LAUSR

We study the microscopic origin of magnetism in suspended and dielectrically embedded CrI 3 monolayer by down-folding minimal generalized Hubbard models from ab initio calculations using the constrained random phase approximation. These models are capable of describing the formation of localized magnetic moments in CrI 3 and of reproducing electronic properties of direct ab initio calculations. Utilizing the magnet force theorem, we find a multi-orbital super-exchange mechanism as the origin of magnetism in CrI 3 resulting from an interplay between ferro- and anti-ferromagnetic Cr-Cr d coupling channels, which is decisively affected by the ligand p orbitals. We show how environmental screening, such as resulting from encapsulation with hexagonal boron nitride, affects the Coulomb interaction in the film and how this controls its magnetic properties. Driven by a non-monotonic interplay between nearest and next-nearest neighbor exchange interactions we find the magnon dispersion and the Curie temperature to be non-trivially affected by the environmental screening.