Microscopic origin of magnetism in monolayer 3d transition metal dihalides

Motivated by the recent wealth of exotic magnetic phases emerging in two-dimensional frustrated lattices, we investigate the origin of possible magnetism in the monolayer family of triangular lattice materials MX2 (M=V, Mn, Ni and X=Cl, Br, I). We first show that consideration of general properties such as filling and hybridization enables to formulate the trends for the most relevant magnetic interaction parameters. In particular, we observe that the effects of spin-orbit coupling (SOC) can be effectively tuned through the ligand elements as the considered 3d transition metal ions do not strongly contribute to the anisotropic component of the intersite exchange interaction. Consequently, we find that the corresponding SOC matrix elements differ significantly from the atomic limit. In the next step and by using two ab initio based complementary approaches, we extract realistic effective spin models and find that in the case of heavy ligand elements, SOC effects manifest in anisotropic exchange and single-ion anisotropy only for specific fillings.