Interplay between interlayer exchange and stacking in CrI$_3$ bilayers

TL;DR

This study investigates how stacking arrangements and interlayer exchange interactions influence the magnetic properties of CrI$_3$ bilayers and bulk, revealing strong dependence on crystal structure, strain, and electronic correlations.

Contribution

It provides a detailed theoretical analysis of stacking-dependent interlayer exchange and hybridization effects in CrI$_3$, explaining experimental observations of magnetic behavior.

Findings

Bulk CrI$_3$ is ferromagnetic in rhombohedral phase.

Interlayer exchange in bilayers can be antiferromagnetic under certain conditions.

Stacking and strain significantly affect magnetic interactions.

Abstract

We address the interplay between stacking and interlayer exchange for ferromagnetically ordered CrI$_3$, both for bilayers and bulk. Whereas bulk CrI$_3$ is ferromagnetic, both magneto-optical and transport experiments show that interlayer exchange for CrI$_3$ bilayers is antiferromagnetic. Bulk CrI$_3$ is known to assume two crystal structures, rhombohedral and monoclinic, that differ mostly in the stacking between monolayers. Below 210-220 Kelvin, bulk CrI$_3$ orders in a rhombohedral phase. Our density functional theory calculations show a very strong dependence of interlayer exchange and stacking. Specifically, the ground states of both bulk and free-standing CrI$_3$ bilayers are ferromagnetic for the rhombohedral phase. In contrast, the energy difference between both configurations is more than one order of magnitude smaller for the monoclinic phase, and eventually becomes antiferromagnetic when either positive strain or on-site Hubbard interactions ($U \geq 3$) are considered. We also explore the interplay between interlayer hybrydization and stacking, using a Wannier basis, and between interlayer hybrydization and relative magnetic alignment for CrI$_3$ bilayers, that helps to account for the very large tunnel magnetoresistance obvserved in recent experiments.