  Around 50 years ago, Doniach [Proc. Phys. Soc. 91, 86 (1967)] predicted the
existence of paramagnons in nearly ferromagnetic materials, recently measured
in bulk Pd [Phys. Rev. Lett. 105, 027207 (2010)]. Here we predict the analogous
effect for single adatoms, namely paramagnetic spin-excitations (PSE). Based on
time-dependent density functional theory, we demonstrate that these overdamped
excitations acquire a well-defined peak structure in the meV energy region when
the adatom's Stoner criterion for magnetism is close to the critical point. In
addition, our calculations reveal a subtle tunability and enhancement of PSE by
external magnetic fields, exceeding by far the response of bulk paramagnons and
even featuring the atomic version of a quantum phase transition. We further
demonstrate how PSE can be detected as moving steps in the $\mathrm{d}I/dV$
signal of state-of-the-art inelastic scanning tunneling spectroscopy, opening a
potential route for experimentally accessing fundamental electronic properties
of non-magnetic adatoms, such as the Stoner parameter.
