  The reversal of spins in a magnetic material as they relax toward equilibrium
is accompanied by the release of Zeeman energy which can lead to accelerated
spin relaxation and the formation of a well-defined self-sustained propagating
spin-reversal front known as magnetic deflagration. To date, studies of
Mn$_{12}$-acetate single crystals have focused mainly on deflagration in large
longitudinal magnetic fields and found a fully spin-reversed final state. We
report a systematic study of the effect of transverse magnetic field on
magnetic deflagration and demonstrate that in small longitudinal fields the
final state consists of only partially reversed spins. Further, we measured the
front speed as a function of applied magnetic field. The theory of magnetic
deflagration, together with a modification that takes into account the partial
spin reversal, fits the transverse field dependence of the front speed but not
its dependence on longitudinal field. The most significant result of this study
is the finding of a partially spin-reversed final state, which is evidence that
the spins at the deflagration front are also only partially reversed.
