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