  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.
