  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.
