Spin Transport Properties of One-Dimensional Benzene Ligand Organobimetallic Sandwich Molecular Wires.

Organometallic sandwich complexes, composed of cyclic hydrocarbon ligands and transition-metal atoms, display unique physical and chemical properties. In this work, the electronic and spin transport properties of one-dimensional (1D) VBz2 ligand bimetallic sandwich complexes, VBz2-TM (TM = Cr, Mn, and Fe), are systematically investigated using density functional theory and nonequilibrium Green's function method. The results show that all the 1D infinite molecular wires [(VBz2)TM]∞ (TM = Cr-Fe) are found to be thermodynamically stable with high binding energies (∼1.0-3.45 eV). In particular, they are predicted to be ferromagnetic half metals. Moreover, the I-V curves exhibit negative differential resistance for one, two, and three VBz2-TM wires at TM = Cr, Mn, and Fe, respectively, which is of great significance for certain electronic applications. Our findings strongly suggest that the benzene ligand bimetallic sandwich molecular wires are good candidates for potential electronics and spintronics.

Introduction

Since the discovery of ferrocene,[1] organometallic sandwich complexes, composed of metal atoms and π-conjugated ligands, have been inspiring ongoing interests because of their excellent electronic and magnetic properties and have become promising candidates for the next generation of electronic and spintronic devices. To date, various organometallic sandwich complexes,[2−55] incorporating organic–monocyclic–hydrocarbon ligands such as Bz(=C6H6),[2−21] Cp(=C5H5),[20−25] COT(=C8H8),[26−30] and so forth and organic–polycyclic–hydrocarbon ligands such as Np(=C10H6),[31,32] Pn(=C8H6),[33,34] coronene (=C24H12),[35] and so forth, have been exemplified; besides, the metal atoms include the 3d transition-metal (TM) atoms and 4f lanthanide metal (Ln) atoms and so forth. In addition, such organometallic sandwich configurations consisting of bimetallic atoms[24,25] or mixed organic ligands[20] are also extensively addressed because of their tunable electronic and magnetic properties. Recently, the one-dimensional (1D) metal trihydride molecular nanowire MH3 (M = Sc, Cr, Mn, and Co) has been shown to have versatile magnetic properties, and the CoH3 nanowire shows the properties of a half metal (HM).[36]

Among the various organometallic sandwich complexes, vanadium(V)–Bz compounds are one of the most extensively studied systems. Experimentally, a stable V6Bz7 molecular chain as long as seven layers was successfully synthesized by the laser vaporization method.[5] Theoretically, Wang et al. investigated an achiral to chiral structure transition for VBz at n = 4,[7,8] which is due to spectral broadening and appearance of new spectra.[8] Besides, multilayer VBz sandwich clusters were predicted to be of great stability, and, in particular, VBz2 is experimentally shown to possess ultrahigh stabilities with high ionization energy.[4,9] The Stern–Gerlach experiment revealed that the magnetic moments of VBz (n = 1–4) are size-dependent at T = 154 and 296 K,[6] which are well elucidated by later density functional theory (DFT) calculation.[7] Using the DFT calculation, Xiang et al.[18] found that the 1D [VBz]∞ wire is a robust ferromagnetic (FM) HM. Maslyuk et al.[19] revealed that it is the direct exchange interaction between V atoms, leading to the FM ground state. Interestingly, such robust FM behaviors can also be conserved in the TM-stacked benzimidazole (Bzim)-modified single-stranded DNA structures.[52] Furthermore, coupling a finite VBz sandwich wire to magnetic (Ni(001) or Co(001)) electrodes makes it act as a nearly perfect molecular spin filter.[19] Moreover, high spin polarizations can be achieved to spin transport through the family of molecular systems the benzene–vanadium clusters sandwiched between carbon nanotube electrodes.[53]

On the other hand, the electronic and magnetic properties of the bimetallic multilayer sandwich complexes have more significant advantages via varying the organic ligands, metallic atoms, and so on. For example, the magnetic moments of TM(FeCp2) (TM = Ti, V, and Mn) are found to increase linearly with their size.[24] 1D [CpTiCpTM]∞ (TM = Cr and Fe), [CpCrCpTM]∞ (TM = Fe and Co), and [CpFeCpCo]∞ biorganometallic sandwich molecular wires (BOSMWs) are robust FM HMs.[25] Moreover, the amplitude and sign of the spin filter efficiency (SFE) of (CpFeCpV) multidecker sandwich clusters were investigated to be varied by choosing the contact condition.[54] Analogous to FeCp2, VBz2 is shown to be quite stable and can act as the building block to bond with other TM atoms forming stable bimetallic sandwich configurations. In our previous study, we investigated that 1D [BzVBzTM]∞ (TM = Sc, Ti, and Cr–Ni) molecular wires show rich electronic and magnetic properties depending on the choice of TM atoms.[14] In this work, we systematically investigate the spin transport behaviors of 1D [(VBz2)TM]∞ (TM = Cr–Fe) BOSMWs. Our results indicate that the bonding between “VBz2” and all the TM atoms in these 1D molecular wires is rather stable. Furthermore, all the studied 1D [(VBz2)TM]∞ (TM = Cr–Fe) BOSMWs are FM HMs. Interestingly, the I–V curves exhibit negative differential resistance (NDR) for one, two, and three 1D VBz2–TM molecular wires at TM = Cr, Mn, and Fe, respectively, which is of great significance for certain electronic devices, such as rectifier diodes.

Results and Discussion

The optimized lattice parameters for 1D [(VBz2)Cr]∞ BOSMW is 7.24 Å, which is a bit longer than that of its 1D [(FeCp2)Cr]∞ analogue (7.16 Å).[24] In contrast, the lattice parameters of 1D [(VBz2)Mn]∞ and [(VBz2)Fe]∞ BOSMWs are 7.02 and 6.92Å, respectively, much shorter than their [(FeCp2)Mn]∞(7.22 Å) and [(FeCp2)V]∞ (7.46 Å) analogues.[24] The distances of V or other TMs to the mass center of Bz rings in these 1D [(VBz2)TM]∞ BOSMWs are 1.722 Å/1.909 Å, 1.674 Å/1.841 Å, and 1.688 Å/1.782 Å at TM = Cr, Mn and Fe, respectively. Moreover, the TM-Bz (including V-Bz) distances in these bimetallic systems are slightly larger than that in [VBz]∞.[18,19] The stabilities of such 1D [(VBz2)TM]∞ BOSMWs are evaluated by calculating the binding energies with the following equationwhere E[ ] is the total energy of the molecular wires, VBz2 molecule, and TM atoms, respectively. The binding energies of these studied 1D [(VBz2)TM]∞ BOSMWs are 1.0, 1.27, and 3.45 eV for TM = Cr, Mn, and Fe, respectively, which is slightly smaller than that of the 1D [(FeCp2)TM]∞ analogues.[24] As shown in the density of state (DOS) plot in Figure a, all the 1D BOSMWs display a striking feature of combining a metallic (spin down) and semiconducting gap (spin up) at different spin channels, indicating that they are robust FM HMs, and such a result is similar to that of [VBz]∞[18,19] and our previous predicted BOSMWs.[14,25]

Figure 1

(a) DOS plots and (d–f) spin density plots of 1D [(VBz2)TM]∞ (TM = Cr, Fe, and Mn) BOSMWs. (b) Scheme of (VBz2)TM(VBz2) cluster connected to two Au(100) electrodes. Here, vertical solid lines present the borders of the central scattering region.

To calculate the electron transport properties through finite VBz2–TM molecular wires, we sandwich four types of clusters having different lengths and anchoring ends: (i) (VBz2)TM, (ii) (VBz2)TMBz, (iii) (VBz2)TMBzV, and (iv) (VBz2)TM(VBz2) (TM = Cr, Fe, and Mn), between two Au(100) electrodes (see Figure b). The distances between different terminated ends and Au(100) surfaces are around 2.60–2.70 Å, varying slightly within 0.05 Å. To quantify the transmission spin polarization, we calculate the SFE aswhere Tmaj(EF) and Tmin(EF) indicate the transmission coefficient of the majority and minority spin channel around the Fermi level, respectively. As shown in Table , the absolute value of SFEs for such 1D (VBz2)–TM molecular wires are in the range of 92–100%, in which the highest SFE is found for (VBz2)Cr, (VBz2)Mn(VBz2), and (VBz2)Fe(VBz2), respectively, ∼100%, and the least one is for (VBz2)FeBzV, ∼92%. Our results indicate that all the studied 1D VBz2–TM molecular wires act as robust spin filters independent of the molecular chain lengths, which are better than those of the FeCp2–V bimetallic wires, whose SFE is found to be sensitive to the choice of the contact condition.[54] In the case of VBz2–Cr complexes, the V–Au or Cr–Au contact is strong for spin-up transport, while the Bz–Au contact prefers spin-down transport (see Table ), showing that the transport behaviors are sensitive to the contact sites. In contract, different cases are envisioned for the VBz2–Mn and VBz2–Fe combinations, in which both contacts prefer the spin-down transport. On the other hand, such spin transport characters of these VBz2 ligand BOSMWs are different from those [(FeCp2)V] analogues.[54]

Table 1

Transmission Coefficient (T) and SFE of Different Clustersa

systems	T(↑)	T(↓)	SFE (%)
(VBz2)Cr	1.4342	0.0035	100
(VBz2)CrBz	0.0103	1.8163	–99
(VBz2)CrBzV	0.9631	0.0058	99
(VBz2)Cr(VBz2)	0.0033	1.8862	–100
(VBz2)Mn	0.0042	0.1693	–95
(VBz2)MnBz	0.0173	1.7523	–98
(VBz2)MnBzV	0.0165	0.9290	–97
(VBz2)Mn(VBz2)	0.0004	1.0800	–100
(VBz2)Fe	0.0103	0.8702	–98
(VBz2)FeBz	0.0524	1.6981	–95
(VBz2)FeBzV	0.0363	0.8671	–92
(VBz2)Fe(VBz2)	0.0005	1.0539	–100

The arrows (↑, ↓) represent the spin-up and spin-down electrons.

To further understand the spin transport characteristics of these 1D VBz2–TM systems, we plot the transmission spectra for different contact configurations in Figures and 3. As shown in Figure a–d, the transport behaviors through (VBz2)Cr and (VBz2)CrBzV clusters under the small bias voltage are mainly determined by the transmission peak originated from the perturbed highest occupied molecular orbitals (HOMO) of the spin-up channel, while in the case of (VBz2)CrBz and (VBz2)Cr(VBz2), the peak of the spin-down channel is dominant around the Fermi level. Also, it should be noted that the narrow peaks for the above two systems appear alternately in both spin-up and spin-down channels, indicating that the spin-up or spin-down transport can be realized by shifting the Fermi level. As shown in Figure e–h, wider spin-down peaks are found to cross the Fermi level for different VBz2–Mn arrangements, showing that they have a stable spin transport channel. Similar results can also be found for the 1D [(VBz2)Fe]∞ system (see Figure ). Moreover, the electronic transport behaviors are slightly affected by the chain lengths, which are consistent with the HM properties of 1D [(VBz2)TM]∞ BOSMWs.

Figure 2

(a–h) Spin-resolved transmission spectra of (VBz2)TM, (VBz2)TMBz, (VBz2)TMBzV, and (VBz2)TM(VBz2) (TM = Cr, Mn), respectively.

Figure 3

(a–d) Spin-resolved transmission spectra of (VBz2)Fe, (VBz2)FeBz, (VBz2)FeBzV, and (VBz2)Fe(VBz2), respectively.

The I–V curves for various finite VBz2–TM molecular wires coupled between two Au(100) electrodes are shown in Figure , and different shapes of the I–V curves are identified. For (VBz2)Cr, striking NDR features appear at around 0.4 V bias voltage. Interestingly, similar NDRs are also found for (VBz2)MnBzV, (VBz2)Mn(VBz2), (VBz2)Fe, (VBz2)FeBzV, and (VBz2)Fe(VBz2). This behavior has gained widespread interest because the NDR is necessary for several electronic components, such as the Esaki and resonant tunneling diodes.[55,56] Finally, we come to the different molecule–electrode coupling for spin-up electrons and spin-down electrons between these VBz2–TM (TM = Cr, Mn and Fe) systems. Taking (VBz2)Cr and (VBz2)Fe as examples, we present their lowest unoccupied molecular orbitals (LUMO), HOMO, and the secondary HOMO (HOMO-1) of the spin-up channel and spin-down channel in Table . For (VBz2)Cr, the LUMO and HOMO orbitals are localized in both spin-up and spin-down channels, particularly the spin-down electron states, which correspond to the small transmission spectra in the spin-up channel and zero transmission spectra in the spin-down channel, showing that the spin-down electron does not contribute to the electronic transport. While for (VBz2)Fe, the spin-up LUMO and HOMO orbitals are localized and does not contribute to the transport; in contrast, the spin-down LUMO and HOMO orbitals extend into both electrodes and induces transmission spectra in Figure a, which contribute to spin transmission at the Fermi level.

Figure 4

I–V curves for (VBz2)TM (the black line), (VBz2)TMBz (the red line), (VBz2)TMBzV (the blue line), and (VBz2)TM(VBz2) (the green line) [TM = (a) Cr, (b) Fe, and (c) Mn] coupled between two Au(100) electrodes.

Table 2

Isosurfaces for LUMO, HOMO, and HOMO-1 Orbitals of (VBz2)Cr and (VBz2)Fe on the Au(100) Surfacesa

The arrows (↑, ↓) represent the spin-up and spin-down electronic states.

Conclusions

In summary, we systematically investigated the structural, electronic, and spin transport behaviors of 1D [(VBz2)TM]∞ (TM = Cr, Fe, and Mn) BOSMWs by DFT and nonequilibrium Green’s function (NEGF) techniques. All the 1D [(VBz2)TM]∞ BOSMWs are energetically stable and are robust FM HMs. Moreover, six VBz2–TM clusters with different lengths and terminals possess NDR, which is essential for electronic applications. Our results indicate that the VBz2–TM combinations display good spin transport behaviors and are potential in future spintronic applications.

Computational Method

The structure optimizations and electronic properties are investigated within the framework of spin-polarized density functional theory as implemented in the Vienna ab initio simulation package.[57,58] The exchange–correlation potentials are treated by the generalized gradient approximation (GGA) parameterized by Perdew, Burke, and Ernzerholf.[59] The interaction between valence electrons and ion cores is described by the projector augmented wave method.[60,61] In our previous studies, we noted that both GGA and GGA + U schemes make negligible difference on the structural, electronic, and magnetic properties for these 3d TM organometallic systems;[20,25] here, we will discuss the results based on the GGA calculations in the whole work. In addition, the DFT-D2 method was adopted in all calculations to take into account the van der Waals interaction.[62] For 1D infinite [(VBz2)TM]∞ wires, periodic boundary conditions are applied along the TM–Bz axis within the unit cell containing two TM atoms and two Bz molecules (Figure a, red dotted line). To avoid the interaction of the nanowires from the adjacent unit cell, the vacuum space opposite to the periodic direction is set as large as 20 Å. The energy cutoff for the plane wave function is 400 eV. Numerical convergence was achieved with a tolerance of 10–6 eV in energy, and the force acting on each atom is less than 0.01 eV/Å. The ions in the periodic unit are allowed to fully relax. The Gaussian smearing technique of width 0.01 eV was used. The reciprocal space is sampled by 1 × 1 × 15 Monkhorst–Pack k-points mesh grids for the geometric optimization, and a much denser k-point grid (1 × 1 × 45) is used for the electronic structure calculation.

The spin transport simulation is carried out with the help of Atomistix Toolkit package.[63,64] The system is described by DFT with the standard nonlocal norm-conserving pseudopotential, and the quantum spin transmission is evaluated by the NEGF technique.[64,65] The wave functions are expanded on a numerical basis set of double-ζ plus polarization for TM atoms and single-ζ plus polarization for other atoms. The convergent results are achieved by using the Monck Horst–Pack grid with 100 k-points in the 1D Brillouin zone. The two-probe system can be divided into three parts, the scattering region, left electrode, and right electrode. To provide that the charge distribution in left and right electrodes are the same as that of the bulk phase, the scattering region is constructed by a VBz2–TM cluster and two(three) surface layers of the left(right) electrodes by including the screening effects in the contact region. The Au(100) surface is represented by a (4 × 4) primitive cell with periodic boundary conditions. To obtain the appropriate distance of the two-probe structural model, the distance between the central cluster and the electrode has been optimized by fixing the cluster and the electrode.