Magnetic Proximity Effects in Transition-Metal Dichalcogenides: Converting Excitons

The two-dimensional character and reduced screening in monolayer transition-metal dichalcogenides (TMDs) lead to the ubiquitous formation of robust excitons with binding energies orders of magnitude larger than in bulk semiconductors. Focusing on neutral excitons, bound electron-hole pairs that dominate the optical response in TMDs, it is shown that they can provide fingerprints for magnetic proximity effects in magnetic heterostructures. These proximity effects cannot be described by the widely used single-particle description but instead reveal the possibility of a conversion between optically inactive and active excitons by rotating the magnetization of the magnetic substrate. With recent breakthroughs in fabricating Mo- and W-based magnetic TMD heterostructures, this emergent optical response can be directly tested experimentally.

Figure 1

(a) Spin-valley coupling in ML TMDs: The conduction (valence) band is spin split in the $K$ valley by $2{\lambda }_{c(v)}$ due to strong spin-orbit coupling with the CB ordering reversed between $\mathrm{Mo}{X}_2$ and $\mathrm{W}{X}_2$; at the $K^{\prime }$ point, all spin orientations are reversed (not shown); emitted or absorbed light has valley-selective helicity, ${\sigma }_{\pm }$. (b) ML TMD on a magnetic substrate. (c) The $K$ and $K^{\prime }$ band edges as the substrate’s magnetization $\mathit{M}$ is rotated, shown for ${\mathrm{MoTe}}_2/\mathrm{EuO}$ parameters. One dark exciton for $K$ and $K^{\prime }$ and the spin direction for selected band edges are depicted.

Figure 2

Absorption spectra of ML ${\mathrm{MoTe}}_2$ on EuO for different polarizations if (a) no proximity-induced, (b) out-of-plane, and (c) in-plane exchange splitting are considered. The insets show the respective single-particle absorptions computed without excitonic effects. $E_g=1.4\mathrm{eV}$.

Figure 3

Evolution of the absorption of ML ${\mathrm{MoTe}}_2$ on EuO as $\mathit{M}$ is rotated from out of plane ($\varphi =0$) to in plane ($\varphi =\pi /2$) and out of plane, but with reversed $\mathit{M}$ ($\varphi =\pi$) for (a) ${\sigma }_{+}$ and (b) ${\sigma }_{-}$. The dashed lines are the peak positions from Eq. (5). The parameters are from Figs. 2 and 2.

Figure 4

Absorption profile of the $A$ peak in ML ${\mathrm{WSe}}_2$ on EuS for (a) ${\sigma }_{+}$ and (b) ${\sigma }_{-}$ and different $\mathit{M}$ directions. (c) The evolution of the bright (dark) excitons as solid (dashed) lines as $\mathit{M}$ is reversed from $\varphi =0$ to $\varphi =\pi$. The size of the circles represents exciton oscillator strengths for selected orientations of $\mathit{M}$ (not to scale).