Figure 3
From: First-principles Dzyaloshinskii–Moriya interaction in a non-collinear framework
DMI calculated when varying the vertical angle of the magnetic moments between \(\theta =60^\circ\) and \(\theta =120^\circ\). On top we have the plot for Cr triangular trimer on Au(111), middle for the triangular trimer of Mn on Au(111) and on bottom the Mn triangular trimer on Ag(111). On the left panels we show results for the DMI part related with the charge-current (\(D^{C}\)), on the right panels we show data for the spin-current dependent part of the DMI (\(D^{S}\)), and the middle panels contain the total DMI. The blue line denotes the \(D_{z}\) component while the red line denotes the in-plane component as \(D_{x}=D_{y}=D_\Vert /\sqrt{2}\). The full line stands for the calculation when the spin-orbit coupling is included, whereas the dashed line denotes the calculation without spin-orbit coupling.
