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  2 /CrBr  3 , leading to a 2D spin-polarized half-metal with carrier densities ranging up to 10 13 cm -2 . 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.