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A first-principles study on magnetic properties of the intrinsic defects in rutile TiO2

Lin Qiao-Lu Li Gong-Ping Xu Nan-Nan Liu Huan Wang Cang-Long

A first-principles study on magnetic properties of the intrinsic defects in rutile TiO2

Lin Qiao-Lu, Li Gong-Ping, Xu Nan-Nan, Liu Huan, Wang Cang-Long
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  • The TiO2 based diluted magnetic semiconductors (DMSs) have aroused the considerable interest as one of the promising candidates for the spintronic devices accommodating both charge and spin of electrons in a single substance. Unfortunately, however, throughout most of the published papers, the question how to clearly elucidate the role of defects which may be played in the experimentally observed room temperature ferromagnetism (RTFM) remains open, especially after a new concept of d0 ferromagnetism. In such a case, to further understand this issue and also to explore the origin of the RTFM in rutile TiO2, we here first perform a first principles calculation on the magnetic properties of the intrinsic defects, namely oxygen vacancy (VO), Ti vacancy (VTi), Ti interstitial (Tiin), oxygen interstitial (Oin) and two complex defects of VO+Oin and VTi+Tiin. Combining the density functional theory and the Perdew-Burke-Ernzerhof functional of the generalized gradient approximation, we calculate various model structures of rutile TiO2 constituted by 48-atom 222 supercell. The cutoff energies in these calculations of the planewave basis are all set to be 340 eV and the Monkhorst-Pack scheme k points are set to be 334 for an irreducible Brillouin zone. The convergence threshold for self-consistent field iteration is 0.145510-6 eV/atom. Structural relaxation is taken into account in each of all calculations. It is found that each defect we created in the structure leads to a lattice expansion and that the positive value for spin up and the negative value for spin down of the density of states (DOS) of the structure without defect are symmetric, suggesting that the perfect rutile TiO2 lattice is nonferromagnetic. For the system with one VO, the total energy of the spin-polarized system is 200 meV lower than that of the non-spin-polarized system, which indicates ferromagnetic behavior in this system. The defect brings in an impurity state near Fermi level located at about 0.71.0 eV down below the conduction band, resulting in an excess of spin up over spin down for the presences of the two localized electrons left by the vacancy. At this point the supercell bears a magnetic moment of about 1.62 B. In contrast, VTi also brings in an impurity state near Fermi level but above the valence band, which reveals a p-type characteristic semiconductor nature. Since a lower total energy requires more spin-up electrons, the asymmetric DOS induces a magnetic moment of 2.47 B. When a neutral Ti occupies an interstitial lattice site, the system requires it to be oxidized into a Ti3+ ion to increase the stabilization of the system. The three delocalized electrons tend to occupy the 3d or 4s orbital of the neighbor Ti4+ ions and then have strong exchange interactions with the 2p electrons of the local O atom. This can distort octahedral symmetry and give rise to a ferromagnetic moment of 3.91 B. Oin defect in the supercell is extremely unstable. It can easily be reduced and escape from the host in terms of an oxygen molecule so that the system is in a manner similar to the perfect lattice, showing no ferromagnetism. It is interesting to note that the properties of the system with the complex defect of one VO and Oin are similar to that of the structure with one VO and the magnetic moment of this system is 1.63 B. For the Ticom complex defect, our results point out the fact that the magnetic properties of the supercell are related to the distance between VTi and Tiin. The spin up and spin down states are symmetric when they are close to each other, while, in addition to some ferromagnetic behavior, the system mainly exhibits antiferromagnetism when the distance increases.
      Corresponding author: Li Gong-Ping, ligp@lzu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11575074, 11304324) and the State Key Laboratory of Crystal Materials at Shandong University Open Foundation, China (Grant No. KF1311).
    [1]

    Dietl T, Ohno H, Matsukura F, Cibert J, Ferrand D 2000 Science 287 1019

    [2]

    Matsumoto Y, Murakami M, Shono T, Fukumura T, Kawasaki M, Ahmet P, Chikyow T, Koshihara S, Koinuma H 2001 Science 291 854

    [3]

    Higgins J S, Shinde S R, Ogale S B, Venkatesan T, Greene R L 2004 Phys. Rev. B 69 073201

    [4]

    Toyosaki H, Fukumura T, Yamada Y, Nakajima K, Chikyow T, Hasegawa T, Koinuma H, Kawasaki M 2004 Nat. Mater. 3 221

    [5]

    Chambers S A, Wang C M, Thevuthasan S, Droubay T, Mccready D E, Lea A S, Shutthanandan V, Windisch C F 2002 Thin Solid Films 418 197

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    Hong N H 2006 J. Magn. Magn. Mater. 303 338

    [7]

    Paul S, Choudhury B, Choudhury A 2014 J. Alloy. Compd. 601 201

    [8]

    Kim D H, Yang J S, Kim Y S, Kim D W, Noh T W, Bu S D, Kim Y W, Park Y D, Pearton S J, Jo Y, Park J G 2003 Appl. Phys. Lett. 83 4574

    [9]

    Kang S H, Quynh H N T, Yoon S G, Kim E T, Lee Z, Radmilovic V 2007 Appl. Phys. Lett. 90 102504

    [10]

    Shutthanandan V, Thevuthasan S, Heald S M, Droubay T, Engelhard M H, Kaspar T C, Mccready D E, Saraf L, Chambers S A, Mun B S, Hamdan N, Nachimuthu P, Taylor B, Sears R P, Sinkovic B 2004 Appl. Phys. Lett. 84 4466

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    Griffin K A, Pakhomov A B, Wang C M, Heald S M, Krishnan K M 2005 Phys. Rev. Lett. 94 157204

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    Santara B, Pal B, Giri P K 2011 J. Appl. Phys. 110 114322

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    Pereira L C J, Nunes M R, Monteiro O C, Silvestre A J 2008 Appl. Phys. Lett. 93 222502

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    Stausholm-Møller J, Kristoffersen H H, Hinnemann B, Madsen G K H, Hammer B 2010 J. Chem. Phys. 133 144708

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    Shi L B, Wang Y P 2016 J. Magn. Magn. Mater. 405 1

    [16]

    Zarhri Z, Houmad M, Ziat Y, El Rhazouani O, Slassi A, Benyoussef A, El Kenz A 2016 J. Magn. Magn. Mater. 406 212

    [17]

    Kim D, Hong J, Park Y R, Kim K J 2009 J. Phys.:Condens. Matter 21 195405

    [18]

    Máca F, Kudrnovsky J, Drchal V, Bouzerar G 2008 Appl. Phys. Lett. 92 212503

    [19]

    Yang K, Dai Y, Huang B, Feng Y P 2010 Phys. Rev. B 81 033202

    [20]

    Iddir H, Ğt S, Zapol P, Browning N D 2007 Phys. Rev. B 75 073203

    [21]

    Na Phattalung S, Smith M F, Kim K, Du M H, Wei S H, Zhang S B, Limpijumnong S 2006 Phys. Rev. B 73 125205

    [22]

    Wang M, Feng M, Zuo X 2014 Appl. Surf. Sci. 292 475

    [23]

    Peng H 2008 Phys. Lett. A 372 1527

    [24]

    Mattioli G, Alippi P, Filippone F, Caminiti R, Amore Bonapasta A 2010 J. Phys. Chem. C 114 21694

    [25]

    Diebold U 2003 Surf. Sci. Rep. 48 53

    [26]

    de Graef M, Mchenry M E 2007 Structure of Materials:An Introduction to Crystallography, Diffraction and Symmetry (Cambridge:Cambridge University Press) p363

    [27]

    Santara B, Giri P K, Imakite K, Fujii M 2014 J. Phys. D:Appl. Phys. 47 215302

    [28]

    Morgan B J, Watson G W 2010 J. Phys. Chem. C 114 2321

    [29]

    Fakhim Lamrani A, Belaiche M, Benyoussef A, El Kenz A, Saidi E H 2010 J. Magn. Magn. Mater. 322 454

    [30]

    Lee H Y, Clark S J, Robertson J 2012 Phys. Rev. B 86 075209

    [31]

    Nolan M, Elliott S D, Mulley J S, Bennett R A, Basham M, Mulheran P 2008 Phys. Rev. B 77 235424

    [32]

    Henderson M A, Epling W S, Peden C H F, Perkins C L 2003 J. Phys. Chem. B 107 534

    [33]

    Yang S, Halliburton L E, Manivannan A, Bunton P H, Baker D B, Klemm M, Horn S, Fujishima A 2009 Appl. Phys. Lett. 94 162114

    [34]

    Santara B, Giri P K, Imakita K, Fujii M 2013 Nanoscale 5 5476

    [35]

    Yosida K 1998 Theory of Magnetism (Berlin:Springer-Verlag) pp87-89

    [36]

    Zhao L, Park S G, Magyari Köpe B, Nishi Y 2013 Math. Comput. Model. 58 275

    [37]

    Zhang Y, Qi Y Y, Hu Y H, Liang P 2013 Chin. Phys. B 22 127101

    [38]

    Rumaiz A K, Ali B, Ceylan A, Boggs M, Beebe T, Shah S I 2007 Solid State Commun. 144 334

    [39]

    Coey J M D, Stamenov P, Gunning R D, Venkatesan M, Paul K 2010 New J. Phys. 12 053025

    [40]

    Finazzi E, Di Valentin C, Pacchioni G 2009 J. Phys. Chem. C 113 3382

    [41]

    Lany S, Zunger A 2009 Phys. Rev. B 80 085202

    [42]

    Kamisaka H, Yamashita K 2011 J. Phys. Chem. C 115 8265

    [43]

    Mulheran P A, Nolan M, Browne C S, Basham M, Sanville E, Bennett R A 2010 Phys. Chem. Chem. Phys. 12 9763

    [44]

    Koudriachova M 2007 Phys. Status Solidi C 4 1205

    [45]

    Zhou S, Čžmár E, Potzger K, Krause M, Talut G, Helm M, Fassbender J, Zvyagin S A, Wosnitza J, Schmidt H 2009 Phys. Rev. B 79 113201

    [46]

    Lai L L, Wu J M 2015 Ceram. Int. 41 12317

    [47]

    Buchholz D B, Chang R P H, Song J Y, Ketterson J B 2005 Appl. Phys. Lett. 87 082504

    [48]

    Ye L H, Freeman A J, Delley B 2006 Phys. Rev. B 73 033203

  • [1]

    Dietl T, Ohno H, Matsukura F, Cibert J, Ferrand D 2000 Science 287 1019

    [2]

    Matsumoto Y, Murakami M, Shono T, Fukumura T, Kawasaki M, Ahmet P, Chikyow T, Koshihara S, Koinuma H 2001 Science 291 854

    [3]

    Higgins J S, Shinde S R, Ogale S B, Venkatesan T, Greene R L 2004 Phys. Rev. B 69 073201

    [4]

    Toyosaki H, Fukumura T, Yamada Y, Nakajima K, Chikyow T, Hasegawa T, Koinuma H, Kawasaki M 2004 Nat. Mater. 3 221

    [5]

    Chambers S A, Wang C M, Thevuthasan S, Droubay T, Mccready D E, Lea A S, Shutthanandan V, Windisch C F 2002 Thin Solid Films 418 197

    [6]

    Hong N H 2006 J. Magn. Magn. Mater. 303 338

    [7]

    Paul S, Choudhury B, Choudhury A 2014 J. Alloy. Compd. 601 201

    [8]

    Kim D H, Yang J S, Kim Y S, Kim D W, Noh T W, Bu S D, Kim Y W, Park Y D, Pearton S J, Jo Y, Park J G 2003 Appl. Phys. Lett. 83 4574

    [9]

    Kang S H, Quynh H N T, Yoon S G, Kim E T, Lee Z, Radmilovic V 2007 Appl. Phys. Lett. 90 102504

    [10]

    Shutthanandan V, Thevuthasan S, Heald S M, Droubay T, Engelhard M H, Kaspar T C, Mccready D E, Saraf L, Chambers S A, Mun B S, Hamdan N, Nachimuthu P, Taylor B, Sears R P, Sinkovic B 2004 Appl. Phys. Lett. 84 4466

    [11]

    Griffin K A, Pakhomov A B, Wang C M, Heald S M, Krishnan K M 2005 Phys. Rev. Lett. 94 157204

    [12]

    Santara B, Pal B, Giri P K 2011 J. Appl. Phys. 110 114322

    [13]

    Pereira L C J, Nunes M R, Monteiro O C, Silvestre A J 2008 Appl. Phys. Lett. 93 222502

    [14]

    Stausholm-Møller J, Kristoffersen H H, Hinnemann B, Madsen G K H, Hammer B 2010 J. Chem. Phys. 133 144708

    [15]

    Shi L B, Wang Y P 2016 J. Magn. Magn. Mater. 405 1

    [16]

    Zarhri Z, Houmad M, Ziat Y, El Rhazouani O, Slassi A, Benyoussef A, El Kenz A 2016 J. Magn. Magn. Mater. 406 212

    [17]

    Kim D, Hong J, Park Y R, Kim K J 2009 J. Phys.:Condens. Matter 21 195405

    [18]

    Máca F, Kudrnovsky J, Drchal V, Bouzerar G 2008 Appl. Phys. Lett. 92 212503

    [19]

    Yang K, Dai Y, Huang B, Feng Y P 2010 Phys. Rev. B 81 033202

    [20]

    Iddir H, Ğt S, Zapol P, Browning N D 2007 Phys. Rev. B 75 073203

    [21]

    Na Phattalung S, Smith M F, Kim K, Du M H, Wei S H, Zhang S B, Limpijumnong S 2006 Phys. Rev. B 73 125205

    [22]

    Wang M, Feng M, Zuo X 2014 Appl. Surf. Sci. 292 475

    [23]

    Peng H 2008 Phys. Lett. A 372 1527

    [24]

    Mattioli G, Alippi P, Filippone F, Caminiti R, Amore Bonapasta A 2010 J. Phys. Chem. C 114 21694

    [25]

    Diebold U 2003 Surf. Sci. Rep. 48 53

    [26]

    de Graef M, Mchenry M E 2007 Structure of Materials:An Introduction to Crystallography, Diffraction and Symmetry (Cambridge:Cambridge University Press) p363

    [27]

    Santara B, Giri P K, Imakite K, Fujii M 2014 J. Phys. D:Appl. Phys. 47 215302

    [28]

    Morgan B J, Watson G W 2010 J. Phys. Chem. C 114 2321

    [29]

    Fakhim Lamrani A, Belaiche M, Benyoussef A, El Kenz A, Saidi E H 2010 J. Magn. Magn. Mater. 322 454

    [30]

    Lee H Y, Clark S J, Robertson J 2012 Phys. Rev. B 86 075209

    [31]

    Nolan M, Elliott S D, Mulley J S, Bennett R A, Basham M, Mulheran P 2008 Phys. Rev. B 77 235424

    [32]

    Henderson M A, Epling W S, Peden C H F, Perkins C L 2003 J. Phys. Chem. B 107 534

    [33]

    Yang S, Halliburton L E, Manivannan A, Bunton P H, Baker D B, Klemm M, Horn S, Fujishima A 2009 Appl. Phys. Lett. 94 162114

    [34]

    Santara B, Giri P K, Imakita K, Fujii M 2013 Nanoscale 5 5476

    [35]

    Yosida K 1998 Theory of Magnetism (Berlin:Springer-Verlag) pp87-89

    [36]

    Zhao L, Park S G, Magyari Köpe B, Nishi Y 2013 Math. Comput. Model. 58 275

    [37]

    Zhang Y, Qi Y Y, Hu Y H, Liang P 2013 Chin. Phys. B 22 127101

    [38]

    Rumaiz A K, Ali B, Ceylan A, Boggs M, Beebe T, Shah S I 2007 Solid State Commun. 144 334

    [39]

    Coey J M D, Stamenov P, Gunning R D, Venkatesan M, Paul K 2010 New J. Phys. 12 053025

    [40]

    Finazzi E, Di Valentin C, Pacchioni G 2009 J. Phys. Chem. C 113 3382

    [41]

    Lany S, Zunger A 2009 Phys. Rev. B 80 085202

    [42]

    Kamisaka H, Yamashita K 2011 J. Phys. Chem. C 115 8265

    [43]

    Mulheran P A, Nolan M, Browne C S, Basham M, Sanville E, Bennett R A 2010 Phys. Chem. Chem. Phys. 12 9763

    [44]

    Koudriachova M 2007 Phys. Status Solidi C 4 1205

    [45]

    Zhou S, Čžmár E, Potzger K, Krause M, Talut G, Helm M, Fassbender J, Zvyagin S A, Wosnitza J, Schmidt H 2009 Phys. Rev. B 79 113201

    [46]

    Lai L L, Wu J M 2015 Ceram. Int. 41 12317

    [47]

    Buchholz D B, Chang R P H, Song J Y, Ketterson J B 2005 Appl. Phys. Lett. 87 082504

    [48]

    Ye L H, Freeman A J, Delley B 2006 Phys. Rev. B 73 033203

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  • Received Date:  02 September 2016
  • Accepted Date:  12 October 2016
  • Published Online:  05 February 2017

A first-principles study on magnetic properties of the intrinsic defects in rutile TiO2

    Corresponding author: Li Gong-Ping, ligp@lzu.edu.cn
  • 1. School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China;
  • 2. Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11575074, 11304324) and the State Key Laboratory of Crystal Materials at Shandong University Open Foundation, China (Grant No. KF1311).

Abstract: The TiO2 based diluted magnetic semiconductors (DMSs) have aroused the considerable interest as one of the promising candidates for the spintronic devices accommodating both charge and spin of electrons in a single substance. Unfortunately, however, throughout most of the published papers, the question how to clearly elucidate the role of defects which may be played in the experimentally observed room temperature ferromagnetism (RTFM) remains open, especially after a new concept of d0 ferromagnetism. In such a case, to further understand this issue and also to explore the origin of the RTFM in rutile TiO2, we here first perform a first principles calculation on the magnetic properties of the intrinsic defects, namely oxygen vacancy (VO), Ti vacancy (VTi), Ti interstitial (Tiin), oxygen interstitial (Oin) and two complex defects of VO+Oin and VTi+Tiin. Combining the density functional theory and the Perdew-Burke-Ernzerhof functional of the generalized gradient approximation, we calculate various model structures of rutile TiO2 constituted by 48-atom 222 supercell. The cutoff energies in these calculations of the planewave basis are all set to be 340 eV and the Monkhorst-Pack scheme k points are set to be 334 for an irreducible Brillouin zone. The convergence threshold for self-consistent field iteration is 0.145510-6 eV/atom. Structural relaxation is taken into account in each of all calculations. It is found that each defect we created in the structure leads to a lattice expansion and that the positive value for spin up and the negative value for spin down of the density of states (DOS) of the structure without defect are symmetric, suggesting that the perfect rutile TiO2 lattice is nonferromagnetic. For the system with one VO, the total energy of the spin-polarized system is 200 meV lower than that of the non-spin-polarized system, which indicates ferromagnetic behavior in this system. The defect brings in an impurity state near Fermi level located at about 0.71.0 eV down below the conduction band, resulting in an excess of spin up over spin down for the presences of the two localized electrons left by the vacancy. At this point the supercell bears a magnetic moment of about 1.62 B. In contrast, VTi also brings in an impurity state near Fermi level but above the valence band, which reveals a p-type characteristic semiconductor nature. Since a lower total energy requires more spin-up electrons, the asymmetric DOS induces a magnetic moment of 2.47 B. When a neutral Ti occupies an interstitial lattice site, the system requires it to be oxidized into a Ti3+ ion to increase the stabilization of the system. The three delocalized electrons tend to occupy the 3d or 4s orbital of the neighbor Ti4+ ions and then have strong exchange interactions with the 2p electrons of the local O atom. This can distort octahedral symmetry and give rise to a ferromagnetic moment of 3.91 B. Oin defect in the supercell is extremely unstable. It can easily be reduced and escape from the host in terms of an oxygen molecule so that the system is in a manner similar to the perfect lattice, showing no ferromagnetism. It is interesting to note that the properties of the system with the complex defect of one VO and Oin are similar to that of the structure with one VO and the magnetic moment of this system is 1.63 B. For the Ticom complex defect, our results point out the fact that the magnetic properties of the supercell are related to the distance between VTi and Tiin. The spin up and spin down states are symmetric when they are close to each other, while, in addition to some ferromagnetic behavior, the system mainly exhibits antiferromagnetism when the distance increases.

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