Fig. 5: Degree of collinearity of the 12:15-MS state in hcp-Fe/Rh/Ir(111).
From: Nano-scale collinear multi-Q states driven by higher-order interactions
a DFT total energies of magnetic states along the geodesic path in spin space from the collinear 12:15-MS state into the non-collinear 27-SkX without (black circles) and with spin–orbit coupling (purple circles). The relative polar angle θ is defined for every atom as θ(x) = θ0 + x(θf − θ0) with x ∈ [0, 1] where the value x = 0 is set for the collinear 12:15-MS state (red filled circle) and x = 1 for the non-collinear hexagonal 27-SkX state (green filled circle). θf refers to the final value of every magnetic moment in the 27-SkX, whereas θ0 is set to 0∘ for upward pointing moments (180∘ for downward pointing moments). The in-plane angles ϕ of the atoms are not changed with the variation of θ, but kept fixed to the values of the 27-SkX. The solid lines connecting the DFT data points serve as a guide to the eye. b–d Simulated SP-STM images of the 12:15-MS state, the energetically lowest 15% canted 12:15-MS state, and the 27-SkX with a tip magnetization in − z direction and 50% spin-polarization based on the model of ref. 33.
