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Valence state determines the band magnetocrystalline anisotropy in 2D 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 on divalent Eu and trivalent Gd intermetallic compounds. We find by X-ray magnetic circular dichroism an out-of-plane easy magetization axis in 2D atom-thick EuAu$_2$. 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 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.