Title: Zero-point spin-fluctuations of single adatoms,
Abstract: Stabilizing the magnetic signal of single adatoms is a crucial step towards
their successful usage in widespread technological applications such as
high-density magnetic data storage devices. The quantum mechanical nature of
these tiny objects, however, introduces intrinsic zero-point spin-fluctuations
that tend to destabilize the local magnetic moment of interest by dwindling the
magnetic anisotropy potential barrier even at absolute zero temperature. Here,
we elucidate the origins and quantify the effect of the fundamental ingredients
determining the magnitude of the fluctuations, namely the ($i$) local magnetic
moment, ($ii$) spin-orbit coupling and ($iii$) electron-hole Stoner
excitations. Based on a systematic first-principles study of 3d and 4d adatoms,
we demonstrate that the transverse contribution of the fluctuations is
comparable in size to the magnetic moment itself, leading to a remarkable
$\gtrsim$50$\%$ reduction of the magnetic anisotropy energy. Our analysis gives
rise to a comprehensible diagram relating the fluctuation magnitude to
characteristic features of adatoms, providing practical guidelines for
designing magnetically stable nanomagnets with minimal quantum fluctuations.