This paper investigates the microscopic origin of magnetism in CrI₃ monolayer, both suspended and dielectrically embedded. Using down-folded generalized Hubbard models derived from ab initio calculations and the constrained random phase approximation (CRPA), the study reveals a multi-orbital super-exchange mechanism driven by ferro- and anti-ferromagnetic Cr-Cr d coupling channels, significantly influenced by ligand p orbitals. Environmental screening, like encapsulation with hexagonal boron nitride, alters Coulomb interactions and magnetic properties, leading to non-trivial effects on magnon dispersion and Curie temperature.

D. Soriano, A. N. Rudenko, M. I. Katsnelson, M. Rösner