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

András Balogh, Zoltán Tajkov, Péter Nemes-Incze, János Koltai

TL;DR

The paper addresses correlation-driven magnetism in ABC-stacked multilayer graphene and its dependence on stacking and mechanical distortions. It develops a tight-binding+$U$ framework with distance-dependent Slater-Koster interlayer hopping and a single universal Hubbard parameter, validated against hybrid-DFT results for 3–8 layer ABC and ABA systems. With a universal value of $U=5.84$ eV, the model reproduces layerwise antiferromagnetic order, where ABC moments grow with thickness while ABA moments peak at the center; mixed ABC-ABA stacks maintain region-specific patterns with boundary perturbations. The study also shows that uniaxial strain and interlayer spacing can tune magnetism in predictable ways, providing a computationally efficient path to explore correlation-driven magnetism across arbitrary graphite polytypes and suggesting experimental routes to realize buried flat-band magnetism.

Abstract

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.

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

TL;DR

The paper addresses correlation-driven magnetism in ABC-stacked multilayer graphene and its dependence on stacking and mechanical distortions. It develops a tight-binding+ framework with distance-dependent Slater-Koster interlayer hopping and a single universal Hubbard parameter, validated against hybrid-DFT results for 3–8 layer ABC and ABA systems. With a universal value of eV, the model reproduces layerwise antiferromagnetic order, where ABC moments grow with thickness while ABA moments peak at the center; mixed ABC-ABA stacks maintain region-specific patterns with boundary perturbations. The study also shows that uniaxial strain and interlayer spacing can tune magnetism in predictable ways, providing a computationally efficient path to explore correlation-driven magnetism across arbitrary graphite polytypes and suggesting experimental routes to realize buried flat-band magnetism.

Abstract

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- 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 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.

Paper Structure

This paper contains 13 sections, 7 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Model and methods
  3. Results
  4. Effects of mechanical distortion
  5. Uniaxial strain in the armchair direction
  6. Deformation of the van der Waals spacing
  7. Conclusion and outlook
  8. The tight-binding model
  9. The model
  10. Fitting procedure
  11. TB+U
  12. Details of the DFT calculations
  13. Simultaneous uniaxial strain and compression

Figures (9)

  • Figure 1: Left column: Comparison between the magnetic moments obtained from the TB+U calculations (red) and the data from Ref. abc_hse (black). Middle column: Comparison between the magnetic moments obtained from the TB+U calculations (blue) and the data from Ref. aba_hse (black). Right column: The structure and numbering of sites in ABC (top) and ABA (bottom) graphene
  • Figure 2: The magnetic structure and geometry of various ABC-ABA mixed stackingss. Empty red (blue) circles represent the magnetic moments for ABC (ABA) graphene multilayers of the same length. Filled green circles represent the magnetic structure of the whole mixed stackings.
  • Figure 3: The value of the maximum magnetic moment in 3-12 layer ABC and ABA multilayers in the case of uniaxial strain along the armchair direction.
  • Figure 4: The value of the maximum magnetic moment in 3-12 layer ABC and ABA multilayers in the case of modified van der Waals separation.
  • Figure 5: The $\theta_i$ angle showed in the AB bilayer. The red arrow is pointing from atom $j$ to atom $i$, while the black arrow is the $z$ axis.
  • ...and 4 more figures