Monolayer*

To magnetize surfaces of topological insulators without damaging their topological feature is a crucial step for the realization of the quantum anomalous Hall effect (QAHE), and still remains as a challenging task. Through density functional calculations, we found that adsorption of a semiconducting two-dimensional van der Waals (2D-vdW) ferromagnetic CrI₃ monolayer can create a sizable spin splitting at the Dirac point of the topological surface states of Bi₂Se₃ films. Furthermore, general rules that connect different quantum and topological parameters are established through model analyses. This work provides a useful guideline for the realization of QAHE at high temperature in heterostructures of 2D-vdW magnetic monolayers and topological insulators.