Fig. 2. Schematic visualizations of the magnetic eigenvectors and their relation with the antibiskyrmion spin structure.

a Top view of NiI₂: the six nearest-neighbors Ni surrounding the central Ni atom are labeled with numbers. Plus and minus indicate iodine atoms above and below nickels plane, respectively. The {ν_α, ν_β, ν_γ} eigenvector basis set is represented on each Ni–Ni pair. b Lateral view of the Ni-I–Ni-I plaquette and relative orientation of the eigenvectors: ν_α (α-red), ν_β (β-green), and ν_γ (γ-blue). c Top and lateral view of the local eigenvectors on the triangular Ni-net to help visualization of the noncoplanarity and noncollinearity in the exchange-tensor principal axes. d In-plane components of the ν_α eigenvector for each magnetic Ni–Ni pair. e Sketches of the anti-biskyrmion spin structure: spins on the magnetic sites of the nearest-neighbors (black arrows) of the central Ni orient according to the in-plane projection of the noncoplanar principal axes (d); spins on the second-nearest neighbor magnetic sites (green arrows) orient following the direction fixed by the interaction accommodating the A2Sk in a spin lattice. Dashed gold lines are guidelines for the eyes delimiting the topological spin pattern and dashed blue (green) lines mark the direction of the six first (second) nearest neighbor Ni, as in Fig. S2c, d. f Zoom on the antibiskyrmion lattice as obtained from the MC simulations: spins orient as drawn in e.