Magnetic edge states in ${\text{MoS}}_2$ characterized using density-functional theory

It is known that the edges of a two-dimensional slab of insulating ${\text{MoS}}_2$ exhibit one-dimensional metallic edge states, the so-called “brim states.” Here, we find from density-functional theory calculations that several edge structures, which are relevant for the hydrodesulfurization process, are magnetic. The magnetism is an edge phenomenon associated with certain metallic edge states. Interestingly, we find that among the two low-index edges, only the S edge displays magnetism under hydrodesulfurization conditions. In addition, the implications of this on the catalytic activity are investigated. Despite large changes in the magnetic moments, a small influence on the adsorption energies is observed. This has implications on the suitability of magnetic measurements for monitoring the catalytic properties.

Figure 1

(Color online) Illustration of the stripe model utilized in our study of the single-layered ${\text{MoS}}_2$ stripe. Shown is the ${\text{MoS}}_2$ structure with 100% sulfur coverage on both the Mo and the S edge, which are indicated in the left figure. To the right a side view of the two edges is shown. The slab consists of 2(6) rows of Mo atoms in the $x\left(y\right)$ direction, also denoted as (2,6). The yellow (light) and blue (gray) balls represent the S and Mo atoms, respectively.

Figure 2

(Color online) Total magnetic moments averaged per edge Mo atom of the considered Mo- and S-edge ferromagnetic structures as a function of the S coverage in blue and red, respectively. Also, presented are the structures together with the 3D spatial localizations of the magnetization $\left({\text{n}}_{\uparrow }-{\text{n}}_{\downarrow }\right)$ in red. The structures with no net magnetic moment are not provided since they are redundant. The color coding of the atoms is the same as in Fig. 1.

Figure 3

(Color online) Visualized in red is the 3D real space localization of the magnetization (for a representative isosurface with the value $0.05/{\text{Å}}^3$) and the local magnetic moments obtained by a Bader analysis (see text for more details). The magnetic states have a pure $d$ character associated with the Mo edge atoms on the S edge. In addition, an order of magnitude smaller magnetization is found on the undimerized S edge atoms on the S edge (not visible for the chosen isosurface). The color coding of the atoms is the same as in Fig. 1.

Figure 4

(Color online) Calculated non-spin-polarized (black solid line) and spin-polarized (red dashed and blue dashed-dotted lines) atom projected DOS for the Mo100S100 structure for (from above) a Mo atom at the Mo edge, in the interior of the stripe, and at the S edge, and an undimerized S atom at the S edge.

Figure 5

(Color online) Calculated non-spin-polarized and spin-polarized LDOS’s for a Mo atom at the Mo edge for the Mo0 structure and a Mo atom at the S edge for the S0 structure.

Figure 6

(Color online) LDOS’s for relevant edge Mo and S atoms of the: (a) S100dd, (b) the S100du, and (c) the S100uu structure.

Figure 7

(Color online) The total magnetic moment per edge Mo atom of the S100dd (100%), the S100du (50%) and the S100uu (0%) structure. Also illustrated is the localization of the magnetism (isosurface with $0.05/{\text{Å}}^3$ is red and isosurface with $-0.05/{\text{Å}}^3$ is purple). The nonmagnetic structure is not shown. For the S100uu structure, the edge S atoms are magnetic.

Figure 8

(Color online) The total magnetic moment per Mo atom as a function of H coverage at the S edge (the Mo edge is H free). Also visualized are the atomic structures and the magnetization in real space of the magnetic stripes (the nonmagnetic ones are not shown). The color coding is the same as in Fig. 2 and the H atoms are represented as black balls.

Figure 9

(Color online) LDOS’s for a Mo atom, an S atom from each S pair for (a) the S100H50s and (b) the S100H100 structure.