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

TL;DR

This study investigates the microscopic origin of magnetism in CrI₃ monolayers, demonstrating how ligand-field effects and environmental screening influence magnetic interactions, exchange mechanisms, and Curie temperature through detailed modeling and ab initio calculations.

Contribution

The paper introduces minimal generalized Hubbard models derived from ab initio data that accurately describe magnetism and electronic properties in CrI₃ monolayers, highlighting the role of ligand orbitals and environmental screening.

Findings

Multi-orbital super-exchange mechanism drives magnetism in CrI₃.

Environmental screening modulates Coulomb interactions and magnetic properties.

Magnon dispersion and Curie temperature are non-trivially affected by dielectric environment.

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.