Tuning magnetic states in CrI$_3$ bilayers via Moir\'e patterns

TL;DR

This paper introduces a mathematical method to generate moiré patterns in twisted CrI$_3$ bilayers and explores how these patterns influence magnetic states and electronic properties, revealing angle-dependent magnetic configurations.

Contribution

A novel mathematical approach to create commensurable moiré patterns in twisted bilayers and analyze their impact on magnetic and electronic properties of CrI$_3$.

Findings

Magnetic configurations depend on the twist angle.

Significant changes in electronic band dispersion occur with different moiré patterns.

Atomic arrangement variations influence energy contributions and magnetic states.

Abstract

Commensurable twisted bilayers can drastically change the magnetic properties of chromium trihalide layered compounds, which opens novel opportunities for tuning magnetic states through layer rotations. Here, we introduce a mathematical approach to obtain moir\'e patterns in twisted hexagonal bilayers by performing a certain commensurable rotation $\theta$ over one layer. To test our approach, we apply it to find moir\'e structures with $\theta=21.79^{\circ}$ and $32.20^{\circ}$ in the phases R$\bar{3}$ and C2/m of CrI$_{3}$. For comparison purposes, we also consider a non-shifted CrI$_{3}$ structure. Electronic and magnetic properties of the so-obtained systems are computed by \textit{Ab-Initio} methodologies. Results show the presence of rotation-angle-dependent magnetic configurations and steep modifications of the dispersion bands due to variations in the nearest and next nearest distances among layers of Cr atoms. Modifications obtained from these commensurable rotations are discussed on the basis of competition among different energy contributions due to changes in the atomic arrangements.