Eu Atomic

Aug 24, 2010 - ... Beijing 100871, P. R. China, and Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska 68182-0266. J. Phys. Chem...
3 downloads 0 Views 3MB Size
Download PDF
J. Phys. Chem. C 2010, 114, 15347–15353

15347

Structural, Electronic, and Transport Properties of Gd/Eu Atomic Chains Encapsulated in Single-Walled Carbon Nanotubes Jing Zhou,†,‡ Xin Yan,† Guangfu Luo,† Rui Qin,† Hong Li,† Jing Lu,*,† Wai Ning Mei,*,‡ and Zhengxiang Gao† State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking UniVersity, Beijing 100871, P. R. China, and Department of Physics, UniVersity of Nebraska at Omaha, Omaha, Nebraska 68182-0266 ReceiVed: June 8, 2010; ReVised Manuscript ReceiVed: July 31, 2010

Structural, electronic, and transport properties of Gd/Eu atomic chains encapsulated in single-walled carbon nanotubes (SWCNTs) are studied by using first-principles density functional theory and the nonequilibrium Green’s function method. We find that the linear single-atom Gd and Eu chains occupy an off-centered position when encapsulated in the (8,0), (10,0), and (6,6) SWCNTs and considerable electrons are transferred from the Gd and Eu chains to the SWCNTs. The resulting composites are all ferromagnetic metals, with the conductivity significantly larger than those of the pristine SWCNTs and the free-standing Gd/Eu linear singleatom atomic chains. The spin polarization of the finite Gd linear single-atom chain at the Fermi level is 67% when encapsulated in the (8,0) SWCNT from the quantum transport calculation. 1. Introduction One-dimensional nanowires have attracted great interest because of their promising applications toward nanoelectronic and nanospintronic devices. Ultrathin nanowires consist of a few-atom chain or even a single-atom chain. The free-standing ultrathin nanowires are often unstable and hard to manipulate directly when fabricating devices. Nanotubes are considered as ideal systems to encapsulate those ultranarrow nanowires due to their spacious and accessible interior. Recently, several elements, such as I,1 La,2 Gd,3 Mo,4,5 and Eu,6 have been reported experimentally to form stable one-dimensional ultrathin nanowires of 1-4 atomic chains in carbon nanotubes (CNTs). These encapsulated ultrathin nanowires exhibit a variety of structures. For example, I forms diameter-dependent polymorphic structures (1-3 helix atom chains).1 La forms a dimer atom chain.2 Gd forms linear single-atom and zigzag double-atom chains in small diameter CNTs (with a diameter of d ) 0.64 nm) and a four-atom chain in large diameter CNTs (d ) 1.17 nm).3 Similarly, Eu forms linear single-atom, zigzag doubleatom, and zigzag square (the cross section of face-centeredcubic structure along the [110] axis) four-atom chains in CNTs with a diameter of d ) 0.76, 1.06, and 1.54 nm, respectively.6 In the theoretical respect, density functional theory (DFT) study has been reported on transition-metal (TM) filled carbon nanotubes.7-12 Strong spin polarization is predicted in Co, Ni, and Fe nanowires encapsulated inside single-walled carbon nanotubes (SWCNTs) as well as considerable magnetic moments. Recently, Parq et al.13 compared the structural properties of four-atom pure Gd nanowire and Gd-carbide nanowires encapsulated in the (14,0) SWCNT, and suggested that the observed four-atom Gd chain encapsulated inside CNTs experimentally3 is a pure planar square Gd nanowire based on the fact that the calculated planar Gd-Gd distance in the pure Gd chain is consistent with the measured distance. * Corresponding author. E-mail: [email protected] (J.L.); physmei@ mail.unomaha.edu (W.N.M.). † Peking University. ‡ University of Nebraska at Omaha.

Several fundamental questions concerning the Gd and Eu atomic chains encapsulated inside CNTs remain unclear: (1) Does the single-atom chain occupy the central or off-centered position inside CNTs? (2) What are the electronic structure and transport properties of single-atom and double-atom Gd/Eu chains encapsulated inside CNTs? (3) How are the magnetic moments of the encapsulated Gd or Eu atoms coupled? (4) Do the encapsulated Gd/Eu chains offer strong spin polarization at the Fermi level as the transition metals do? In this work, we investigated the structural, electronic, and transport properties of the ultrathin single-atom and doubleatom Gd and Eu chains encapsulated in the SWCNTs by using the DFT method and nonequilibrium Green’s function method. We locate the favorable position of the Gd and Eu atoms in the SWCNTs. The electronic, magnetic, and transport properties differ greatly between the free-standing and encapsulated Gd and Eu chains. 2. Computational Details The measured Gd-Gd and Eu-Eu separations of the singleatom chains along the tube axis are found to be 0.41 ( 0.13 and 0.467 ( 0.019 nm,6 respectively, when encapsulated in CNTs, both of which are larger than those of their respective bulk crystal of 0.350/0.357 (for bcc and hcp structures, respectively) and 0.397 nm, respectively. The period of the zigzag SWCNT is about 4.26 Å, and the double period of the armchair SWCNT is about 4.92 Å. In light of the commeasurable condition, we put the Gd atomic chains in the zigzag SWCNT and Eu atomic chains inside both the zigzag and armchair SWCNTs. In our supercell model, the periodicities are 2 and 4 times those of the zigzag and armchair SWCNTs, respectively. The shortest interatomic distances between adjacent supercells are greater than 7.5 Å. We choose the (8,0) SWCNT with d ) 6.26 Å (close to the experimental value of 6.4 Å3) to encapsulate single-atom and double-atom Gd chains and the (10,0) and (6,6) SWCNTs with d ) 7.83 and 8.14 Å (close to the experimental value of 7.6 Å6), respectively, to encapsulate the single-atom Eu chain. We use the REl chain to denote the

10.1021/jp105274v  2010 American Chemical Society Published on Web 08/24/2010

15348

J. Phys. Chem. C, Vol. 114, No. 36, 2010

Zhou et al.

TABLE 1: Binding Energy per Gd/Eu Atom, Energy Difference between FM and AFM States per Gd/Eu Atom, Localized Magnetic Moment (M) per Gd/Eu Atom, Nearest Gd/Eu-Carbon Distance (dGd/Eu-C), Axial Gd/Eu Separation (daxial), and Mulliken Charge (Q) per Gd/Eu Atom of Gd/Eu Atomic Chains Encapsulated in SWCNTs Calculated by Using GGA and GGA+U Methods (the Binding Energy and Energy Difference between the FM and AFM States Are Changed Little with Increasing Plane-Wave Cutoff Energy and Number of k Points, as Shown in the Supporting Information) c

Gd1 @(8,0) SWCNT Gd1off@(8,0) SWCNT Gd2z@(8,0) SWCNT Eu1c@(10,0) SWCNT Eu1off@(10,0) SWCNT Eu1c@(6,6) SWCNT Eu1off@(6,6) SWCNT

method

Eb (eV)

EFM - EAFM (eV)

M (µB)

GGA GGA+U GGA GGA+U GGA GGA+U GGA GGA GGA GGA

-2.49 -2.44 -3.26 -3.16 -3.26 -3.16 -0.94 -1.62 -0.85 -1.29

0.05 0.06 -0.06 -0.06 -0.06 -0.07 0.01 -0.02 0.01 -0.02

7.42 7.52 7.78 7.78 7.83 7.83 7.12 7.64 7.04 7.60

daxial (Å)

Qa (e)

3.31

4.33

2.54

4.33

1.87 1.83 2.12 2.11 1.95,b 1.93c 1.95,b 1.93c 1.25 1.61 1.15 1.64

dGd/Eu-C (Å)

2.47,b 2.48c 4.05 2.73 4.09 2.77

4.38 4.26 4.26 4.92 4.93

a We estimate that the charges of the Gd and Eu atoms from the natural population analysis are about 1e larger than those from Mulliken population analysis according to the previous results for Gd@C6017 and [email protected] Therefore, the valence electrons of the encapsulated Gd and Eu atoms, especially the Gd atom, in SWCNTs are highly ionized. b The chain with the Gd atom located over the centers of the hexagons on SWCNTs. c The chain with the Gd atom located over the middle of the axial C-C bond SWCNTs.

chain consisting of l rare-earth (RE) atoms. The REl chain encapsulated in (m,n) SWCNT is simply denoted as REl@(m,n) SWCNT. RE1c@(m,n) SWCNT and RE1off@(m,n) SWCNT denote the RE1 chain occupying the central and off-centered position of the nanotube, respectively. Gd2z@(8,0) SWCNT denotes the zigzag Gd2 chain encapsulated in the (8,0) SWCNT. We perform spin-polarized calculations by using the ultrasoft pseudopotential plane-wave method implemented in the CASTEP14 package. All the calculations were performed with the generalized gradient approximation (GGA) of Perdew-Wang 1991 (PW91) for the exchange-correlation energy. Geometry optimization is performed for both the atomic positions and the lattice constant along the tube axis with a plane wave cutoff energy of 220 eV for the Gd/SWCNT composites and 390 eV for the Eu/SWCNT composites using two k points, until the maximum atomic force is less than 0.01 eV/Å. The single point energy calculation is performed with a larger cutoff energy of 400 eV for Gd/SWCNT composites and 480 eV for Eu/SWCNT composites using six k points. The transport calculations are based on the DFT and nonequibrium Green’s function method embedded in the ATK2008.10 code.15,16 The norm-conserving pseudopotentials of Troullier-Martins type and a mesh cutoff of 200 Ry are adopted. The single-ζ plus polarization basis set (SZP) is employed for Gd atoms, and the single-ζ basis set (SZ) is employed for C atoms. 3. Results and Discussion In Table 1, we summarize the essential results such as the calculated binding energies per Gd/Eu atom, energy differences between the ferromagnetic (FM) and antiferromagnetic (AFM) states per Gd/Eu atom, the nearest Gd/Eu-C distance, the Gd/ Eu separation along the tube axis, the localized magnetic moment on the Gd/Eu atom, and the Mulliken charge per Gd/ Eu atom. The optimized configurations of all the studied Gd/Eu atomic chains encapsulated in the SWCNTs are shown in Figure 1. No Peierls distortion has been found in all the encapsulated Gd/ Eu chains. The off-centered positions (Figure 1b, e, and g) of the linear single-atom Gd and Eu chains inside the SWCNT are more stable than the centered ones (Figure 1a, d, and f) by 0.44-0.77 eV per metal atom from Table 1. We have calculated

Figure 1. Optimized structures of the Gd and Eu chains encapsulated in the SWCNTs. Gray ball, C; green ball, Gd; dark pink ball, Eu.

the total energy of the single-atom Gd chain encapsulated in the (8,0) SWCNT using the Perdew-Burke-Ernzerhof (PBE) form of the exchange-correlation functional. The off-centered position of the Gd chain inside the (8,0) SWCNT remains more stable than the centered one by 0.88 eV per Gd atom, compared with a value of 0.77 eV from the PW91 form. In Gd@C60, the Gd atom also prefers the off-centered position.17 The SWCNTs in both the Gd1off@(8,0) SWCNT and Eu1off@(10,0) SWCNT are distorted by the encapsulation of the off-centered Gd/Eu chain, with aspect ratios of 1.18 and 1.03, respectively. By contrast, there is no appreciable distortion for the SWCNT in the Eu1off@(6,6) SWCNT and for the SWCNTs with the central single-atom chain. In the off-centered Gd1 and Eu1 composites, both the Gd and Eu atoms prefer to locate over the centers of the hexagons of the SWCNT sidewall; the same location preference is also calculated by Parq et al.13 The nearest Gd/ Eu-C distance is 2.54, 2.73, and 2.77 Å in the Gd1off@(8,0)

Gd/Eu Atomic Chains Encapsulated in SWCNTs

J. Phys. Chem. C, Vol. 114, No. 36, 2010 15349

Figure 2. Spin-resolved band structures of the pristine SWCNTs and infinite free-standing and encapsulated Gd chains in the ground state. The two bands pointed by arrows of the Gd chain in Gd1off@(8,0) SWCNT are widened compared with those in the free-standing chain. Blue, majority spin; red, minority spin.

Figure 3. Spin-resolved band structures of the pristine SWCNTs and the infinite free-standing and encapsulated Eu1 chains in the ground state. Blue, majority spin; red, minority spin.

SWCNT, Eu1off@(10,0) SWCNT, and Eu1off@(6,6) SWCNT, respectively. The distance between the Gd chain and SWCNT wall is 2.27 Å in the Gd1off@(8,0) SWCNT, which is close to a value of 2.28 Å in the pure four-atom Gd chain encapsulated in the (14,0) SWCNT.13 In the Gd2z@(8,0) SWCNT, the (8,0) SWCNT is severely distorted with a larger aspect ratio of 1.34 than that in the Gd1off@(8,0) SWCNT. The Gd atoms in one

atom chain locate over the centers of the hexagons of the SWCNT sidewall with the nearest Gd-C distance of 2.47 Å, and the Gd atoms in the other chain locate over the middle of the axial C-C bond with the nearest Gd-C distance of 2.48 Å. The nearest Gd-C distances in the Gd-SWCNT composites are close to those in Gd@C60 and Gd3N@C80 of 2.4717 and 2.38-2.42 Å,18 respectively.

15350

J. Phys. Chem. C, Vol. 114, No. 36, 2010

Zhou et al.

Figure 4. Atom- and spin-resolved partial DOS of the infinite (a) Gd1off@(8,0) SWCNT, (b) Eu1off@(10,0) SWCNT, and (c) Eu1off@(6,6) SWCNT in ground states.

Figure 5. Electron density in the plane passing through the Gd/Eu atom in the (a) Gd1off@(8,0) SWCNT, (b) Gd2z@(8,0) SWCNT, and (c) Eu1off@(10,0) SWCNT. Gray ball, C; green ball, Gd; dark pink ball, Eu.

The binding energy of the REl atomic chains encapsulated in SWCNT is defined as

Eb ) (Etot - nREERE - ESWCNT)/nRE

(1)

Etot represents the total energies of the REl-SWCNT composites. ERE and ESWCNT are the total energy of the isolated RE atom and pristine SWCNT, respectively, and nRE is the number of RE atoms per supercell. Thus, Eb can be used to check the stability of the system studied. From Table 1, the formations of Gd and Eu atomic chains encapsulated in SWCNTs are all exothermic with binding energies of -0.85 to -3.26 eV per Gd/Eu atom, respectively. The binding energies of Gd chains encapsulated in SWCNTs (-2.44 to -3.26 eV) are about twice those of the Eu chains (-0.85 to -1.62 eV) and thus have a much higher thermal stability than the latter. The binding energy of Gd in C60 is -3.27 eV,17 quite close to the value of the offcentered Gd chain inside the SWCNT. The free-standing Gd1/Gd2 atomic chains of the same axial Gd separation with the encapsulated atomic chain are all ferromagnetically coupled with a magnetic moment of M ) 8.66 µB/Gd atom, and the AFM state is 0.11 eV/Gd atom higher in energy. After being inserted into SWCNTs, the Gd1off@(8,0) SWCNT and Gd2z@(8,0) SWCNT are also ferromagnetically ordered with a reduced magnetic moment of M ) 7.78-7.83 µB/Gd atom, and the AFM coupling is 0.06 eV/Gd atom less stable in both the Gd1off@(8,0) SWCNT and Gd2z@(8,0) SWCNT. This FM-AFM energy difference is larger than the room temperature of 0.026 eV and suggests that the FM state can be stabilized in the Gd1off@(8,0) SWCNT and Gd2z@(8,0) SWCNT at room temperature. By contrast, the Gd atoms are antiferromagnetically coupled when they locate in the center of the SWCNT. On the other hand, the free-standing linear Eu1 atomic chains are both ferromagnetically coupled with M ) 7.34 and 7.00 µB/Eu atom, respectively, when the axial separation is as that in the (10,0) and (6,6) SWCNTs, and the

AFM state is 0.03 and 0.02 eV/Eu atom higher in energy, respectively. After being inserted into SWCNTs, the Eu1off@(10,0) SWCNT and Eu1off@(6,6) SWCNT remain ferromagnetically ordered with an increased magnetic moment of M ) 7.64 and 7.60 µB/Eu atom, and the AFM states are both 0.02 eV/Eu atom less stable. Interestingly, both the Gd and Eu atoms are antiferromagnetically coupled when they locate in the center of the SWCNTs. The DFT-GGA calculations are known to underestimate the on-site correlation effects between 4f electrons of rare-earth atoms, which are important in predicting the magnetic interaction. Hence, we have also performed calculations within the GGA+U scheme by using the ultrasoft pseudopotential plane wave method implemented in CASTEP.14 The recommended Hubbard parameter U is 6.0 eV for the Gd atom. The main results of the two methods are compared in Table 1. The inclusion of the Hubbard U term causes the binding energy to slightly decrease by 0-0.1 eV and the energy difference between the FM and AFM states to slightly increase by 0-0.01 eV, thus stabilizing the FM states. The localized magnetic moment per Gd atom is nearly intact. Water-soluble Gd-based metallofullerenes (Gd@C82(OH)x, Gd@C60[C(COOH)10], Gd@C60(OH)x) have attracted recent interest19-21 as a possible new generation of magnetic resonance imaging (MRI) contrast agents because they not only can produce proton relaxivities greater than commercially available MRI contrast agents but also are safer than the latter because the toxic Gd ions are completely encaged inside the fullerenes and do not dissociate under physiological conditions. Since more Gd and Eu ions are encapsulated and ferromagnetically coupled inside the (8,0), (10,0), and (6,6) SWCNTs, much larger proton relaxivities than Gd@C82/Gd@C60 may be obtained in Gd1off@(8,0) SWCNT, Gd2z@(8,0) SWCNT, Eu1off@(10,0) SWCNT, and Eu1off@(6,6) SWCNT. Exceptional large proton relaxivities are expected to remain at room temperature for Gd1off@(8,0) SWCNT and Gd2z@(8,0) SWCNT. If so, SWCNTs

Gd/Eu Atomic Chains Encapsulated in SWCNTs

Figure 6. Transmission spectra of the infinite Gd1off@(8,0) SWCNT as a function of energy.

doped by Gd single-atom or zigzag double-atom chains may serve as a novel MRI contrast agent. We show the ground-state band structures of the pristine (8,0) SWCNT and free-standing and encapsulated Gd1/Gd2 atomic chains of the same axial Gd separation in Figure 2. The pristine (8,0) SWCNT is semiconducting with a band gap of ∼0.5 eV, and the free-standing linear Gd1 atomic chain is metallic in both spin channels with two bands in the majority spin and one band in the minority spin crossing the Fermi level (Ef). The Gd1off@(8,0) SWCNT is metallic with six bands crossing Ef in both spin channels as a result of the charge transfer from Gd atoms to the SWCNT. The free-standing linear Gd2 atomic chain is also metallic in both

J. Phys. Chem. C, Vol. 114, No. 36, 2010 15351 spin channels with four bands in the majority spin and two bands in the minority spin crossing Ef. As for the Gd2z@(8,0) SWCNTs, there are six and seven bands crossing Ef in the majority and the minority spin, respectively. By comparing the band structures of the pristine SWCNTs, free-standing atomic chains, and the composites, we find that the total band structure is not a simple sum of the two constituents. In other words, electron filling is nonrigid and there is orbital hybridization between the Gd chains and SWCNTs. Moreover, the spin degeneracy in the conduction band structure of the SWCNTs is lifted. The ground-state band structures of the pristine (10,0) and (6,6) SWCNTs and free-standing and encapsulated Eu1 atomic chains are shown in Figure 3. In the band structure of the freestanding linear Eu1 atomic chain with the same axial separation as encapsulated in the (10,0) SWCNT, both the majority and minority spins are metallic with one band crossing Ef. In Eu1off@(10,0) SWCNT, both the majority and minority spins are metallic but with four and three bands crossing Ef, respectively. The free-standing linear Eu1 atomic chains with the same axial separation as encapsulated in (6,6) SWCNT are semiconducting with a band gap of ∼1 and ∼0.6 eV in majority and minority spin channels, respectively. As for the Eu1off@(6,6) SWCNT shown in Figure 3f, both the majority and minority spins are metallic with the same number of three bands crossing Ef, respectively. By comparing the band structures of the pristine SWCNTs, free-standing Eu1 atomic chains, and the Eu1off@(10,0) and Eu1off@(6,6) SWCNT, the rigid filling approximation remains invalid. The spin degeneracy of the SWCNT conduction band is also lifted by Eu atomic chain doping.

Figure 7. (a) Two-probe model of a four-unit cell of linear Gd1off@(8,0) SWCNT coupled to the (001) surface of nonmagnetic bcc Li metal electrodes. Transmission spectra of the four-unit-cell (b) pristine (8,0) SWCNT and (c) Gd1off@(8,0) SWCNT. (d) The spin-resolved local density of states (LDOS) at Ef of the four-unit-cell Gd1off@(8,0) SWCNT. Gray ball, C; green ball, Gd; purple ball, Li.

15352

J. Phys. Chem. C, Vol. 114, No. 36, 2010

In Figure 4a, we show the atom-resolved partial density of states (PDOS) of the infinite ground-state Gd1off@(8,0) SWCNT, and we find that the DOS of both majority and minority spin at Ef are primarily contributed from the C 2p rather than Gd 5d orbitals. The total state density at Ef is quite close in both spin channels, and this even distribution is quite different from the situation of TM atom filled SWCNTs,7 in which the DOS at Ef is spin polarized because the majority and minority spins are both primarily contributed from the spin-polarized TM 3d orbitals. The PDOS of the Eu1off@(10,0) SWCNT and Eu1off@(6,6) SWCNT are shown in Figure 4b and c, respectively, and the states around Ef in both spin channels are also mostly contributed by the C 2p rather than Eu 5d orbitals. Thus, both of the infinite Gd and Eu atomic chains encapsulated in the SWCNTs exhibit very little spin polarization at Ef. Parq et al.13 also show that there is little spin polarization at Ef in the PDOS of Gd4@(14,0) SWCNT. The Mulliken population analysis shows that significant electrons are transferred from the Gd/Eu atoms to C atoms, suggestive of strong ionic bonding between the Gd/Eu atoms and SWCNTs. The charges per Gd atom are 2.12e and 1.93-1.95e in Gd1off@(8,0) SWCNT and Gd2z@(8,0) SWCNT, respectively, which are slightly larger than the ones per Eu atom in Eu1off@(10,0) SWCNT and Eu1off@(6,6) SWCNT of ∼1.6e. The larger charge transfer from the Gd atom to the SWCNT is responsible for the stronger binding between the Gd atom and the SWCNT than that between the Eu atom and the SWCNT. For the same reason, the larger charge transfer between offcentered Gd/Eu chains and SWCNT than the centered position is responsible for the stronger binding of the off-centered position. Figure 5a-c shows the calculated electron density in a plane containing all Gd/Eu atoms in Gd1off@(8,0) SWCNT, Gd2z@(8,0) SWCNT, and Eu1off@(10,0) SWCNT, respectively. There is an appreciable electron accumulation between the Gd/ Eu atom and adjacent C atoms, but it is not as apparent as that between C-C atoms. This suggests a relatively weak covalent bonding between Gd/Eu and adjacent C atoms in addition to the dominant ionic interaction between the Gd/Eu atom and the adjacent C atoms. Such a weak covalent bonding together with an increase in charge transfer (0.25e per Gd atom and 0.36-0.49e per Eu atom) stabilizes the off-centered displacement of Gd and Eu chains inside SWCNTs. The off-centered position should still be favored over the centered position if changing the SWCNT radius because the stronger interaction between Gd/Eu and SWCNT in the off-center position is independent of the tube radius. The transmission spectra of the ground-state infinite Gd1off@(8,0) SWCNT are provided in Figure 6. The conductance G at Ef for both the majority and minority spins is 6G0 (G0 ) e2/h) due to the six bands across Ef in each spin channel, resulting in a total conductance of 12G0, which is twice larger than that (4G0) at Ef of the ordinary pristine metallic SWCNTs. The conductance G at Ef should be 13G0, 7G0, and 6G0 for Gd1z@(8,0) SWCNT, Eu1off@(10,0) SWCNT, and Eu1off@(6,6) SWCNT, respectively, in terms of the number of bands across Ef. Therefore, Gd/Eu encapsulated SWCNTs are more suitable for nanoscale conductive wire than pure SWCNTs. Next, we study the transport property of a four-unit-cell-long pristine (8,0) SWCNT cluster and Gd1off@(8,0) SWCNT cluster coupled to two Li(001) surfaces, respectively, as shown in Figure 7a. The shortest distance between the Li and C atoms is set as the noncovalent interaction distance of ∼3 Å. The transmission coefficients of the Gd1off@(8,0) SWCNT cluster (Figure 7c) around Ef are much larger than those of the pristine (8,0)

Zhou et al. SWCNT cluster (Figure 7b) and furthermore differ significantly between the majority and minority spins. The spin polarization of the electron current is defined as

ξ)

Tv(Ef) - TV(Ef) Tv(Ef) + TV(Ef)

(2)

where Tv(Ef) and TV(Ef) are the transmission coefficients at Ef of the majority and minority spin channels, respectively. The calculated ξ is 67%, suggesting an effective spin filter of the Gd1off@(8,0) SWCNT cluster. The difference in the transmission between the two spin channels is also reflected from a difference in the local density of states (LDOS) at Ef, as shown in Figure 7d. The majority spin has a larger LDOS at Ef than the minority spin. 4. Conclusions In this work, we investigate the geometrical structures and electronic and transport properties of the infinite ultrathin Gd and Eu atomic chains encapsulated in SWCNTs using DFT and the nonequilibrium Green’s function method. We find that these linear single-atom Gd and Eu chains both prefer locating offcentered when encapsulated in SWCNTs. The encapsulated Gd and Eu atomic chains both exhibit considerable localized magnetic moment. Substantial electrons are transferred from Gd and Eu atoms to SWCNTs. The composites are all ferromagnetic metals with significantly larger conductivity than those of the pristine SWCNTs and free-standing Gd/Eu atomic chains. We also find a large spin polarization of 67% of the finite Gd1off@(8,0) SWCNT at Ef from the quantum transport calculation. Acknowledgment. This work was supported by the NSFC (Grant Nos. 90206048, 20771010, 10774003, 90606023, and 20731160012), National 973 Projects (Nos. 2006CB932701, 2007AA03Z311, and 2007CB936200, MOST of China), Fundamental Research Funds for the Central Universities, Program for New Century Excellent Talents in University of MOE of China, National Foundation for Fostering Talents of Basic Science (No. J0630311), and Nebraska Research Initiative (No. 4132050400). Supporting Information Available: Benchmark of binding energy per Gd atom of off-centered single-atom Gd chains encapsulated in (8,0) SWCNT as a function of cutoff energy and k-point, respectively. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Guan, L. H.; Suenaga, K.; Shi, Z. J.; Gu, Z. N.; Iijima, S. Nano Lett. 2007, 7, 1532. (2) Guan, L.; Suenaga, K.; Okubo, S.; Okazaki, T.; Lijima, S. J. Am. Chem. Soc. 2008, 130, 2162. (3) Kitaura, R.; Imazu, N.; Kobayashi, K.; Shinohara, H. Nano Lett. 2008, 8, 693. (4) Meunier, V.; Muramatsu, H.; Hayashi, T.; Kim, Y. A.; Shimamoto, D.; Terrones, H.; Dresselhaus, M. S.; Terrones, M.; Endo, M.; Sumpter, B. G. Nano Lett. 2009, 9, 1487. (5) Muramatsu, H.; Hayashi, T.; Kim, Y. A.; Shimamoto, D.; Endo, M.; Terrones, M.; Dresselhaus, M. S. Nano Lett. 2008, 8, 237. (6) Kitaura, R.; Nakanishi, R.; Saito, T.; Yoshikawa, H.; Awaga, K.; Shinohara, H. Angew. Chem. 2009, 48, 8298. (7) Yang, C. K.; Zhao, J.; Lu, J. P. Phys. ReV. Lett. 2003, 90, 257203. (8) Jo, C. J. Phys. D 2009, 42, 105008. (9) Jo, C.; Il Lee, J. J. Magn. Magn. Mater. 2008, 320, 3256. (10) Jang, Y. R.; Lee, J. I. Phys. Status Solidi B 2007, 244, 4407.

Gd/Eu Atomic Chains Encapsulated in SWCNTs (11) Ivanovskaya, V. V.; Kohler, C.; Seifert, G. Phys. ReV. B 2007, 75, 075410. (12) Jo, C. L.; Lee, J. I.; Jang, Y. R. Phys. Status Solidi C 2004, 3264. (13) Parq, J. H.; Yu, J.; Kim, G. J. Chem. Phys. 2010, 132, 054701. (14) Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert, M. J.; Refson, K.; Payne, M. C. Z. Kristallogr. 2005, 220, 567. (15) Taylor, J.; Guo, H.; Wang, J. Phys. ReV. B 2001, 63, 245407. (16) Brandbyge, M.; Mozos, J. L.; Ordejon, P.; Taylor, J.; Stokbro, K. Phys. ReV. B 2002, 65, 165401. (17) Lu, J.; Mei, W. N.; Gao, Y.; Zeng, X. C.; Jing, M. W.; Li, G. P.; Sabirianov, R.; Gao, Z. X.; You, L. P.; Xu, J.; Yu, D. P.; Ye, H. Q. Chem. Phys. Lett. 2006, 425, 82.

J. Phys. Chem. C, Vol. 114, No. 36, 2010 15353 (18) Lu, J.; Sabirianov, R. F.; Mei, W. N.; Gao, Y.; Duan, C. G.; Zeng, X. C. J. Phys. Chem. B 2006, 110, 23637. (19) Toth, E.; Bolskar, R. D.; Borel, A.; Gonzalez, G.; Helm, L.; Merbach, A. E.; Sitharaman, B.; Wilson, L. J. J. Am. Chem. Soc. 2005, 127, 799. (20) Sitharaman, B.; Bolskar, R. D.; Rusakova, I.; Wilson, L. J. Nano Lett. 2004, 4, 2373. (21) Kato, H.; Kanazawa, Y.; Okumura, M.; Taninaka, A.; Yokawa, T.; Shinohara, H. J. Am. Chem. Soc. 2003, 125, 4391.

JP105274V