Fig. 3: Theoretical model of the H, T phase diagram based on continuous multi-Q manifolds.

a Continuous manifold of multi-Q M-orderings, depicted as a variational space on a spherical shell. b–e Magnetic structures consistent with the symmetry and topological properties suggested by the combination of MCD and MLD measurements. The size and color of the blue dots on the right side of each panel represent the magnitude of the Fourier components (∣Δ_ν∣²). f, g Theoretical temperature-field (H ∥ c) phase diagram derived from classical Monte-Carlo simulations of the realistic anisotropic spin model for Co_1/3TaS₂ (Eqs. (2) and (3)). The color code in f indicates \({r}_{\Delta }\equiv \frac{{\Delta }_{2}+{\Delta }_{3}}{{\Delta }_{1}}\), where Δ₃ ≤ Δ₂ ≤ Δ₁. Spin configurations of the Phases I--III are depicted in c, b, and e, respectively. h Evolution of the four spin-sublattice configurations throughout Phases II, I, and III, transitioning from a three-fold symmetric triple-Q (3Q) state to a stripe-like single-Q (1Q) state via a distorted tetrahedral alignment.