Predictive design of intrinsic half-metallicity in zigzag tungsten dichalcogenide nanoribbons

Realization of half-metallicity with a sizable minority-spin gap and ferromagnetic ordering has been a central research emphasis in the development of next-generation spintronic devices. To date, only three-dimensional half-metals have been achieved experimentally, while their counterparts based on two-dimensional (2D) materials remain to be materialized despite extensive efforts based on various predictive designs. This standing challenge is largely due to stringent requirements to establish ferromagnetic order in low-dimensional systems. Here we use first-principles approaches to show that atomically thin zigzag tungsten dichalcogenide $\mathrm{W}{X}_2$ ($X=\mathrm{S}$, Se) nanoribbons preserving the stoichiometry of $\mathrm{W}:X=1:2$ stand as highly appealing intrinsic half-metallic systems, without invoking the prevailing approaches of applying an external electric field, chemical modification, or carrier doping. The readily accessible half-metallicity is attributed to distinctly different edge reconstructions, insulating along the X-terminated edges and metallic along the self-passivated W-terminated edges; the latter are further characterized by a robust spin-polarized electron transmission channel. These findings are expected to provide indispensable elemental building blocks for spintronic applications purely based on 2D materials.

Figure 1

(a) Top view (upper panel) and side views (right and bottom panels) of a rectangle-shaped $\mathrm{W}{X}_2$ ($X=\mathrm{S},\mathrm{Se}$) nanoribbon with coexisting zigzag and armchair edges. (b) Top view (left panel) and side view (right panel) of the optimized atomic structures of 8-ZZ $\mathrm{W}{X}_2$ nanoribbons. The reconstructed structures along the W-terminated and X-terminated edges are indicated by the red dashed rectangles, respectively. The atoms included in the supercell calculations are indicated by the blue solid rectangle.

Figure 2

Evolutions of the (a, c) temperature and (b, d) total energy of the 8-ZZ $\mathrm{W}{\mathrm{S}}_2$ and $\mathrm{WS}{\mathrm{e}}_2$ nanoribbons during the AIMD simulations at 300 K and up to 15 ps. The insets in (a, c) show the top (left panels) and side (right panels) views of the atomic structures after 15-ps AIMD.

Figure 3

(a, d) Spin-unresolved band structure, (b, e) spin-resolved band structure and DOS (including both total and partial), and (c, f) spatial charge density distribution of the spin-resolved triply folded I-u band crossing the Fermi level at the Γ point of an 8-ZZ $\mathrm{W}{\mathrm{S}}_2$ and $\mathrm{WS}{\mathrm{e}}_2$ nanoribbon, respectively. The red color in the charge density plots of (c) and (f) denotes the spin-up states.

Figure 4

Atom-resolved distributions of the magnetic moments on (a) the W and S atoms of an 8-ZZ $\mathrm{W}{\mathrm{S}}_2$ nanoribbon and (b) the W and Se atoms of an 8-ZZ $\mathrm{WS}{\mathrm{e}}_2$ nanoribbon. In both cases, only moments with absolute values $>0.005{\mu }_{\mathrm{B}}$ are displayed, with the red (up) and blue (down) arrows indicating opposite spin orientations. Sizable magnetic moments are distributed on the W and X atoms along the W-terminated edges of the $\mathrm{W}{X}_2$ nanoribbons, with no magnetism along the X-terminated edges.

Figure 5

Spin-resolved band structures of reconstructed 8-ZZ (a) $\mathrm{W}{\mathrm{S}}_2$ and (b) $\mathrm{WS}{\mathrm{e}}_2$ nanoribbons calculated using the HSE06 hybrid functional. Band structures of the reconstructed 8-ZZ (c) $\mathrm{W}{\mathrm{S}}_2$ and (d) $\mathrm{WS}{\mathrm{e}}_2$ nanoribbons calculated using the PBE functional with and without SOC.

Figure 6

Optimized structures of the reconstructed $n$-ZZ $\mathrm{W}{\mathrm{S}}_2$ and $\mathrm{WS}{\mathrm{e}}_2$ nanoribbons with $n=3$,4,5,…,12. The edge reconstructions are highlighted in the dashed rectangles.

Figure 7

Energy difference ($\mathrm{\Delta }{E}_{\mathrm{mag}}$) between the nonmagnetic and ferromagnetic states as a function of the ribbon width ($n$) for the zigzag (a) $\mathrm{W}{\mathrm{S}}_2$ and (b) $\mathrm{WS}{\mathrm{e}}_2$ nanoribbons.

Figure 8

Spin-resolved band structures of (a–c) $n$-ZZ $\mathrm{W}{\mathrm{S}}_2$ nanoribbons with $n=4$, 5, and 12, and (d–f) $n$-ZZ $\mathrm{WS}{\mathrm{e}}_2$ nanoribbons with $n=4$, 5, and 12, respectively.