Chiral magnetic interactions in graphene nanoribbons on topological insulator substrates

It is known that the interplay between strong spin-orbit coupling and broken inversion symmetry can lead to chiral configurations in low-dimensional magnetic systems deposited on heavy-element surfaces. This phenomenon is due to the Dzyaloshinskii-Moriya interaction, which favours noncollinear magnetic structures. Here we show by ab initio simulations that this interaction leads to a twisting of the two antiferromagnetically coupled edge-state spins of a zigzag graphene nanoribbon deposited on the topological insulator ${\mathrm{Sb}}_2{\mathrm{Te}}_3$. To our knowledge, this is the first report of a chiral magnetic structure formed by a pair of one-dimensional states. This effect results in a finite net magnetization in the nanoribbons, which could lead to applications such as spin filters in graphene-based spintronics devices.

Figure 1

Atomistic models. (a) Side and (b) top view of the GNR on ${\mathrm{Sb}}_2{\mathrm{Te}}_3$(111) after relaxation. A thick slab of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ is considered in the DFT simulations, but only five atomic layers are shown here for the sake of clarity. The red arrows render the spin structure formed by the edge states in the lowest-energy configuration obtained. The directions of the edge magnetic moments deviate slightly from the $y$ axis due to the DMI. The blue dashed lines in (b) depict the $yz$ and $xz$ planes: the first one is an exact mirror plane, whereas the mirror symmetry with respect to the second one is broken by the atomic layers beneath the topmost Te layer of the substrate. The blue rectangle in (b) indicates the actual supercell employed in the simulations. In this and the following figure, Sb, Te, and C atoms are rendered with yellow, green, and black spheres, respectively.

Figure 2

Magnetic properties. (a) Nonspin-polarized and (b) spin-polarized PDOS for the $\mid j$=3/2,$l=1\rangle$+$\mid j=1/2$, $l=1\rangle$ spin-angle functions of the three edge C atoms of the GNR (black lines) and the nearest neighbor Te atoms (dashed red lines). The peak at ${\mathrm{E}}_F$ in (a) corresponds to the edge state. The PDOS in (b) correspond to the magnetic configuration shown in Fig. 1. The non-spin-polarized PDOS for the edge C atoms of a freestanding monohydrogenated GNR is also shown in (a) for the sake of comparison (dashed blue line). (c)–(e) Isovalue surfaces of the spin polarization density along $x$ (c), $y$ (d), and $z$ (e) for the magnetic configuration in Fig. 1. The red (blue) surface indicates spin up (down) density, corresponding to $\pm 4\times {10}^{-5}{\mu }_B$/(a.u.)${}^3$. The plots clearly show that the $y$ and $z$ components form an AFM configuration across the GNR, whereas the $x$ components of the two edge spins are parallel.