Giant proximity exchange and flat Chern band in 2D magnet-semiconductor heterostructures.

van der Waals (vdW) heterostructures formed by two-dimensional (2D) magnets and semiconductors have provided a fertile ground for fundamental science and spintronics. We present first-principles calculations finding a proximity exchange splitting of 14 meV (equivalent to an effective Zeeman field of 120 T) in the vdW magnet-semiconductor heterostructure MoS /CrBr , leading to a 2D spin-polarized half-metal with carrier densities ranging up to 10 cm. We consequently explore the effect of large exchange coupling on the electronic band structure when the magnetic layer hosts chiral spin textures such as skyrmions. A flat Chern band is found at a "magic" value of magnetization [Formula: see text] for Schrödinger electrons, and it generally occurs for Dirac electrons. The magnetic proximity-induced anomalous Hall effect enables transport-based detection of chiral spin textures, and flat Chern bands provide an avenue for engineering various strongly correlated states.