[Paper Review] Environmental Screening and Ligand-Field Effects to Magnetism in CrI$_3$ Monolayer

David Soriano, А. Н. Руденко+2 more|arXiv (Cornell University)|Mar 8, 2021

2D Materials and ApplicationsMaterials Science63 references35 citations

TL;DR

This study reveals that magnetism in CrI3 monolayers arises from a multi-orbital super-exchange mechanism driven by interplay between ferro- and antiferromagnetic Cr-Cr coupling channels, with ligand (I) p-orbitals playing a decisive role. Environmental screening—particularly from hexagonal boron nitride encapsulation—non-monotonically modulates Coulomb interactions, thereby tuning the magnon dispersion and Curie temperature through dielectric effects on the exchange couplings.

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.

Motivation & Objective

• To understand the microscopic origin of magnetism in CrI3 monolayers under varying environmental conditions.
• To investigate how dielectric screening from encapsulation (e.g., hBN) modifies Coulomb interactions and magnetic exchange couplings.
• To determine the role of ligand (I) p-orbitals in mediating magnetic exchange via multi-orbital super-exchange.
• To quantify the impact of environmental screening on the Curie temperature and magnon dispersion in 2D CrI3.

Proposed method

• Constructed minimal generalized Hubbard models using ab initio DFT and constrained RPA to derive accurate Coulomb tensors.
• Down-folded two models: one with only Cr d-orbitals (d-only) and another including I p-orbitals (d+p) to capture ligand-field effects.
• Solved the models within mean-field Hartree-Fock theory to obtain spin-resolved quasi-particle band structures.
• Applied the magnetic force theorem to compute orbitally resolved exchange interactions.
• Used the Wannier Function Continuum Electrostatics (WFCE) approach to include environmental screening effects from dielectric encapsulation.
• Analyzed the non-monotonic dependence of exchange couplings on nearest- and next-nearest-neighbor interactions under varying dielectric screening.

Experimental results

Research questions

• RQ1 How do ligand p-orbitals influence the magnetic exchange pathways in CrI3 monolayers?
• RQ2 What is the role of multi-orbital super-exchange in stabilizing ferromagnetism in CrI3?
• RQ3 How does dielectric screening from hBN encapsulation alter the effective Coulomb interactions and magnetic exchange couplings?
• RQ4 To what extent does environmental screening tune the Curie temperature and magnon dispersion in CrI3?
• RQ5 Can Coulomb engineering via encapsulation be used to control magnetic properties in 2D van der Waals magnets?

Key findings

• Magnetism in CrI3 monolayers originates from a multi-orbital super-exchange mechanism involving competing ferromagnetic and antiferromagnetic Cr-Cr coupling channels.
• The ligand (I) p-orbitals are essential in mediating and tuning the exchange interactions, particularly through t2g-t2g and t2g-eg hybridization pathways.
• Environmental screening from dielectric encapsulation non-monotonically modifies the effective Coulomb interaction, leading to non-trivial changes in exchange couplings.
• The Curie temperature and magnon dispersion in CrI3 are strongly and non-monotonically tunable via dielectric screening, with optimal tuning near intermediate screening strengths.
• The d+p model, which includes I p-orbitals, provides a more accurate description of magnetic exchange than the d-only model, especially under screening.
• The study demonstrates that Coulomb engineering via encapsulation is a viable route to control magnetic ground states and magnonic excitations in 2D CrI3.