  Time resolved measurements of the linear magneto-optical Kerr rotation reveal
that, in the {\it 3d} ferromagnets Fe, Co and Ni, the amplitude of the
demagnetization increases linearly with the fluence of the light. We
rationalize this phenomenon as being linearly driven by the increase in
temperature, the electron-phonon and electron-magnon scattering, and a
reduction of the inter-atomic exchange. The amplitude of the latter phenomenon,
which until the present study has been widely overlooked, is obtained through
\textit{ab initio} density functional theory calculations, and is argued to be
the principal source of demagnetization in Ni and Co, while still contributing
largely in Fe.
