Magnetic ordering tendencies in hexagonal boron nitride-bilayer graphene moir\'e structures

TL;DR

This study investigates magnetic ordering in moiré structures formed by aligned hexagonal boron nitride and bilayer graphene, revealing a dominant antiferromagnetic instability influenced by Coulomb interactions and moiré-induced band gaps.

Contribution

It provides a detailed atomistic Hubbard model analysis of magnetic tendencies in hBN-BG moiré structures, highlighting the impact of band gaps on magnetic ordering thresholds.

Findings

Antiferromagnetic ordering is the dominant magnetic instability.

Critical interaction strength U_c is slightly higher in systems with moiré-induced band gaps.

Magnetic order can influence the observable single-particle gap sizes.

Abstract

When hexagonal boron nitride (hBN) and graphene are aligned at zero or small twist angle, a moir\'e structure is formed due to the small lattice constant mismatch between the two structures. In this work, we analyze magnetic ordering tendencies, driven by onsite Coulomb interactions, of encapsulated bilayer graphene (BG) forming a moir\'e structure with one (hBN-BG) or both hBN layers (hBN-BG-hBN), using the random phase approximation. The calculations are performed in a fully atomistic Hubbard model that takes into account all $\pi$-electrons of the carbon atoms in one moir\'e unit cell. We analyze the charge neutral case and find that the dominant magnetic ordering instability is uniformly antiferromagnetic. Furthermore, at low temperatures, the critical Hubbard interaction $U_c$ required to induce magnetic order is slightly larger in those systems where the moir\'e structure has caused a band gap opening in the non-interacting picture, although the difference is less than 6%. Mean-field calculations are employed to estimate how such an interaction-induced magnetic order may change the observable single-particle gap sizes.