Introduction

One-dimensional (1D) monatomic metals or molecular nanowires have attracted tremendous interest in recent decades owing to their promising potential for next-generation nanoelectronics1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23. The quantization of their conductance in multiple units of \({G}_{0}=2{e}^{2}/h\) is a signature of ballistic transport in a 1D nanowire. Previous studies have demonstrated that noble metals, such as Au, Ag, and Cu, can exhibit quantum conductance of 1\({G}_{0}\) in the monatomic wires, which is indicative of a single-spin-degenerate channel24,25,26. When the metallic nanowire is magnetic, a half-integer conductance of 0.5\({G}_{0}\) may be observed because of the lifted spin degeneracy, suggesting a single-spin channel. Enormous efforts have been devoted to the search for 1D magnetic nanowires that exhibit a half-integer conductance, as it simplifies the processes of the production, detection, and manipulation of fully spin-polarized current. For instance, detecting the spin current can be accomplished by simply measuring a half-integer quantized conductance plateau, without the need of sophisticated techniques, such as an external magnetic field or top-gate bias2,11,15. Furthermore, benefiting from the potential to precisely control and monitor spin transport in a single-spin channel, these 1D magnetic systems can be utilized for versatile applications, including spin-qubit quantum computer27, spin filter28,29,30,31, and magnetic random access memory32,33.

Rodrigues et al. first observed half-integer conductance in a monatomic Co nanowire and claimed that such an effect originated from a single fully spin-polarized channel2. However, subsequent experimental and theoretical studies questioned this outcome34,35,36,37,38,39,40,41,42,43,44, and argued, instead, that the 0.5\({G}_{0}\) conductance may be caused by the contamination of H2 in the Co nanowire37. For most transition metal wires, many d bands cross the Fermi level in both majority and minority spin channels, and thus a complete spin polarization appears to be impossible34,35,36,38,39,40,41,42,43,44. Furthermore, from a practical point of view, monatomic metal wire is inherently unstable and readily contaminated by ambient gas. Consequently, many researchers have redirected their attention to exploring other 1D systems, such as 1D organic, organometallic, and inorganic nanowires. Although several experimental works have claimed the observation of half-integer conductance in 1D quantum systems5,15,45, they relied heavily on sophisticated techniques to create a single-spin channel, such as an external magnetic field or gate voltage. For instance, 1D GaAs nanowire, through the modulation of top-gate bias, would exhibit a half-integer quantum conductance5. Theoretical studies have proposed that 1D multidecker organometallic sandwich molecular wires (SMWs) can exhibit half-metallicity property with a single d band crossing the Fermi level, e.g., (MnBz)∞7,9, (VCp)∞9,10 and (CoH3)∞21. However, because of the high-symmetry structure of SMWs, this d band is actually a two-fold degenerate band e1 (\({d}_{{xz}}\), \({d}_{{yz}}\)) or e2 (\({d}_{{xy}}\), \({d}_{{x}^{2}-{y}^{2}}\)), resulting in two ballistic conductance channels. In other words, these SMWs still exhibit an integer conductance quantization of 1G0. To date, the existence of a 1D nanowire that intrinsically displays a half-integer conductance without utilizing sophisticated techniques remains an unsolved puzzle.

In this work, we have proposed that 1D SMW composed of Cobalt atoms and fulvalene (\({{\rm{C}}}_{10}{{\rm{H}}}_{8}\)) molecules, referred to as (CoFul)∞, can exhibit a half-integer conductance quantization of 0.5 G0. Our calculations demonstrate that the introduction of fulvalene enhances the physical and chemical stabilities of the (CoFul)∞ nanowire. In addition, the fulvalene provides a mechanism of symmetry-selective filtering, which creates a single-spin channel responsible for the half-integer conductance quantization. Besides, this (CoFul)∞ nanowire favors a ferromagnetic ground state with a magnetic moment of 1\({\mu }_{B}\) localized at the Co atom, which may serve as a perfect 1D Ising spin-1/2 chain46. When arranged in a 2D nanowire array, the (CoFul)∞ exhibits a high Curie temperature of 267 K, making it feasible for room-temperature applications. With exceptional features above, the (CoFul)∞ nanowire offers an invaluable platform for verifying previously proposed fundamental theories, such as the quantum communication protocol through single-spin-qubit transiting in 1D ferromagnet47, single-spin inelastic tunneling spectroscopy48,49 and spin dynamics theory of 1D Ising single-spin chain50,51,52,53. Furthermore, a class of (TMFul)∞ nanowires, derived from the (CoFul)∞, exhibit a broad range of electronic and magnetic properties, holding great potential for multifunctional spintronics applications. To showcase this potential, we have designed a molecular magnetic tunneling junction (MTJ)31 utilizing the (CoFul)∞ nanowire. Benefiting from the spin transmitting confined in a single open spin channel, this MTJ exhibits exceptional performance, with an impressive spin filter efficiency (SFE) of nearly 100% and a staggering tunneling magneto-resistance (TMR) of up to ~107%. To the best of our knowledge, these outcomes represent the best record in the field of molecular MTJs thus far.

Results

Stability of 1D (CoFul)∞ nanowire and feasibility of experimental design

Prior to showcasing the features of 1D (CoFul)∞ nanowire, we first elucidate why a pure monatomic Co nanowire fails to give a complete spin current. The optimized lattice constant of the Co nanowire is 2.16 Å, as shown in Fig. 1a, and two initial magnetic configurations are taken into account for a double-unit-cell containing two Co atoms: ferromagnetic state (FM) and antiferromagnetic state (AFM). Consistent with previous works1,36,41,43,54, the Co nanowire favors the FM phase, having an exchange energy (\({\Delta E}_{{\rm{ex}}}={E}_{{\rm{AFM}}}-{E}_{{\rm{FM}}}\)) of 0.98 eV and a magnetic moment of 2.13 \({\mu }_{B}\) per Co atom. The conductivity of the Co nanowire can be described by the Landauer formula \(G={G}_{0}/2{\sum }_{n,\sigma }{T}_{n,\sigma }\), where \({T}_{n,\sigma }\) is the transmission coefficient of the nth conduction channel for a spin \(\sigma\). Generally, under the ballistic regime, the conductance can be determined directly by counting the total number of conduction channels, i.e., the total number of dispersive bands crossing the Fermi level. As shown in Fig. 1b, the spin-polarized band structure of the Co nanowire reveals that the bands near the Fermi level are primarily dominated by the d orbitals of Co. Only one ballistic conductance channel, arising from the hybridization of s orbital and \({d}_{{z}^{2}}\) orbital, is present for the majority spin, yielding a conductance of \({G}_{0}/2\). For the minority spin, six ballistic conductance channels exist, stemming from the degenerate \({d}_{{xz}}\) and \({d}_{{yz}}\) orbitals, the degenerate \({d}_{{xy}}\) and \({d}_{{x}^{2}-{y}^{2}}\) orbitals, and two s-\({d}_{{z}^{2}}\) hybridized orbitals. These conductance channels collectively result in a total conductance of 3.5G0. Due to the co-contribution of both the majority and minority spins, the electrons propagating along the Co nanowire are not fully spin-polarized.

Fig. 1: The atomic structure and electronic and transport properties of the Co nanowire.
figure 1

a The optimized atomic structure of 1D Co nanowire and b the corresponding spin-polarized band structure and tunneling conductance.

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To attain a complete spin-polarized current, a fulvalene molecule (\({{\rm{C}}}_{10}{{\rm{H}}}_{8}\)) is inserted between two adjacent Co atoms in the Co nanowire, therefore generating a Cobalt-fulvalene sandwich nanowire, referred to as (CoFul)∞. This arrangement is made possible in the experiment, as demonstrated in previous experimental works55, that a planer fulvalene ligand linking two metal atoms will emerge after fusing two metallocene (M(C5H5)2) molecules. Moreover, a recent experiment56 has successfully synthesized metallocene polymers with more than two metallocene molecules. Drawing on similar strategies, it is feasible to experimentally fabricate a 1D (CoFul)∞ nanowire by polymerizing Cobaltocene (Co(C5H5)2) molecules (Fig. 2a). The optimized lattice constant of the (CoFul)∞ nanowire is determined to be 5.33 Å, while the calculated perpendicular Co-Cyclopentadiene distance is 1.71 Å. The H-C bond lengths are found to be 1.09 Å, and the C-C bond lengths range from 1.43 Å to 1.44 Å. We preliminarily evaluate the electronic stability of the (CoFul)∞ nanowire using the binding energy, defined as \({E}_{{\rm{b}}}={E}_{{\rm{w}}}-{E}_{{\rm{Co}}}-{E}_{{\rm{Ful}}}\), where \({E}_{{\rm{w}}}\), \({E}_{{\rm{Co}}}\) and \({E}_{{\rm{Ful}}}\) represent total energies of the nanowire, Co atom, and fulvalene molecule, respectively. The binding energy is calculated to be –6.1 eV, indicating good electronic stability. At room temperature of 300 K, the ab initio molecular dynamics (AIMD) simulations are performed to assess the thermodynamic stability of the (CoFul)∞ nanowire, and the phonon dispersion is also calculated to confirm the dynamic stability. As illustrated in Supplementary Figs. 1, 2, the results suggest that the structure is thermally and dynamically stable. Finally, we access the (CoFul)∞ nanowire’s chemical stability through the adsorption of O2, and the results show that the O2 cannot be adsorbed (more details can be seen in Supplementary Figs. 3 and 4). The sheltering effect of the fulvalene renders the Co atom inert in the ambient air. These findings highlight the role of the fulvalene in stabilizing both the physical and chemical stabilities of the (CoFul)∞ nanowire.

Fig. 2: The atomic structure and electronic, magnetic and transport properties of the (CoFul)∞ nanowire.
figure 2

a Schematic for the synthesis of the 1D (CoFul)∞ nanowire from the polymerization of Cobaltocene molecules. b The spin-polarized band structure, conductivity and c spin charge density isosurface of the (CoFul)∞ nanowire. d The Co lone pair hybrid bond (1c bond) consists of \({d}_{{yz}}\) orbital with occupancy of 0.49 |e| and \({d}_{{xz}}\) orbital with occupancy of 0.48 |e| responsible for the 1 \({\mu }_{B}\) magnetic moment in the (CoFul)∞ nanowire. e The side views and top views of the wavefunctions of the \({d}_{{yz}}\) band and f the \({d}_{{xz}}\) band in the band structure shown in b.

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Magnetic, electronic, and transport properties

Next, we investigate the magnetism and conductivity of the (CoFul)∞ nanowire. Similarly, the (CoFul)∞ also prefers the FM phase and a magnetic moment of 1 \({\mu }_{B}\) is predominantly localized at the Co atom (Fig. 2c). Since the axis orientation of the \({d}_{{z}^{2}}\) orbital of Co is not aligned with the z-direction of the unit cell, the utilization of the conventional projected density of states (PDOS) analysis based on the coordinates of the unit cell, is inapplicable in this system. To decipher the orbital nature of the magnetic moment, we employ a more advanced analysis technique, namely the solid state adaptive natural density partitioning (SSAdNDP) (see Supplementary Fig. 5 for details)57. Our analysis reveals that the 1 \({\mu }_{B}\) magnetic moment is derived from the hybrid \({d}_{{yz}}\) and \({d}_{{xz}}\) orbital of Co with occupation numbers of 0.49 |e| and 0.48 |e| , respectively (Fig. 2d). The band structure of the (CoFul)∞ nanowire also corroborates this finding. As depicted in Fig. 2b, the (CoFul)∞ exhibits half-metallicity, in which the majority spin channel is metallic while the minority spin channel shows an indirect band gap of 1.87 eV. Similar to the situation of Co nanowire, the bands near the Fermi level are also dominated by the d orbitals of Co. The behavior of the frontier bands near the Fermi level can be explained by crystal field theory combined with molecular orbital theory as follows. It’s noteworthy that the principal symmetry axis of the (CoFul)∞ nanowire is along the x-axis, resulting in higher C2h symmetry instead of the lower Ci symmetry when either y-axis or z-axis is considered as the principal axis. The \({d}_{{yz}}\), \({d}_{{z}^{2}}\) and \({d}_{{x}^{2}-{y}^{2}}\) orbitals of Co exhibit symmetry with respect to C2 operation, possessing Ag symmetry, while the \({d}_{{xz}}\) and \({d}_{{xy}}\) orbitals are antisymmetric and thus exhibit Bg symmetry. Under the C2h crystal field, the d orbitals of Co experience energy level split due to their different coupling strengths with the \(\pi\) orbitals of the fulvalene. For instance, since the orbital lobes of \({d}_{{xy}}\) and \({d}_{{x}^{2}-{y}^{2}}\) are parallel to the fulvalene plane (Supplementary Fig. 6), their overlap with the \(\pi\) orbitals of fulvalene is minimal, resulting in two localized \({d}_{{xy}}\) and \({d}_{{x}^{2}-{y}^{2}}\) bands located far from the Fermi level in both the majority and the minority spin channels. The least overlap between \({d}_{{z}^{2}}\) orbital and \(\pi\) orbital can be anticipated since the orbital lobes of \({d}_{{z}^{2}}\) are pointed towards the “holes” of the carbocycles. Consequently, a localized \({d}_{{z}^{2}}\) band is formed with an energy level lower than that of all other d bands. On the contrary, the remaining \({d}_{{yz}}\) orbital and \({d}_{{xz}}\) orbital of Co, vertically oriented toward the carbocycles, have appreciable coupling with the \(\pi\) orbitals of fulvalene (Fig. 2e, f), which give rise to two half-occupied bands at the Fermi level in the majority spin channel. The flat dxz band, mainly composed of the localized Bloch states, makes little contribution to the conductivity in realistic electronic devices, as will be demonstrated later. Thus, only the dispersive dyz band contributes a single-spin conductance channel, characterized by a conductance plateau of 0.5 G0 around the Fermi level (Fig. 2b). In the minority spin channel, both the \({d}_{{yz}}\) and \({d}_{{xz}}\) bands are unoccupied, displaying a semiconductor behavior.

To elucidate why originally degenerate \({d}_{{yz}}\) and \({d}_{{xz}}\) bands in the Co nanowire (Fig. 1b) are split into a dispersive \({d}_{{yz}}\) band and a flat \({d}_{{xz}}\) band, respectively, in the (CoFul)∞ nanowire (Fig. 2b), we compare the wavefunctions of the \({d}_{{yz}}\) and \({d}_{{xz}}\) bands of the (CoFul)∞ nanowire (Fig. 2e, f) with the frontier molecular orbitals of fulvalene (Fig. 3a). Due to symmetry matching, only the LUMO (Ag symmetry) and HOMO-1 (Bg symmetry) of fulvalene exhibit nonzero overlap with the \({d}_{{yz}}\) (Ag symmetry) and \({d}_{{xz}}\) (Bg symmetry) orbitals of Co, respectively. The HOMO-1 of fulvalene is highly localized and no electron density resides on the exocyclic C-C double bond between the two five-membered rings (Fig. 3a). Thus, two adjacent Co atoms cannot interact with each other through the localized HOMO-1 of fulavelne (the top view of Fig. 2f), rendering a flat \({d}_{{xz}}\) band at the Fermi level. The situation is opposite for the dyz band because strong interaction between two adjacent Co atoms is facilitated through the diffused LUMO (the top view of Fig. 2e), yielding an open ballistic conductance channel. These findings demonstrate that the fulvalene acts as a mediator of the interaction between the Co atoms, and this mediation is orbital-selective: the majority of d orbitals are blocked, while only permitting the \({d}_{{yz}}\) orbital to form the long-range interaction between the adjacent Co atoms.

Fig. 3: The molecular orbitals of the fulvalene and the electron configuration and Curie temperature of the (CoFul)∞ nanowire.
figure 3

a The LUMO and HOMO-1 of the fulvalene. b The PDOS and the d orbital occupation diagram of Co in the (CoFul)∞ nanowire. The PDOS in the left panel is obtained from the band structure in Fig. 2b. The direction of the arrow in the right panel represents the majority spin or minority spin and the full-filled or half-filled ball represents full occupation or half occupation, respectively. c The variation of the total magnetic moment per unit cell of the 2D (CoFul)∞ nanowire array with respect to the temperature.

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To investigate the feasibility of achieving quantized half-integer conductance in realistic electronic devices, we have examined the transport properties of finite-sized (CoFul)n nanowires connected between two bulk Co(111) electrodes. The devices are constructed by connecting (CoFul)n nanowires of varying lengths ((CoFul)3, (CoFul)5, (CoFul)7 and (CoFul)9) to the hollow sites of the Co(111) surfaces, as depicted in Supplementary Fig. 7. The transport calculations demonstrate that as the length of the (CoFul)n nanowire increases, the conductance of the device rapidly converges to 0.5 G0 (Supplementary Fig. 8a), and the (CoFul)7 nanowire is sufficiently long to exhibit half-integer conductance. To unravel the underlying transport mechanism responsible for the observed half-integer conductance, we have calculated the tunneling eigenchannel of the (CoFul)7 device. As shown in Supplementary Fig. 8b, the tunneling eigenchannel consists of only the dyz orbitals of Co and the dispersive \(\pi\) orbitals of fulvalenes, which is consistent with the conduction mechanisms of 1D infinite (CoFul)∞ nanowire.

Origin of magnetic moment and half-metallicity

We have proposed a simplified schematic model to elucidate the origin of the magnetic moment and half-metallicity in the (CoFul)∞ nanowire. The d orbital occupation diagram of Co is constructed based on the PDOS of Co in the (CoFul)∞ nanowire. As illustrated in Fig. 3b, the energy level of each d orbital in the right panel is aligned with the peak position of corresponding d orbital in the PDOS in the left panel. The occupation of each d orbital is determined by integrating the PDOS of the corresponding d orbital below the Fermi level. The Co possesses nine valence electrons (3d74s2), and according to the Hückel rule, two electrons will be captured by the fulvalene to form a stable aromatic configuration of 4 m + 2 electrons. Six other electrons occupy the \({d}_{{x}^{2}-{y}^{2}}\), \({d}_{{xy}}\), and \({d}_{{z}^{2}}\) orbitals in both the majority and minority spin channels (Fig. 3b). Lastly, the remaining one electron will half-occupy the degenerate \({d}_{{yz}}\) and \({d}_{{xz}}\) orbitals, respectively, in the majority spin channel, which is responsible for the magnetic moment of 1 \({\mu }_{B}\) and the appearance of half-metallicity. On the other hand, the degenerate \({d}_{{yz}}\) and \({d}_{{xz}}\) orbitals in the minority spin channel are unoccupied, leading to the semiconducting characteristic.

For comparison, we have also performed calculations using the PBE + U scheme58. The Hubbard parameter Ueff = U-J is set to 3.3 eV for Co, which has been widely used in previous reports59,60,61,62. The results demonstrate that the main signatures, including the half-integer conductance and FM ground state with a magnetic moment of 1 \({\mu }_{B}\), are still preserved. In comparison with the results of PBE functional, the differences are a widened band gap of the minority spin channel from 1.87 eV to 3.24 eV (Supplementary Fig. 9) and a slight increase of \({\Delta E}_{{\rm{ex}}}\) from 0.103 eV to 0.112 eV.

In order to gain further insights of the magnetic interactions, we have also investigated the exchange couplings of the (CoFul)∞ nanowire. The exchange coupling of the (CoFul)∞ nanowire was studied using the Ising model \(H=-{\sum }_{\left\langle i,j\right\rangle }{{JS}}_{i}{S}_{j}-{\sum }_{\left\langle \left\langle i,j\right\rangle \right\rangle }{{J}^{{\prime} }S}_{i}{S}_{j}\), where \(J\) and \({J}^{{\prime} }\) represent the exchange couplings for the nearest-neighbor and next nearest-neighbor sites, respectively, and \({S}_{i}\) denotes the magnetic moment at each site. To obtain the exchange couplings, we have considered three magnetic configurations: FM, AFM1 and AFM2 in a (1 × 1 × 4) supercell, as displayed in the Supplementary Fig. 10. By mapping the total energies obtained by PBE + U scheme to the Ising spin Hamiltonian, the exchange couplings can be determined,

$${E}_{{\rm{FM}}}={E}_{0}-4J{\left|S\right|}^{2}-4{J}^{{\prime} }{\left|S\right|}^{2}$$
(1)
$${E}_{{\rm{AFM}}1}={E}_{0}+4J{\left|S\right|}^{2}-4{J}^{{\prime} }{\left|S\right|}^{2}$$
(2)
$${E}_{{\rm{AFM}}2}={E}_{0}+4{J}^{{\prime} }{\left|S\right|}^{2}$$
(3)

where \({E}_{0}\) is the ground state energy independent of the spin configuration and S is the spin on each Co atom. The calculated values of \(J\) and \({J}^{{\prime} }\) are 28 meV and 4.2 meV, respectively, for the (CoFul)∞ nanowire. Clearly, the nearest-neighbor exchange coupling dominates in the (CoFul)∞ nanowire. Similarly, applying the same procedure, the \(J\) and \({J}^{{\prime} }\) of the Co nanowire are estimated to be 32.4 meV and 8.1 meV, respectively.

Notably, the possibility of Peierls transition needs to be assessed since if a partially filled band crosses the Fermi level exactly at the wavevector \(k={\rm{\pi }}/2c\) (c is the lattice constant), a structural distortion of dimerization may happen because of the strong electron-phonon interaction63. In this case, we duplicate the unit cell and optimize lattice of the supercell structure. Actually, no dimerization occurs, revealing that the coupling between the Co and the fulvalene is strong enough to prevent the Peierls transition.

It is worth noting that a recent wonderful theoretical work has also reported a half-metallic nanowire, (CoH3)∞21, capable of producing 100% spin-polarized current. In that system, the bands crossing the Fermi level in the majority spin channel are two-fold degenerate \({d}_{{xy}}\) and \({d}_{{x}^{2}-{y}^{2}}\) bands, contributing two ballistic conductance channels instead of single ballistic channel.

Finally, we have also investigated the electronic and magnetic properties of a class of (TMFul)∞ nanowires constructed by substituting the metal atom with all other 3d-block transition metals. As summarized in Supplementary Table 1, the (TMFul)∞ nanowires display diverse electrical and magnetic properties. Among them, (ScFul)∞, (TiFul)∞, (MnFul)∞ and (NiFul)∞ favor the AFM ground states, while (VFul)∞ and (CrFul)∞ prefer the FM ground state. The (FeFul)∞ is non-magnetic (NM) with a largest band gap of 2.96 eV. Interestingly, the band gap values span evenly between 0 and 3 eV. Thanks to their diverse characteristics, this class of (TMFul)∞ nanowires have great prospects in a wide range of applications, including transistors, optoelectronics and magnetic memory devices. Although this category of (TMFul)∞ nanowires present diverse characteristics, in this work, we pay particular attention to the (CoFul)∞ nanowire that displays half-integer conductance quantization.

Curie temperature and spintronic device performance

To develop practical spintronics with the (CoFul)∞ nanowire, understanding the variation of magnetic moment with regard to temperature is crucial. Despite the Mermin-Wagner theorem64 suggesting that long-range magnetic ordering is unlikely in an infinite 1D chain at nonzero temperature, many studies have demonstrated that the magnetic ordering can be stabilized in a stacking nanowire bundle or a 2D nanowire array, where the interchain coupling plays a key role in this behavior65,66,67,68. For instance, an experimental study showed that a weak interchain coupling of 0.1 K (0.009 meV) was strong enough to establish long-range Ferromagnetic ordering in quasi-1D p-NPNN nanowire65. On the basis of this discovery, we build a 2D (CoFul)∞ nanowire array and then perform a Monte Carlo (MC) simulation69,70 to determine its Curie temperature (\({T}_{{\rm{c}}}\)) based on the Ising model \(H=-{\sum }_{\left\langle i,j\right\rangle }{{JS}}_{i}{S}_{j}\), where \(J\) is the nearest-neighbor exchange parameter. The optimal interchain distance of the 2D (CoFul)∞ nanowire array is determined from the curve of the total energy versus interchain distance. For each fixed interchain distance, we optimized the structure using the DFT + D3 scheme71 to include the van der Waals interactions, and then obtained the total energy after the optimization. The results are shown in Supplementary Fig. 11, and the optimal interchain distance is estimated to be 6.5 Å. The intrachain exchange coupling \({J}_{1}\) and the interchain exchange coupling \({J}_{2}\) of the 2D nanowire array (Supplementary Fig. 12) are calculated to be 28 meV and 2.1 meV, respectively, by PBE + U scheme. In the MC simulation, we use a (100 × 100) supercell and perform 1 × 109 loops to achieve the average magnetic moment for each temperature value. The temperature dependence of the average magnetic moment per unit cell is shown in Fig. 3c, with an estimated \({T}_{{\rm{c}}}\) of 267 K. This value is significantly higher than that of quasi-1D CrSbSe3 nanowire (95 K)68.

The characteristics of the (CoFul)∞ nanowire offer exciting opportunities for spintronic applications. Here, we exemplarily showcase how well it performs as a spin filter or spin valve device. As illustrated in Fig. 4a, a molecular magnetic tunneling junction (MTJ)31 is constructed by coupling benzene between two (CoFul)∞ nanowire electrodes. The structure of the entire molecular junction has been optimized and the results show that the benzene favors a coplanar configuration with the cyclopentadiene cycles (Supplementary Fig. 13). The spin-filter efficiency (SFE) and tunneling magneto-resistance (TMR) of the device are assessed using the following formulas:

$${\rm{SFE}}=\frac{\left({I}_{\uparrow }-{I}_{\downarrow }\right)}{\left({I}_{\uparrow }+{I}_{\downarrow }\right)}\times 100 \%$$
(4)
$${\rm{TMR}}=\frac{\left({I}_{{\rm{P}}}-{I}_{{\rm{AP}}}\right)}{{I}_{{\rm{AP}}}}\times 100 \%$$
(5)

where the \({I}_{\uparrow }\) and \({I}_{\downarrow }\) are majority spin and minority spin currents, respectively, and the \({I}_{{\rm{P}}}\) and \({I}_{{\rm{AP}}}\) are the currents in parallel and anti-parallel magnetic configurations, respectively. Our spin transport simulations show that the SFE is nearly 100% even when the current reaches up to 7 \(\mu A\) (Supplementary Fig. 14). Additionally, a staggering TMR of ~107% is recorded throughout the whole bias range, which, to the best of our knowledge, represents the best record in the field of molecular MTJs to date. (Fig. 4b). In this device, a huge TMR can be achieved without compromising the current’s strength. It has addressed a critical limitation observed in many previously reported organic-semiconductor-based MTJs72, namely, an extremely low on-state current is produced in order to achieve a huge TMR, which is detrimental to real device operation. These findings show that the (CoFul)∞ nanowire can function flawlessly as a spin filter or spin valve device. For comparison, the TMRs of other 3D, 2D, and 1D molecular MTJ systems are as follows: bulk Ni (600%)31, bulk Co (60%)73, 2D Fe3GeTe2 (6 × 103%)74, Co nanowire (2 × 104%)75, (CoCp2)∞ nanowire (25%)76 and Fe3O4 nanowire (2 × 104%)77. Notably, Kim et al. theoretically predicted that quasi-1D graphene nanoribbon (GNR) would exhibit an amazing TMR of 106%78,79. However, the GNR still confronts challenges for practical application because experimental works have demonstrated that the graphene exhibits no signs of ferromagnetism at any temperature80,81. The absence of ferromagnetic behavior is ascribed to weak ferromagnetic exchange coupling among the magnetic moments in carbon-based materials82,83.

Fig. 4: The atomic structure and transport properties of the (CoFul)∞-benzene-(CoFul)∞ device.
figure 4

a The schematic structures of the (CoFul)∞-benzene-(CoFul)∞ device in parallel and anti-parallel magnetic configurations. b The I–V curves of the (CoFul)∞-benzene-(CoFul)∞ device in parallel and anti-parallel magnetic configurations (left vertical axis) and the derived TMR ratio (right vertical axis).

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The giant TMR observed in the (CoFul)∞-based MTJ is primarily attributed to the characteristic of single-spin channel transport in the (CoFul)∞ electrodes. Generally, the transport in an MTJ is dominated by two key factors, namely, the coupling between the molecule and electrodes, and the matching of Bloch states between two electrodes. For the parallel magnetic configuration, the transport is dominated by the coupling between the molecule and electrodes because the Bloch states in two electrodes are already well matched. According to the tunneling eigenchannel analysis (Supplementary Fig. 15b)84, the LUMO of benzene can strongly couple with the Bloch states of the \({d}_{{yz}}\) bands in the electrodes, resulting in a conductance of 0.49 G0 at the Fermi level for the majority spin (Supplementary Fig. 15a). Considering the fact that the benzene is connected to the electrodes through the C-C single bonds, the conductance limit of this MTJ is restricted strictly to 0.5 G0 for either majority spin or minority spin, regardless of how many spin channels are available for transport in the electrodes. In other words, the conductance of this MTJ in the parallel magnetic configuration has already been maximized with the help of the strong coupling between the LUMO of benzene and the \({d}_{{yz}}\) bands of electrodes. In contrast, the transport in the anti-parallel magnetic configuration is dominated by the mismatch of Bloch states between two electrodes. Since only single-spin channel is available for transport in the electrodes, combined with a large energy mismatch between the \({d}_{{yz}}\) band of the majority spin in the left electrode and the \({d}_{{yz}}\) band of the minority spin in the right electrode, the conductance of this MTJ is minimized to a mere 2.8 × 10−6 G0 (Supplementary Fig. 15c). Evidently, the \({d}_{{yz}}\) band serves opposing roles in the parallel and anti-parallel magnetic configurations: it maximizes the transport in the parallel magnetic configuration through strong coupling with the LUMO of benzene while simultaneously minimizing the transport in the anti-parallel magnetic configuration via a large mismatch between the \({d}_{{yz}}\) bands of two electrodes. This mechanism results in a staggering TMR observed in this molecular MTJ.

Discussion

In conclusion, using the first-principles methods, we have investigated the electronic, magnetic, and transport properties of the (CoFul)∞ nanowire. The (CoFul)∞ nanowire is a half-metallic ferromagnet that exhibits single-spin channel transport characteristics, and its magnetic moment arises from the half-occupied \({d}_{{yz}}\) and \({d}_{{xz}}\) orbitals of the Co atom. By comparing with a pure Co nanowire, we have demonstrated that the incorporation of fulvalene has three-fold effects in the (CoFul)∞ nanowire: (1) stabilization of the structure and reduction of environmental contamination; (2) establishment of a single ballistic conductance channel by splitting the two-fold degenerate \({d}_{{yz}}\) and \({d}_{{xz}}\) bands and blocking one of these two conductance channels; (3) maintaining the superexchange coupling between adjacent Co atoms. Furthermore, a class of (TMFul)∞ nanowires exhibit an abundance of desirable properties, making them attractive candidates for multifunctional spintronics. In this work, we particularly focus on the spintronic device performance of the (CoFul)∞ nanowire. Benefiting from the spin transmitting confined in a single open spin channel, the (CoFul)∞-based molecular MTJ can function flawlessly as a spin filter or spin valve device.

Methods

First-principles calculations details

All first-principles calculations based on the spin-polarized density functional theory (DFT) were carried out by using the Vienna ab Initio Simlation Package (VASP)85,86. The Projector augmented wave pseudopotentials87 for the core and the Perdew-Burke-Ernzerhof (PBE) format88 of the generalized gradient approximation (GGA) for the exchange-correlation functional were adopted. The DFT-D3 scheme71 was used to account for the van der Waals interaction. We set the kinetic energy cutoff to be 520 eV, and optimized the structures until the forces were below 0.01 eV/Å. To eliminate the interaction between the nanowire and its images, the vacuum spaces in the x and y directions were set to be 20 Å. The Brillouin Zones of the Co nanowire and the (CoFul)∞ nanowire were sampled by 1 × 1 × 23 and 1 × 1 × 9 k points, respectively, in the Monkhorst-Pack scheme. In order to assess the thermal dynamic stability, AIMD simulations were performed in the canonical ensemble with Nosé-Hoover thermostat (NVT). In the AIMD simulations, a (1 × 1 × 2) supercell was used and each time-step of 1 fs was adopted for a total duration of 2 ps at 300 K. For the analysis of the chemical bonding pattern in the (CoFul)∞ nanowire, we used the SSAdNDP scheme57 by projecting the delocalized plane-wave basis set from the VASP code to a localized Karlsruhe def2-SVP basis set.

Transport properties calculations details

All the transport calculations were performed with the steady-state (SS)-DFT89,90,91,92. In the transport simulations, Troullier-Martins pseudopotentials93 for the core and double-\(\zeta\) polarized (DZP) basis set were employed. The tunneling eigenchannel analysis was done by the software INELASTICA94.