Abstract

Removing valley degeneracy is a necessary condition for manipulating valley degrees of freedom and storing information in future spintronics. Magnetic proximity effect has been demonstrated to be an effective way to introduce exchange interactions, especially in the case of two-dimensional (2D) van der Waals (vdW) heterostructures. We have explored the electronic properties and the valley physics of 2D ${\mathrm{WSe}}_{2}/{\mathrm{CrI}}_{3}$ using first-principles calculations. Our results show that a valley splitting of 2 meV is achieved in ${\mathrm{WSe}}_{2}/{\mathrm{CrI}}_{3}$ heterostructures thanks to the coexistence of inversion and time-reversal symmetry breaking. This value corresponds to an effective magnetic field of \ensuremath{\sim}10 T in experiments. Moreover, we demonstrate that the valley splitting is a robust feature regardless of the stacking configuration and the thickness of ${\mathrm{CrI}}_{3}$. Most importantly, by reversing the magnetization in the ${\mathrm{CrI}}_{3}$ layer, the valley splitting and polarization at ${K}^{+}$ and ${K}^{\ensuremath{-}}$ points are completely switchable. Our findings provide fundamental insights into the magnetoelectric spin-orbit coupling based spintronics applications of 2D vdW heterostructures.

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