Phase coexistence of clusters and islands: europium on graphene

The adsorption and equilibrium surface phases of europium (Eu) on graphene on Ir(111) are investigated in the temperature range from 35 to 400K and for coverages ranging from a small fraction of a saturated monolayer to the second layer by scanning tunnelling microscopy. Using density functional theory including 4f-shell Coulomb interactions and modelling of electronic interactions, excellent agreement with the experimental results for the equilibrium adsorbate phase, adsorbate diffusion and work function is obtained. Most remarkably, at 300 K in an intermediate coverage range a phase of uniformly distributed Eu clusters (size 10-20 atoms) coexists in two-dimensional equilibrium with large Eu-islands in a (root 3 x root 3)R30 degrees structure. We argue that the formation of the cluster phase is driven by the interplay of three effects. Firstly, the metallic Eu-Eu binding leads to the local stability of (root 3 x root 3)R30 degrees structures. Secondly, electrons lower their kinetic energy by leaving the Eu clusters, thereby doping graphene. Thirdly, the Coulomb energy penalty associated with the charge transfer from Eu to graphene is strongly reduced for smaller clusters.