Spin Spirals in Surface Alloys on Ru(0001): A First-principles Study

We have used ab initio density functional theory to compute the magnetic ground states of the surface alloy systems FeAu$_2$/Ru(0001) and MnAu$_2$/Ru(0001). For both systems, we find that the lowest energy magnetic configuration corresponds to a left-rotating spin spiral, in which the sense of rotation is determined by the Dzyaloshinskii-Moriya interaction. These spirals are lower in energy than the ferromagnetic configuration by 3-4 meV per nm$^2$. We also find that FeAu$_2$/Ru(0001) has a significantly high magnetic anisotropy energy, of the order 1 meV per Fe atom. By comparing with the corresponding freestanding alloy monolayers, we find that the presence of the Ru substrate plays a significant role in determining the magnetic properties of the surface alloy systems.