Stability and magnetic behavior of exfoliable nanowire one-dimensional materials

Low-dimensional materials can display enhanced electronic, magnetic, and quantum properties. We use the topological scaling algorithm to identify all sufficiently metastable materials in the Materials Project database to identify bulk crystals with one-dimensional (1D) structural motifs: Five hundred fifty-one crystals that are within 50 meV ${\mathrm{atom}}^{-1}$ of the thermodynamic hull display 1D motifs, where 293 of these contain $d$-valence elements, which we focus on in this work. After exfoliating nanowires from 263 of these materials and calculating their thermodynamic stability using density functional theory, 103 nanowires meet per-atom and per-Ångström thermodynamic stability criteria. We illustrate for three nanowire systems that a variety of local minima can be present in these systems, demonstrating one case of a Peierls distortion. The wires display a broad diversity of electronic and magnetic properties of these nanowires, with 14 metals, 7 half-metals, and 82 semiconductors and insulators, and 41 nanowires displaying magnetic moments ranging from 0.1 to $5{\mu }_B$ per $d$-valence species when assuming ferromagnetic order. A subset of these chains are investigated for the impact of magnetic ordering, identifying 1D ${\mathrm{FeCl}}_3$ to be most stable in an antiferromagnetic state. The electronic and magnetic properties of the identified 1D materials could enable applications in spintronic and quantum devices.

Figure 1

The structure of bulk tellurium with a three-atom unit cell consists of 1D structural motifs, highlighted by the single chain of blue atoms. Exfoliation of such a material can lead to a 1D material, which corresponds to an inorganic polymer or nanowire. This Te nanowire forms a three-fold-symmetric helical coil, denoted as 3H-Te.

Figure 2

Distribution of structural motifs identified by the TSA as a function of the scaling of the bond length, i.e., the sum of empirical atomic radii. The figure is limited to materials which are reported as within 50 meV ${\mathrm{atom}}^{-1}$ of the thermodynamic hull. For materials where a heterostructure was identified (i.e., the composition of individual structural motifs does not match the materials composition), each bonding network with a unique composition is categorized separately. The number of conventionally networked materials increases rapidly up to a scaling of about $+10$%. We select a scaling of $+20$% to capture almost all covalent, ionic, and metallic bonds but not bridge the majority of van der Waals gaps.

Figure 3

Effect of periodic boundary conditions on the dimensionality of structural motifs. The phosphorous bipartite structure comprises two separate bonding networks represented in red and blue. (a) The crystal structure consists of two networks of linked rodlike motifs. The top and bottom sets of atoms form equivalent structures that are related by a ${90}^{\circ }$ rotation and connected through bridging phosphorous atoms. (b) The top-down view shows the bipartite network structure. Panels (c) and (d) display $6\times 6$ supercells of the unit cell, constructed from $2\times 2$ and $3\times 3$ supercells, respectively. The region within the black lines represents the primitive cell of the crystal. The dashed lines represent the bottom rods, solid lines represent the top rods, and dots represent the points at which the upper and lower rods connect. The green circles highlight the conflicting network connectivity for the $3\times 3$ supercell (d), which shows the blue bonding network incorrectly connected to the red bonding network.

Figure 4

Density scatter plots showing the nanowire distribution for (a) the exfoliation energy, (b) the elliptical nanowire cross section, and (c) the average magnetic moment normalized by the number of $d$-valence elements as a function of the line tension. The black circle represents single-chain 3H-Te, which provides an empirical stability criterion indicated by the light blue region.

Figure 5

Examples of structural distortions observed in this work. These correspond to [(a) and (b)] ${\mathrm{MoBr}}_3$, [(c) and (d)] ${\mathrm{NbCl}}_3\mathrm{O}$, and [(e) and (f)] HgO. The low-energy phase of ${\mathrm{MoBr}}_3$ and ${\mathrm{NbCl}}_3\mathrm{O}$ are shown in (b) and (d), respectively. The lowest-energy HgO nanowires differ for the exfoliation energy and line tension stability criteria.

Figure 6

Electronic structure of the stable nanowires. The nanowires exhibit a variety of electronic structures, illustrated by the band structure of (a) metallic ${\mathrm{TcBr}}_3$, (b) half-metallic ${\mathrm{VBr}}_3$, and semiconducting ${\mathrm{MoI}}_3\mathrm{O}$ with the spin channels denoted by solid blue and dashed red lines. (d) The 103 identified stable nanowires comprise 14 metals, 7 half-metals, and 82 semiconductors and insulators, shown in order of increasing band gap. The red diamonds (blue circles) indicate that the spin channel corresponds to the majority (minority) electron carrier. Black squares indicate both band gaps are equal, with magnetic (nonmagnetic) nanowires are shown with an empty (filled) markers. Metals are ordered alphabetically and half-metals/insulators are ordered by band gap. The red, green, and orange shadings indicate metallic, half-metallic, and semiconducting nanowires, such as shown in the example band structures [(a)–(c)]. Staggered-gap and straddling-gap insulators are plotted with dashed black and dotted green lines, respectively.