  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 $MX_2$
($M$={V, Mn, Ni}, $X$={Cl, Br, I}). We first show that consideration of general
properties such as filling and hybridization enables to formulate 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 3$d$ transition metal ions do not
strongly contribute to the anisotropic component of the inter-site exchange
interaction. Consequently, we find that the corresponding SOC matrix-elements
differ significantly from the atomic limit. In a next step and by using two
complementary approaches based on first principles, 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.
