Goodenough-Kanamori-Anderson rules in 2D magnet: A chemical trend in MCl2 with M=V, Mn, and Ni

Density-functional-theory calculations were performed to investigate the magnetism in a series of triangular-lattice monolayer MCl2 (M=V, Mn, and Ni). The magnetic stability manifests a distinct chemical trend; VCl2 and MnCl2 show the antiferromagnetic ground states and NiCl2 shows the ferromagnetic ground state. The microscopic mechanism behind the magnetic interaction is explained by the so-called Goodenough-Kanamori-Anderson rules and by the virtual-hopping process through the hopping integrals between the 3d-orbital maximally localized Wannier functions. Our result highlights the role of the direct exchange interaction and the superexchange interaction in the magnetic stabilization in two-dimensional magnets.