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. 2020 Dec 15;1(2):147–155. doi: 10.1021/jacsau.0c00049

Atomic Wires of Transition Metal Chalcogenides: A Family of 1D Materials for Flexible Electronics and Spintronics

Chanjuan Shang 1, Li Fu 1, Si Zhou 1,*, Jijun Zhao 1
PMCID: PMC8395661  PMID: 34467280

Abstract

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As analogues of two-dimensional (2D) layered materials, searching for one-dimensional (1D) van der Waals wired materials as 1D Lego blocks for integration and device applications has been pursued. Motivated by the recently synthesized atomic wires of molybdenum chalcogenide, here we explored the structures and stability of 66 atomic wires of 3d, 4d, and 5d transition metal chalcogenides in the M6X6 stoichiometry (M = transition metal, X = chalcogen). After high-throughput first-principles calculations, 53 unprecedented and experimentally feasible M6X6 wires have been identified. Diverse functionalities are found in these 1D materials, including semiconductors, metals, and ferromagnets with high Young’s modulus and large fracture strain. Notably, six kinds of M6X6 wires are robust ferromagnets with Curie temperatures up to 700 K, which can be further elevated under axial strains. Moreover, these M6X6 atomic wires possess high stability and resistance to oxidation, humidity, and aggregation; both merits are desirable for device applications. This large family of 1D materials with definite structures and rich properties allows atomically precise integration for flexible electronics and spintronics.

Keywords: atomic wire, transition metal chalcogenide, ferromagnetism, Curie temperature, flexible electronics

1. Introduction

The emergence of two-dimensional (2D) materials has opened unprecedented opportunities for exploring new physics and developing innovative devices. With van der Waals (vdW) layered structures and diverse properties, 2D materials serve as Lego blocks that allow for integration to create desired functionality.1 Extending such a concept to even lower dimensions, i.e. from 2D vdW layered to one-dimensional (1D) vdW wired materials, is also exciting but remains challenging.2,3 Atomic wires made of transition metal chalcogenides (TMCs), with a general formula of M6X6 (M = Mo, W; X = S, Se, Te), are a kind of 1D material with atomically precise structures (see Figure 1a).4,5 The M6X6 wires can be stacked parallelly into a hexagonal crystal with vdW interaction between each other.6,7 Different from 2D transition metal dichalcogenides (TMDs) for which the systems in 2H phase are commonly semiconductors,8 TMC atomic wires usually exhibit metallic behavior.9,10 Compared with carbon nanotubes that are structurally and electronically ambiguous,11 M6X6 wires have well-defined electronic structures and physical properties for a given stoichiometry, which is a distinct advantage for practical uses.

Figure 1.

Figure 1

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(a) Structures of Mo6S6 atomic wires from different perspectives as a representative of 1D M6X6 wires. (b) Phonon dispersion of Fe6S6 atomic wires. (c) Top view structures of various M6S6 (M = 3d, 4d, and 5d transition metal elements) wires with similar structural features found for the corresponding M6Se6 and M6Te6 wires.

So far, quasi-1D batches of molybdenum chalcogenide wires have been widely obtained in bulk inorganic synthesis using various counterions (such as alkali metals or iodine) to stabilize these atomic wires.12,13 Free bundles of Mo6S6 wires without counterions,14 aligned and equally spaced arrays of Mo6S6 wires on Cu(111) substrate,15 as well as heterostructures of 1D Mo6Te6 and 2D MoTe2 have also been reported.16 Recently, isolated Mo6Te6 and Sn6Se6 wires were fabricated inside single-wall carbon nanotubes.17−20 Individual wires of MX (M = Mo, W; X = S, Se), MoSxSe1–x, and MoxW1–xS alloys14 were also synthesized by sculpting their monolayer counterparts. These atomic wires exhibit self-adaptive connections to the monolayers and remain conductive under severe mechanical deformation. In addition, rotational twisting, axial kinking, and branching of individual M6X6 wires, as well as well-ordered junction structures that connect multiple atomic wires, have been achieved.14 The maturing fabrication techniques enable the access to many kinds of subnanometer-width atomic wires. On the theoretical side, great efforts have been made to understand the electronic, transport, and mechanical properties of the metallic TMC wires6,10 and to explore the effects of intercalation and heteroatom doping on their physical properties, especially the possibility of band gap opening.21

Despite the above successes, all previous experimental and theoretical studies only focused on limited kinds of M6X6 wires, i.e. molybdenum chalcogenides and tungsten chalcogenides. Because many 2D TMDs with multiple structural phases and diverse properties have been synthesized in the laboratory,22 it is natural to ask whether the other transition metal elements besides Mo and W are able to form stable 1D chalcogenide wires. If so, what would be their geometrical structures? How about their electronic and mechanical properties compared to Mo6X6 and W6X6 atomic wires as well as the 2D TMD counterparts? Is it possible to design 1D TMC wires with desired band structures for a specific device application?

To address the above intriguing questions, here for the first time, we systematically explore atomic wires of transition metal chalcogenides in the stoichiometry of M6X6 (X = S, Se, Te; M = 3d, 4d, and 5d elements), a total of 66 1D systems, using high-throughput first-principles calculations. By revealing their structures and stabilities, 53 unreported TMC wires that are possible to exist in ambient condition and feasible for experimental synthesis have been predicted. The electronic structures of various M6X6 wires are examined to screen the 1D semiconductors and ferromagnets, whose carrier mobility and Curie temperature are evaluated, respectively. We further investigate the mechanical properties of TMC atomic wires, elucidate the regulation of strain engineering of the ferromagnetic exchange strength, and propose a number of 1D flexible ferromagnets with high Curie temperature for spintronics.

2. Computational Methods

Spin polarized density functional theory (DFT) calculations were performed by the Vienna Ab-initio Simulation Package (VASP)23,24 using the planewave basis set with an energy cutoff of 500 eV and the projector augmented wave (PAW)25,26 potentials to describe the electron–ion interactions. The generalized gradient approximation (GGA)27 parametrized by Perdew, Burke, and Ernzerhof (PBE) was adopted for the exchange-correlation functional.28 The unit cells of M6X6 wires were periodic along the z axis, and a vacuum space of 20 Å was added in the other two directions to eliminate interaction between the atomic wire and its replica. The Brillouin zone was sampled by a 1 × 1 × 8 k-point grid based on the Monkhorst–Pack scheme.29 All 1D structures were fully optimized for both ionic and cell degrees of freedom with the converge criteria of 10–6 eV for energy and 0.005 eV Å–1 for force, respectively. Then, the phonon dispersions of all M6X6 wires were computed by the supercell method as implemented in the Phonopy program.30 Because the PBE functional is known to underestimate the band gap of a semiconductor, we also calculated the electronic band structures of the semiconducting M6X6 wires using the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional.31

3. Results and Discussion

3.1. Structure and Stability of 1D M6X6 Atomic Wires

Figure 1a presents the atomic structures of Mo6X6 (X = S, Se, Te) wires, which were synthesized in the laboratory. The 1D unit cell is composed of an octahedral Mo6 unit with the faces capped by six X atoms, and each X atom is coordinated with three Mo atoms. The calculated Mo–Mo and Mo–X bond lengths are 2.67–2.77 and 2.49–2.86 Å, respectively, in good agreement with the previous theoretical reports (see Table S1 for a comparison of the geometrical parameters).6,32 Based on these known Mo6X6 wires, we constructed 1D structural models for the other 3d, 4d, and 5d transition metal chalcogenide wires. The elements Tc and La are excluded, as Tc is radioactive and unsuitable for practical uses. La is an f-block element and has relatively larger atomic size, such that the conventional DFT methods may not correctly predict the geometrical and electronic structures of La chalcogenide wires.33 The optimized structures of all the considered TMC atomic wires are displayed in Figure 1c. Generally speaking, M6X6 wires composed of group VIB, VIIB, and VIII elements almost keep the hexagonal symmetry of Mo6X6 and W6X6. For early and middle transition metal elements (group IIIB, IVB, and VB), their 1D M6X6 wires exhibit notable deformation with lower symmetry, i.e. the triangular angle between M–M bonds (defined in Figure 1a) varies from 68° to 78°. This is related to the fewer d electrons and larger atomic radius of the group IIIB, IVB, and VB transition metal atoms. After donating electrons to the S atoms, the M–M bonds are relatively weak; thus, structural deformation from the symmetric octahedral M6 backbone can help maximize the M–S and M–M interactions. For a given transition metal element M, its sulfide, selenide, and telluride wires with the M6X6 stoichiometry have similar structures, with the M–X bond length increasing as X goes from S, Se, to Te. The detailed geometrical parameters and bond overlap population analysis of various TMC atomic wires are given by Table S2.

The energetic stability of 1D M6X6 atomic wires is described by the binding energy Eb per atom, defined as

3.1. 1

where EM and EX are the energies of an isolated transition metal atom and chalcogen atom, respectively; EM6X6 is the total energy of the TMC wire per M6X6 formula. To further assess the feasibility for experimental synthesis of each TMC atomic wire from thermodynamic point of view, we computed the formation energy Eform per atom by comparing the binding energy of the M6X6 wire to the sum of cohesive energies (Ecoh) of the elemental crystals of transition metal and chalcogen as follows

3.1. 2

By definition, a positive Eform means that formation of the M6X6 wire is exothermic. As presented in Table 1, most of the M6X6 atomic wires have Eform = 0.03–1.54 eV/atom, suggesting that they can be produced from the corresponding bulk precursors. The only exceptions are Re6Te6, Mn6X6, and Os6X6 (X = S, Se, and Te), which nevertheless have positive Eb values and thus could still be synthesized from atomic M and X sources.

Table 1. Binding Energies (Eb), Formation Energies (Eform), and Optimized Lattice Constants (c) of 1D M6X6 Atomic Wires.

  Eb (eV)
 Eform (eV)
 c (Å)
  S Se Te S Se Te S Se Te
Sc 5.34 4.91 4.40 1.52 1.34 0.95 4.86 5.02 5.25
Y 5.38 4.99 4.52 1.54 1.40 1.05 5.25 5.41 5.66
Ti 5.64 5.19 4.70 1.14 0.95 0.57 4.46 4.60 4.77
Zr 6.09 5.68 5.21 1.18 1.02 0.66 4.82 4.97 5.16
Hf 6.10 5.67 5.20 1.07 0.90 0.54 4.73 4.87 5.05
V 5.12 4.70 4.28 0.78 0.61 0.31 4.20 4.31 4.45
Nb 5.92 5.52 5.12 0.81 0.67 0.38 4.55 4.65 4.79
Ta 6.50 6.11 5.72 0.64 0.50 0.23 4.52 4.62 4.75
Cr 4.86 4.47 4.11 0.55 0.41 0.17 4.03 4.13 4.22
Mo 5.92 5.57 5.25 0.52 0.43 0.22 4.36 4.45 4.59
W 6.11 5.77 5.44 0.33 0.25 0.03 4.37 4.46 4.57
Mn 4.09 3.71 3.34 –0.24 –0.36 –0.61 4.10 4.22 4.33
Re 5.64 5.33   0.11 0.06   4.40 4.36  
Fe 4.65 4.29   0.35 0.26   4.07 4.19  
Ru 5.63 5.39 5.21 0.09 0.10 0.05 4.39 4.46 4.52
Os 5.77 5.51 5.33 –0.22 –0.22 –0.28 4.45 4.51 4.54
Co 4.73 4.40 4.15 0.27 0.20 0.05 4.00 4.16 4.26
Ni 4.42 4.10 3.87 0.31 0.25 0.13 4.08 4.23 4.40
Pd 3.62 3.43   0.15 0.22   4.48 4.63  
Pt 4.44 4.24 4.17 0.03 0.09 0.13 4.50 4.65 4.84
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The phonon dispersions of all the M6X6 wires were computed to characterize their dynamic stability (Figure 1b and Figure S1). Among 66 explored systems, only 3 of them, including Re6Te6, Fe6Te6, and Pd6Te6, are dynamically unstable with negative phonon bands. In addition, after full optimization, Rh6X6 and Ir6X6 (X = S, Se, and Te) undergo severe structural deformation; thus, we will not consider them further. All of the other TMC wires are dynamically stable without imaginary frequency in the entire phonon bands. We also confirmed that these M6X6 wires can be well segregated, i.e. they interact with each other through vdW interaction. The equilibrium distance between two neighboring M6X6 wires is above 3.3 Å (see the potential energy curve of wire–wire interaction for Fe6S6 in Figure 2b). Similarly, weak interaction was reported for Mo6S6 wires in its 3D crystalline phase with an interwire distance of about 4.4 Å from GGA calculation without dispersion correction.32

Figure 2.

Figure 2

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(a) Energy profile during AIMD simulation of Fe6S6 atomic wire at 300 K (inset: side-view snapshot structure of Fe6S6 at 10 ps). (b) Interaction energy as a function of wire–wire distance for two Fe6S6 wires. (c, d) Energy diagrams for dissociation of O2 and H2O molecules on the Fe6S6 wire, respectively. The structures of initial state (IS), transition state (TS), and final state (FS) are shown as insets. The numbers indicate the kinetic barrier (middle) and heat of reaction (right).

The thermal stability of M6X6 wires was then assessed by ab initio molecular dynamics (AIMD) simulations, as presented by Figure 2a and Figure S2. Taking the Fe6S6 wire as representative, at 300 K, it retains the 1D structures after 10 ps without any noticeable distortion, i.e. the variations of M–M and M–X bond lengths are within 0.8 Å. The energy profile of AIMD simulation shows oscillation between two states, which are higher in energy by about 0.27 and 0.84 eV per Fe6S6 formula relative to the equilibrium state at 0 K, respectively. These two high-energy states exhibit some deviations from the symmetric ground state structure. Their geometrical and electronic structures are presented in Figure S3 and Table S3. The electronic density of states is only slightly changed, and the local magnetic moment at the Fe atom remain the same, suggesting that structural deformation at finite temperatures would not much affect the electronic and magnetic properties of these TMC atomic wires.

Furthermore, we investigated the environmental stability of the Fe6S6 wire and found O2 and H2O molecules are physisorbed on it with vertical distance of over 2.76 Å above the wire surface. Dissociation of either O2 or H2O involves a kinetic barrier of 1.89 eV (Figures 2c, d). We also examined the oxygen resistance for some other M6X6 wires, such as Fe6Se6, Co6S6, Co6Se6, and Co6Te6. As will be shown later, these systems are ferromagnets. They exhibit reasonable stability with kinetic barriers of 0.80–1.66 eV for O2 dissociation, and their wired structures remain intact upon interaction with O2 molecule. For reference, we also explored two semiconducting systems, Mo6Te6 and W6Te6. Dissociation of the O2 molecule involves a barrier of 0.73 eV on Mo6Te6 and is barrierless on W6Te6. Moreover, the adsorbed O atoms severely destruct the wired structure of W6Te6. The detailed reaction diagrams and transition states are presented in Figure S4. Our calculations reveal that some of the TMC atomic wires have reasonable stability against oxidation and humidity, while some may be vulnerable in air.

Based on the above results, most of the 3d, 4d, and 5d transition metal chalcogenide atomic wires have sufficient energetic and dynamic stabilities to be synthesized in the laboratory. They exhibit satisfactory thermal stability and are against aggregation to keep their wire character and unique properties. Some of them are environmentally stable. Therefore, these 1D vdW-wired materials with rich chemical compositions may serve as Lego blocks for materials design and device integration.

3.2. Electronic Properties

The electronic structures of all the M6X6 atomic wires are comprehensively investigated. Among them, we found three semiconductors (Cr6Te6, Mo6Te6, and W6Te6) and six metallic magnets (Co6S6, Co6Se6, Co6Te6, Fe6S6, Fe6Se6, and Re6S6), while the others exhibit nonmagnetic metallic behavior. In the following two subsections, we will focus on the 1D semiconducting and magnetic wires.

Figure 3a displays the 1D electronic band structures of Cr6Te6, Mo6Te6, and W6Te6 wires from HSE06 calculations. Cr6Te6 and Mo6Te6 are indirect semiconductors with band gap of 0.70 and 0.50 eV, respectively, and W6Te6 has a narrow indirect gap of 0.24 eV (with almost flat bands near the Γ point), which can be compared with the previously reported values of 0.39, 0.23, and 0.25 eV calculated by the PBE functional, respectively.6 Their valence band maximum (VBM) and conduction band minimum (CBM) are dominated by the d orbitals of transition metal atoms and partly contributed from the p orbitals of chalcogen atoms, which can be also seen from the band decomposed charge density in Figure 3c. We further analyzed the effective masses of electron carriers along the principal axis of the semiconducting wires, which are 0.50 m0, 1.18 m0, and 5.00 m0 (m0 is the electron rest mass) for Cr6Te6, Mo6Te6, and W6Te6, and the electron mobilities estimated by the Takagi model34 are 34, 13, and 14 cm2V–1s–1, respectively (Figure 3b). As this model only accounts for the long-wavelength longitudinal acoustic phonon scattering, the carrier mobility is underestimated,35−37 and the realistic carrier mobility of these three atomic wires would be even smaller. Therefore, our proposed 1D semiconducting and metallic TMC wires may be used as electrode or conducting wire integrated with 2D TMD channels in the electronic and optoelectronic devices.

Figure 3.

Figure 3

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(a) Orbital-projected electronic band structures of Cr6Te6, Mo6Te6, and W6Te6 atomic wires calculated by the HSE hybrid functional. The blue line represents the p-orbitals of chalcogenide atoms, and light purple, dark purple, and green lines represent the d-orbitals of Cr, Mo, and W, respectively. The Fermi levels are set to zero. (b) Band gap (Eg), electron effective mass (m*/m0), and electron mobility (μ) of Cr6Te6, Mo6Te6, and W6Te6 atomic wires. The color scheme is the same as that in panel a. (c) Partial charge densities of VBM and CBM of Cr6Te6 with an isosurface value of 0.03 e/Å3 (left panel: top view; right panel: side view). Cr, Mo, and W atoms are represented by light purple, dark purple, and green, respectively.

To gain more insights into the origin of metallic behavior of the other TMC atomic wires, we examined the projected electronic band structures of Cr6X6 (X = S, Se, and Te) given by Figure S5 and Table S4. As the X atom changes from Te to Se and S, the electronegativity increases, indicating stronger interaction between the p orbitals of the X atom and the d orbitals of the transition metal atom. As expected, Bader charge analysis shows electron transfer of 0.40, 0.58, and 0.76 from each Cr atom to Te, Se, and S atoms, respectively. Consistently, for Cr6S6 and Cr6Se6, the bottom conduction band from p orbitals of chalcogen atoms moves downward, which touches or even crosses the Fermi level and results in substantial overlap with the valence d bands of the Cr atom. As a consequence, the atomic wires of Cr (Mo and W) sulfides and selenides become metals.

3.3. Magnetic Properties

From our high-throughput screening, atomic wires of Co6S6, Co6Se6, Co6Te6, Fe6S6, Fe6Se6, and Re6S6 are predicted to be magnetic for the first time. For each system, we compared the energies of ferromagnetic (FM), antiferromagnetic (AFM), and ferrimagnetic states. All six magnetic wires prefer FM order as the ground state. The electronic band structure of a representative system Fe6S6 is given by Figure 4a, which exhibits metallic behavior with strong polarization for the two spin channels. The magnetism is originated from the unpaired d electrons of the transition metal atoms, and the magnetic moment per transition metal atom is around 1.71–2.02 μB for Fe6X6 (X = S, Se), 0.97–1.18 μB for Co6X6 (X = S, Se, Te), and 0.62 μB for Re6S6, respectively. As illustrated by Figure 4b, the crystal field of M6X6 wire leads to the splitting of d orbitals into five components (dz2, dx2–y2, dxy, dyz, and dxz). Taking Fe6S6 as an example, among the five d components, dxz and dyz orbitals are degenerate, so as for dxy and dx2–y2. Because the Fe atom has eight valence electrons, the spin-up channels of the five d orbitals are occupied, while the spin-down states of dxy/dx2–y2 orbitals are empty, resulting in an on-site magnetic moment of 2 μB on the Fe atom. Similarly, the magnetic moment of about 1 μB on the Co atom of Co6X6 can be understood by the crystal field splitting of the d states plotted in Figure S6.

Figure 4.

Figure 4

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(a) Spin-polarized band structure (left) and projected density of states (PDOS) (right) of the Fe6S6 atomic wire. (b) Fe-3d orbital splitting in the crystal field of Fe6S6. (c) Spin density distribution of Fe6S6 in the ferromagnetic ground state and two lowest antiferromagnetic states with an isosurface value of 0.3 e/Å3. Purple and green represent spin-up and spin-down densities, respectively. (d) Magnetic moment on each transition metal atom (top panel) and exchange energy (bottom panel) of the six magnetic M6X6 wires.

To characterize the robustness of ferromagnetism in these 1D materials, we define the exchange energy Em as the difference between the energies of ferromagnetic state (EFM per M6X6 formula) and the lowest-energy antiferromagnetic state (EAFM per M6X6 formula):38,39

3.3. 3

As revealed in Figure 4d, these six magnetic wires have large exchange energies up to 108 meV per transition metal atom (equal to 650 meV per M6X6 formula). In addition, the Curie temperatures of these six atomic wires are calculated from Monte Carlo (MC) simulations based on the Ising model, in which the Hamiltonian operator is written as

3.3. 4

where Jij is the exchange coupling parameter between site i and site j; Si and Sj are the magnetic moments at site i and site j, respectively. Here, we considered only the exchange interaction between the nearest M–M neighbors, and the exchange coupling parameter is represented by J. After considering three possible AFM spin configurations, the lowest-energy ones are determined for the six M6X6 wires, i.e. AFM1 for Co6S6, Co6Se6, and Co6Te6 and AFM2 for Fe6S6, Fe6Se6, and Re6S6, as displayed in Figure 4c. Based on eq 4 and using the energies of FM and AFM states, we obtained J = 2–34 meV (see Table S5 for details). Then, MC simulations were performed to estimate the Curie temperature (TC) of these six magnetic M6X6 wires using a 1 × 1 × 30 supercell. The heat capacity (C) per formula unit of each TMC atomic wire was computed based on the Heisenberg model after the system reached equilibrium at a given temperature.

Figure 5a plots the heat capacity versus temperature, and the peak of the C(T) curve corresponds to TC for second-order magnetic transition. Excitingly, high Curie temperatures of 655, 705, and 485 K are obtained for Co6S6, Co6Se6, and Co6Te6 wires, respectively, far above room temperature. Meanwhile, Fe6S6 and Fe6Se6 have relatively lower Curie temperatures of 165 and 245 K, respectively. Similar to our recent finding for bilayer CrI3 that suitable semiconductor substrate can steer the exchange energy and thus rise the Curie temperature,38 the Curie temperature of TMC atomic wires follows a linear relation with both exchange energy and exchange coupling parameter, as shown by Figure 5b. Noticeably, the exchange energies and Curie temperatures of Co6X6 and Fe6X6 wires are much larger than the values of 2D semiconducting and metallic ferromagnets reported in the experiment, e.g. CrI3 monolayer with Em = 28 meV per Cr atom and measured Curie temperature of about 45 K,40 as well as Fe3GeTe241 and CrGeTe342 monolayers having calculated Em = 76 and 20 meV per transition metal atom and measured TC of about 130 and 52 K, respectively. The strong FM coupling of the TMC atomic wires is attributed to their metallic behavior and large density of states at the Fermi level, which signifies itinerant ferromagnetism under the Stoner model.43

Figure 5.

Figure 5

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(a) Heat capacity C as a function of temperature for the magnetic M6X6 atomic wires from Monte Carlo simulations. (b) Curie temperature TC as a function of exchange energy Em (left) and exchange coupling parameter J (right).

The intrinsic ferromagnetism is a uniqueness for the above 1D TMC wires. In comparison, most of 2D TMDs are nonmagnetic, and strategies such as heteroatom doping are necessary to induce local magnetic moments. Some TMD monolayers (e.g., CrTe2) can have intrinsic ferromagnetism, which, however, is a metastable state.44−46 The 1D TMC wires not only exhibit high Curie temperatures, but also have satisfactory thermal and environmental stabilities. They can keep their 1D identity against agglomeration, superior to the 1D atomic metal chains that have to be stabilized on certain substrates.47 Therefore, atomic wires of Co6X6 (X = S, Se, Te) and Fe6X6 (X = S, Se) are 1D ferromagnets with many merits for integration of room-temperature spintronic devices.48

3.4. Mechanical Properties and Strain Engineering of Ferromagnetism

To explore the potential of the 1D M6X6 wires for flexible electronics and spintronics, we examined the mechanical properties of the semiconducting and ferromagnetic TMC wires, i.e. M6Te6 (M = Cr, Mo, and W), Co6X6 (X = S, Se and Te), and Fe6X6 (X = S and Se). Here, we did not discuss the Re6S6 wire because the magnetic moment of Re6S6 is relatively small and unstable under small perturbation. By applying uniaxial strains from −2% (compressive) to 2% (extensive) along the principal axis of atomic wires, the Young’s modulus is calculated using the formula:

3.4. 5

where V0 is the equilibrium volume of the atomic wire and ES is the energy of the atomic wire under strain ε. As presented in Figure 6b, the explored semiconducting and magnetic M6X6 wires possess appreciable Young’s modulus of 347–662 GPa. The breaking strength (σ) and fracture strain (ε) determined from the stress–strain curves are in the range of 39–59 GPa and 16–24%, respectively, as displayed in Figure 6a (the detailed calculation method is given in the Supporting Information). Table 2 summarizes the key mechanical parameters compared with those of typical 1D and 2D nanostructures such as carbon nanotubes and TMD monolayers. Note that the Young’s modulus and breaking strength of the present M6X6 atomic wires even approach two-thirds of those of single-wall carbon nanotubes (Y ∼ 1 TPa, σ ∼ 95 GPa),49 which is known as the strongest and stiffest 1D material. On the other hand, 2D TMDs have relatively lower Young’s modulus, i.e. Y ∼ 270 GPa for MoS2 and WS2 monolayers.50,51

Figure 6.

Figure 6

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(a) Strain–stress curves and (b) Young’s modulus (Y) of the semiconducting and magnetic M6X6 atomic wires. (c) Exchange energy as a function of strain for the six magnetic M6X6 wires. (d) Relative energy ΔE between FM and AFM states under different strains for Co6X6 (X = S, Se, Te). The color scheme is given in panel b.

Table 2. Young’s Modulus (Y), Breaking Strength (σ), and Fracture Strain (ε) of Semiconducting and Magnetic M6X6 Atomic Wires Compared with Some Synthetic Low-Dimensional Materials and Bulk Solids.

  Y (GPa) σ (GPa) ε (%)
Cr6Te6 486 45 16
Mo6Te6 558 50 18
W6Te6 562 59 20
Co6S6 637 55 24
Co6Se6 463 46 22
Co6Te6 347 39 24
Fe6S6 662 54 16
Fe6Se6 506 44 16
graphene52 1000 130 13
carbon nanotubes49,53 1000 95 6.3
monolayer MoS250 270 30 11
WS2 nanotubes54 152 16.3 10
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The modulation of electronic structures and magnetic properties under uniaxial strains were then examined for the above atomic wires. Our calculations show that the band gaps of semiconducting Cr6Te6, Mo6Te6, and W6Te6 wires vary very little (within 0.2 eV) under uniaxial strains up to ±2%. Under compressive and tensile strains below 2%, the 5 magnetic wires remain ferromagnetic. Interestingly, the exchange energy of various 1D magnetic wire changes with strain in different manners. As displayed in Figure 6c, Em of the sulfide atomic wires (Co6S6 and Fe6S6) generally increases with the strain (or 1D cell parameter of nanowire); the opposite trend is observed for Fe6Se6 and Co6Te6, while Em of Co6Se6 remains almost the same under strain. As revealed by Figure 6d, it is the stability of the AFM state that determines the exchange energy of these 1D magnetic wires. Taking Co6X6 for instance, the AFM state of Co6S6 becomes more (less) stable under compressive (tensile) strains, while Co6Te6 follows the reverse behavior. As a result, the strength of ferromagnetic coupling of these TMC wires can be tuned by up to 100 meV under strains, which would further elevate the Curie temperature. Based on the above results, our proposed TMC atomic wires have superior mechanical properties compared to many other low-dimensional materials. Moreover, their electronic and magnetic properties are robust under strains, enabling them to be used for flexible electronics and spintronics.

4. Conclusion

In summary, motivated by the synthetic atomic wires of molybdenum chalcogenides, we explored the possibility for 3d, 4d, and 5d transition metal and chalcogen (S, Se, and Te) elements to form 1D M6X6 wires with well-defined geometrical structures. By high-throughput DFT calculations, we identified 57 M6X6 atomic wires (53 of them are predicted for the first time) with satisfactory dynamic and thermal stabilities and diverse electronic band structures, most of which could be synthesized from their bulk transition metal and chalcogen precursors. Some of them may be stable in air. Impressively, five systems (Co6S6, Co6Se6, Co6Te6, Fe6S6, and Fe6Se6) are 1D ferromagnets with Curie temperature up to 700 K, and the ferromagnetic order is robust under tensile and compressive strains. They also have high elasticity and stiffness, with Young’s modulus and breaking stress up to 662 and 59 GPa, respectively. Our theoretical work proposes a family of stable 1D vdW-wired materials with rich physical properties. They may offer the opportunity for exploring new states of matter under quantum size effect and manufacturing nanodevices at atomic precision.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (11974068, 91961204) and the Fundamental Research Funds for the Central Universities of China (DUT20LAB110). The authors acknowledge the computer resources provided by the Shanghai Supercomputer Center and the Supercomputing Center of Dalian University of Technology.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.0c00049.

  • Details of geometrical parameters and bonding properties (Tables S1–S4), magnetic properties (Table S5), structural stability (Figures S1–S4), and electronic properties (Figures S5 and S6) (PDF)

The authors declare no competing financial interest.

Supplementary Material

au0c00049_si_001.pdf (1,015.8KB, pdf)

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