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At the heart of current information nanotechnology lies the search for idealplatforms hosting the smallest possible magnets, i.e. single atoms withmagnetic moments pointing out-of-plane, as requested in a binary-type ofmemory. For this purpose, a 2D material such as graphene would be an idealsubstrate thanks to its intrinsic low electron and phonon densities, as well asits 6-fold symmetry. Here we investigate, from first-principles, a fundamentalmechanism detrimental for the magnetic stability: the zero-pointspin-fluctuations modifying the effective energy landscape perceived by thelocal spin moments of 3$d$ and 4$d$ transition metal atoms deposited on a freestanding graphene. Utilizing time-dependent density functional theory and byvirtue of the fluctuation-dissipation theorem, these spontaneous quantumfluctuations are found to be negligible for most of the 3$d$ elements, instrong contrast to the 4$d$ atoms. Surprisingly, we find that such fluctuationscan promote the magnetic stability by switching the easy direction of themagnetic moment of Tc from being initially in-plane to out-of-plane. Theadatom-graphene complex gives rise to impurity states settling in some casesthe magnetocrystalline anisotropy energy --- the quantity that defines theenergy barrier protecting the magnetic moments and, consequently, thespin-excitation behavior detectable with inelastic scanning tunnelingspectroscopy. A detailed analysis is provided on the impact of electron-holeexcitations, damping and lifetime of the spin-excitations on the dynamicalbehavior of the adsorbed magnetic moments on graphene.

Spontaneous and externally driven quantum spin fluctuations of 3d and 4d single atoms adsorbed on graphene