Here we carry out a first-principles time-dependent calculation to investigate how fast electrons actually move under laser excitation and how large the electron transport affects demagnetization on the shortest time scale. To take into account the transport effect, we implement the intraband transition in our theory. In the bulk fcc Ni, we find the effect of the spin transport on the demagnetization is extremely small, no more than 1%. The collective electron velocity in Ni is 0.4 $rm AA/fs$, much smaller than the Fermi velocity, and the collective displacement is no more than 0.1 $rm AA$. But this does not mean that electrons do not travel fast; instead we find that electron velocities at two opposite crystal momenta cancel each other. We follow the $Gamma$-X line and find a huge dispersion in the velocities in the crystal momentum space. In the Fe/W(110) thin film, the overall demagnetization is larger than Ni, and the Fermi velocity is higher than Ni. However, the effect of the spin transport is still small in the Fe/W(110) thin film. Based on our numerical results and existing experimental findings, we propose a different mechanism that can explain two latest experimental results. Our finding sheds new light on the effect of ballistic transport on demagnetization.
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