Effect of the valence state on the band magnetocrystalline anisotropy in two-dimensional rare-earth/noble-metal compounds

In intermetallic compounds with zero orbital momentum (L=0) the magnetic anisotropy and the electronic band structure are interconnected. Here, we investigate this connection in divalent Eu and trivalent Gd intermetallic compounds. We find by x-ray magnetic circular dichroism an out-of-plane easy magnetization axis in two-dimensional atom-thick EuAu_{2}. Angle-resolved photoemission spectroscopy and density-functional theory prove that this is due to strong f-d band hybridization and Eu^{2+} valence. In contrast, the easy in-plane magnetization of the structurally equivalent GdAu_{2} is ruled by spin-orbit-split d bands, notably Weyl nodal lines, occupied in the Gd^{3+} state. Regardless of the L value, we predict a similar itinerant electron contribution to the anisotropy of analogous compounds.