The role of stacking and strain in mean-field magnetic moments of multilayer graphene

Rhombohedral or ABC stacked multilayer graphene hosts a correlated magnetic ground state at charge neutrality, making it one of the simplest systems to investigate strong electronic correlations. We investigate this ground state in multilayer graphene structures using the Hubbard model in a distance dependent Slater-Koster tight binding framework. We show that by using a universal Hubbard-$U$ term, we can accurately capture the spin polarization predicted by hybrid density functional theory calculations for both hexagonal (ABA) and rhombohedral (ABC) stackings. Using this $U$ value, we calculate the magnetic moments of 3-8 layers of ABC and ABA graphene multilayers. We demonstrate that the structure and magnitude of these magnetic moments are robust when heterostructures are built from varying numbers of ABC and ABA multilayers. By applying different types of mechanical distortions, we study the behaviour of the magnetism in graphene systems under uniaxial strain and pressure. Our results establish a computationally efficient framework to investigate correlation-driven magnetism across arbitrary stacking configurations of graphite polytypes.

💡 Research Summary

This paper presents a computationally efficient framework for investigating correlation‑driven magnetism in multilayer graphene with arbitrary stacking configurations. Using a distance‑dependent Slater‑Koster tight‑binding (TB) model augmented by an on‑site Hubbard‑U term (TB+U), the authors fit a single universal Hubbard parameter, U = 5.84 eV, to magnetic moments obtained from hybrid density‑functional (PBE0) calculations for both rhombohedral (ABC) and Bernal (ABA) stackings in 3–8‑layer systems. The fitted TB+U model reproduces the layer‑resolved magnetic moments of the LAF (layer antiferromagnetic) ground state with high fidelity, capturing two distinct spatial patterns: in ABC stacks the moment magnitude decays from the outermost layers toward the interior, while in ABA stacks the moments increase toward the central layers.

Beyond pure stackings, the study examines mixed structures composed of alternating ABC and ABA segments (denoted R_M‑B_N‑R_M′). The magnetic texture of each segment remains largely unchanged, but the interface induces a non‑local influence: increasing the number of ABC layers progressively suppresses the central‑enhanced magnetism of the adjacent ABA region, indicating that the magnetic order of one domain can affect the other over several layers.

Mechanical deformations are then explored in two regimes. First, a modest ±1 % uniaxial strain applied along the armchair direction shows that tensile strain enhances magnetic moments in both stackings, whereas compressive strain can completely quench the ABA magnetism while the ABC magnetism persists, reflecting the different sensitivities of in‑plane hopping to strain. Second, a ±5 % variation of the interlayer spacing (simulating hydrostatic pressure) reveals a universal trend: expanding the interlayer distance reduces interlayer hopping, weakens electronic correlations, and diminishes the magnetic moments; compressing the layers has the opposite effect, strengthening the LAF order across all layer numbers and both stackings.

Overall, the work demonstrates that a single Hubbard‑U value suffices to describe the mean‑field magnetic behavior of multilayer graphene across a wide range of stacking orders, layer counts, and mechanical perturbations. This TB+U approach offers a low‑cost alternative to expensive hybrid‑DFT calculations, enabling large‑scale simulations of realistic heterostructures, twisted multilayers, and domain‑wall configurations. The findings provide quantitative guidance for experimental efforts aiming to tune magnetism in graphene‑based van‑der‑Waals systems via stacking engineering, strain, or pressure.