TM)-doped oxide semiconductors, such as TM-doped TiO2 [1–3], ZnO [3–5], SnO2 [6–32] and In2O3 [33,34], have been reported to be room-temperature ferromagnets. SnO2 is an important oxide semiconductor with a wide band gap. The high-temperature ferromagnetism in TM-doped SnO2 films was first reported by Ogale et al. [6], who reported a high Curie temperature of 650 K and a giant magnetic moment of 7.5 mB/Co in a 5% Co-doped thin film sample. Room-temperature ferromagnetism was subsequently reported in SnO2 doped with V [14,15], Cr [7,16,17], Mn [7,18,30], Fe [7,17–22] and Ni [7,23–25]. Co-doped SnO2 system has been investigated most extensively and room-temperature ferromagnetism was found in Co-doped SnO2 films and nano-particles prepared by a variety of growth methods [7–13,20,26–29,31–32]. The reported magnetic moments in Co-doped SnO2 range from 0.04 mB/Co [31] to the value as high as 5.0 mB/Co [7], which are all less than 7.5 mB/Co [6]. It was
Corresponding author. Tel.: +86 043188499047; fax: +86 043188499073.
E-mail address: [email protected] (Y. Yan). 0304-8853/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2009.05.013
found that the ferromagnetic properties of TM-doped SnO2, such as the magnetic moment and Curie temperature, are sensitive to the sample preparation methods and conditions. The giant moment of 7.5 mB/Co [6] in Sn1xCoxO2d (x ¼ 0.05) film has not been reproduced even at the lab where it allegedly originated [35]. Therefore, besides the doping TM ions, other factors should be responsible for ferromagnetic properties in TM-doped SnO2. More and more experimental results suggest that oxygen vacancies play a crucial role in the ferromagnetism of TM-doped SnO2. Recently it is shown that depositing under different oxygen partial pressure [13,24] and annealing under different atmospheres [13,15] strongly influence the ferromagnetism of TM-doped SnO2 films. Hays et al. [11] found that substitution of Sn ions with Co ions result in the reduction in the oxygen content of ferromagnetic Co-doped SnO2 powders. Theoretically, several first-principle computational investigations based on local-spin density approximation (LSDA) and generalized gradient approximation (GGA) have been reported on the magnetic properties of TM-doped SnO2 [36–40]. It is known that LSDA or GGA often yield incorrect behavior for strongly correlated magnetic systems. As there exists strongly correlated interaction in the TM 3d shell, the calculations for TM-doped TiO2 [41] and ZnO [42–45] within LSDA and GGA scheme suffer from improper description of the electronic structure and the ferromagnetic behavior, and the incorporating of on-site Coulomb interaction between the TM 3d electrons into
ARTICLE IN PRESS H. Wang et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
LSDA and GGA can give improved results. Therefore, the inclusion of the Coulomb interaction between the electrons in the TM-3d shell is necessary for the TM 3d electrons. More recently, several reports for TM-doped ZnO and In2O3 suggest that band-gap correction of the host oxide is needed for the correct description of magnetism in transition-metal-doped wide-gap oxides [46–48]. A self-consistent band-gap correction can be achieved by applying a Coulomb U on s orbital to raise the conduction band minimum (CBM) level [48–50]. In this work, we perform first-principle calculations within GGA [51] and GGA+U [52–54] schemes for Co-doped SnO2 with and without oxygen vacancies and investigate the effect of Co dopants and oxygen vacancies on the electronic structure and the magnetic properties of Co-doped SnO2. Moreover, we correct the band gap of SnO2 for all calculations by applying a Coulomb U on O 2s orbital to study the impact of band-gap underestimation on the ferromagnetic mechanism.
3115
[52]as n 1 n n 1 n þ ; 3d" þ ; 1 2 2 2 2 2 2 n 1 n n 1 n F þ ; þ F þ ; 1 , 2 2 2 2 2 2
U ¼ 3d"
(3)
where e3dm is the spin-up 3d eigenvalue at the central atom, eF is the Fermi energy. Using Eq. (3) the parameter U for Co can be calculated by performing FLAPW calculations, where the exchange parameter for Co is set to the typical value of J ¼ 1 eV [53,54,57]. An effective interaction parameter Ueff ¼ UJ for Co, or simply UCo, was introduced. The Sn-4d level is at around 20 eV below the Fermi energy (EF), which indicates that the correlations on the Sn d states do not affect the magnetic properties, so the implement of Ueff for Sn d electrons is ignored.
3. Results and discussions 2. Computational details In this paper calculations are performed, using the FLAPW method as implemented in WIEN2k code [55]. The exchange and correlation effects are treated with GGA [51] and GGA+U [52–54]. The size of basis sets was controlled by the parameter RmtKmax, where Rmt is the smallest muffin tin radius in the unit cell and Kmax is the magnitude of the largest K vector in reciprocal space. In our calculations RmtKmax was taken to be seven. The number of kpoints in the whole Brillouin zone was increased until the total energy was well converged. SnO2 has a tetragonal rutile structure with a ¼ 4.737 A˚ and c ¼ 3.186 A˚ [56]. Each Sn atom is in the central site of an octahedron formed from four rectangular basal O atoms (O1) and two vertex O atoms (O2). Supercell built of 2 2 2 unit cells was used in the calculations for Co-doped system. In the supercell Sn atoms are replaced by Co atoms, since X-ray photoelectron diffraction (XPD) and XAS cobalt L edge spectra show that Co atoms occupy substitutional Sn sites in Co-doped SnO2 [8,12]. In all calculations we kept the lattice parameters fixed at experimental values [56] of undoped SnO2 and fully relax the internal coordinates until the forces on the ions are below 0.05 eV/A˚. The LSDA+U [53,54] total-energy functional can be written as ^ ¼ ELSDA ðrÞ þ Eee ðnÞ ^ Edc ðnÞ, ^ Etot ðr; nÞ
(1)
LSDA
where E (r) is the standard LSDA functional of the spin charge ˆ is the local orbital occupation number rÞ (s ¼ m,k), n density rs ð~ matrix, Eee is the intra-atomic electron–electron interaction energy for d (f) electrons, and Edc is the ‘double-counting’ term. In this work the double-counting term is taken to satisfy the fully localized limit [54], which approximately removes the selfinteraction of the electrons, hence it is often referred to as the self-interaction corrected (SIC) version. The potential which are added to the LSDA potential for the orbital m has the following expression [54]: 1 DV SIC m;s ¼ ðU JÞð2I nm;s Þ,
The case of isolated Co substitution in 2 2 2 supercell is first investigated. The corresponding Co concentration is 6.25%, which is close to the experimental concentration for thin films [6,7,9,13]. Applying the method of Anisimov and Gunnarsson to Sn15CoO32, the effective interaction for Co UCo ¼ 4.08 eV is obtained by performing FLAPW calculations. For a more straightforward comparison, we use the same value of UCo for all calculations in the paper. The calculated density of states (DOS) of Sn15CoO32 by GGA and GGA+UCo are presented in Fig. 1. Comparing with the GGA results, the addition of the effective UCo enlarges the splitting between the filled and empty states of Co3d, which causes the transition from half-metallic to insulating state. Fig. 1(b) shows that the occupied Co-3d states, which were localized in the gap by GGA, shift down in energy and hybridize with the valence band. The calculated magnetic moments by GGA and GGA+UCo are listed in Table 1. The magnetic moments of Co calculated by GGA is 0.76 mB, which is consistent with value of 0.78 mB calculated by Wang et al. [37]. After UCo correction the magnetic moments are more local at Co site. The 3d electrons located in the muffin tin sphere of Co calculated by GGA and GGA+UCo are all about 6.7, which suggests that the charge state of Co is close to +2, in agreement with the XPS and X-ray absorption spectroscopy (XAS) measurement results for Co-doped SnO2 [8,11–13]. To study the magnetic ordering in Co-doped SnO2, the cases with two Co ions substituting the near and far cation sites in the
(2)
where U and J are on-site Coulomb and exchange interactions for electrons with the given angular momentum l, nm,s is the corresponding occupation of m orbital. In a 3d electron system with n 3d electrons per atom, the parameter U is defined as the energy cost for moving a 3d electron between two atoms which both initially had n 3d electrons. To calculate parameter U, Anisimov and Gunnarsson [52] constructed a supercell and set the hopping integrals to the 3d shell of the central atom equal to zero. The number of 3d electrons on one of the atoms in the supercell is varied. According to Slater’s transition-state rule, U is expressed
Fig. 1. Total and Co-3d DOS for Co-doped SnO2 calculated by GGA (a) and GGA+UCo (b). The lines and shaded plots represent total and Co-3d DOS, respectively. The Fermi level EF is set to 0.0 eV.
ARTICLE IN PRESS 3116
H. Wang et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
Table 1 Magnetic moments of Co atoms (MCo) and its nearest neighbor O atoms (M O1 and M O2 ), and total magnetic moments of the supercell (MSC).
Table 2 The energies difference DE per Co atom for three configurations calculated by GGA and GGA+UCo.
System
MCo (mB)
M O1 ðmB Þ
M O2 ðmB Þ
MSC (mB)
Configuration
N-1
N-2
F
Sn15CoO32 (GGA) Sn15CoO32 (GGA+UCo)
0.76 1.05
0.02 0.02
0.06 0.02
1.00 1.00
DE (meV) (GGA) DE (meV) (GGA+UCo)
36.0 2.4
11.0 0.4
1.0 2.2
Table 3 The energies difference DE per Co atom and magnetic moments of two Co atoms and the supercell for FM/AFM alignment of two Co spins for F configuration with oxygen vacancies.
Fig. 2. (Color online) The schematic 48-atom supercell (2 2 2) of SnO2. Red and gray balls represent O and Sn atoms, respectively.
supercells are considered. For near configurations there are two spatial arrangements, in which two Co atoms are separated by a single O atom. As shown in Fig. 2, the first substitutional Co atom is fixed at 1 site and the second occupies 2 and 3 sites, respectively. For far configuration two Co atoms are separated by –O–Sn–O–, in which the second Co occupies the 4 site. The relaxed Co–Co distance for the three spatial arrangements is 3.186, 3.591 and 7.418 A˚, named N-1, N-2 and F configurations, respectively. The energy differences DE (EAFMEFM) between antiferromagnetic (AFM) and ferromagnetic (FM) alignments for three configurations were calculated by GGA and GGA+UCo. The calculated DE per Co atom for three configurations is listed in Table 2. The GGA results show that ground state for near configurations is FM state, which is in agreement with the result calculated by Wang et al. [37]. In contrast with the GGA calculations, the calculated results by GGA+UCo show that the ferromagnetic coupling between Co spins for near configurations is significantly weakened and the coupling for N-1 configuration is weak AFM. The values of DE calculated by GGA+UCo for three configurations in Table 2 suggest that the exchange interaction between the dopant Co spins alone, without taking into account other factors, cannot yield the ferromagnetism. Many experimental results suggest that oxygen vacancies play a crucial role for turning the ferromagnetism in DMS [11,13,15,24]. Moreover, Kılıc- and Zunger [58] predicted that the formation energy of oxygen vacancy (VO) in pure SnO2 is surprisingly low. Therefore the effect of VO on electronic and magnetic properties in Co-doped SnO2 is investigated. The formation energy of oxygen vacancy in undoped (Sn16O31) and doped (Sn15CoO31) system are first calculated. For Sn15CoO31 one oxygen atom is removed from Co contained octahedron and Sn contained octahedron in the supercell, respectively. The calculated formation energy of VO for Co-doped
Configuration
DE (meV)
MCo1 (mB)
MCo (mB)
MSC (mB)
F (GGA) F (GGA+UCo)
10.0 23.6
1.50/1.51 1.81/1.81
1.50/1.50 1.81/1.81
2.94/0.00 2.86/0.00
system with vacancy near Co is lower than that for undoped system and doped system with vacancy near Sn by 280 and 740 meV, respectively. This means that the doped systems will have more oxygen vacancies near Co. In this connection, the measurements of absorption and Raman spectra show that the oxygen vacancies tend to form a near-neighbor complex with the Co atoms in Co-doped SnO2 [32]. Because of the large Co–Co distance due to low Co concentration in Co-doped SnO2, the long-range FM exchange is prerequisite for room-temperature ferromagnetism in DMS. For that the role of oxygen vacancies in tuning exchange interaction between Co spins with large Co–Co distance is investigated. In far configuration an oxygen vacancy is introduced near each Co atom to compensate Sn4+ and Co2+ ion charge difference and vacancies near Co at 1 and 4 sites are located in the Co–VO–Sn–VO–Co chain. The energies difference DE per Co atom between AFM and FM alignments and magnetic moments are listed in Table 3. Both results calculated by GGA and GGA+UCo show that the presence of vacancies near Co strongly increases the magnetic moment of Co, in agreement with the calculated results by Wang et al. [37]. The calculated magnetic moments for F configuration with and without oxygen vacancies by GGA+UCo are 1.81 and 1.05 mB/Co, which is consistent qualitatively with experimental value of 2.37 and 0.91 mB/Co for vacuum and air annealed films [13]. The presence of vacancies also increase DE to a positive value, which indicates that vacancies can induce a FM coupling between two Co spins with large Co–Co distance. Moreover, the energy difference calculated by GGA+UCo is larger than that by GGA, meaning that UCo enhances the FM stability of the system with oxygen vacancies. This is explained in detail below. Fig. 3 is DOS of FM alignment for F configuration without and with oxygen vacancies calculated by GGA+UCo. Fig. 3 shows that the electrons offered by oxygen vacancies form a spin-polarized impurity band in the gap and the impurity band hybridize with Co-3d states near EF, which yields about 0.07 electrons transfer per Co atom from the impurity states to the Co-3d states. Fig. 4 is DOS of FM alignment for F configuration with oxygen vacancies calculated by GGA. Comparing Fig. 3(b) and 4 we see that the addition of UCo enlarge the split between filled and empty Co-3d states, which modifies the hybridization of the impurity and Co3d states in the gap and causes the larger spin split of Co-3d and impurity states near EF. As a result the impurity states are more localized near EF and its hybridization with Co-3d states yields more electrons transfer. The electrons of spin-split impurity band deduced by oxygen vacancies mediate long-range FM interaction between two separated Co atoms and Curie temperature can be boosted by increasing the donor electron density in the vicinity of
ARTICLE IN PRESS H. Wang et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
3117
Fig. 3. Total and Co-3d DOS of FM alignment for F configuration calculated by GGA+UCo. (a) Without oxygen vacancies and (b) with oxygen vacancies. The lines and shaded plots represent total and the sum of two Co-3d DOS, respectively. Arrows indicate impurity states induced by oxygen vacancies.
Fig. 5. (Color online) The spin density distribution of F configuration in (11 0) plane calculated by GGA+UCo. (a) Without O vacancies and (b) with O vacancies.
Fig. 4. Total and Co-3d DOS for F configuration with oxygen vacancies calculated by GGA. The lines and shaded plots represent total and the sum of two Co-3d DOS, respectively.
the magnetic impurity, as is proposed by Coey et al. [5,7,59]. Therefore, more charge transfer from the impurity to the Co-3d states and larger spin split of Co-3d and impurity states induced by the addition of UCo enhance FM coupling for F configuration with oxygen vacancies. Fig. 5 shows the spin density distribution in (11 0) plane passing Co impurity and its near VO for the F configuration without and with oxygen vacancies, respectively. The distribution show that polarized components mainly locate at atoms around VO and polarization of atoms around two near VO connect each other, which is absent in the case without oxygen vacancies. This spin density distribution also fit the polaron-pair picture of spin-split donor impurity-band model [59]. In order to study the impact of band-gap underestimation on the ferromagnetic ordering in Co-doped SnO2, the band gap for all calculations are corrected by applying a Coulomb U on O 2s orbital to raise the CBM level. With an additional Coulomb repulsive potential (UO ¼ 24 eV) on O-2s, the electronic structure description of valence band and conduction band is consistent with experiment [60,61] and the corrected band gap of pure SnO2 is
3.54 eV, which is close to the experimental value of 3.6 eV. Fig. 6 shows that the calculated DOS of SnO2 by GGA+UCo+UO is in agreement with the overall shape of the measured curves [60,61]. The results of F configuration without and with oxygen vacancies calculated by GGA+UCo+UO are listed in Table 4. The results listed in Table 4 show that the presence of vacancies increase DE to a positive value, which indicates that after band-gap correction vacancies can also induce a FM coupling between two Co spins with large Co–Co distance. Fig. 7 is the DOS of FM alignment for F configuration without and with oxygen vacancies calculated by GGA+UCo+UO. Figs. 3(a) and 7(a) show that the correction of the band gap just raises the conduction band and the unoccupied Co3d states are all in the gap or the bottom of conduction band, which means that the additional electrons will preferentially occupy the Co-3d states in the gap even when the band gap is not corrected. It is seen from Figs. 3(b) and 7(b) that whether the band gap is corrected or not, the electrons offered by oxygen vacancies form an spin-split impurity band in the gap, and the impurity states hybridize with the Co-3d states near EF. GGA+UCo+UO calculations show that the hybridization at EF also yields electrons transfer from the impurity to the Co-3d states. These results suggest that the conclusions derived from GGA+UCo+UO calculations are kept consistent with that derived from GGA+UCo calculations.
4. Conclusions The effective interaction UCo between the localized Co-3d electrons is calculated by performing FLAPW calculations. Incorporating of UCo caused the ground state of Co-doped SnO2 transition from half-metallic to insulating state and the magnetic coupling between the nearest neighbor Co spins transition from FM to weak AFM coupling. The exchange interaction between the doping Co spins alone cannot induce ferromagnetism in Co-doped SnO2. Oxygen vacancies near Co strongly increase the magnetic moment of Co and induce a long-range FM interaction between largely separated Co atoms. Moreover, the addition of UCo obviously enhances the FM stability for Co-doped SnO2 with
ARTICLE IN PRESS 3118
H. Wang et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
Fig. 6. The measured and calculated DOS of SnO2. (a) Valence band DOS measured by XPS [60]. (b) O 2p DOS measured by SXE (solid and dash–dotted lines) and SXA (solid line) [61]. Two SXE spectra are shown: hv ¼ 550.4 eV (solid line), above the absorption threshold, and hv ¼ 534.7 eV (dash–dotted line), at the first absorption peak. (c) Valence band DOS calculated by GGA+UCo+UO. (d) O 2p DOS calculated by GGA+UCo+UO.
Table 4 The energies difference DE per Co atom and magnetic moments of two Co atoms and the supercell for FM/AFM alignment for F configuration without and with oxygen vacancies calculated by GGA+UCo+UO. Configuration
DE (meV)
MCo1 (mB)
MCo (mB)
MSC (mB)
F (without VO) F (with VO)
0.9 15.2
1.02/1.03 1.77/1.77
1.02/1.03 1.77/1.77
2.00/0.00 1.99/0.00
Fig. 7. Total and Co-3d DOS of FM alignment for F configuration calculated by GGA+UCo+UO. (a) Without oxygen vacancies and (b) with oxygen vacancies. The lines and shaded plots represent total and the sum of two Co-3d DOS, respectively. Arrows indicate impurity states induced by oxygen vacancies.
oxygen vacancies. The calculations show that long-range FM interaction in Co-doped SnO2 with oxygen vacancies can be understood by the spin-split impurity-band model by Coey et al. [5,59]. The DFT band-gap underestimation of SnO2 is corrected for all calculations by applying a Coulomb UO on O 2s orbital and the obtained conclusions are consistent with that derived from GGA+UCo calculations.
Acknowledgments This work was supported by the Specialized Research fund for the Doctoral Program of Higher Education (No. 200801830010) and the National Found for Fostering Talents of Basic Science (Grant no. J0730311). References [1] Matsumoto, M. Murakami, T. Shono, T. Hasegawa, T. Fukumura, M. Kawasaki, P. Ahmet, T. Chikyow, S. Koshihara, H. Koinuma, Science 291 (2001) 854. [2] A. Chambers, S. Thevuthasan, R.F.C. Farrow, R.F. Marks, J.U. Thiele, L. Folks, M.G. Samant, A.J. Kellock, N. Ruzycki, D.L. Ederer, U. Diebold, Appl. Phys. Lett. 79 (2001) 3467. [3] A. Chambers, Surf. Sci. Rep. 61 (2006) 345. [4] K. Ueda, H. Tabata, T. Kawai, Appl. Phys. Lett. 79 (2001) 988. [5] M. Venkatesan, C.B. Fitzgerald, J.G. Lunney, J.M.D. Coey, Phys. Rev. Lett. 93 (2004) 177206. [6] S.B. Ogale, R.J. Choudhary, J.P. Buban, S.E. Lofland, S.R. Shinde, S.N. Kale, V.N. Kulkarni, J. Higgins, C. Lanci, J.R. Simpson, N.D. Browning, S. Das Sarma, H.D. Drew, R.L. Greene, T. Venkatesan, Phys. Rev. Lett. 91 (2003) 077205. [7] C.B. Fitzgerald, M. Venkatesan, L.S. Dorneles, R. Gunning, P. Stamenov, J.M.D. Coey, P.A. Stampe, R.J. Kennedy, E.C. Moreira, U.S. Sias, Phys. Rev. B 74 (2006) 115307. [8] A. Lussier, J. Dvorak, Y.U. Idzerda, S.B. Ogale, S.R. Shinde, R.J. Choudary, T. Venkatesan, J. Appl. Phys. 95 (2004) 7190. [9] K. Gopinadhan, D.K. Pandya, S.C. Kashyap, S. Chaudhary, J. Appl. Phys. 99 (2006) 126106. [10] A. Punnoose, J. Hays, V. Gopal, V. Shutthanandan, Appl. Phys. Lett. 85 (2004) 1559. [11] J. Hays, A. Punnoose, R. Baldner, M.H. Engelhard, J. Peloquin, K.M. Reddy, Phys. Rev. B 72 (2005) 075203. [12] M. Batzill, J.M. Burst, U. Diebold, Thin Solid Films 484 (2005) 132. [13] X.F. Liu, Y. Sun, R.H. Yu, J. Appl. Phys. 101 (2007) 123907. [14] Nguyen Hoa Hong, Joe Sakai, Physica B 358 (2005) 265. [15] Jun Zhang, R. Skomski, L.P. Yue, Y.F. Lu, D.J. Sellmyer, J. Phys. Condens. Matter 19 (2007) 256204. [16] Nguyen Hoa Hong, Joe Sakai, W. Prellier, Awatef Hassini, J. Phys. Condens. Matter 17 (2005) 1697. [17] Wendong Wang, Zhenjun Wang, Yuanjia Hong, Jinke Tang, Minghui Yu, J. Appl. Phys. 99 (2006) 08M115. [18] C.B. Fitzgerald, M. Venkatesan, A.P. Douvalis, S. Huber, J.M.D. Coey, T. Bakas, J. Appl. Phys. 95 (2004) 7390. [19] J.M.D. Coey, A.P. Douvalis, C.B. Fitzgerald, M. Venkatesan, Appl. Phys. Lett. 84 (2004) 1332. [20] A. Punnoosea, J. Hays, J. Appl. Phys. 97 (2005) 10D321. [21] A. Punnoose, J. Hays, A. Thurber, M.H. Engelhard, R.K. Kukkadapu, C. Wang, V. Shutthanandan, S. Thevuthasan, Phys. Rev. B 72 (2005) 054402.
ARTICLE IN PRESS H. Wang et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 3114–3119
[22] A. Punnoose, K.M. Reddy, J. Hays, A. Thurber, M.H. Engelhard, Appl. Phys. Lett. 89 (2006) 112509. [23] Nguyen Hoa Hong, Antoine Ruyter, W. Prellier, Joe Sakai, Ngo Thu Huong, J. Phys. Condens. Matter 17 (2005) 6533. [24] Nguyen Hoa Hong, Joe Sakai, Ngo Thu Huong, Nathalie Poirot, Antoine Ruyter, Phys. Rev. B 72 (2005) 045336. [25] P.I. Archer, D.R. Gamelin, J. Appl. Phys. 99 (2006) 08M107. [26] A. Punnoose, M.H. Engelhard, J. Hays, Solid State Commun. 139 (2006) 434. [27] S.K. Misra, S.I. Andronenko, K.M. Reddy, J. Hays, A. Punnoose, J. Appl. Phys. 99 (2006) 08M106. [28] X.F. Liu, R.H. Yu, J. Appl. Phys. 102 (2007) 083917. [29] A. Bouaine, N. Brihi, G. Schmerber, C. Ulhaq-Bouillet, S. Colis, A. Dinia, J. Phys. Chem. C. 111 (2007) 2924. [30] K. Gopinadhan, S.C. Kashyap, D.K. Pandya, S. Chaudhary, J. Appl. Phys. 102 (2007) 113513. [31] K. Gopinadhan, S.C. Kashyap, D.K. Pandya, S. Chaudhary, J. Phys. Condens. Matter 20 (2008) 125208. [32] V.G. Kravets, L.V. Poperenko, J. Appl. Phys. 103 (2008) 083904. [33] J. Philip, A. Punnoose, B.I. Kim, K.M. Reddy, S. Layne, J.O. Holmes, B. Satpati, P.R. Leclair, T.S. Santos, J.S. Moodera, Nat. Mater. 5 (2006) 298. [34] J. Philip, N. Theodoropoulou, G. Berera, J.S. Moodera, B. Satpati, Appl. Phys. Lett. 85 (2004) 777. [35] S.A. Chambers, Surf. Sci. Rep. 61 (2006) 345. [36] X.L. Wang, Z. Zeng, X.H. Zheng, H.Q. Lin, J. Appl. Phys. 101 (2007) 09H104. [37] X.L. Wang, Z.X. Dai, Z. Zeng, J. Phys. Condens. Matter 20 (2008) 045214. [38] S.J. Hu, S.S. Yan, X.X. Yao, Y.X. Chen, G.L. Liu, L.M. Mei, Phys. Rev. B 75 (2007) 094412. [39] C.E. Rodrı´guez Torres, L. Errico, F. Golmar, A.M. Mudarra Navarro, A.F. Cabrera, S. Duhalde, F.H. Sa´nchez, M. Weissmann, J. Magn. Magn. Mater. 316 (2007) e219.
3119
[40] Hongxia Wang, Yu Yan, Y.Sh. Mohammed, Xiaobo Du, Lei Lu, Hanmin Jin, J. Magn. Magn. Mater 321 (2009) 337. [41] X.S. Du, Q.X. Li, H.B. Su, J.L. Yang, Phys. Rev. B 74 (2006) 233201. [42] P. Gopal, N.A. Spaldin, Phys. Rev. B 74 (2006) 094418. [43] S.J. Hu, S.C. Yan, M.W. Zhao, L.M. Mei, Phys. Rev. B 73 (2006) 245205. [44] L.M. Huang, A.L. Rosa, R. Ahuja, Phys. Rev. B 74 (2006) 075206. [45] T. Chanier, M. Sargolzaei, I. Opahle, R. Hayn, K. Koepernik, Phys. Rev. B 73 (2006) 134418. [46] S. Lany, H. Raebiger, A. Zunger, Phys. Rev. B 77 (2008) 241201. [47] H. Raebiger, S. Lany, A. Zunger, Phys. Rev. Lett. 101 (2008) 027203. [48] A. Walsh, J.L.F.D. Silva, S.H. Wei, Phys. Rev. Lett. 100 (2008) 256401. [49] C. Persson, S. Mirbt, Brazilian J. Phys. 36 (2006) 286. [50] T.R. Paudel, W.R.L. Lambrecht, Phys. Rev. B 77 (2008) 205202. [51] J.P. Perdew, Y. Wang, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [52] V.I. Anisimov, O. Gunnarsson, Phys. Rev. B 43 (1991) 7570. [53] V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44 (1991) 943. [54] V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyzyk, G.A. Sawatzky, Phys. Rev. B 48 (1993) 16929. [55] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Liutz, in: K. Schwarz (Ed.), WIEN2k, An augmented plane wave plus local orbitals program for calculating crystal properties, Technical University, Wien, Austria, 2001. [56] R.W.G. Wyckoff, second ed., Crystal Structures, vol. I, Interscience, New York, 1963, p. 239. [57] A.I. Liechtenstein, V.I. Anisimov, J. Zaanen, Phys. Rev. B 52 (1995) R5467. [58] C. Kılıc-, A. Zunger, Phys. Rev. Lett. 88 (2002) 095501. [59] J.M.D. Coey, M. Venkatesan, C.B. Fitzgerald, Nat. Mater. 4 (2005) 173. [60] L. Kover, G. Moretty, Z. Kovacs, R. Sanjines, I. Csemy, G. Margaritondo, J. Palinkas, H. Adachi, J. Vac. Sci. Technol. A 13 (1995) 1382. [61] C. McGuinness, C.B. Stagarescu, P.J. Ryan, J.E. Downes, D. Fu, K.E. Smith, Phys. Rev. B 68 (2003) 165104.