Fig. 6: Comparison of selected magnetic states.
From: Nano-scale collinear multi-Q states driven by higher-order interactions
a, b Upper panels show the total energies for fcc-Fe/Rh/Ir(111) and hcp-Fe/Rh/Ir(111), respectively, with respect to the FM reference state; red squares are DFT values (violet dots include spin–orbit coupling), black circles are obtained via the atomistic spin model with DFT parameters for the magnetic interactions. On the upper axis the non-collinear states and on the lower axis the corresponding collinear states are specified (background colors serve to group the states, which have the same Q-vectors). In the lower panels the total energy of the spin model (black circles in upper panel) is decomposed into the contributions from the Heisenberg exchange, the two-site four-spin interaction (biquadratic), the three-site four-spin interaction (3-Spin) and the four-site four-spin interaction (4-Spin). Filled (open) circles indicate collinear (non-collinear) states. Note that for the calculation of total energies within the spin model the DMI and the MAE were taken into account (not shown here). The lines connecting the data points serve as a guide to the eye.
