Valence state determines the band magnetocrystalline anisotropy in 2D rare-earth/noble-metal compounds

As Eu and Gd are zero-orbital-momentum ($L=0$) rare-earth atoms, their crystalline intermetallic alloys illustrate the connection between electron bands and magnetic anisotropy. Here we find out-of-plane anisotropy in 2D atom-thick EuAu$_2$ by X-ray magnetic circular dichroism. Angle-resolved photoemission and density-functional theory prove that this is due to strong $f-d$ band hybridization and Eu$^{2+}$ valence. In contrast, the in-plane anisotropy of the structurally-equivalent GdAu$_2$ is ruled by spin-orbit-split $d$-bands, notably Weyl nodal lines, occupied in the Gd$^{3+}$ state. Irrespectively of $L$, we predict a similar itinerant electron contribution to the anisotropy of analogous compounds.