  The stability of a magnetic deflagration front in a collection of molecular
magnets, such as Mn_12-acetate, is considered. It is demonstrated that
stationary deflagration is unstable with respect to one-dimensional
perturbations if the energy barrier of the magnets is sufficiently high in
comparison with the release of Zeeman energy at the front; their ratio may be
interpreted as an analogue to the Zeldovich number, as found in problems of
combustion. When the Zeldovich number exceeds a certain critical value, a
stationary deflagration front becomes unstable and propagates in a pulsating
regime. Analytical estimates for the critical Zeldovich number are obtained.
The linear stage of the instability is investigated numerically by solving the
eigenvalue problem. The nonlinear stage is studied using direct numerical
simulations. The parameter domain required for experimental observations of the
pulsating regime is discussed.
