  Despite intense experimental effort, theoretical proposals and modeling
approaches, a lack of consensus exists about the intrinsic mechanisms driving
ultrafast magnetization dynamics in 3$d$ ferromagnets. In this work, we find
evidence of electron-phonon mediated spin-flip as the driving mechanism for the
ultrafast magnetization dynamics in all three 3$d$ ferromagnets; nickel, iron
and cobalt. We use a microscopic three temperature model with parameters
calculated from first-principles, which has been validated by direct comparison
to the electron and lattice dynamics extracted from previous experiments. By
direct comparison to the experimentally measured magnetization dynamics for
different laser fluence, we determine the spin-flip probability of each
material. In contrast to previous findings but in agreement to ab-initio
predictions, we find that relatively small values of the spin-flip probability
enable ultrafast demagnetization in all three 3$d$ ferromagnets.
