Fig. 2: DFT total energies of spin states in Fe/Ir-3/Re(0001).

Energy dispersion of spin spirals obtained via DFT along the high-symmetry lines \(\overline{{\rm{M}}}\)-\(\overline{\Gamma }\)-\(\overline{{\rm{K}}}\)-\(\overline{{\rm{M}}}\) with and without including SOC displayed by filled red and gray circles, respectively. The solid line represents a fit of the atomistic model to the DFT values. The total energies of the two uudd states and the 3Q state calculated via DFT are marked. The self-consistently calculated DFT total energies including SOC for the three spin lattices (Fig. 3) are also marked. All energies are given with respect to the FM state. In the inset the unit cells of the magnetic contrast is shown with the magnetic unit cell vectors a₁ and a₂ and a_M and a_K in purple and black, respectively obtained based on the experimental SP-STM images (cf. Fig. 1). The Brillouin zone is also sketched as an inset and the spin spiral vectors q₁, q₂, q_K and q_M are indicated. Dashed gray lines indicate the experimentally determined absolute values of q_K and q_M.