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Electronic structure and magnetic properties of Cr monodoped and (Cr, Al) codoped ZnO
Physica B 407 (2012) 464–467
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Electronic structure and magnetic properties of Cr monodoped and (Cr, Al) codoped ZnO Y.F. Chen a,b,n, F.F. Zhou c, Q.G. Song a, H.Y. Yan a, X. Yang a, T. Wei a a
College of Science, Civil Aviation University of China, Tianjin 300300, People’s Republic of China Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Institute of Advanced Materials Physics and Faculty of Science, Tianjin University, Tianjin 300072, People’s Republic of China c Center of Information Management, Zhongzhou University, Zhengzhou 450044, People’s Republic of China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 June 2011 Received in revised form 26 August 2011 Accepted 12 November 2011 Available online 17 November 2011
Using first-principles calculations based on density functional theory, we investigated systematically the electronic structures and magnetic properties of Cr monodoped and (Cr, Al) codoped in ZnO. The results indicate that Cr monodoped in ZnO favors a spin-polarized state with a total magnetic moment of 7.50mB per supercell and the magnetic moment mainly comes from the unpaired 3d electrons of Cr atoms. In addition, it was found that the ferromagnetic exchange interaction between Cr atoms is shortranged in Cr monodoped ZnO. Interestingly, the ferromagnetic stability can be enhanced significantly by codoping AlZn. We think that the enhancement of ferromagnetic stability should be attributed to the additional electrons introduced by AlZn codoping. & 2011 Elsevier B.V. All rights reserved.
Keywords: Diluted magnetic semiconductors First-principles Magnetic moment Electronic structure
1. Introduction Spintronics is currently an active area of research because spin-based multifunctional electronic device has several advantages over the conventional charge-based devices regarding data-processing speed, nonvolatility, higher integration densities, etc. [1]. The impending need to obtain such device has led to growing interest in developing and designing spintronic materials. The diluted magnetic semiconductors (DMSs) combine ferromagnetism (FM) with the conductivity properties of semiconductors. Therefore, DMSs are ideal materials for applications in spintronics where not only the electron charge but also the spin of the charge carrier is used for information processing. The ideal DMSs should exhibit ferromagnetism at room temperature for practical applications and have a homogeneous distribution of the magnetic dopants. Since Dietl et al. theoretically predicted that room temperature (RT) ferromagnetism might exist in wide-band-gap semiconductors [2], ZnO doped with transition metal (TM) has been extensively studied [3–6] due to its abundance and environment-friendly nature and also due to its potential as a suitable optoelectronic material [7,8] with a wide band gap ( 3.34 eV) and high excitation binding energy of 60 meV. At present, RT FM has been found [9–11], however, experimental results are quite contradictory, there are still some reports indicating no sign of FM [12,13]. In
n
Corresponding author. E-mail address: [email protected] (Y.F. Chen).
0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.11.015
addition, some studies indicate that the RT ferromagnetism in TMdoped oxides may come from precipitation of magnetic clusters or from secondary magnetic phases [14,15]. These extrinsic magnetic behaviors are undesirable for practical applications. Up to the present, the origin of ferromagnetism in oxide DMSs remains a very controversial topic. Among of the TMs, Cr is particularly attractive. Cr was chosen as the preferred TM dopant by several research groups because (1) theoretical research on Cr-based ferromagnetic semiconductors supports the prospect of producing FM; (2) among the impurity phases related to Zn–Cr–O system, Cr metal, Cr2O3, Cr3O4 and ZnCr2O4 are antiferromagnetic, thus eliminating any role of Cr precipitates in yielding spurious FM and (3) the only ferromagnetic oxide of Cr, CrO2 with a Curie temperature (TC) of 386 K, However, the half-metallic CrO2 is not a stable phase under normal condition. CrO2 is usually synthesized under high pressure and is easy to decompose into Cr2O3 when heated at atmospheric pressure [16]. However, compared with the widely studied Coor Mn-doped ZnO systems, both theoretical and experimental researches on Cr-doped ZnO are scarce. Moreover, the experimental results on the studies of Cr doped ZnO are in conflict with each other. Extensive researches were carried out by Venkatesan et al. [17] and Ueda et al. [18] and no sign of FM was observed in Cr doped ZnO. On the contrary, some other studies indicate that Cr-doped ZnO films are ferromagnetic at room temperature [19]. In addition, codoping, i.e., the simultaneous presence of two kinds of defects, has attracted attention primarily because of the
Y.F. Chen et al. / Physica B 407 (2012) 464–467
possibility of using it to solve the asymmetry doping problem of ZnO. It has been found that ferromagnetism in DMS can be enhanced by codoping. For an instance, Sluiter et al. [20] used this approach to promote the FM stability and increase the Curie temperature of ZnO-based ferromagnets. Therefore, codoping was viewed as a potential means to specify the availability of carriers to mediate ferromagnetism. Recently, it has been reported that additional electrons introduced by Al doping can stabilize the ferromagnetic state in Co-doped ZnO [21]. All of these expressions above motivate us to focus on the electronic structure and magnetic properties of Cr monodoped and (Cr, Al) codoped ZnO. In this work, we investigated systematically the electronic structures and magnetic properties in Cr monodoped and (Cr, Al) codoped ZnO using first-principle calculations. We found that FM exchange interaction between Cr atoms is short-ranged in Cr monodoped ZnO system. Interestingly, the FM stability can be enhanced significantly by codoping AlZn. The mechanism of ferromagnetism is discussed.
465
Fig. 1. Schematic illustration of wurtzite 2 2 2 supercell ZnO with 12.5% Cr dopant in the near (a) and far (b) arrangements, where larger (gray) balls, small (red) balls and green balls stand for Zn, O and dopant Cr, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
2. Computational methods Total energy and electronic structure calculations were performed using density functional theory (DFT) with a plane-wave expansion of the wave function [22] as implemented in the Cambridge Serial Total Energy Package (CASTEP) code. Ultrasoft pseudopotentials [23] were used to replace nuclei, the valenceelectron configurations for the O, Zn, Cr and Al atoms were chosen as 2s22p4, 3d104s2, 3s23p63d54s1 and 3s23p1, respectively, all represented in a reciprocal space. The generalized gradient approximation with the Perdew–Burke–Ernzerhof scheme [24] was adopted for the exchange-correlation potential. The electron wave function was expanded in plane waves with a cutoff energy of 420 eV, and a Monkhorst–Pack grid [25] with parameters of 4 4 2 was used for irreducible Brillouin zone sampling. The crystal structure and the atomic coordinates were fully relaxed without any restriction using the Broyden–Fletcher–Goldfarb–Shanno method [26]. In the geometry optimization process, the energy change, as well as the maximum tolerances of the force, stress and displacement were set as 5 10 6 eV/atom, ˚ 0.02 GPa and 0.0005 A. ˚ The test calculations with 0.01 eV/A, higher cutoff energies and denser k-point grids were also performed, and the overall results remained unchanged. Then the electronic structures were calculated on the basis of the optimized supercells.
3. Results and discussion ˚ c¼ 5.315 A) ˚ for The calculated lattice constants (a¼3.281 A, wurtzite ZnO are in good agreement with the experimental values ˚ c¼5.21 A) ˚ [27], which indicates the calculation model (a¼3.25 A, and parameters are reasonable. Based on the unit cell, a 2 2 2 supercell of ZnO was constructed, in which two Zn atoms were substituted with two Cr atoms. This gives a dopant concentration of 12.5% and allows for calculation of the relative energies of ferromagnetic (FM) and antiferromagnetic (AFM) orderings. As described in Ref. [28], two spatial arrangements were explored, namely, near (Cr atoms separated by one O atom) and far (Cr atoms separated by –O–Zn–O–), as shown in Fig. 1. In each case, the energy difference between FM and AFM orderings, DE¼EAFM EFM, was used as an indicator of the magnetic stability. If DE is negative, the AFM configuration is more stable and vice versa. The calculated results show that the magnetic moments of the two Cr dopants favor FM coupling, and the energy of the FM state is 278 and 26 meV lower than that of the corresponding AFM state for near and far
Fig. 2. Band structures of the up spin (a) and the down spin (b) of ZnO doped with 12.5% of Cr. Fermi level is set to zero.
configurations, respectively. The decreasing of DE with increasing Cr separation distance shows that the FM exchange interaction between Cr atoms is short-ranged. In addition, the calculated results also indicate that the far configuration has larger total energy than the near configuration. This suggests that Cr atoms have a tendency to cluster together around O atoms, which is in excellent agreement with previous theoretical studies [4,28,29]. This is also similar to the behavior of Cr in ZnO thin film [30] and other compounds [31–33]. Fig. 2 presents the band structure of the defective system of Zn14Cr2O16. It can be seen that the spin splitting occurs between up spin and down spin channels near the Fermi level, which implies that the Cr dopants can order magnetism in the ZnO hosts. The total magnetic moment is 7.50mB per 2 2 2 supercell. In addition, it can also be seen that the Zn14Cr2O16 system is metallic for the Fermi energy passes through both up-spin component and down-spin component as shown in Fig. 2(a) and (b), respectively. This is different from the one reported by Wang et al. [4], where the authors found that the system of Cr doped in ZnO is half-metallic. It also is found that the impurity band merges with the conduction band at higher carrier concentrations and Cr dopant acts as a donor in ZnO. Evidently, the Cr dopant is found to be the main contributor to the ferromagnetic of the Cr-doped ZnO. To further study the contribution of different atoms in the system for ferromagnetism, we calculated the total density of states (DOS) and partial DOS for the Zn14Cr2O16 system. Fig. 3 presents the total density of states (DOS) and partial DOS for the 12.5% concentration of Cr doping system. One can see that the
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Fig. 3. The total DOS for the Cr-doped ZnO with doped concentration 12.5% is shown in (a), (b) shows the partial DOS of 3d state for Cr atom and (c) shows the 2p DOS for the O atom, respectively. The positive (negative) channel represents the up (down) spin, respectively. The Fermi level is set to 0 eV.
O 2p states (Fig. 3(b)) overlap obviously with those of Cr 3d (Fig. 3(c)) near the Fermi level, suggesting a strong exchange interaction between them. This strong interaction results in the splitting of the energy levels near the Fermi level. The asymmetrical DOS between the up and down-spin channels near the Fermi level suggests the magnetic properties of such defective system, resulting in a magnetic moment of 7.50mB per supercell. The local moment at Cr is about 3.84mB per atom; the O atom bridging the two Cr atoms is antiferromagnetically polarized and carries a magnetic moment of 0.08mB mainly coming from O 2p orbitals. Namely, the two Cr atoms couple ferromagnetically to each other but antiferromagnetically to their nearest neighbor O atoms. This is in good agreement with the result in Ref. [29]. In addition, one can also see that major hybridizations occur between Cr-3d and O-2p orbitals, forming bonding tb and antibonding ta states, with a nonbonding e state lying between the two states. This is similar to the one reported in the Ref. [21]. To explore the effect of (Cr, Al) codoped on the electronic structure and magnetic properties in ZnO, we focus on the case of (Cr, Al)-codoped ZnO. For (Cr, Al)-codoped ZnO system, the calculation model was obtained by substituting a Zn atom with one Al atom in the far configuration, as shown in Fig. 4. To determine whether the defective system is order magnetically or not, both FM and AFM orderings were calculated for the configuration. Our calculation results indicate that FM state is more stable than AFM state with a total energy difference of 73 meV. Interestingly, according to the total energy calculation of FM and AFM states for Cr monodoped ZnO and (Cr, Al) codoped ZnO in the far configuration, we found that the total energy difference favoring ferromagnetic state for the former is 47 meV lower than that of the latter. This fact reveals the FM stability is enhanced significantly by Al codoping. In order to avoid the effect of insufficient k-points and lower cut-off energy, we have a test calculation using 4 4 4 k-points and higher cut-off energy of 450 eV, which verifies that the former k-mesh and cut-off energy provide good convergence with respect to total energy differences and magnetic moment formation. To understand the effect of Al codoping on the electronic structure and magnetic properties of Cr doped ZnO. Fig. 5 presents the total DOS of (Cr, Al) codoped ZnO system and partial DOS of Cr 3d and Al 3p for (Cr, Al) codoped in ZnO system, as well as partial DOS of Cr 3d for Cr monodoped ZnO system. One can see that the Cr 3d states (Fig. 5(b)) overlap obviously with those of Al
Fig. 4. Schematic illustration of wurtzite 2 2 2 supercell ZnO with 12.5% Cr dopant, where larger (gray) balls, small (red) balls and green balls stand for Zn, O and dopant Cr, respectively, and dopant Al is labeled individually. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
Fig. 5. The total DOS of (Cr, Al) codoped ZnO system and partial DOS of Cr 3d and Al 3p for (Cr, Al) codoped ZnO system, as well as partial DOS of Cr 3d for Cr monodoped in ZnO system. The positive (negative) channel represents the up (down) spin, respectively. The Fermi level is set to 0 eV.
3p (Fig. 5(d)) near the Fermi level, which indicates that there exist strong hybridization between Al-3p and Cr-3d states. After hybridization between Al-3p and Cr-3d states, a portion of the Al-3p electrons could occupy the empty states of Cr-3d states, which results in electron transition occurring between Cr 3d and Al 3p and then leads to the increase of the electron number in Cr 3d in the Zn13AlCr2O16 system. In addition, a noticeable change occurs in the partial DOS of 3d states of Cr atoms around the Fermi level. In Zn14Cr2O16, one can see that a pseudogap appears in Cr 3d state, while the pseudogap of Cr 3d in Zn13AlCr2O16 is invisible. Fig. 6 presents a three-dimensional (3D) iso-surface of the average spin charge density of 0.05 e/A˚ 3. It clearly indicates that the magnetic moment is mainly contributed by spin polarized Cr atoms. The unpaired 3d electrons of Cr are responsible for the spin density on Cr atoms. However, our calculation indicates AlZn has no contribution to the total magnetic moment directly, as can
Y.F. Chen et al. / Physica B 407 (2012) 464–467
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Acknowledgments This research has been financially supported by the National Natural Science Foundation of China (Grant no. 60979008) and the Fundamental Research Funds for the Central Universities (Grant no. ZXH2010D014). The authors are grateful to Prof. H.L. Bai and Dr. W.B. Mi for helpful discussion. References
Fig. 6. A 3D iso-surface of the average spin charge density of 0.05 e/A˚ 3 for Zn13Cr2AlO16, where larger (gray) balls, small (red) balls and green balls stand for Zn, O and dopant Cr, respectively. And dopant Al is labeled individually. Blue shells represent the 3D iso-surface. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
be seen from Fig. 6. Based on our calculation results, AlZn is a donor defect and it can introduce electrons in ZnO. Therefore, one can think that the enhancement of ferromagnetic state in Zn13 AlCr2O16 system should be attributed to the additional electrons introduced by AlZn. Furthermore, it is the additional electrons that enhance the FM stability.
4. Conclusions In summary, the electronic structures and magnetic properties of Cr-monodoped and (Cr, Al)-codoped ZnO have been investigated systematically using first-principles calculations based on DFT. The results indicate that monodoping of Cr in ZnO favors a spinpolarized state with a magnetic moment of 7.50mB per supercell and the magnetic moment mainly comes from the unpaired Cr 3d electrons. In addition, it has been found that FM exchange interaction between Cr atoms is short-ranged in Cr monodoped in ZnO. Interestingly, by codoping AlZn, the FM stability can be enhanced significantly with a total energy difference of 73 meV in the far configuration. Based on AlZn is a donor defect and it can generate electrons in ZnO, therefore, we think that the enhancement of FM stability in Zn13Cr2AlO16 system should be attributed to the additional electrons introduced by codoping AlZn.
[1] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. Von Molnar, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488. [2] T. Dietl, H. Ohno, F. Matsujura, J. Cibert, D. Ferrand, Science 287 (2000) 1019. [3] D. Mukherjee, T. Dhakal, H. Srikanth, P. Mukherjee, S. Witanachchi, Phys. Rev. B 81 (2010) 205202. [4] F.G. Wang, Z.Y. Pang, L. Lin, S.J. Fang, Y. Dai, S.H. Han, J. Magn. Magn. Mater. 321 (2009) 3067. [5] O. Mounkachi, A. Benyoussef, A. El Kenz, E.H. Saidi, E.K. Hlil, J. Appl. Phys. 106 (2009) 093905. [6] M.H.N. Assadi, Y.B. Zhang, S. Li, J. Appl. Phys. 105 (2009) 043906. [7] D.M. Bagnall, Y.F. Chen, Z. Zhu, T. Yao, S. Koyama, M.Y. Shen, T. Goto, Appl. Phys. Lett. 70 (1997) 2230. [8] Z.K. Tang, G.K.L. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, Y. Segawa, Appl. Phys. Lett. 72 (1998) 3270. [9] D. Chakraborti, J. Narayan, J.T. Prater, Appl. Phys. Lett. 90 (2007) 062504. [10] L.J. Zhuge, X.M. Wu, Z.F. Wu, X.M. Chen, Y.D. Mengd, Scr. Mater. 60 (2009) 214. [11] B.K. Roberts, A.B. Pakhomov, K.M. Krishnan, J. Appl. Phys. 103 (2008) 07D133. [12] Z.W. Jin, T. Fukumura, M. Kawasaki, K. Ando, H. Saito, T. Sekiguchi, Y.Z. Yao, M. Murakami, Y. Matsumoto, T. Hasegawa, H. Koinuma, Appl. Phys. Lett. 78 (2001) 3824. [13] W. Li, Q.Q. Kang, Z. Lin, W.S. Chu, D.L. Chen, Z.Y. Wu, Y. Yan, D.G. Chen, F. Huang, Appl. Phys. Lett. 89 (2006) 112507. [14] J.H. Park, M.G. Kim, H.M. Jang, S. Ryu, Y.M. Kim, Appl. Phys. Lett. 84 (2004) 1338. [15] S. Deka, R. Pasricha, P.A. Joy, Phys. Rev. B 74 (2006) 033201. [16] Y.P. Chen, K. Ding, L. Yang, B. Xie, F.Q. Song, J.G. Wan, G.H. Wang, M. Han, Appl. Phys. Lett. 92 (2008) 173112. [17] M. Venkatesan, C.B. Fitzgerald, J.G. Lunney, J.M.D. Coey, Phys. Rev. Lett. 93 (2004) 177206. [18] K. Ueda, H. Tabata, T. Kawai, Appl. Phys. Lett. 79 (2001) 988. [19] H. Liu, X. Zhang, L.Y. Li, Y.X. Wang, K.H. Gao, Z.Q. Li, R.K. Zheng, S.P. Ringer, B. Zhang, X.X. Zhang, Appl. Phys. Lett. 91 (2007) 072511. [20] M.H.F. Sluiter, Y. Kawazoe, P. Sharma, A. Inoue, A.R. Raju, C. Rout, U.V. Waghmare, Phys. Rev. Lett. 94 (2005) 187204. [21] T. Zhang, L.X. Song, Z.Z. Chen, E.W. Shi, L.X. Chao, H.W. Zhang, Appl. Phys. Lett. 89 (2006) 172502. [22] M.D. Segall, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717. [23] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [24] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [25] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [26] B.G. Pfrommer, M. Cote, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997) 233. [27] E.H. Kisi, M.M. Elcombe, Acta Crystallogr. 45 (1989) 1867. [28] P. Gopal, N.A. Spaldin, Phys. Rev. B 74 (2006) 094418. [29] Q. Wang, Q. Sun, P. Jena, Y. Kawazoe, Appl. Phys. Lett. 87 (2005) 162509. [30] Q. Wang, Q. Sun, P. Jena, Y. Kawazoe, Phys. Rev. B 79 (2009) 115407. [31] Q. Wang, A.K. Kandalam, Q. Sun, P. Jena, Phys. Rev. B 73 (2006) 115411. [32] Q. Wang, Q. Sun, P. Jena, Y. Kawazoe, Phys. Rev. B 73 (2006) 205320. [33] Q. Wang, Q. Sun, P. Jena, J.Z. Yu, R. Note, Y. Kawazoe, Phys. Rev. B 72 (2005) 045435.
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Physica B journal homepage: www.elsevier.com/locate/physb
Electronic structure and magnetic properties of Cr monodoped and (Cr, Al) codoped ZnO Y.F. Chen a,b,n, F.F. Zhou c, Q.G. Song a, H.Y. Yan a, X. Yang a, T. Wei a a
College of Science, Civil Aviation University of China, Tianjin 300300, People’s Republic of China Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Institute of Advanced Materials Physics and Faculty of Science, Tianjin University, Tianjin 300072, People’s Republic of China c Center of Information Management, Zhongzhou University, Zhengzhou 450044, People’s Republic of China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 June 2011 Received in revised form 26 August 2011 Accepted 12 November 2011 Available online 17 November 2011
Using first-principles calculations based on density functional theory, we investigated systematically the electronic structures and magnetic properties of Cr monodoped and (Cr, Al) codoped in ZnO. The results indicate that Cr monodoped in ZnO favors a spin-polarized state with a total magnetic moment of 7.50mB per supercell and the magnetic moment mainly comes from the unpaired 3d electrons of Cr atoms. In addition, it was found that the ferromagnetic exchange interaction between Cr atoms is shortranged in Cr monodoped ZnO. Interestingly, the ferromagnetic stability can be enhanced significantly by codoping AlZn. We think that the enhancement of ferromagnetic stability should be attributed to the additional electrons introduced by AlZn codoping. & 2011 Elsevier B.V. All rights reserved.
Keywords: Diluted magnetic semiconductors First-principles Magnetic moment Electronic structure
1. Introduction Spintronics is currently an active area of research because spin-based multifunctional electronic device has several advantages over the conventional charge-based devices regarding data-processing speed, nonvolatility, higher integration densities, etc. [1]. The impending need to obtain such device has led to growing interest in developing and designing spintronic materials. The diluted magnetic semiconductors (DMSs) combine ferromagnetism (FM) with the conductivity properties of semiconductors. Therefore, DMSs are ideal materials for applications in spintronics where not only the electron charge but also the spin of the charge carrier is used for information processing. The ideal DMSs should exhibit ferromagnetism at room temperature for practical applications and have a homogeneous distribution of the magnetic dopants. Since Dietl et al. theoretically predicted that room temperature (RT) ferromagnetism might exist in wide-band-gap semiconductors [2], ZnO doped with transition metal (TM) has been extensively studied [3–6] due to its abundance and environment-friendly nature and also due to its potential as a suitable optoelectronic material [7,8] with a wide band gap ( 3.34 eV) and high excitation binding energy of 60 meV. At present, RT FM has been found [9–11], however, experimental results are quite contradictory, there are still some reports indicating no sign of FM [12,13]. In
n
Corresponding author. E-mail address: [email protected] (Y.F. Chen).
0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.11.015
addition, some studies indicate that the RT ferromagnetism in TMdoped oxides may come from precipitation of magnetic clusters or from secondary magnetic phases [14,15]. These extrinsic magnetic behaviors are undesirable for practical applications. Up to the present, the origin of ferromagnetism in oxide DMSs remains a very controversial topic. Among of the TMs, Cr is particularly attractive. Cr was chosen as the preferred TM dopant by several research groups because (1) theoretical research on Cr-based ferromagnetic semiconductors supports the prospect of producing FM; (2) among the impurity phases related to Zn–Cr–O system, Cr metal, Cr2O3, Cr3O4 and ZnCr2O4 are antiferromagnetic, thus eliminating any role of Cr precipitates in yielding spurious FM and (3) the only ferromagnetic oxide of Cr, CrO2 with a Curie temperature (TC) of 386 K, However, the half-metallic CrO2 is not a stable phase under normal condition. CrO2 is usually synthesized under high pressure and is easy to decompose into Cr2O3 when heated at atmospheric pressure [16]. However, compared with the widely studied Coor Mn-doped ZnO systems, both theoretical and experimental researches on Cr-doped ZnO are scarce. Moreover, the experimental results on the studies of Cr doped ZnO are in conflict with each other. Extensive researches were carried out by Venkatesan et al. [17] and Ueda et al. [18] and no sign of FM was observed in Cr doped ZnO. On the contrary, some other studies indicate that Cr-doped ZnO films are ferromagnetic at room temperature [19]. In addition, codoping, i.e., the simultaneous presence of two kinds of defects, has attracted attention primarily because of the
Y.F. Chen et al. / Physica B 407 (2012) 464–467
possibility of using it to solve the asymmetry doping problem of ZnO. It has been found that ferromagnetism in DMS can be enhanced by codoping. For an instance, Sluiter et al. [20] used this approach to promote the FM stability and increase the Curie temperature of ZnO-based ferromagnets. Therefore, codoping was viewed as a potential means to specify the availability of carriers to mediate ferromagnetism. Recently, it has been reported that additional electrons introduced by Al doping can stabilize the ferromagnetic state in Co-doped ZnO [21]. All of these expressions above motivate us to focus on the electronic structure and magnetic properties of Cr monodoped and (Cr, Al) codoped ZnO. In this work, we investigated systematically the electronic structures and magnetic properties in Cr monodoped and (Cr, Al) codoped ZnO using first-principle calculations. We found that FM exchange interaction between Cr atoms is short-ranged in Cr monodoped ZnO system. Interestingly, the FM stability can be enhanced significantly by codoping AlZn. The mechanism of ferromagnetism is discussed.
465
Fig. 1. Schematic illustration of wurtzite 2 2 2 supercell ZnO with 12.5% Cr dopant in the near (a) and far (b) arrangements, where larger (gray) balls, small (red) balls and green balls stand for Zn, O and dopant Cr, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
2. Computational methods Total energy and electronic structure calculations were performed using density functional theory (DFT) with a plane-wave expansion of the wave function [22] as implemented in the Cambridge Serial Total Energy Package (CASTEP) code. Ultrasoft pseudopotentials [23] were used to replace nuclei, the valenceelectron configurations for the O, Zn, Cr and Al atoms were chosen as 2s22p4, 3d104s2, 3s23p63d54s1 and 3s23p1, respectively, all represented in a reciprocal space. The generalized gradient approximation with the Perdew–Burke–Ernzerhof scheme [24] was adopted for the exchange-correlation potential. The electron wave function was expanded in plane waves with a cutoff energy of 420 eV, and a Monkhorst–Pack grid [25] with parameters of 4 4 2 was used for irreducible Brillouin zone sampling. The crystal structure and the atomic coordinates were fully relaxed without any restriction using the Broyden–Fletcher–Goldfarb–Shanno method [26]. In the geometry optimization process, the energy change, as well as the maximum tolerances of the force, stress and displacement were set as 5 10 6 eV/atom, ˚ 0.02 GPa and 0.0005 A. ˚ The test calculations with 0.01 eV/A, higher cutoff energies and denser k-point grids were also performed, and the overall results remained unchanged. Then the electronic structures were calculated on the basis of the optimized supercells.
3. Results and discussion ˚ c¼ 5.315 A) ˚ for The calculated lattice constants (a¼3.281 A, wurtzite ZnO are in good agreement with the experimental values ˚ c¼5.21 A) ˚ [27], which indicates the calculation model (a¼3.25 A, and parameters are reasonable. Based on the unit cell, a 2 2 2 supercell of ZnO was constructed, in which two Zn atoms were substituted with two Cr atoms. This gives a dopant concentration of 12.5% and allows for calculation of the relative energies of ferromagnetic (FM) and antiferromagnetic (AFM) orderings. As described in Ref. [28], two spatial arrangements were explored, namely, near (Cr atoms separated by one O atom) and far (Cr atoms separated by –O–Zn–O–), as shown in Fig. 1. In each case, the energy difference between FM and AFM orderings, DE¼EAFM EFM, was used as an indicator of the magnetic stability. If DE is negative, the AFM configuration is more stable and vice versa. The calculated results show that the magnetic moments of the two Cr dopants favor FM coupling, and the energy of the FM state is 278 and 26 meV lower than that of the corresponding AFM state for near and far
Fig. 2. Band structures of the up spin (a) and the down spin (b) of ZnO doped with 12.5% of Cr. Fermi level is set to zero.
configurations, respectively. The decreasing of DE with increasing Cr separation distance shows that the FM exchange interaction between Cr atoms is short-ranged. In addition, the calculated results also indicate that the far configuration has larger total energy than the near configuration. This suggests that Cr atoms have a tendency to cluster together around O atoms, which is in excellent agreement with previous theoretical studies [4,28,29]. This is also similar to the behavior of Cr in ZnO thin film [30] and other compounds [31–33]. Fig. 2 presents the band structure of the defective system of Zn14Cr2O16. It can be seen that the spin splitting occurs between up spin and down spin channels near the Fermi level, which implies that the Cr dopants can order magnetism in the ZnO hosts. The total magnetic moment is 7.50mB per 2 2 2 supercell. In addition, it can also be seen that the Zn14Cr2O16 system is metallic for the Fermi energy passes through both up-spin component and down-spin component as shown in Fig. 2(a) and (b), respectively. This is different from the one reported by Wang et al. [4], where the authors found that the system of Cr doped in ZnO is half-metallic. It also is found that the impurity band merges with the conduction band at higher carrier concentrations and Cr dopant acts as a donor in ZnO. Evidently, the Cr dopant is found to be the main contributor to the ferromagnetic of the Cr-doped ZnO. To further study the contribution of different atoms in the system for ferromagnetism, we calculated the total density of states (DOS) and partial DOS for the Zn14Cr2O16 system. Fig. 3 presents the total density of states (DOS) and partial DOS for the 12.5% concentration of Cr doping system. One can see that the
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Fig. 3. The total DOS for the Cr-doped ZnO with doped concentration 12.5% is shown in (a), (b) shows the partial DOS of 3d state for Cr atom and (c) shows the 2p DOS for the O atom, respectively. The positive (negative) channel represents the up (down) spin, respectively. The Fermi level is set to 0 eV.
O 2p states (Fig. 3(b)) overlap obviously with those of Cr 3d (Fig. 3(c)) near the Fermi level, suggesting a strong exchange interaction between them. This strong interaction results in the splitting of the energy levels near the Fermi level. The asymmetrical DOS between the up and down-spin channels near the Fermi level suggests the magnetic properties of such defective system, resulting in a magnetic moment of 7.50mB per supercell. The local moment at Cr is about 3.84mB per atom; the O atom bridging the two Cr atoms is antiferromagnetically polarized and carries a magnetic moment of 0.08mB mainly coming from O 2p orbitals. Namely, the two Cr atoms couple ferromagnetically to each other but antiferromagnetically to their nearest neighbor O atoms. This is in good agreement with the result in Ref. [29]. In addition, one can also see that major hybridizations occur between Cr-3d and O-2p orbitals, forming bonding tb and antibonding ta states, with a nonbonding e state lying between the two states. This is similar to the one reported in the Ref. [21]. To explore the effect of (Cr, Al) codoped on the electronic structure and magnetic properties in ZnO, we focus on the case of (Cr, Al)-codoped ZnO. For (Cr, Al)-codoped ZnO system, the calculation model was obtained by substituting a Zn atom with one Al atom in the far configuration, as shown in Fig. 4. To determine whether the defective system is order magnetically or not, both FM and AFM orderings were calculated for the configuration. Our calculation results indicate that FM state is more stable than AFM state with a total energy difference of 73 meV. Interestingly, according to the total energy calculation of FM and AFM states for Cr monodoped ZnO and (Cr, Al) codoped ZnO in the far configuration, we found that the total energy difference favoring ferromagnetic state for the former is 47 meV lower than that of the latter. This fact reveals the FM stability is enhanced significantly by Al codoping. In order to avoid the effect of insufficient k-points and lower cut-off energy, we have a test calculation using 4 4 4 k-points and higher cut-off energy of 450 eV, which verifies that the former k-mesh and cut-off energy provide good convergence with respect to total energy differences and magnetic moment formation. To understand the effect of Al codoping on the electronic structure and magnetic properties of Cr doped ZnO. Fig. 5 presents the total DOS of (Cr, Al) codoped ZnO system and partial DOS of Cr 3d and Al 3p for (Cr, Al) codoped in ZnO system, as well as partial DOS of Cr 3d for Cr monodoped ZnO system. One can see that the Cr 3d states (Fig. 5(b)) overlap obviously with those of Al
Fig. 4. Schematic illustration of wurtzite 2 2 2 supercell ZnO with 12.5% Cr dopant, where larger (gray) balls, small (red) balls and green balls stand for Zn, O and dopant Cr, respectively, and dopant Al is labeled individually. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
Fig. 5. The total DOS of (Cr, Al) codoped ZnO system and partial DOS of Cr 3d and Al 3p for (Cr, Al) codoped ZnO system, as well as partial DOS of Cr 3d for Cr monodoped in ZnO system. The positive (negative) channel represents the up (down) spin, respectively. The Fermi level is set to 0 eV.
3p (Fig. 5(d)) near the Fermi level, which indicates that there exist strong hybridization between Al-3p and Cr-3d states. After hybridization between Al-3p and Cr-3d states, a portion of the Al-3p electrons could occupy the empty states of Cr-3d states, which results in electron transition occurring between Cr 3d and Al 3p and then leads to the increase of the electron number in Cr 3d in the Zn13AlCr2O16 system. In addition, a noticeable change occurs in the partial DOS of 3d states of Cr atoms around the Fermi level. In Zn14Cr2O16, one can see that a pseudogap appears in Cr 3d state, while the pseudogap of Cr 3d in Zn13AlCr2O16 is invisible. Fig. 6 presents a three-dimensional (3D) iso-surface of the average spin charge density of 0.05 e/A˚ 3. It clearly indicates that the magnetic moment is mainly contributed by spin polarized Cr atoms. The unpaired 3d electrons of Cr are responsible for the spin density on Cr atoms. However, our calculation indicates AlZn has no contribution to the total magnetic moment directly, as can
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Acknowledgments This research has been financially supported by the National Natural Science Foundation of China (Grant no. 60979008) and the Fundamental Research Funds for the Central Universities (Grant no. ZXH2010D014). The authors are grateful to Prof. H.L. Bai and Dr. W.B. Mi for helpful discussion. References
Fig. 6. A 3D iso-surface of the average spin charge density of 0.05 e/A˚ 3 for Zn13Cr2AlO16, where larger (gray) balls, small (red) balls and green balls stand for Zn, O and dopant Cr, respectively. And dopant Al is labeled individually. Blue shells represent the 3D iso-surface. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).
be seen from Fig. 6. Based on our calculation results, AlZn is a donor defect and it can introduce electrons in ZnO. Therefore, one can think that the enhancement of ferromagnetic state in Zn13 AlCr2O16 system should be attributed to the additional electrons introduced by AlZn. Furthermore, it is the additional electrons that enhance the FM stability.
4. Conclusions In summary, the electronic structures and magnetic properties of Cr-monodoped and (Cr, Al)-codoped ZnO have been investigated systematically using first-principles calculations based on DFT. The results indicate that monodoping of Cr in ZnO favors a spinpolarized state with a magnetic moment of 7.50mB per supercell and the magnetic moment mainly comes from the unpaired Cr 3d electrons. In addition, it has been found that FM exchange interaction between Cr atoms is short-ranged in Cr monodoped in ZnO. Interestingly, by codoping AlZn, the FM stability can be enhanced significantly with a total energy difference of 73 meV in the far configuration. Based on AlZn is a donor defect and it can generate electrons in ZnO, therefore, we think that the enhancement of FM stability in Zn13Cr2AlO16 system should be attributed to the additional electrons introduced by codoping AlZn.
[1] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. Von Molnar, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488. [2] T. Dietl, H. Ohno, F. Matsujura, J. Cibert, D. Ferrand, Science 287 (2000) 1019. [3] D. Mukherjee, T. Dhakal, H. Srikanth, P. Mukherjee, S. Witanachchi, Phys. Rev. B 81 (2010) 205202. [4] F.G. Wang, Z.Y. Pang, L. Lin, S.J. Fang, Y. Dai, S.H. Han, J. Magn. Magn. Mater. 321 (2009) 3067. [5] O. Mounkachi, A. Benyoussef, A. El Kenz, E.H. Saidi, E.K. Hlil, J. Appl. Phys. 106 (2009) 093905. [6] M.H.N. Assadi, Y.B. Zhang, S. Li, J. Appl. Phys. 105 (2009) 043906. [7] D.M. Bagnall, Y.F. Chen, Z. Zhu, T. Yao, S. Koyama, M.Y. Shen, T. Goto, Appl. Phys. Lett. 70 (1997) 2230. [8] Z.K. Tang, G.K.L. Wong, P. Yu, M. Kawasaki, A. Ohtomo, H. Koinuma, Y. Segawa, Appl. Phys. Lett. 72 (1998) 3270. [9] D. Chakraborti, J. Narayan, J.T. Prater, Appl. Phys. Lett. 90 (2007) 062504. [10] L.J. Zhuge, X.M. Wu, Z.F. Wu, X.M. Chen, Y.D. Mengd, Scr. Mater. 60 (2009) 214. [11] B.K. Roberts, A.B. Pakhomov, K.M. Krishnan, J. Appl. Phys. 103 (2008) 07D133. [12] Z.W. Jin, T. Fukumura, M. Kawasaki, K. Ando, H. Saito, T. Sekiguchi, Y.Z. Yao, M. Murakami, Y. Matsumoto, T. Hasegawa, H. Koinuma, Appl. Phys. Lett. 78 (2001) 3824. [13] W. Li, Q.Q. Kang, Z. Lin, W.S. Chu, D.L. Chen, Z.Y. Wu, Y. Yan, D.G. Chen, F. Huang, Appl. Phys. Lett. 89 (2006) 112507. [14] J.H. Park, M.G. Kim, H.M. Jang, S. Ryu, Y.M. Kim, Appl. Phys. Lett. 84 (2004) 1338. [15] S. Deka, R. Pasricha, P.A. Joy, Phys. Rev. B 74 (2006) 033201. [16] Y.P. Chen, K. Ding, L. Yang, B. Xie, F.Q. Song, J.G. Wan, G.H. Wang, M. Han, Appl. Phys. Lett. 92 (2008) 173112. [17] M. Venkatesan, C.B. Fitzgerald, J.G. Lunney, J.M.D. Coey, Phys. Rev. Lett. 93 (2004) 177206. [18] K. Ueda, H. Tabata, T. Kawai, Appl. Phys. Lett. 79 (2001) 988. [19] H. Liu, X. Zhang, L.Y. Li, Y.X. Wang, K.H. Gao, Z.Q. Li, R.K. Zheng, S.P. Ringer, B. Zhang, X.X. Zhang, Appl. Phys. Lett. 91 (2007) 072511. [20] M.H.F. Sluiter, Y. Kawazoe, P. Sharma, A. Inoue, A.R. Raju, C. Rout, U.V. Waghmare, Phys. Rev. Lett. 94 (2005) 187204. [21] T. Zhang, L.X. Song, Z.Z. Chen, E.W. Shi, L.X. Chao, H.W. Zhang, Appl. Phys. Lett. 89 (2006) 172502. [22] M.D. Segall, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717. [23] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [24] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [25] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [26] B.G. Pfrommer, M. Cote, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997) 233. [27] E.H. Kisi, M.M. Elcombe, Acta Crystallogr. 45 (1989) 1867. [28] P. Gopal, N.A. Spaldin, Phys. Rev. B 74 (2006) 094418. [29] Q. Wang, Q. Sun, P. Jena, Y. Kawazoe, Appl. Phys. Lett. 87 (2005) 162509. [30] Q. Wang, Q. Sun, P. Jena, Y. Kawazoe, Phys. Rev. B 79 (2009) 115407. [31] Q. Wang, A.K. Kandalam, Q. Sun, P. Jena, Phys. Rev. B 73 (2006) 115411. [32] Q. Wang, Q. Sun, P. Jena, Y. Kawazoe, Phys. Rev. B 73 (2006) 205320. [33] Q. Wang, Q. Sun, P. Jena, J.Z. Yu, R. Note, Y. Kawazoe, Phys. Rev. B 72 (2005) 045435.