  Avalanches of the magnetization, that is to say an abrupt reversal of the
magnetization at a given field, have been previously reported in the spin-ice
compound Dy$_{2}$Ti$_{2}$O$_{7}$. This out-of-equilibrium process, induced by
magneto-thermal heating, is quite usual in low temperature magnetization
studies. A key point is to determine the physical origin of the avalanche
process. In particular, in spin-ice compounds, the origin of the avalanches
might be related to the monopole physics inherent to the system. We have
performed a detailed study of the avalanche phenomena in three single crystals,
with the field oriented along the [111] direction, perpendicular to [111] and
along the [100] directions. We have measured the changing magnetization during
the avalanches and conclude that avalanches in spin ice are quite slow compared
to the avalanches reported in other systems such as molecular magnets. Our
measurements show that the avalanches trigger after a delay of about 500 ms and
that the reversal of the magnetization then occurs in a few hundreds of
milliseconds. These features suggest an unusual propagation of the reversal,
which might be due to the monopole motion. The avalanche fields seem to be
reproducible in a given direction for different samples, but they strongly
depend on the initial state of magnetization and on how the initial state was
achieved.
