We investigate the stability and electronic properties of single Co atoms on graphene with near-exact many-body calculations. A frozen-orbital embedding scheme was combined with auxiliary-field quantum Monte Carlo calculations to increase the reach in system sizes. Several energy minima are found as a function of the distance h between Co and graphene. Energetics only permit the Co atom to occupy the top site at h=2.2 Å in a high-spin 3d(8)4s(1) state, and the van der Waals region at h=3.3 Å in a high-spin 3d(7)4s(2) state. The findings provide an explanation for recent experimental results with Co on free-standing graphene.
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