Interplay between Structure and Magnetism in ${\mathrm{Mo}}_{12}{\mathrm{S}}_9{\mathrm{I}}_9$ Nanowires

We investigate the equilibrium geometry and electronic structure of ${\mathrm{Mo}}_{12}{\mathrm{S}}_9{\mathrm{I}}_9$ nanowires using ab initio density functional calculations. The skeleton of these unusually stable nanowires consists of rigid, functionalized Mo octahedra, connected by flexible, bistable sulfur bridges. This structural flexibility translates into a capability to stretch up to $\approx 20\%$ at almost no energy cost. The nanowires change from conductors to narrow-gap magnetic semiconductors in one of their structural isomers.

Figure 1

Structural properties of ${\mathrm{Mo}}_{12}{\mathrm{S}}_9{\mathrm{I}}_9$ nanowires. (a) Atomic arrangement within a unit cell. Planes normal to the wire axis are denoted by A, A′, B, C, D. (b) Binding energy as a function of the lattice constant $a$. (c) Optimized interplane distances as a function of $a$. (d) Optimum values of the Mo-S-Mo bond angle $\Theta$ as a function of $a$. Values in the two sulfur bridges per unit cell are distinguished by different symbols. Dashed lines in (b)–(d) are guides to the eye.

Figure 2

Electronic band structures $E(k)$ of ${\mathrm{Mo}}_{12}{\mathrm{S}}_9{\mathrm{I}}_9$ nanowires with lattice constants (a) $a=11.0\AA$, (b) $a=12.3\AA$, and (c) $a=13.8\AA$. Solid lines represent majority and dashed lines minority spin bands. Bands crossing the Fermi level are emphasized by heavy lines. Densities of states of nanowires with (d) $a=11.0\AA$, (e) $a=12.3\AA$, and (f) $a=13.8\AA$, convoluted with 0.01 eV wide Gaussians. The Fermi level lies at $E_F=0$.

Figure 3

Contour plots depicting the charge distribution in a ${\mathrm{Mo}}_{12}{\mathrm{S}}_9{\mathrm{I}}_9$ nanowire at $a=11.0\AA$. (a) Total charge density contour at $\rho =0.05\mathrm{el}/a_0^3$. (b) Difference charge density $\Delta \rho (\mathbf{r})$, indicating regions of charge depletion and excess with respect to the superposition of isolated atoms. (c) $\rho =1.0\times {10}^{-3}\mathrm{el}/a_0^3$ charge density contour associated with states close to the Fermi level, $E_F-0.05\mathrm{eV}<E<E_F+0.05\mathrm{eV}$. (d) Difference spin density ${\rho }_{\uparrow }(\mathbf{r})-{\rho }_{\downarrow }(\mathbf{r})$, showing regions of excess majority spin $\uparrow$. Contour plots (b) and (d) are depicted in a plane, which contains the wire axis.