  We extend spin-lattice relaxation theory to incorporate the use of pulsed
magnetic fields for probing the hysteresis effects and magnetization steps and
plateaus exhibited, at low temperatures, by the dynamical magnetization of
magnetic molecules. The main assumption made is that the lattice degrees of
freedom equilibrate in times much shorter than both the experimental time scale
(determined by the sweep rate) and the typical spin-lattice relaxation time. We
first consider the isotropic case (a magnetic molecule with a ground state of
spin $S$ well separated from the excited levels and also the general isotropic
Heisenberg Hamiltonian where all energy levels are relevant) and then we
include small off-diagonal terms in the spin Hamiltonian to take into account
the Landau-Zener-St\"{u}ckelberg (LZS) effect. In the first case, and for an
$S=1/2$ magnetic molecule we arrive at the generalized Bloch equation recently
used for the magnetic molecule \{V$_6$\} in Phys. Rev. Lett. 94, 147204 (2005).
An analogous equation is derived for the magnetization, at low temperatures, of
antiferromagnetic ring systems. The LZS effect is discussed for magnetic
molecules with a low spin ground state, for which we arrive at a very
convenient set of equations that take into account the combined effects of LZS
and thermal transitions. In particular, these equations explain the deviation
from exact magnetization reversal at $B\approx 0$ observed in \{V$_6$\}. They
also account for the small magnetization plateaus (``magnetic Foehn effect''),
following the LZS steps, that have been observed in several magnetic molecules.
Finally, we discuss the role of the Phonon Bottleneck effect at low
temperatures and specifically we indicate how this can give rise to a
pronounced Foehn effect.
