Tuning paramagnetic spin-excitations of single adatoms

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.