Half-Metallic Sandwich Molecular Wires with Negative Differential

Dec 2, 2010 - ... Japan Science and Technology Agency, 4-1-8 Honcho Kawagushi, Saitama, Japan, Center for Tsukuba Advanced Research Alliance, Universi...
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J. Phys. Chem. C 2010, 114, 21893–21899

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Half-Metallic Sandwich Molecular Wires with Negative Differential Resistance and Sign-Reversible High Spin-Filter Efficiency Lu Wang,†,‡,¶ Xingfa Gao,‡ Xin Yan,† Jing Zhou,†,¶ Zhengxiang Gao,† Shigeru Nagase,*,‡ Stefano Sanvito,§ Yutaka Maeda,|,⊥ Takeshi Akasaka,# Wai Ning Mei,¶ and Jing Lu*,† State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking UniVersity, Beijing 100871, People’s Republic of China, Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan, School of Physics and CRANND, Trinity College, Dublin 2, Ireland, Department of Chemistry, Tokyo Gakugei UniVersity, Tokyo 184-8501, Japan, PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho Kawagushi, Saitama, Japan, Center for Tsukuba AdVanced Research Alliance, UniVersity of Tsukuba, Ibaraki 305-8577, Japan, Department of Physics, UniVersity of Nebraska at Omaha, Omaha, Nebraska 68182-0266, United States ReceiVed: June 1, 2010; ReVised Manuscript ReceiVed: NoVember 18, 2010

Using density functional theory and nonequilibrium Green’s function method, we construct organometallic nanowires that consist of Fe or V atoms sandwiched between composite molecules (Cp*FeCp*, where Cp* is C5(CH3)5). For the first time, we demonstrate that half-metallicity, negative differential resistance, and sign-reversible high spin-filter capability can coexist remarkably in one organometallic nanowire (FeCp* wire). This renders FeCp* wire promising in electronics and spintronics. Introduction Organic molecules, such as metallocenes and metal-benzene complexes, have attracted much attention in recent years motivated by their potential applications in nanoscale electronics and spintronics as well as a tool to understand the operational principles of organic spintronics.1,2 It is well-known that due to their weak spin-orbit and hyperfine interactions,3,4 carbon-based materials have considerably long spin relaxation lengths5 and spin lifetimes,6 which make them extremely interesting as potential replacements for the inorganic materials used in spintronic devices.7 Even more intriguing will be the possibility of constructing an all-organic device, where all the elements, including the magnets, are made of organometallic molecules. Recently, half-metallicity was predicted to occur in onedimensional (1D) transition metal (TM)-benzene (Bz) sandwich wires [e.g., (VBz)∞ and (MnBz)∞], metallocene wires [e.g., (VCp)∞, (FeCp)∞, and (VBzVCp)∞, where Cp is cyclopentadienyl], and transition metal-borazine wires.8-18 Among them, 1D TM-Bz and metallocene wires can be considered as the limiting case (n f ∞) of synthesized multidecker TMnBzn+1 and TMnCpn+1 sandwich clusters. On the basis of the transport calculations, finite-size clusters made of these half-metallic organic wires often display high spin-filter efficiency (SFE)12-14,19 at zero bias, hence suggesting potential application as spin-filters. In addition to the high SFE, negative differential resistance (NDR) is also predicted to appear in finite multidecker ferrocene cluster FenCpm.13 Since NDR is an extremely valuable property for electronic devices, such as instance amplifiers, logic gates, memory, and fast switch devices,20,21 ferrocene clusters are frequently studied materials. Furthermore, we notice that when * Address correspondence to [email protected], [email protected]. † Peking University. ‡ Institute for Molecular Science. ¶ University of Nebraska at Omaha. § Trinity College. | Tokyo Gakugei University. ⊥ Japan Science and Technology Agency. # University of Tsukuba.

comparing with Cp ligand, pentamethylcyclopentadienyl ligand [C5(CH3)5 or Cp* in short] is a stronger donor and harder to remove from metal substrates, consequently its metal complexes demonstrated enhanced thermal stability.22 Moreover, multidecker VnFen+1Cp*2n+2 clusters with n up to 4 have been synthesized by reacting V vapor with FeCp*2 since 2000.23 Anchored in all these fascinating properties, we are encouraged to pursue an extensive theoretical study on the structural, electronic, and transport properties of the multidecker sandwich complexes VnFen+1Cp*2n+2 and Fe2n+1Cp*2n+2 (n ) 1-3). We find that all the examined multidecker clusters are in linear staggered structures and ferromagnetic in ground states. Particularly, the infinitely long 1D (FeCp*)∞ wire is a ferromagnetic half-metal. More importantly we find that Fe3Cp*2 and Fe5Cp*4 clusters attached to gold electrodes exhibit both high SFE and negative differential resistance (NDR). Furthermore, it is found that the sign of spin current in the Au-Fe5Cp*4-Au system can be altered by changing the bias. Undoubtedly, this biasinduced spin polarization reversal is highly desirable in logic spintronic devices and has been reported recently only in the Fe/GaAs(001) interface,24,25 in which all the components are inorganic compounds, due to an interfacial minority-spin resonant state.26 However, to the best of our knowledge, this profound phenomenon has not been reported in molecular wires. Finally a remark regarding the material manufacture: since the multidecker VnFen+1Cp*2n+2 clusters were synthesized a decade ago, we believe that the Fe2n+1Cp*2n+2 could also be fabricated by using a similar technique. Computational Details The geometry optimization and the electronic structure are calculated by using spin-unrestricted density functional theory (DFT) as implemented in SIESTA.27 The generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form is employed for the exchange-correlation functional.28 Optimized basis sets of the double-ζ quality including polarization functions (DZP) are adopted with the real-space mesh cutoff

10.1021/jp105027y  2010 American Chemical Society Published on Web 12/02/2010

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400 Ry. We use 20 × 20 × c Å supercell cells for all the structures. In the case of the finite multidecker clusters, the lattice parameter c is chosen to be 15 Å larger than the cluster lengths. c is about 6.7 and 7.2 Å for the infinite (FeCp*)∞ and (VCp*FeCp*)∞ wires, respectively. And the 1 × 1 × 100 Monkhorst-Pack29 k-point grid is used in order to sample the 1D Brillouin zone. Geometry optimization is performed without any symmetry constraint until the forces acting on each atom are smaller than 0.01 eV/Å. Different spin-multiplicity states have been considered carefully. The DFT method has been extensively used to study transition metal sandwich structures. The calculated distance between two Cp rings of the eclipsed ferrocene is the same as the experimental value (3.338 Å).13,30 The calculated vertical ionization potentials (VIPs) and average total magnetic moments for the multidecker VnBzn+1 sandwich structures are also in good agreement with the measured values in the previous study.31 As a test of the DFT, we optimized the structure of the eclipsed ferrocene within the DFT and GGA-PBE by using SIESTA code. The calculated C-C and Fe-C bond lengths are 1.44 and 2.02 Å, respectively, in good agreement with the experimental values (1.43 and 2.06 Å).32 Double-ζ basis sets plus double polarization functions (DZDP) have also been tested (see the Supporting Information), and the results basically agree with the DZP calculations except for a large change in the binding energy. The large changes in binding energies indicate that large basis set is required to obtain reliable binding energy for the examined systems. We also calculated the VIPs of the isolated VnFen+1Cp*2n+2 clusters by using the double numerical atomic basis set plus polarization (DNP) implemented in the DMol3 package.33,34 The calculated VIPs are 5.99, 3.05, and 2.69 eV, which agree with the experimental values of 5.88, 3.39 ( 0.10, and 3.15 ( 0.11 eV for n ) 0, 1, and 2, respectively.23 DFT+U calculations were also carried out within the planewave basis set (see the Supporting Information). In brief, we obtained very similar geometries and electronic properties at different theoretical levels by using several DFT codes and present the details in the following section. To carry out the transport calculations we build a two-probe device model, in which the outer Fe atoms of the Fe3Cp*2 and Fe5Cp*4 are covalently bonded to the Au(100) surface electrodes. (Since Au is used as an electron reservoir, we assume the Au(100) surface is in its unreconstructed structure, as proposed in the previous electron transport calculations.35,36) The size of the electrode supercell is 16.3 × 16.3 × 8.2 Å. We calculate the transport properties with the SMEAGOL code,37-39 which is based on DFT and the nonequilibrium Green’s function (NEGF) method. The pseudopotentials, basis set, and exchangecorrelation functional are set to be the same as those used in the electronic structure calculations. The Green’s function and self-energies are calculated for the central scattering region (the extended molecule) consisting of the cluster and four layers of Au atoms on each side. The electrodes are semi-infinite bulk structures, and a Monkhorst-Pack29 5 × 5 × 100 k-point grid is used for the calculation of their electronic structure. For the transport calculations, the Monkhorst-Pack29 5 × 5 k-point grid is employed in order to sample the two-dimensional Brillouin zone perpendicular to the transport direction. We apply an equivalent cutoff of 400 Ry for the real space grid. In the NEGF self-consistent loop the charge density is integrated over 50 energy points along the semicircle in the complex plane, 25 along the complex line parallel to the real axis, while 25 poles are used for the Fermi distribution.28,29

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Figure 1. Total magnetic moments (S) of the optimized structures of the (a) Fe2n+1Cp*2n+2 (n ) 1-3) and (b) VnFen+1Cp*2n+2 (n ) 1-3) clusters in the ground state as a function of the cluster size n. Blue spheres are Fe; red spheres are V; gray spheres are C; and white spheres are H. Lengths of the arrows indicate the magnitudes of the localized TM atoms magnetic moments.

Results and Discussions The optimized structures of multidecker Fe2n+1Cp*2n+2 (n ) 1-3) and VnFen+1Cp*2n+2 (n ) 1-3) clusters are shown in Figure 1. All the optimized clusters are in a linear staggered structure with C5V symmetry because the spatial repulsion due to the CH3 group is rather significant in the eclipsed structure. On the contrary, the most stable V2n+1Cp2n+2 (n ) 1-3) and VnFen+1Cp2n+2 clusters are all in eclipsed structure.14 We also performed additional vibrational frequency analysis for the Fe3Cp*2, Fe3Cp*4, Fe5Cp*4, Fe5Cp*6, and VFe2Cp*4 clusters by using DMol3 code.33,34 All the examined structures have no imaginary frequency and are local energy minima. To understand the stability of the cluster systems, we first calculate the binding energies (Eb) of the clusters defined as:

Eb[Fen(FeCp*2)m] ) E[Fen(FeCp*2)m] - nE[Fe] mE[FeCp*2]

(1)

Eb[Vn(FeCp*2)m] ) E[Vn(FeCp*2)m] - nE[V] mE[FeCp*2]

(2)

where E[ ] is the total energy of Fen(FeCp*2)m, Vn(FeCp*2)m, Fe(V) atom, and FeCp2*, respectively. The calculated binding energies are listed in Table 1. We notice that the formation of these multidecker sandwich clusters is either strongly or moderately exothermic with Eb ranging from -2.0 to -10.7 eV. We learn from the high-level MP2 method that the π-π stacking interaction between the two adjacent Cp* rings is about 0.1 eV, which is 1 order of magnitude smaller than the covalent/ ionic interaction between the metal atom and Cp* ring. Even though the GGA fails to correctly describe the π-π stacking interaction between the two adjacent Cp* rings, we anticipate the effects of π-π stacking interaction on the binding energies and electronic structures to be insignificant. Furthermore, the exothermic process and linear structure feature suggest that the multidecker sandwich Fe2n+1Cp*2n+2 clusters are possible to synthesize and the freestanding 1D (FeCp*)∞ and (VCp*FeCp*)∞ are mechanically stable. The absolute binding energies of Fe2n+1Cp*2n+2 and VnFen+1Cp*2n+2 clusters are significantly larger than those of V2n+1Cp2n+2 and Vn(FeCp2)n+1 clusters with the same n at the same calculation level.14 For

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TABLE 1: Binding Energy (Eb), Total Magnetic Moment j V) and (S), Average Localized Magnetic Moment on the V (S j Fe) Atoms, and HOMO-LUMO Gap for the Majority Fe (S (∆maj) and Minority (∆min) Spin in the Ground State for All the Examined Multidecker Clusters and 1D Wires Eb (eV) S (µB) SjFe (µB) SjV (µB) ∆maj (eV) ∆min (eV) Fe3Cp*4 Fe5Cp*6 Fe7Cp*8 Fe3Cp*2 Fe5Cp*4 VFe2Cp*4 V2Fe3Cp*6 V3Fe4Cp*8 (FeCp*)∞ (VCp*FeCp*)∞ a

-3.6 -7.2 -10.5 -2.0 -5.3 -3.8 -7.9 -10.7 -3.7a -4.4a

2.0 4.0 6.0 8.0 10.0 5.0 10.0 11.0 2.0a 5.0a

0.73 0.88 0.95 2.73 2.05 0.75 1.10 1.05 1.11 1.89

3.33 3.22 2.36 3.08

1.10 0.61 0.51 0.80 0.67 0.50 0.19 0.27 metallic 1.11 (0.82b)

1.22 0.94 0.86 0.20 0.48 2.53 1.93 0.14 0.74 (0.29b) 1.36 (1.78b)

Each supercell (containing two TM atoms). b GGA+U level.

example, Eb[V(FeCp*2)2] is -3.8 eV while Eb[V(FeCp2)2] is merely -1.9 eV.14 Therefore we conclude that the Fe2n+1Cp*2n+2 and VnFen+1Cp*2n+2 clusters are more thermodynamically stable than V2n+1Cp2n+2 and Vn(FeCp2)n+1 clusters, as mentioned in the introduction. On the basis of the spin-polarized studies, the high spin state is always energetically preferable in all the examined clusters suggesting that the transition metal atoms in these clusters are ferromagnetically (FM) ordered in the ground state. We list all the ground-state total magnetic moments (S) of the multideckers and average localized magnetic moments of the transition metal atoms in Table 1. S of Fe2n+1Cp*2n+2 increases linearly with the cluster size for n ) 1-3 whereas S of VnFen+1Cp*2n+2 increases nonlinearly with the cluster size for n ) 1-3. We ascribe the nonlinear behavior of S in VnFen+1Cp*2n+2 to the fact that the localized magnetic moment around the V atom is about 3.2-3.3 µB in VnFen+1Cp*2n+2 with n ) 1-2 but drastically decreased to about 2.3-2.4 µB at n ) 3, whereas the average localized magnetic moment around the Fe atom is about 0.7-1.1 µB. The quasi-one-dimensional structure and increasing total magnetic moment with the cluster size have been previously reported for the multideckers VnBzn+1,31 V2n+1Cp2n+2, Vn(FeCp2)n+1, and V2nAntn+1.14 In addition, we present the comparison of calculated charge and localized magnetic moment of Fe and V atoms in V3Fe4Cp*8 and V3Fe4Cp8 in Table S2 in the Supporting Information. We notice that Cp* transfers more electrons to Fe and V atoms than those of Cp, as we stated in the Introduction section that Cp* is a stronger donor than Cp, which we believe originates from the long-range interactions between the additional methyl group in Cp* and Fe/V atoms. In Figure 2, we present the optimized geometries of the 1D (FeCp*)∞ and (VCp*FeCp*)∞ wires. Both of them maintain the staggered structure. In contrast, the most stable 1D (FeCp)∞, (VCp)∞, and (VCpFeCp)∞ wires still adopt an eclipsed structure.13,14 The distances between two nearest C pentagonal rings are 3.36, 3.79, and 3.44 Å, in the (FeCp*)∞, Cp*VCp* unit, and Cp*FeCp* unit for the (VCp*FeCp*)∞ wire, respectively, which are quite similar to the corresponding distances between two nearest Cp rings: that is 3.34, 3.73, and 3.41 Å in the (FeCp)∞ and (VCpFeCp)∞ wires, repsectively.13,14 Hence we notice that replacing H in Cp by CH3 does not change the entire structure of 1D wires significantly. Similarly the binding energies (Eb) per unit cell (containing two TM atoms) of 1D wires are defined as:

Eb[(FeCp*)∞] ) E[(FeCp*)∞] - E[Fe] - E[FeCp*2]

(3) Eb[(VCp*FeCp*)∞] ) E[(VCp*FeCp*)∞] - E[V] E[FeCp*2] (4) where E[ ] is the total energy of (FeCp*)∞/(VCp*FeCp*)∞ per unit cell, Fe/V atom, and FeCp2*, respectively. The calculated binding energies are -3.7 and -4.4 eV per unit cell for the (FeCp*)∞ and (VCp*FeCp*)∞ wires, respectively, indicating that the formation of these 1D wires is also exothermic. In addition, binding energy of the FM state (FeCp*)∞ wire is 0.16 eV per Fe atom lower than that of the antiferromagnetic (AFM) state, while the FM state of the (VCp*FeCp*)∞ wire is 0.09 and 0.12 eV per transition metal atom lower in total energy than its ferrimagnetic (FIM) and AFM states, respectively. Therefore, we expect that both 1D (FeCp*)∞ and (VCp*FeCp*)∞ wires are ferromagnetic in the ground state. We display the spin-resolved band structure, the density of states (DOS), and the corresponding spin density isosurface of the 1D (FeCp*)∞ wire in Figure 3, parts a, b, and c, respectively, and observe that the majority spin-band of the (FeCp*)∞ wire is metallic with two bands crossing the Fermi level (Ef) and providing two ballistic conductance channels. In contrast, the minority spin-band is semiconducting with a moderate indirect band gap of 0.74 eV. Thus, the 1D (FeCp*)∞ wire is a halfmetallic ferromagnet, where the current is 100% spin-polarized around Ef. We also notice that the half-metallicity is stronger in the (FeCp*)∞ wire than in the (FeCp)∞ wire because the band gap of the semiconducting channel for (FeCp*)∞ is much larger than that (0.1 eV) for the (FeCp)∞ wire at the DFT level.13 This feature is based on the band structure near Ef: that is most of the bands are the 2p orbitals of C and 3d orbitals from the Fe atoms, which are split by the strong C5V crystalline field into a singlet dz2 and two doublets dxy/dx2-y2 and dxz/dyz orbitals. In the majority spin-band, the dz2 and the two adjacent Cp* rings are fully occupied, while the dxz- and dyz-dominated bands are only partially occupied, whereas in the minority spin-band, the dz2-, dxy-, and dx2-y2-dominated bands are all fully occupied, yet the dxz- and dyz-dominated bands are pushed above the Fermi level and thus remain empty. Therefore, the total magnetic moment per unit cell is 1.0 µB, and is strongly localized around the Fe atoms. On the basis of the Mulliken population, we obtained the local magnetic moment of Fe about 1.11 µB, slightly smaller than that of the V atom (1.28 µB) in the (VBz)∞ wire.12 The localized magnetic moment distributed over the Cp* ring in the (FeCp*)∞ wire is -0.11 µB, originating from Fe3d-C2p orbital hybridization. We display the spin-resolved band structure, density of states (DOS), and spin density isosurface of the 1D (VCp*FeCp*)∞ wire in Figure 3, parts d, e, and f, respectively, and notice that the majority spin-band of the 1D (FeCp*)∞ wire has a direct band gap of 1.16 eV at the X-point, whereas the minority spinband has a direct band gap of 1.30 eV also at the X-point. From the calculated band structure, we deduced that the (VCp*FeCp*)∞ wire is a ferromagnetic semiconductor with the total magnetic moment of 5.0 µB per unit cell. On the basis of our previous work,14 we notice that the (VCpFeCp)∞ wire is also a ferromagnetic semiconductor with band gaps 1.4 and 1.1 eV for the majority and minority spin channels, respectively. In both systems, the magnetic moments are mainly localized over the two TM atoms, with the local magnetic moments of V and Fe about 3.05 and 1.92 µB, respectively, while that distributed over the Cp* ring is negligible.

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Figure 2. Structures of the optimized infinite 1D (a) (FeCp*)∞ and (b) (VCp*FeCp*)∞ wires. Blue spheres are Fe; red spheres are V; gray spheres are C; and white spheres are H.

Figure 3. (a, d) Spin-resolved band structures of the infinite 1D (a) (FeCp*)∞ and (d) (VCp*FeCp*)∞ wires. (b, e) Spin-resolved total and local density of states of the infinite 1D (b) (FeCp*)∞ and (e) (VCp*FeCp*)∞ wires. (c, f) Isosurface plot of spin density for (c) (FeCp*)∞ and (f) (VCp*FeCp*)∞ wires. Isosurfaces for 0.02 e/Å3 are red; isosurfaces for -0.02 e/Å3 are green.

An additional remark regarding our method: the DFT calculations are known to underestimate the on-site correlation effects between 3d electrons of TM atoms, therefore we reinforce our findings by performing DFT+U calculations for the two infinite sandwich nanowires with U - J ) 3 and 2 eV for the V and Fe atoms, respectively, and present the resulting electronic structures in the Supporting Information. Generally speaking, the half-metal identification for the 1D (FeCp*)∞ wire is robust against the details of the calculations except for the band gap of the semiconducting channel decreasing from 0.74 to 0.29 eV due to the rise of the dxy- and dx2-y2-dominated bands in the minority spin channel. In contrast, the band gap in the majority spin channel increased due to the downshifts of dz2-,

dxy-, and dx2-y2-dominated bands in the half-metallic 1D (VCp)∞ wire.14 The ferromagnetic semiconductor identification for the 1D (VCp*FeCp*)∞ also remains valid with a band gap of 0.82 and 1.78 eV for the majority and minority spin channels, respectively. Next, we study the electronic conduction through the finite FenCp*m multideckers by performing the spin-polarized transport calculations. Experimentally, (FeCp*VCp*) clusters can be terminated at a Cp* ring or metal atom,23 which allows one to choose freely the anchoring group. In our two-probe model, we assign the finite Fe5Cp*4 and Fe3Cp*2 clusters to covalently coupled to nonmagnetic metal electrodes [Au(100)] on the top site by the outer Fe atoms, as shown in the inset of Figure 4,

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Figure 4. (a, c) I-Vbias curve of the (a) Fe3Cp*2 and (c) Fe5Cp*4 clusters coupled to the gold electrode surface. Inset: The corresponding two-probe models. (b, d) Spin-filter efficiency for the (b) Fe3Cp*2 and (d) Fe5Cp*4 clusters as a function of the bias voltage.

parts a and c, respectively. Then both the Au-Fe3Cp*2-Au and Au-Fe5Cp*4-Au structures are optimized, in which the nearest distance between the Fe and Au atoms is about 2.5 Å. We define the spin-filter efficiency at zero bias as:

SFE ) [Tmaj(Ef) - Tmin(Ef)]/[Tmaj(Ef) + Tmin(Ef)],

(5) where Tmin and Tmaj represent the transmission coefficient of the minority and majority spin channels, respectively. A positive value for the SFE denotes a conductance dominated by the majority spins, while a negative one indicates that the minority spins dominate. It turned out the calculated SFE at zero bias is -57% and -67% for the Fe3Cp*2 and Fe5Cp*4 clusters, respectively. These values are smaller than that calculated previously for Fe3Cp2 (83%).13 On the basis of the band structure study, Figure 3a, we notice that the SFE for the infinitely long 1D (FeCp*)∞ wire at zero bias is 100% and its conductance is entirely governed by the majority spins, because there are two bands crossing the Fermi surface at majority spins, yet there is a finite gap at the minority side. However, in the finite Fe3Cp*2 or Fe5Cp*4 cluster cases, the HOMO-LUMO gap is only about 0.20 or 0.51 eV for the minority-spins and they are smaller than those of the majority ones, 0.80 and 0.65 eV for Fe3Cp*2 and Fe5Cp*4, respectively. Thus the transmissions for the minorityspin channels in the finite clusters are larger than those for the majority, and consequently the SFE signs for the Fe3Cp*2 and Fe5Cp*4 clusters are primarily determined by the minority spins. Generally speaking, the infinite (FeCp*)∞ wire and the finite clusters have different electronic properties and hence lead to different transport properties. Actually devices work at finite bias, and hence the spinpolarized current Iσ at the finite bias is calculated by using the Landauer-Bu¨ttiker formula:38,40

Iσ )

e h

∫-∞+∞ Tσ(E, Vbias)[fL(E, Vbias) - fR(E, Vbias)] dE (6)

where Tσ(E,Vbias) represents the spin-resolved transmission coefficient calculated at the bias voltage Vbias, and fL(E,Vbias) and fR(E,Vbias) are the Fermi distribution functions for the left and right electrodes, respectively. Here we present the calculated I-Vbias curves in parts a and c of Figure 4 for the Au-Fe3Cp*2-Au and Au-Fe5Cp*4-Au models, respectively. The total current Itotal of both systems initially increases with Vbias. Then a remarkable negative differential resistance (NDR) appears in the bias range of 0.6-0.8 and 0.65-0.70 V for the Au-Fe5Cp*4-Au and Au-Fe3Cp*2-Au systems, respectively. To further understand the nature of the observed NDR, we plot the total transmission spectra T(E,Vbias) of the Au-Fe5Cp*4-Au system at the different biases in Figure 5. Three significant peaks in T(E,Vbias)0), P1, P2, and P3, representing the conductance channels in the extended molecule, are located around -0.45, 0.03, and 0.45 eV, respectively. When Vbias increases, these peaks gradually shift toward the low-energy side, accompanied by a change in heights. When Vbias reaches 0.55 V, the P3 peak drifts into the bias window, causing a significant raise in the electrical current. Then, when Vbias further increases to 0.80 V, the P3 peak in the bias window is strongly suppressed, probably because of a change in its effective coupling to the leads under bias.41 This reduction in transmission is only partially compensated by the P4 peak shifting into the bias window and results in a decline of the electrical current. Different from eq 5, we define the spin-filter efficiency at the finite bias voltage in terms of the spin-resolved currents:

SFE ) (Imaj - Imin)/(Imaj + Imin)

(7)

where Imaj and Imin represent majority and minority current, respectively. Then we present the SFE verses Vbias curves of the Au-Fe3Cp*2-Au and Au-Fe5Cp*4-Au models in Figure 4, parts b and d, respectively. First, we notice that the sign of SFE for Au-Fe3Cp*2-Au remains negative throughout the 0-1 V bias range with a high average value of -61%, a minimum value of -83% locates at Vbias ) 0.5 V. Yet the SFE of Au-Fe5Cp*4-Au is negative for Vbias from 0.00 to 0.50 V with an average value of -53%, then it turns positive with an average

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Wang et al. Conclusion In summary, we demonstrated that the organometallic multidecker sandwich complexes Fe2n+1Cp*2n+2 and VnFen+1Cp*2n+2 are linear staggered ferromagnetic clusters up to n ) 3. The infinite 1D (FeCp*)∞ wire is a half-metallic ferromagnet, whereas the (VCp*FeCp*)∞ wire is only a ferromagnetic semiconductor. In addition, we also found that the finite multidecker sandwich Fe3Cp*2 and Fe5Cp*4 clusters, when attached to gold electrodes, show high spin-filter efficiency. In particular we also noticed a sign-controlled spin-filter effect in the Fe5Cp*4 cluster. Most importantly, both the clusters display negative differential resistance. All these features observed in our work are desirable features with ample applications in electronics and spintronics devices, indicating that the investigation of organometallic nanowires is a fruitful direction to find more promising materials in nanoscale applications.

Figure 5. Transmission spectra of the Fe5Cp*4 cluster coupled to gold electrodes at the bias voltages of (a) 0, (b) 0.30, (c) 0.55, and (d) 0.80 V.

value of 74% when Vbias exceeds 0.50 V, which means the current is dominated by the majority spins. This indicates clearly that spin-polarization of the current could be controlled by increasing the bias voltage without resorting to external magnetic field. Such a sign-reversal effect is extremely attractive and of great potential applications in spintronic logic devices, where the spin signal is monitored by the bias voltage. Such a spinpolarization inversion was previously found in Fe/GaAs(001) interfaces24,25 and earlier theoretical study,26 but is demonstrated for the first time on devices constructed from organic molecules. The reversibility of this remarkable sign-switchable SFE and possible hysteresis loop are important issues needed to be verified experimentally, and we encourage further study along this exciting direction. The spin-polarized transmission spectra shown in Figure 5 can also be used to explain the bias-voltage-controlled spinfilter effect: at zero bias, the P2 peak in transmission around Ef is dominated by the minority spin, and SFE is nagative. With the increasing bias voltage, the P2 peak gradually shifts toward the lower energy. At Vbias ) 0.3 V, the P2 peak remains in the bias window and the sign of SFE remains negative. When Vbias reaches 0.55 V, the P2 peak shifts away from the bias window and the P3 peak dominated by the majority spin moves into the bias window. As a result, the spin current is primarily occupied by the majority spin. Finally when Vbias arrives at 0.80 V, the P3 peak remains in the bias window but a fraction of the P4 peak dominated by the majority spin progresses into the bias window. Hence the spin-polarization of the current is governed by the interplay between different spectral amplitudes of the P3 and P4 peaks, yet the spin current remains dominated by the majority spin.

Acknowledgment. The work in Japan was supported by the Grant-in-Aid for Scientific Research on Priority Area and Next Generation Super Computing Project (Nanoscience Program) from the MEXT and the Iketani Science and Technology Foundation. The work in China was supported by the NSFC (Grant Nos. 10774003, 10474123, 10434010, 90606023, and 20731160012), National 973 Projects (Nos. 2002CB613505 and 2007CB936200, MOST of China), Fundamental Research Funds for the Central Universities, National Foundation for Fostering Talents of Basic Science (No. J0630311), and Program for New Century Excellent Talents in University of MOE of China. The work in the USA was funded by the Nebraska Research Initiative (No. 4132050400). And the Smeagol project (SS) is sponsored by Science Foundation of Ireland. Supporting Information Available: Electronic properties of the most stable structures of the examined Fen(FeCp*2)m and Vn(FeCp*2)m multidecker clusters calculated with a larger DZDP basis set and the spin-resolved electronic band structure of the 1D (FeCp*)∞ and (VCpFeCp*)∞ wires at the GGA+U level. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Naber, W. J. M.; Faez, S.; van der Wiel, W. G. J. Phys. D: Appl. Phys. 2007, 40, R205. (2) Miyajima, K.; Yabushita, S.; Knickelbein, M. B.; Nakajima, A. J. Am. Chem. Soc. 2007, 129, 8473. (3) Sanvito, S. J. Mater. Chem. 2007, 17, 4455. (4) Sanvito, S.; Rocha, A. R. J. Comput. Theor. Nanosci. 2006, 3, 624. (5) Tsukagoshi, K.; Alphenaar, B. W.; Ago, H. Nature 1999, 401, 572. (6) Kikkawa, J. M.; Awschalom, D. D. Nature 1999, 397, 139. (7) Szulczewski, G.; Sanvito, S.; Coey, M. Nat. Mater. 2009, 8, 693. (8) Kurikawa, T.; Takeda, H.; Hirano, M.; Judai, K.; Arita, T.; Nagao, S.; Nakajima, A.; Kaya, K. Organometallics 1999, 18, 1430. (9) Miyajima, K.; Muraoka, K.; Hashimoto, M.; Yasuike, T.; Yabushita, S.; Nakajima, A.; Kaya, K. J. Phys. Chem. A 2002, 106, 10777. (10) Miyajima, K.; Nakajima, A.; Yabushita, S.; Knickelbein, M. B.; Kaya, K. J. Am. Chem. Soc. 2004, 126, 13202. (11) Xiang, H. J.; Yang, J. L.; Hou, J. G.; Zhu, Q. S. J. Am. Chem. Soc. 2006, 128, 2310. (12) Maslyuk, V. V.; Bagrets, A.; Meded, V.; Arnold, A.; Evers, F.; Brandbyge, M.; Bredow, T.; Mertig, I. Phys. ReV. Lett. 2006, 97, 097201. (13) Zhou, L. P.; Yang, S. W.; Ng, M. F.; Sullivan, M. B.; Tan, V. B. C.; Shen, L. J. Am. Chem. Soc. 2008, 130, 4023. (14) Wang, L.; Cai, Z. X.; Wang, J. Y.; Lu, J.; Luo, G. F.; Lai, L.; Zhou, J.; Qin, R.; Gao, Z. X.; Yu, D. P.; Li, G. P.; Mei, W. N.; Sanvito, S. Nano Lett. 2008, 8, 3640. (15) Zhu, L. Y.; Wang, J. L. J. Phys. Chem. C 2009, 113, 8767. (16) Koleini, M.; Paulsson, M.; Brandbyge, M. Phys. ReV. Lett. 2007, 98, 197202. (17) Shen, L.; Yang, S. W.; Ng, M. F.; Ligatchev, V.; Zhou, L. P.; Feng, Y. P. J. Am. Chem. Soc. 2008, 130, 13956.

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