Longitudinal and transverse spin relaxation times of magnetic single adatoms: an ab initio analysis

We present a systematic ab initio investigation of the longitudinal and transverse spin relaxation times of magnetic single adatoms deposited on metallic substrates. Our analysis based on time-dependent density functional theory shows that the longitudinal time, $T_{\parallel }$, is of order femtosecond while the transverse time, $T_{\perp }$, is of order picosecond, i.e. $T_{\perp }\gg T_{\parallel }$. This comes as a consequence of the different energy scales of the corresponding processes: $T_{\parallel }$ involves spin-density excitations of order eV, while $T_{\perp }$ is governed by atomic spin-excitations of order meV. Comparison to available inelastic scanning tunneling spectroscopy $\mathrm{d}I\mathrm{/}\mathrm{d}V$ experimental curves shows that the order of magnitude of $T_{\perp }$ agrees well with our results. Regarding $T_{\parallel }$, the time scale calculated here is several orders of magnitude faster than what has been measured up to now; we therefore propose that an ultrafast laser pulse measuring technique is required in order to access the ultrafast spin-dynamics described in this work.