Electronic and magnetic properties of early transition

Electronic and magnetic properties of early transition-metal substituted iron-cyclopentadienyl sandwich molecular wires: Parity-dependent halfmetallicity Yuanchang Li, Gang Zhou, Jian Wu, and Wenhui Duan Citation: J. Chem. Phys. 135, 014702 (2011); doi: 10.1063/1.3604817 View online: http://dx.doi.org/10.1063/1.3604817 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v135/i1 Published by the AIP Publishing LLC.

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THE JOURNAL OF CHEMICAL PHYSICS 135, 014702 (2011)

Electronic and magnetic properties of early transition-metal substituted iron-cyclopentadienyl sandwich molecular wires: Parity-dependent half-metallicity Yuanchang Li, Gang Zhou, Jian Wu, and Wenhui Duana) Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China

(Received 13 February 2011; accepted 7 June 2011; published online 1 July 2011) Electronic and magnetic properties of early transition metals (V, Ti, Sc)-Fek Cpk+1 sandwich molecular wires (SMWs) are investigated by means of ab initio calculations. It is found that all SMWs favor a ferromagnetic ground state. Significantly, V-Fek Cpk+1 SMWs are either half-metallic or semiconducting, dependent upon the parity (even or odd) of the number (k) of Fe atoms in the unit cell of SMWs. This parity oscillation of conductive properties results from the combined effects of the bandfolding and gap-opening at the Brillouin-zone boundary of one-dimensional materials. In contrast, Sc-Fek Cpk+1 and Ti-Fek Cpk+1 SMWs are always semiconducting. Our work may open up the way toward half metal/semiconductor heterostructures with perfect atomic interface. © 2011 American Institute of Physics. [doi:10.1063/1.3604817] I. INTRODUCTION

Molecular magnets are intensively studied during the last decade due to the observed quantum phenomena1–4 and their potential applications in quantum computing and information storage technologies.5–9 With the recent discovery of magnetic metal-benzene sandwich clusters Mn (C6 H6 )m (M = Al, Sc, Ti, and V),10, 11 linear transition metal (TM)-ligand complexes have received increasing attention. They not only have promising improved performance and enhanced functionality for next-generation spintronic devices, but also possess the advantages of normal organic materials (e.g., cheap, low-weight, and mechanically flexible). Subsequent theoretical studies showed that quasi-one-dimensional organometallic sandwich molecular wires (SMWs), such as transition metal-benzene, -cyclopentadienyl (Cp) and -fullerenes, do exhibit spin filter effects and half-metallicity.12–19 On the other hand, doping provides a viable way to tailor the properties of nanomaterials for new applications.20 An improved two-laser vaporization, for example, made it realistic to dope titanium (Ti) or vanadium (V) species into grown iron-cyclopentadienyl (FeCp) complexes,21 forming different metal centers. In this perspective, the constituent metal species and their ratio then play an essential role in determining their quantum properties. Currently, information on the structures and properties of doped TMFek Cpk+1 SMWs is very limited, except for a few reports on TM-FeCp2 (TM = Sc, Ti, V, and Mn) SMWs.17, 22 Although both VCp and FeCp SMWs are half-metallic,15 VFeCp2 SMW is semiconducting.17, 22 In other words, there must exist a complex interaction between different TM species centers, which frustrates their own half-metallicity. Understanding this interaction and the underlying physical mechanism is significant for manipulating the electronic and magnetic properties of such one-dimensional materials. a) Author to whom correspondence should be addressed. Electronic mail.

[email protected]. 0021-9606/2011/135(1)/014702/5/$30.00

In this work, we systematically studied electronic and magnetic properties of early transition metal (TM = V, Sc, and Ti)-doped FeCp SMWs and explored the underlying mechanism using ab initio calculations. We found that Sc-Fek Cpk+1 and Ti-Fek Cpk+1 SMWs are ferromagnetic semiconductor, while V-Fek Cpk+1 SMWs are either ferromagnetic half-metal or semiconductor with the variation of doping concentration. As a result, promising halfmetal/semiconductor junctions with ideal heterointerface can be obtained for spintronic devices.

II. METHODOLOGICAL DETAILS AND MODEL

All structure optimizations and total energy calculations are performed within the framework of spin-polarized density functional theory as implemented in the Vienna ab initio simulation package.23 The exchange-correlation energy and the electron-ion interaction are described, respectively, by the Perdew-Burke-Ernzerhof 24 generalized gradient approximation and the projector-augmented wave25 potential. A supercell model with the periodical boundary condition is adopted. The separation between the two neighboring SMWs is at least 10 Å, which is sufficient to make interwire interaction negligible. All structure optimizations are made without any symmetry constraint until the residual force on each atom is less than 0.01 eV/Å. Local magnetic moments are calculated using Bader analysis.26 The binding energy of TM-Fek Cpk+1 SMW is defined as E b = E TM−Fek Cpk+1 − E TM − E Fek Cpk+1 , where E TM , E Fek Cpk+1 , and E TM−Fek Cpk+1 are, respectively, the total energies of the TM atom, Fek Cpk+1 complex, and formed SMW. A negative value of E b means an exothermic reaction, implying the formed SMW is more stable than separate TM and Fek Cpk+1 .

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J. Chem. Phys. 135, 014702 (2011) Unit cell of V-Fe5Cp6 SMW

Cp1

Fe1

Fe2

Fe3

Fe2

Fe1

Cp2

Cp3

Cp4

Cp3

Cp2

Cp1

Unit cell of V-Fe6Cp7 SMW

FIG. 1. Selected representatives of two kinds of one-dimensional SMWs with different symmetry planes. Top: V-Fe5 Cp6 SMW, with the mirror plane through Fe; down: V-Fe6 Cp7 SMW, with the mirror plane through Cp. Red, purple, cyan, and white balls denote carbon, iron, vanadium, and hydrogen, respectively. The region between two adjacent V atoms indicates the unit cell. The dashed lines denote the mirror symmetry planes.

III. RESULTS AND DISCUSSION

According to the parity (odd or even) of k, TM-Fek Cpk+1 SMWs can be divided into two classes with different mirror symmetry planes [i.e., the planes through Fe (odd k) or Cp (even k)]. As an example, geometries of V-Fe5 Cp6 and V-Fe6 Cp7 SWMs are shown in Fig. 1, where the Fe atoms and Cps are denoted by the distance from the V atom as Fe1 , Fe2 , Fe3 , and Cp1 , . . ., Cp4 . Note that both two classes of SMWs have the same D5h symmetry. Table I shows structural, electronic, and magnetic properties of a series of V-Fek Cpk+1 SMWs (k = 1–6), with the V concentration of 50%, 33.3%, 25%, 20%, 16.7%, and 14.3%.27 It is found that the segment of Fek Cpk+1 in the V-Fek Cpk+1 SMWs is elongated in comparison to isolated Fek Cpk+1 molecule, but such an elongation decreases with the increase of k. Simultaneously, the C–C bonds in Cp rings are also stretched, which occurs in organometallic complexes frequently.28 Relative stabilities of the doped SMWs can be evaluated in terms of the binding energy E b . Except for V-FeCp2 SMW, all the other five SMWs have larger E b than 3.0 eV (see Table I). The relatively small E b (∼ 2.79 eV) of V-FeCp2 SMW is due to the hyperstability of ferrocene, which satisfies the 18-electron rule. Note that V-FeCp2 complexes have been successfully assembled.21 Our energetics results indicate the feasibility of synthesizing V-Fek Cpk+1 SMWs. From Table I, it is interesting to find that the SMWs with even k are half-metallic, substantially distinct from the semiconducting character of the SMWs with odd k. In other words, half-metallicity exhibits a peculiar odd-even oscillatory be-

havior with respect to k. The half-metal energy gaps29 are 0.37, 0.35, and 0.34 eV for k = 2, 4, and 6, respectively, showing a decreasing trend with increasing k. Due to strong crystal field of the D5h symmetry, 3d orbitals of TM atoms split into 2-fold degenerate dxy and dx2 −y2 orbitals (e2 ), a singlet dz2 orbital (a1 ), and 2-fold degenerate dxz and dyz orbitals (e1 ).14–16 Projected density of states (PDOS) of TM 3d orbitals (e2 , e1 , and a1 ) of VFeCp2 and VFe2 Cp3 SMWs are shown in Fig. 2, which typically represent the characters for the odd-/evennumbered SMWs (i.e., k is odd/even). Our detailed molecular orbital analysis shows that the bands across the Fermi level in even-numbered VFe2 Cp3 SMW are composed of 85% Fe and V e1 orbitals (see Fig. 2(b)), and 15% Cp 2 p orbitals (not shown in the figure), indicating the dominant contribution of the TM 3d orbitals. Furthermore, V exhibits similar behavior both in the odd- and even-numbered SMWs. Its contributions to PDOS are always in majority spin, and its three electron states (one a1 and two e2 ) have nearly the same energy, locating at 1.5–1 eV below the Fermi level. This PDOS distribution is like the case of VCp2 molecule. More importantly, the distance between the two Cp rings adjacent to V is very close to that in the VCp2 molecule, as if V-Fek Cpk+1 was composed of Fek Cpk−1 and VCp2 alternatively, rather than the Fek Cpk+1 and V. This implies that the behavior of the host Fe atoms will be affected significantly. It should be noted that in VCp SMW, the e2 orbitals of the V are the highest occupied orbitals,15 while the e1 level is fully unoccupied. However, in V-Fek Cpk+1 SMWs with even k, V’s minority-spin electrons transfer from a1 and e2 orbitals to Cps, filling the π orbitals then forming a stable aromatic configuration such as benzene, and simultaneously, some electrons are transferred from organic ligand to V’s empty e1 orbitals. Such a donation/backdonation mechanism results in considerable electron hopping from the occupied a1 and e2 orbitals to the empty high-lying e1 orbitals, leading to a finite DOS at the Fermi level. This substantial difference from the VCp SMW also reveals the sophisticated interaction between the impurity V and the host Fe atoms. As shown in Table I, all the six V-Fek Cpk+1 SMWs exhibit a ferromagnetic ground state with an integer magnetic moment per unit cell. Starting from 5 μ B of V-FeCp2 , the total magnetic moment uniformly increases by 1 μ B when one more “FeCp” unit is added to the supercell. The coupling between the TMs is always ferromagnetic. Although all the local moments on V atoms are close to 3 μ B , they are different on Fe atoms: the local moments on the two equivalent Fe1 atoms, which share the same Cp ring with the V atom (see Fig. 1), are

TABLE I. Optimized lattice constant (c), binding energy (E b ), total magnetic moment per unit cell (M), local moment on V (MV ), sum of local moment on Fe atoms (MFe ), half-metal energy gap (), band gaps for majority (maj ), and minority (min ) spin for one-dimensional V-Fek Cpk+1 SMWs. System V-FeCp2 V-Fe2 Cp3 V-Fe3 Cp4 V-Fe4 Cp5 V-Fe5 Cp6 V-Fe6 Cp7

c (Å)

E b (eV)

M (μ B )

MV (μ B )

MFe (μ B )

HM

7.368 10.768 14.155 17.590 20.989 24.395

−2.79 −3.14 −3.02 −3.10 −3.02 −3.07

5 6 7 8 9 10

3.0 3.1 2.8 3.0 2.8 2.9

2.0 3.0 4.3 5.0 6.3 7.2

no yes no yes no yes

(eV)

0.37 0.35 0.34

maj (eV)

min (eV)

1.95 metallic 1.34 metallic 0.98 metallic

1.50 1.44 1.36 1.19 1.07 0.96


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Fe

2

2

0

0

-2 -4

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4 2

2

e2 e1 a1

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e2 e1 a1

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e1

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J. Chem. Phys. 135, 014702 (2011)

-2

0

M

Γ

e1

-1

0

1

2

FIG. 2. Projected density of states (PDOS) of Fe/V 3d orbitals (e2 , e1 , and a1 ) of (a) VFeCp2 and (b) VFe2 Cp3 SMWs, which typically represent the characters for the odd-/even-numbered SMWs. The Fermi level (red dashed line) is set at zero.

both about 1.5 μ B ; while they are nearly 1.0 μ B on the other Fe atoms. The long-range ferromagnetism in such systems is mainly due to the spin exchange coupling interaction between the valence electrons of V/Fe and the 2p electrons of Cp.15, 30 Then, we turn to the physical origin of the odd-even oscillatory behavior of electronic properties of SMWs (i.e., the oscillation between the half-metallic and semiconducting properties). TM-Fek Cpk+1 SMW can be considered to be formed by substitutionally doping one TM atom in the supercell of k + 1 unit cells of FeCp SMW. Therefore, the band structure of TM-Fek Cpk+1 SMW can be analyzed in terms of doping effect on the folded band structure of host FeCp SMW (note: different k corresponds to different Brillouin-zone folding). In principle, a perturbation to the system has its major effects on only those electronic states near the Brillouin-zone boundary, which may lead to the degeneracy removal and gap opening.31 Previous works14, 16 and our calculations have both shown that FeCp SMW is a half-metal: its minority-spin channel is semiconducting with fully occupied e2 and a1 orbitals around the Fermi level and a visible gap; while the majority-spin channel is metallic, where e2 and a1 orbitals are fully filled and e1 orbitals crossing the Fermi level are partially occupied. For this reason, we only focus on the majority-spin band structure in the following. Taking the simplest V-FeCp2 and V-Fe2 Cp3 as representatives of the odd-k and even-k SMWs, we schematically show semiconducting and half-metallic characteristics in Fig. 3. The left panel of Fig. 3 corresponds to the majority-spin bands of FeCp SMW. For V-FeCp2 , the host bands (corresponding to Fe2 Cp2 ) fold at the M point and the folded band structure is shown in the top of the middle panel of Fig. 3. It can be seen that now the Fermi level is just at the folded Brillouin-zone boundary (i.e., the X point), where the two subbands of e1 orbitals are degenerate. The substitution of the V for Fe will lower the symmetry (and perturb the crystal field) of the system and thus lift the degeneracy at the boundary of the Brillouin zone. In principle, such a degeneracy-lift effect is universal for TM doping into FeCp SMWs. Thus, a gap is opened at the X point (see the top of the

Γ

X

X

Γ

X

e1

-1

Energy (eV)

X

e1 -2 Γ

e1 X Γ

FIG. 3. Schematic representation of band-folding and impurity doping leading to the odd-even oscillatory behavior. Only the majority spin channel responsible for half-metallicity is shown, since the minority spin channel is always semiconducting. Left: majority spin channel of the host FeCp SMW. The e1 state of the Fe crosses the Fermi level and the M denotes the middle point between and X . Middle: folded majority spin bands for host SMWs with the supercell containing two (top)/three (bottom) unit cells, qualitatively corresponding to the situations of SMWs with odd/even k. Right: majority spin bands for V-FeCp (top) and V-Fe2 Cp3 (bottom) where V-doping lifts the degeneracy at the Brillouin-zone boundary.

right panel of Fig. 3), and V-FeCp2 shows semiconducting behavior. In contrast, for V-Fe2 Cp3 , the host bands fold at (1/3) and (2/3) of original X, and the resulting bands are shown in the bottom of the middle panel of Fig. 3. A basic feature is that the subband of e1 orbitals crosses the Fermi level at the middle of the folded Brillouin zone, which will not be influenced by the doping-induced degeneracy removal (or gap-opening) at the Brillioun-zone boundary (see the bottom of the right panel of Fig. 3). Therefore, the half-metallicity is always preserved. In a word, if the host bands fold at M point, the subbands will cross the Fermi level at the Brillioun-zone boundary, then the doping can induce a gap opening and the semiconducting behavior; while, when the folding happens at points other than M, the half-metallicity is preserved. Hence, it can be expected that all the V-Fek Cpk+1 SMWs with even k are half-metallic. Half-metal energy gap, which is the distance between the Fermi level and the conduction band bottom in insulating spin channel in the present case, is an important parameter of half metals that determines the practical application in spintronics device.32 This gap, as well as the magnetic moment of the SMW, may be tuned by changing the impurity species and concentration. One key point to determine the unique oddeven oscillatory behavior of the SMWs is the band-folding point (related to the size of the supercell). This suggests that such behavior could also be achieved by doping other TMs. Indeed, our ab initio calculations reveal similar odd-even oscillatory behavior in Ni-Fek Cpk+1 SMWs (k = 1–4). On the other hand, doping of some other TMs may induce much more complicated effect on the band structure around


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J. Chem. Phys. 135, 014702 (2011)

Energy (eV)

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Sc e1

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e1

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0

e1 e1

-1

-1

V -2 Γ

-2

X

Γ

-2

X

Γ

X

-2

Γ

X

-2

Γ

X

-2

Γ

X

FIG. 4. Spin-polarized band structure of (a) Sc-Fe2 Cp3 , (b) Ti-Fe2 Cp3 , and (c) V-Fe2 Cp3 SMWs. Left (black solid), majority spin; right (red dot), minority spin. The blue dashed line represents the Fermi level. The magenta letters mark the bands dominated by the substituting TMs.

the Fermi level, rather than mere band-folding and degeneracy removal. In fact, substitutional doping may introduce new electronic states around the Fermi level, especially when the ratio of TM to Fe is high. This will totally change the occupation around the Fermi level and shift the Fermi level greatly, and consequently destroy the half-metallicity of the SMWs, which is clearly reflected by the comparison among the band structures of TM-Fe2 Cp3 (TM = Sc, Ti, and V) in Fig. 4. In contrast to V-Fe2 Cp3 , Sc-Fe2 Cp3 and Ti-Fe2 Cp3 SMWs exhibit the semiconducting behavior. It is the location of the substitutional TM bands that makes the difference. The bands dominated by V mainly lie between the energies of −1.49 and −1.26 eV, lower than the e1 orbitals of Fe, as shown in Fig. 4(c), which guarantees the preservation of the half-metallicity from FeCp SMW. Differently, the states contributed by doped Sc and Ti are both present around the top of the valence bands and intercalate into the e1 subbands of Fe, as shown in Figs. 4(a) and 4(b). Thus, half-metallicity of the host FeCp SMW is destroyed in Sc-Fe2 Cp3 and Ti-Fe2 Cp3 SMWs. As discussed above, V-Fek Cpk+1 may be regarded as composed of Fek Cpk−1 and VCp2 alternatively. A “VCp2 ” cluster has a relatively stable valence electron configuration (three electrons with the same spin direction), and thus its states are deep away from the Fermi level. For Sc or Ti doped SMWs, however, there are not enough electrons to enable the stable valence electron configuration of “ScCp2 ” or “TiCp2 .” Therefore, the bands contributed by Sc and Ti have higher energies and appear around the Fermi level, determining the semiconducting characteristic of SMWs. One can reasonably expect that all the Sc or Ti doped SMWs are semiconducting irrespective to the value of k, although the location and number of the bands contributed by the dopants are dependent on k. This is also confirmed by our further ab initio calculations for k = 3 and 4. In principle, doping can be achieved during the growth from the finite multidecker sandwich cluster.21 More importantly, the species and concentration of TM dopant should be tunable via control of precursors introduced in the growth process. This provides a way to obtain half-metal/semiconductor heterojunctions for sensor, memory, and logic device applications by doping SMWs with different TM species and varied concentration. Such heterojunctions have perfect atomic interface, which is advantageous for device applications based on these doped SMWs.

IV. CONCLUSION

In conclusion, using ab initio calculations, we demonstrate that the dopant species and concentration play a central role in the preservation of half-metallicity of early TM doped FeCp SMWs. We find an intriguing odd-even oscillatory behavior of electronic properties/half-metallicity with respect to different doping concentration in V-Fek Cpk+1 SMWs. This unique oscillation is revealed to originate from the dopinginduced degeneracy removal at the Brillouin-zone boundary. Our work also suggests that half-metal/semiconductor heterostructures with perfect atomic interface can be achieved from one-dimensional TM-Fek Cpk+1 SMWs by controlling doping TM species and concentration. This makes such SMWs attractive candidates for the spintronics application. ACKNOWLEDGMENTS

We acknowledge the support of the Ministry of Science and Technology of China (Grant Nos. 2011CB606405 and 2011CB921901) and the National Natural Science Foundation of China. 1 S.

Hill, R. S. Edwards, N. Aliaga-Alcalde, and G. Christou, Science 302, 1015 (2003). 2 S. Bertaina, S. Gambarelli, T. Mitra, B. Tsukerblat, A. Müller, and B. Barbara, Nature (London) 453, 203 (2008). 3 M. Mannini, F. Pineider, P. Sainctavit, C. Danieli, E. Otero, C. Sciancalepore, A. M. Talarico, M.-A. Arrio, A. Cornia, D. Gatteschi, and R. Sessoli, Nature Mater. 8, 194 (2009). 4 R.-Q. Wang, L. Sheng, R. Shen, B. Wang, and D. Y. Xing, Phys. Rev. Lett. 105, 057202 (2010). 5 M. Leuenberger and D. Loss, Nature (London) 410, 789 (2001). 6 F. Troiani, A. Ghirri, M. Affronte, S. Carretta, P. Santini, G. Amoretti, S. Piligkos, G. Timco, and R. E. P. Winpenny, Phys. Rev. Lett. 94, 207208 (2005). 7 A. Ardavan, O. Rival, J. J. L. Morton, S. J. Blundell, A. M. Tyryshkin, G. A. Timco, and R. E. P. Winpenny, Phys. Rev. Lett. 98, 057201 (2007). 8 R. Xiao, D. Fritsch, M. D. Kuz’min, K. Koepernik, H. Eschrig, M. Richter, K. Vietze, and G. Seifert, Phys. Rev. Lett. 103, 187201 (2009). 9 J. Ribas-Arino, T. Baruah, and M. R. Pederson, J. Chem. Phys. 123, 044303 (2005). 10 K. Miyajima, A. Nakajima, S. Yabushita, M. B. Knichelbein, and K. Kaya, J. Am. Chem. Soc. 126, 13202 (2004). 11 K. Miyajima, S. Yabushita, M. B. Knichelbein, and A. Nakajima, J. Am. Chem. Soc. 129, 8473 (2007). 12 H. J. Xiang, J. L. Yang, J. G. Hou, and Q. S. Zhu, J. Am. Chem. Soc. 128, 2310 (2006). 13 M. Koleini, M. Paulsson, and M. Brandbyge, Phys. Rev. Lett. 98, 197202 (2007).


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14 L. P. Zhou, S. W. Yang, M.-F. Ng, M. B. Sullivan, V. B. C. Tan, and L. Shen,

23 G.

J. Am. Chem. Soc. 130, 4023 (2008). 15 L. Shen, S. W. Yang, M.-F. Ng, V. Ligatchev, L. P. Zhou, and Y. P. Feng, J. Am. Chem. Soc. 130, 13956 (2008). 16 X. Shen, Z. L. Yi, Z. Y. Shen, X. Y. Zhao, J. L. Wu, S. M. Hou, and S. Sanvito, Nanotechnology 20, 385401 (2009). 17 L. Wang, Z. X. Cai, J. Y. Wang, J. Lu, G. F. Luo, L. Lai, J. Zhou, R. Qin, Z. X. Gao, D. Yu, G. P. Li, W. N. Mei, and S. Sanvito, Nano Lett. 8, 3640 (2008). 18 H. Weng, T. Ozaki, and K. Terakura, Phys. Rev. B 79, 235118 (2009). 19 X. Xu and H. S. Kang, J. Chem. Phys. 128, 074707 (2008). 20 G. Zhou and W. H. Duan, J. Nanosci. Nanotechnol. 5, 1421 (2005); D. J. Norris, A. L. Efros, and S. C. Erwin, Science 319, 1776 (2008). 21 S. Nagao, A. Kato, A. Nakajima, and K. Kaya, J. Am. Chem. Soc. 122, 4221 (2000). 22 X. Y. Zhang, J. L. Wang, Y. Gao, and X. C. Zeng, ACS Nano 3, 537 (2009).

24 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).

Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).

25 P.

E. Blöchl, Phys. Rev. B 50, 17953 (1994); G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). 26 G. Henkelman, A. Arnaldsson, and H. Jónsson, Comput. Mater. Sci. 36, 254 (2006). 27 In the situations of k = 1 or 2, the notion of doping may not be appropriate, however, we found the underlying physics is still valid. 28 T. Yasuike and S. Yabushita, J. Phys. Chem. A 103, 4533 (1999). 29 F. W. Zheng, G. Zhou, Z. R. Liu, J. Wu, W. H. Duan, B. L. Gu, and S. B. Zhang, Phys. Rev. B 78, 205415 (2008). 30 K. Sato, P. H. Dederichs, H. Katayama-Yoshida, and J. Kudrnovsky, J. Phys.: Condens. Matter 16, S5491 (2004). 31 N. W. Ashcroft and M. D. Mermin, Solid State Physics (Holt, Rinehart, and Winston, New York, 1976). 32 W. E. Pickett and J. S. Moodera, Phys. Today 54, 39 (2001); W. E. Pickett and H. Eschrig, J. Phys.: Condens. Matter 19, 315203 (2007).
