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The role of spin-orbit interaction in the ultrafast demagnetization of small iron clusters

The ultra-fast demagnetization of small iron clusters initiated by an intense optical excitation is studied with time-dependent spin density functional theory (TDSDFT). In particular we investigate the effect of the spin-orbit interaction on the onset of the demagnetization process. It is found that the initial rate of coherent spin loss is proportional to the square of the atomic spin-orbit coupling constant, $λ$. A simplified quantum spin model comprising spin-orbit interaction and a local time-dependent magnetic field is found to be the minimal model able to reproduce our {\it ab initio} results. The model predicts the $λ^2$ dependence of the onset rate of demagnetization when it is solved either numerically or analytically in the linear response limit. Our findings are supported by additional TDSDFT simulations of clusters made of Co and Ni.