Valley polarization in magnetically doped single-layer transition-metal dichalcogenides

We demonstrate that valley polarization can be induced and controlled in semiconducting single-layer transition-metal dichalcogenides by magnetic doping, which is important for spintronics, valleytronics, and photonics devices. As an example, we investigate Mn-doped ${\mathrm{MoS}}_2$ by first-principles calculations. We study how the valley polarization depends on the strength of the spin orbit coupling and the exchange interaction and discuss how it can be controlled by magnetic doping. Valley polarization by magnetic doping is also expected for other honeycomb materials with strong spin orbit coupling and the absence of inversion symmetry.

Figure 1

(a) Side view and (b) top view of single-layer ${\mathrm{MoS}}_2$ for a $4\times 4$ supercell. The red and blue circles represent Mn doping on top of Mo and on top of the hollow site, respectively. (c) Brillouin zone corresponding to the $1\times 1$ unit cell (blue) and $4\times 4$ supercell (red), where the $K$ and $K^{\prime }$ points of the unit cell, respectively, are folded onto the $K$ and $K^{\prime }$ points of the supercell.

Figure 2

Formation energy for various impurities in ${\mathrm{MoS}}_2$ as a function of the S chemical potential.

Figure 3

Total spin polarized density of states (DOS) for Mn-doped single-layer ${\mathrm{MoS}}_2$ without spin orbit coupling. (a), (b), and (c) refer to the Mn${}_{\mathrm{Mo}}$, Mn${}_{\mathrm{S}}$, and Mn${}_{\mathrm{HT}}$ systems, respectively.

Figure 4

Electronic band structures for single-layer ${\mathrm{MoS}}_2$: (a) without doping and without spin orbit coupling, (b) with Mn${}_{\mathrm{Mo}}$ doping and without spin orbit coupling, (c) without doping and with spin orbit coupling, (d) with Mn${}_{\mathrm{Mo}}$ doping and with spin orbit coupling [inverted spin polarization in (e)], and (f) with B${}_{\mathrm{S}}$ doping and with spin orbital coupling. Red and blue color indicates spin up and down, respectively.

Figure 5

Schematic view of the band structure of single-layer ${\mathrm{MoS}}_2$ near the $K$ and $K^{\prime }$ points: (a) pristine without spin orbit coupling, (b) with exchange field and without spin orbit coupling, (c) pristine with spin orbit coupling, and (d) with exchange field and with spin orbit coupling. (e) Same as (d) but with inverted spin polarization.