Tetrahedral Core in a Sea of Competing Magnetic Phases in Graphene

We demonstrate the emergence of a robust tetrahedral magnetic ground state in monolayer graphene doped to the van Hove singularity (vHS). This noncoplanar, gapped spin configuration - featuring four equally inclined moments - has been previously identified as a candidate instability. Here, not only do we confirm its stability across all finite interactions using fully self-consistent, real-space-resolved calculations, but we also go beyond earlier work by charting the full surrounding phase diagram. In doing so, we unravel a cascade of symmetry-broken magnetic states - pseudo-tetrahedral, planar, collinear, and modulated textures - which we classify using spin structure factors and vector order parameters. These results stem from unrestricted Hartree-Fock simulations on large supercells with dense k-point sampling, enabling us to resolve interaction-driven magnetic and charge inhomogeneities. Our findings connect directly with recent ARPES and doping experiments near the vHS in graphene, and establish the tetrahedral state as the central correlated instability in this regime, offering predictive insight into emergent magnetism in correlated Dirac materials.