Fig. 4

Spin model parameters and stabilization of helical ordering based on ab-initio calculations. a Isotropic Heisenberg interactions (top) and magnitude of the z-component of Dzyaloshinskii–Moriya vectors (bottom) as a function of inter-atomic distance. Red and blue circles denote inter- and intra-plane interactions, respectively. b Energy per unit cell of the (Γ₅) state with a helical modulation propagating along the c direction as computed with the spin model parameters in a. The blue curve corresponds to a purely isotropic model, the green curve to a spin model including also first nearest neighbor DM interactions, and the red curve refers to including all calculated DM interactions. The inset shows the contribution from the DM interactions to the spin-spiral energy for both cases. The nearest neighbor case (the green line) fits perfectly to a function Acos(k_zc/2)