Microscopic understanding of magnetic interactions in bilayer CrI$_3$

TL;DR

This study provides a microscopic analysis of magnetic interactions in bilayer CrI$_3$, revealing the orbital interactions responsible for ferromagnetic order and suggesting ways to achieve antiferromagnetic states for device applications.

Contribution

The paper offers a detailed microscopic understanding of inter-layer magnetic couplings in bilayer CrI$_3$, highlighting the orbital interactions that stabilize ferromagnetism and proposing methods to induce antiferromagnetism.

Findings

Ferromagnetic ground state confirmed by van der Waals functionals and magnetic force response.

Orbital interactions, especially $e_g$-$t_{2g}$, stabilize ferromagnetism.

High-temperature monoclinic stacking may lead to antiferromagnetic order.

Abstract

We performed the detailed microscopic analysis of the inter-layer magnetic couplings for bilayer CrI$_3$. As the first step toward understanding the recent experimental observations and utilizing them for device applications, we estimated magnetic force response as well as total energy. Various van der Waals functionals equivocally point to the ferromagnetic ground state for the low-temperature structured bilayer CrI$_3$ which is further confirmed independently by magnetic force response calculations. The calculated orbital-dependent magnetic forces clearly show that $e_g$-$t_{2g}$ interaction is the key to stabilize this ferromagnetic order. By suppressing this ferromagnetic interaction and enhancing antiferromagnetic orbital channels of $e_g$-$e_g$ and $t_{2g}$-$t_{2g}$, one can realize the desirable antiferromagnetic order. We showed that high-temperature monoclinic stacking can be the case. Our results provide unique information and insight to understand the magnetism of multi-layer CrI$_3$ paving the way to utilize it for applications.