  The ultra-fast magnetisation relaxation rates during the laser-induced
magnetisation process are analyzed in terms of the Landau-Lifshitz-Bloch (LLB)
equation for different values of spin $S$. The LLB equation is equivalent in
the limit $S \rightarrow \infty$ to the atomistic Landau-Lifshitz-Gilbert (LLG)
Langevin dynamics and for $S=1/2$ to the M3TM model [B. Koopmans, {\em et al.}
Nature Mat. \textbf{9} (2010) 259]. Within the LLB model the ultra-fast
demagnetisation time ($\tau_{M}$) and the transverse damping ($\alpha_{\perp}$)
are parameterized by the intrinsic coupling-to-the-bath parameter $\lambda$,
defined by microscopic spin-flip rate. We show that for the phonon-mediated
Elliott-Yafet mechanism, $\lambda$ is proportional to the ratio between the
non-equilibrium phonon and electron temperatures.
  We investigate the influence of the finite spin number and the scattering
rate parameter $\lambda$ on the magnetisation relaxation rates. The relation
between the fs demagnetisation rate and the LLG damping, provided by the LLB
theory, is checked basing on the available experimental data. A good agreement
is obtained for Ni, Co and Gd favoring the idea that the same intrinsic
scattering process is acting on the femtosecond and nanosecond timescale.
