Environmental Screening and Ligand-Field Effects to Magnetism in CrI${}_3$ Monolayer

Abstract

We present a detailed study on the microscopic origin of magnetism in suspended and dielectrically embedded CrI${}_3$ monolayer. To this end, we down-fold two distinct minimal generalized Hubbard models with different orbital basis sets from \emph{ab initio} calculations using the constrained random phase approximation. Within mean-field approximation, we show that these models are capable of describing the formation of localized magnetic moments in CrI${}_3$ and of reproducing electronic properties of full \emph{ab initio} calculations. We utilize the magnetic force theorem to study microscopic magnetic exchange channels between the different orbital manifolds. We find a multi-orbital super-exchange mechanism as the origin of magnetism in CrI${}_3$ resulting from a detailed interplay between effective ferro- and anti-ferromagnetic Cr-Cr $d$ coupling channels, which is decisively affected by the ligand (I) $p$ orbitals. We show how environmental screening such as resulting from encapsulation with hexagonal boron nitride (hBN) of the CrI${}_3$ monolayer affects the Coulomb interaction in the film and how this successively controls its magnetic properties. Driven by a non-monotonic interplay between nearest and next-nearest neighbour exchange interactions we find the magnon dispersion and the Curie temperature to be non-trivially affected by the environmental dielectric screening.

13 pages, 7 figures

References in corpus (10)

• Enhancement of Carrier Mobility in Semiconductor Nanostructures by Dielectric Engineering
• Excitons versus electron-hole plasma in monolayer transition metal dichalcogenide semiconductors
• Physical origin of giant excitonic and magneto-optical responses in two-dimensional ferromagnetic insulators
• Relativistic exchange interactions in CrX${}_3$ (X=Cl, Br, I) monolayers
• Magnetic Skyrmions in Atomic Thin CrI${}_3$ Monolayer
• Microscopic origin of ferromagnetism in trihalides CrCl${}_3$ and CrI${}_3$
• Strength of effective Coulomb interaction in two-dimensional transition-metal Halides MX${}_2$ and MX${}_3$ (M=Ti, V, Cr, Mn, Fe, Co, Ni; X=Cl, Br, I)
• Magnetic polaron and antiferro-ferromagnetic transition in doped bilayer CrI${}_3$
• Spin caloritronics in a CrBr${}_3$-based magnetic van der Waals heterostructure
• Random Phase Approximation for gapped systems: role of vertex corrections and applicability of the constrained random phase approximation