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Density Functional Study of Boron-Doped Anatase TiO2 Kesong Yang, Ying Dai,* and Baibiao Huang School of Physics, State Key Laboratory of Crystal Materials, Shandong UniVersity, Jinan 250100, People’s Republic of China ReceiVed: August 26, 2010; ReVised Manuscript ReceiVed: October 5, 2010
Our first-principles calculations demonstrate that the substitutional B anion and B cation doped TiO2 both produce a spin magnetic moment of 1.0 µB despite their different mechanisms. The former is due to that the three electrons of B2- (s2p3) at the O site occupy the two low-energy B 2p orbitals preferentially, leaving an unpaired electron, whereas the later results from a hole in the O 2p orbital introduced by the replacement of B3+ for Ti4+. In addition, an alternative path to produce a magnetic ground state was proposed on the basis of the substitutional X-doped TiO2 with X@Ti (X ) B, Al, Ga, and In). 1. Introduction In recent years, so-called “d0” magnetism has challenged our conventional understanding of the origin of magnetism;1 that is, the magnetism is not caused by partially filled d orbitals. So far, experimental “d0” magnetism has been observed in two classes of semiconductor materials. One consists of such undoped oxides2-10 and nitrides11 as HfO2, In2O3, SnO2, TiO2, CeO2, Al2O3, ZnO, MgO, and GaN, and the other C- or N-doped oxides12-16 and C-doped nitrides.17 Correspondingly, numerous theoretical attempts have also been made to understand the origin of “d0” magnetism.18-22 It has been widely accepted that the former is probably due to the cation vacancies, which introduce some holes in O 2p or N 2p orbitals with spin magnetic moments,18-20 though the cation vacancies are difficult to form owing to the large formation energy. In contrast, the later is because the electronegativity of the host anion in the semiconductor is weaker than the substitutional dopant, which introduces sufficient holes in the 2p orbitals of the dopant and results in the spontaneous spin-polarization.18,21,22 Consequently, the spinpolarization could be found in lots of 2p-light element doped oxides and nitrides. However, most of these 2p-light elements are focused on C and N elements.23-30 Lately, Peng et al. studied the substitutional Be- and B-doped AlN and ZnO besides C and N and concluded that the magnetic moment per dopant in µB is the atomic number difference between the dopant and host anion atom, and thus, the spin moments of 2.0 and 3.0 µB were obtained in B-doped wurtzite-type AlN and ZnO, respectively.21 As a consequence, it can be inferred that a spin-polarization ground state could also be obtained in substitutional B anion doped TiO2.31 Although numerous experimental attempts were made to improve the optical absorption and photocatalytic activity of boron-doped TiO2,32-34 few studies have been done on its magnetic property. Particularly, it should be noted that the symmetry of the local crystal structure of TiO2 is different from that of wurtzite-type ZnO (BTi3 vs BZn4, C2V vs Td symmetry), and this will result in a different splitting behavior of B 2p orbitals. A different spin magnetic moment may then be obtained. Therefore, a clear understanding of the magnetic * To whom correspondence should be addressed. E-mail: daiy60@ sina.com.
property of B-doped TiO2 as well as the relationship between the spin moment and symmetry of the local crystal structure is essential. In principle, substitutional boron-doped TiO2 has two possible ways, that is, B at the O site (B@O) and B at the Ti site (B@Ti). Substitutional B-doped TiO2 with B@O and an interstitial B-doped structure forming a Ti-O-B chemical environment have been reported in experiments,32-34 but a typical substitutional B-doped TiO2 with B@Ti has not been observed yet. However, it is a general consensus that, in doped TiO2 with a main group nonmetal element (except high-electronegativity fluorine and low-electronegativity silicon), replacing an O atom is energetically preferable under Ti-rich conditions, and replacing a Ti atom is energetically preferable under O-rich conditions.35,36 Therefore, a substitutional B-doped TiO2 with B@Ti is also expected to form under O-rich conditions. In this work, we studied the magnetic properties of B-doped TiO2 with B@O and B@Ti and found that the substitution of B3+ for Ti4+ could produce a spin magnetic moment of 1.0 µB, resulting from a hole in the O 2p orbital, and we further proposed an alternative path to produce a magnetic ground state on the basis of the substitutional X-doped TiO2 with X@Ti (X ) B, Al, Ga, and In). Therefore, it is expected that this work will provide some new insights into the preparation of ferromagnetic materials. Besides this, we also demonstrate the magnetic property of substitutional B anion doped TiO2 and found that the mechanism of its spin-polarized electronic states is different from that of B cation doped TiO2. 2. Computational Details We simulated substitutional B-doped TiO2 using a 48-atom 2 × 2 × 1 supercell, shown in Figure 1. B-doped TiO2 with B@O was modeled by replacing one O atom with one B atom, and this is equal to a doping level about 3.13%, which is comparable to the experimental doping concentration of 3.23%.33 B-doped TiO2 with B@Ti was modeled by replacing one Ti atom with one B atom, which corresponds to a doping level of 6.25%. The ultrasoft pseudopotential was used for electron-ion interactions and the generalized gradient approximation (GGA) parametrized by Perdew and Wang (PW91) was used for the exchange-correlation functional.37,38 The cutoff energy of 400 eV for the plane-wave basis set and a 2 × 2 × 2 k-point set centered at the Γ point were used to reproduce the accurate
10.1021/jp108092h 2010 American Chemical Society Published on Web 11/01/2010
Density Functional Study of Boron-Doped Anatase TiO2
Figure 1. 48-atom 2 × 2 × 1 supercell of the anatase phase employed to define substitutional B anion doped TiO2. The larger and small spheres represent the Ti and O atoms, respectively. The O atoms labeled 0-9 are the sites to be replaced with B atoms.
Figure 2. (a) Total DOS plot of one-B doped anatase TiO2. (b) Partial DOS plot of the B 2px, B 2py, and B 2pz states. (c) Partial DOS plot of Ti 3d states. The dotted line represents the Fermi level at 0 eV. To make the impurity states more visible, the intensity of the integral B 2p states in (a) was multiplied by a factor 10.
results.25 The atomic positions of the doped structures were relaxed by performing first-principles spin-polarized DFT electronic structure calculations with the Vienna Ab inito Simulation Package.39,40 All the atomic positions were fully optimized until all components of the residual forces were smaller than 0.025 eV/Å, and the convergence threshold for self-consistent-field iteration was set at 10-6 eV. The density of states (DOS) of the B-doped TiO2 structure was obtained by the tetrahedron method with the Blo¨chl correction. 3. Results and Discussion 3.1. B-Doped TiO2 with B@O. The calculated total density of states (TDOS) and partial DOS for one-B-atom doped anatase TiO2 with B@O are presented in Figure 2. The intensity of the integral B 2p states in Figure 2a was multiplied by a factor of 10 to make the impurity states more visible. As in the case of C- and N-doped TiO2,24,25 the substitution of B for O results in an obvious spin-polarization. Most of the B 2p states are localized in the band gap just below the conduction band, and the Fermi level is pinned in the middle of the states, thus indicating a metallic property of the B-doped TiO2. The interaction between the B dopant and adjacent Ti atoms results in a strong hybridization of B 2p states and Ti 3d states, and the induced spin-polarized B 2p states also lead to a spinsplitting behavior of Ti 3d states of adjacent titanium atoms
J. Phys. Chem. C, Vol. 114, No. 46, 2010 19831 around the B dopant, which is shown in Figure 2c. This indicates that the magnetic orbital describing the B center extends to the adjacent Ti atoms, and the spin density plot (not shown here) of one-B doped TiO2 also shows that most of the spin density is contributed by the B dopant and three adjacent Ti. With respect to the local Cartesian coordinate defined in Figure 1, the up-spin and down-spin B 2px states as well as the up-spin B 2pz states are both occupied, but the up-spin and down-spin B 2py states and down-spin B 2pz states are not. This indicates that the doped B ion in anatase TiO2 should have its electron configuration like the B2- (s2p3) anion, thus leading to a net magnetic moment of 1.0 µB. Further test calculations for the substitutional B-doped 216-atom 3 × 3 × 2 TiO2 supercell show nearly the same spin-polarized electronic characteristics, indicating that the spin-polarization is due to the intrinsic property of B-doped TiO2 rather than the interaction between the dopants. Furthermore, nonspin-polarized DFT calculations carried out for one-B-atom doped TiO2 show that the spin-polarized state is more stable than the nonspin-polarized state by about 71 meV, thereby indicating that the ground state of B-doped TiO2 should be magnetic. These results are in good agreement with the experimentally observed boron-based paramagnetic species induced by the unpaired B 2p electrons through an electron paramagnetic resonance (EPR) study.41 It is worthwhile to mention that the calculated spin magnetic moment of B-doped TiO2 is different from that of B-doped ZnO in which a magnetic moment of 3.0 µB per B dopant was obtained,21 though the doped B dopants both replace O atoms, and the authors concluded that the magnetic moment per dopant (in µB) is equal to the difference of the atomic numbers of the dopant and the substituted atom in light of their theoretical calculations for AlN- and ZnO-based semiconductors.21 However, we carried out further fixed-spin-moment calculations for one-B-atom doped anatase TiO2 (with fixed moments of 1, 2, and 3 µB on B) and confirmed that the lowest total energy occurs when the B dopant has 1.0 µB. Therefore, our theoretical calculations for B-doped TiO2 do not support the conclusion mentioned above. This discrepancy is due to the fact that the TiO2 and ZnO have different local crystal structures around the boron dopant. In boron-doped ZnO, the local BZn4 has a local Td symmetry and three electrons of B2- (s2p3) occupy the 3-fold degenerate p orbital in the Td surroundings, thus generating a magnetic moment of 3.0 µB. In boron-doped TiO2, the “Tshaped” BTi3 local structure has a local C2V symmetry and thus the 3-fold degenerate p orbitals of the B atom will be split into three nondegenerate energy levels. The three electrons of B2(s2p3) will occupy the lower-energy pz and px orbitals preferably, thus producing a magnetic moment of 1.0 µB, which is reflected in Figure 2b. As a consequence, besides the difference in the fundamental properties between the dopant and the host anion, the symmetry of the local structure is also an important and nonignorable factor to judge the generated spin magnetic moment. Next, to examine the magnetic coupling interaction between two spin-polarized B2- ions in B-doped anatase TiO2, we considered 10 different unique arrangements of two-B-atom doped models (using a 48-atom 2 × 2 × 1 anatase phase supercell) as in the case of C- and N-doped TiO2. The relative positions of the two B atoms are shown in terms of 10 O positions, labeled 0-9, in Figure 1. The 10 different configurations are obtained by replacing two B for the two O positions at (0,1), (0,2), (0,3), (0,4), (0,5), (0,7), (0,8), (0,9), (1,6), and (3,8). These structures are labeled as (i,j) for convenience. To evaluate the relative stability of the ferromagnetic and antifer-
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TABLE 1: Values of the B · · · B Distance, the Relative Energies, E and Emag, and the Total Magnetic Moment under Ferromagnetic Alignment Per Cell Calculated for the (i,j) Structure of the Two-B-Atom Doped Anatase TiO2a (i,j)
B · · · B (Å)
∆E (eV)
Emag (meV)
(µB)
(0,1) (0,2) (0,3) (0,4) (0,5) (1,6) (0,7) (0,8) (0,9) (3,8)
1.498 1.479 1.700 1.525 3.776 3.776 4.321 4.870 6.064 6.992
1.46 1.04 0.00 2.19 6.99 6.37 6.20 1.51 0.69 7.14
0 0 0 0 -27 17 0 0 0 8
0 0 0 0 2.2 2.0 0 0 0 2.0
a
For each (i,j) structure, the energy of the lower-energy state (either FM or AFM) is given with respect to that of the (0,1) structure; i.e., ∆E ) E (i,j) - E (0,3). For each (i,j) structure, the energy of the FM state is given with respect to that of the AFM state; i.e., Emag ) E (FM) - E (AFM).
romagnetic alignments between the magnetic moments around the two B dopants, further spin-polarized calculations are carried out for the parallel and antiparallel arrangements of the spin magnetic moments on the two B ions. For each structure, the optimized B · · · B distances of two-B-atom doped anatase and the relative energy ∆E (the lower-energy state, i.e., the FM or AFM state, was used) with respect to the energy of the (0,3) structure are listed in Table 1. Also listed for each (i,j) configuration are the relative energy Emag of the FM state with respect to that of the AFM states, Emag ) E (FM) - E (AFM), and the total magnetic moment under ferromagnetic alignment of the supercell. Table 1 shows that the structures (0,1), (0,2), (0,3), and (0,4), in which the B · · · B distances are much closer to the typical bond length of a boron cluster (1.48-1.7 Å),42 are nonmagnetic. These structures are relatively more stable than other magnetic structures [(0,5), (1,6), and (3,8)], indicating that the B atoms prefer to form a cluster through direct BB bonding interactions. In fact, the clustering of boron has been widely reported in silicon,43,44 and the clustering of dopants was found in the case of C-doped ZnO12 and TiO2,24 indicating that it may be a general trend to form a cluster for dopants. For the structures (0,8) and (0,9), the doped boron atoms are displaced from the oxygen sites after geometrical relaxation, forming an interstitial B-like structure, and the spin magnetic moment vanishes. It is also noted that energy differences ∆E of the (0,8) and (0,9) configurations are close to those of (0,1), (0,2), and (0,3) configurations, thus indicating that the interstitial B-doped structures are also relatively easy to form, as in the case of the previous theoretical calculations.45 These interstitial boron structures are in good agreement with Chen et al.’s experiments in which a possible chemical structure like Ti-O-B induced by interstitial B doping was found.34 As shown by the results listed in Table 1, with respect to the C- and N-doped ZnO12,23 and TiO2,24-26,46 the coupling interaction between the magnetic orbitals of boron ions is very weak. For the (0,5) structure, the FM state is more stable than the AFM state by 27 meV, whereas the AFM state is energetically preferred for the (1,6) structure by 17 meV; the magnetic energy difference becomes negligible for the (3,8) configuration in which the B · · · B distance is close to 7 Å. The three-dimensional spin density distribution plots around each B site for the (0,5) and (1,6) structures are shown in Figure 3a,b, respectively. For the (0,5) configuration, the magnetic orbitals of the two B dopants have a substantial
Figure 3. Spin density distribution of two-B-atom doped anatase TiO2: (a) FM coupling for the (0,5) structure and (b) AFM coupling for the (1,6) structure.
Figure 4. Calculated total DOS plot of substitutional B cation doped anatase TiO2. The dotted line represents the Fermi level at 0 eV.
through-space π-type spin superexchange interaction, thereby causing an FM coupling, and a direct through-space overlap via the middle Ti ion takes place in the (1,6) configuration, thus leading to an AFM coupling. For the (0,7) configuration, two boron atoms form a linear B-Ti-B structure, and the total spin moment is reduced to zero, similar to the case of the linear C-Ti-C configuration in carbon-doped TiO2,24 in which the total spin moment under ferromagnetic alignment is reduced to 2.0 µB from 4.0 µB. Therefore, our calculated results indicate that the B anion doping may be not an effective way to produce d0 ferromagnetism in TiO2. 3.2. B-Doped TiO2 with B@Ti. To examine the electronic and magnetic properties of B cation doped TiO2, the DOS of substitutional B-doped TiO2 with the B@Ti site is calculated and shown in Figure 4. It is found that the valence band is spinpolarized and the Fermi level crosses the down-spin states, resulting in a spin magnetic moment of 1.0 µB and a half-metallic property. The electronic characteristic is similar to the case of undoped TiO2 with a Ti vacancy despite the different spin magnetic moment. This indicates that the doped B has an electron configuration resembling that of a B3+ (1s22s02p0) cation, and the replacement of B3+ for Ti4+ introduces one hole in the O 2p orbital, that is, producing an unpaired electron, thus generating the spin moment of 1.0 µB. In addition, our calculations for substitutional X3+-doped TiO2 (X ) Al, Ga, and In) also show the similar spin-polarized electronic state and a spin moment of 1.0 µB is obtained, and further calculations for substitutional cation doping in TiO2 by alkali metals of group
Density Functional Study of Boron-Doped Anatase TiO2
J. Phys. Chem. C, Vol. 114, No. 46, 2010 19833 with Al (Ga, In)@Ti is even lower than that of an oxygen vacancy, indicating that it is more effective to substitute the Ti using a less electronegative X atom. Therefore, our proposed alternative path to produce a magnetic ground state in TiO2 by substituting the Ti4+ with a low-valence-state cation may be more effective than producing the isolated Ti vacancy with a high formation energy. 4. Conclusions
Figure 5. Formation energies as a function of the oxygen chemical potential (µO) for substitutional B (Al, Ga, and In)-doped TiO2 and undoped TiO2 with a Ti vacancy.
I and alkaline earth metals of group II indicate that three and two holes are introduced in the O 2p orbitals, and spin moments of 3.0 µB and 2.0 µB are obtained, respectively. As a result, our results indicate that the substitutional doping by low-valencestate cations in oxides could introduce some holes in O 2p orbitals and induce a spin-polarized ground state, and the calculated magnetic moment per dopant (in µB) is the valence state difference between the dopant and the host cation. Therefore, our theoretical study provides a possible alternative route to produce the ferromagnetism rather than using the isolated cation vacancies, and this rule could be expanded into other oxides or nitrides. Next, we assess the relative stability of an isolated Ti vacancy and X3+-doped structures (X ) B, Al, Ga, and In) by comparing their formation energies, which are calculated from Ef ) Edef - Ebulk + µTi and Ef ) Edef - Ebulk + µTi - µX, respectively. Edef (Ebulk) is the total energy of the anatase TiO2 with (without) defects, whereas µXand µTi are the chemical potentials of the substitutional dopants (X ) B, Al, Ga, and In) and Ti. The chemical potential µTi depends on whether TiO2 is grown under O-rich or Ti-rich growth conditions,47 and µX was obtained according to µX ) (1/2)µ(X2O3) - (3/4)µ(O2). The calculated formation energies are shown as a function of the oxygen chemical potential (µO) in Figure 5. It should be noted that an absolute value of the oxygen chemical potential in the x axis was used, whereas µO ) -5 eV corresponds to the oxygenrich limit and µO ) -9.6 eV corresponds to the oxygen-poor limit. We could obtain the following conclusions according to the change trend of the formation energies: (1) Although the formation of an isolated titanium vacancy is energetically more favorable under the O-rich than under the O-poor growth condition, its formation energy is still much larger than that of an oxygen vacancy for the entire range of oxygen chemical potentials, indicating that the formation of a titanium vacancy is much more difficult than an oxygen vacancy. (2) The formation energy of substitutional X-doped TiO2 with X@Ti is much smaller than that of an isolated titanium vacancy under both O-poor and O-rich growth conditions, indicating that the substitutional doping of X@Ti is more favorable than an isolated titanium vacancy. (3) For X-doped TiO2 with X@Ti, the doping is energetically preferred under the O-rich than O-poor growth condition and becomes easier from B to Al, Ga, and In. In addition, under O-rich growth conditions, the formation energy of doped TiO2
We studied the electronic and magnetic properties of substitutional B-doped anatase TiO2 with B@O and B@Ti, respectively. It is found that substitutional B anion and B cation doped TiO2 both produce a spin magnetic moment of 1.0 µB, though their origins are different. For substitutional B anion doped TiO2, the three electrons of B2- (s2p3) at the O site occupy the two low-energy degenerate B 2p orbitals, thus resulting in a spin moment of 1.0 µB. For substitutional B cation doped TiO2, the replacement of B3+ for Ti4+ introduces a hole in the O 2p orbital and leads to a spontaneous spin-polarization. In addition, we also proposed an alternative path to produce a magnetic ground state by replacing the Ti4+ ion using a low-valence-state cation, and the generated spin moment per dopant (in µB) should be the valence state difference between the dopant and the host cation. Acknowledgment. This work is supported by the National Science Foundation of China under Grant Nos. 10774091 and 20973102, the National Basic Research Program of China (973 program, 2007CB613302), and the Natural Science Foundation of Shandong Province under Grant No. Y2007A18. References and Notes (1) Coey, J. M. D. Solid State Sci. 2005, 7, 660. (2) Venkatesan, M.; Fitzgerald, C. B.; Coey, J. M. D. Nature 2004, 430, 630. (3) Hong, N. H.; Sakai, J.; Poirot, N.; Brize´, V. Phys. ReV. B 2006, 73, 132404. (4) Hong, N. H.; Poirot, N.; Sakai, J. Phys. ReV. B 2008, 77, 033205. (5) Hassini, A.; Sakai, J.; Lopez, J. S.; Hong, N. H. Phys. Lett. A 2008, 372, 3299. (6) Yoon, S. D.; Chen, Y.; Yang, A.; Goodrich, T. L.; Zuo, X.; Arena, D. A.; Ziemer, K.; Vittoria, C.; Harris, V. G. J. Phys.: Condens. Matter 2006, 18, L355. (7) Yoon, S. D.; Chen, Y.; Yang, A.; Goodrich, T. L.; Zuo, X.; Ziemer, K.; Vittoria, C.; Harris, V. G. J. Magn. Magn. Mater. 2007, 309, 171. (8) Rumaiz, A. K.; Ali, B.; Ceylan, A.; Boggs, M.; Beebe, T.; Shah, S. I. Solid State Commun. 2007, 144, 334. (9) Sundaresan, A.; Bhargavi, R.; Rangarajan, N.; Siddesh, U.; Rao, C. N. R. Phys. ReV. B 2006, 74, 161306. (10) Sundaresan, A.; Rao, C. N. R. Nano Today 2009, 4, 96. (11) Madhu, C.; Sundaresan, A.; Rao, C. N. R. Phys. ReV. B 2008, 77, 201306(R). (12) Pan, H.; Yi, J. B.; Shen, L.; Wu, R. Q.; Yang, J. H.; Lin, J. Y.; Feng, Y. P.; Ding, J.; Van, L. H.; Yin, J. H. Phys. ReV. Lett. 2007, 99, 127201. (13) Yu, C.-F.; Lin, T.-J.; Sun, S.-J.; Chou, H. J. Phys. D: Appl. Phys. 2007, 40, 6497. (14) Zhou, S.; Xu, Q.; Potzger, K.; Talut, G.; Gro¨tzschel, R.; Fassbender, J.; Vinnichenko, M.; Grenzer, J.; Helm, M.; Hochmuth, H.; Lorenz, M.; Grundmann, M.; Schmidt, H. Appl. Phys. Lett. 2008, 93, 232507. (15) Ye, X. J.; Zhong, W.; Xu, M. H.; Qi, X. S.; Au, C. T.; Du, Y. W. Phys. Lett. A 2009, 373, 3684. (16) Wen, Q.-Y.; Zhang, H.-W.; Yang, Q.-H.; Gu, D.-E.; Li, Y.-X.; Liu, Y.-L.; Shen, J.; Xiao, J. Q. IEEE Trans. Magn. 2009, 45, 4096. (17) Yu, L.; Wang, Z.; Guo, M.; Liu, D.; Dai, Y.; Huang, B. Chem. Phys. Lett. 2010, 487, 251. (18) Peng, H.; Xiang, H. J.; Wei, S.-H.; Li, S.-S.; Xia, J.-B.; Li, J. Phys. ReV. Lett. 2009, 102, 017201. (19) Pemmaraju, C. D.; Sanvito, S. Phys. ReV. Lett. 2005, 94, 217205. (20) Dev, P.; Xue, Y.; Zhang, P. Phys. ReV. Lett. 2008, 100, 117204. (21) Peng, X.; Ahuja, R. Appl. Phys. Lett. 2009, 94, 102504. (22) Yang, K.; Wu, R.; Shen, L.; Feng, Y. P.; Dai, Y.; Huang, B. Phys. ReV. B 2010, 81, 125211.
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