Graphene Exhibits Robust Tetrahedral Magnetism at the Van Hove Singularity, Charting a Cascade of Symmetry-broken States

The search for novel magnetic states in two-dimensional materials receives a significant boost from new research revealing a robust tetrahedral magnetic ground state within graphene. Maxime Lucas, Arnaud Ralko, and Andreas Honecker, alongside their colleagues at CY Cergy Paris Université and the Institut Néel, demonstrate the stability of this unique configuration, characterised by four mutually perpendicular magnetic moments, across a range of interactions. Their work goes beyond previous theoretical predictions by mapping the complete surrounding magnetic phase diagram, identifying a cascade of related states including pseudo-tetrahedral, planar, and modulated textures. These findings connect directly with experimental observations from angle-resolved photoemission spectroscopy and doping experiments, establishing the tetrahedral state as a key correlated instability in graphene and offering valuable insight into the emergence of magnetism in similar materials.

The research focuses on the van Hove singularity, a specific electronic state in graphene where interactions between electrons are dramatically enhanced, potentially leading to novel magnetic behavior. Scientists confirm the stability of a unique, noncoplanar magnetic configuration, featuring four mutually orthogonal magnetic moments, across a range of interaction strengths using large-scale computational modeling. They comprehensively map the surrounding magnetic phase diagram, revealing a cascade of symmetry-broken magnetic states including pseudo-tetrahedral, planar, collinear, and modulated textures.

Graphene Magnetism via Electronic Structure Calculations

This material details a computational investigation into the magnetic properties of graphene, exploring how different magnetic phases emerge depending on the number of electrons and the strength of interactions between them. The study aims to understand the complex interplay between electronic structure and magnetism, potentially revealing ways to control and manipulate magnetic order for future spintronic devices. Scientists employed Density Functional Theory, a powerful computational method, to model the system, focusing on behavior near the van Hove Singularity, where enhanced electronic interactions are expected. They meticulously calculated the spin structure factor to characterize the magnetic order, identifying the periodicity of the magnetic arrangement.

The team emphasizes the importance of using a sufficiently fine grid of points during the calculations to ensure accurate results, particularly when determining the true ground state magnetic configuration. They demonstrate that a coarse grid can lead to incorrect conclusions about the stability of different magnetic phases. The authors constructed a detailed magnetic phase diagram, identifying different magnetic phases and the boundaries between them using multiple order parameters. They present real-space snapshots of the magnetic configurations for different phases, such as stripe, ferrimagnetic, Y/Y*, and tetrahedral, visualizing the arrangement of spins on the graphene lattice.

Tetrahedral Magnetism Emerges in Doped Graphene

This work reveals a robust tetrahedral magnetic ground state in monolayer graphene when doped to the van Hove singularity, a point where electronic interactions are dramatically enhanced. Scientists confirmed the stability of this noncoplanar magnetic configuration, featuring four mutually orthogonal magnetic moments, across a range of interaction strengths using large-scale computational modeling. The research goes beyond previous studies by comprehensively charting the surrounding magnetic phase diagram, identifying a cascade of symmetry-broken magnetic states including pseudo-tetrahedral, planar, collinear, and modulated textures. These findings stem from unrestricted Hartree-Fock simulations performed on extensive supercells with dense sampling of the electronic structure, allowing researchers to resolve interaction-driven magnetic and charge inhomogeneities.

At a doping level of 0. 75, corresponding to quarter filling, the team definitively identified the tetrahedral magnetic order, a gapped state exhibiting exact tetrahedral symmetry. The simulations demonstrate that this tetrahedral state remains stable and well-defined, even with variations in the on-site Coulomb interaction. Further analysis reveals a complex phase diagram dependent on both doping level and interaction strength. Below the van Hove singularity, the team identified distinct magnetic phases compatible with a 2×2 graphene supercell, including canted tetrahedral states, planar ferrimagnetic states, and collinear magnetic phases. Above the van Hove singularity, more complex magnetic orders emerge, characterized by dominant magnetic structure factors at specific points in the electronic Brillouin zone. These detailed calculations provide a fundamental understanding of emergent magnetism in correlated Dirac materials like graphene and offer predictive insight into the behavior of similar systems.

Graphene’s Tetrahedral Magnetism and Phase Cascade

This research establishes a comprehensive magnetic phase diagram for monolayer graphene doped near the van Hove singularity. Through unrestricted calculations, scientists demonstrate the emergence of a robust tetrahedral magnetic order at a doping level of 0. 75, confirming its stability across a range of interaction strengths. This noncoplanar arrangement, characterized by four mutually orthogonal magnetic moments, represents a rare and nontrivial spin configuration within a simple theoretical model. Beyond identifying this central magnetic state, the team mapped a cascade of symmetry-broken magnetic phases that appear as doping levels are adjusted away from the van Hove singularity. These include various textures, such as pseudo-tetrahedral, planar, collinear, and modulated arrangements, all classified using detailed analysis of spin structure. Importantly, the research also reveals signatures of interaction-induced charge redistribution, suggesting a coupling between magnetic ordering and charge degrees of freedom, potentially leading to more complex intertwined states.