Ultra-fast spin avalanches in crystals of molecular magnets in terms of magnetic detonation

Recent experiments (Decelle et al., Phys. Rev. Lett. 102, 027203 (2009)) discovered an ultra-fast regime of spin avalanches in crystals of magnetic magnets, which was three orders of magnitude faster than the traditionally studied magnetic deflagration. The new regime has been hypothetically identified as magnetic detonation. Here we demonstrate the possibility of magnetic detonation in the crystals, as a front consisting of a leading shock and a zone of Zeeman energy release. We study the dependence of the magnetic detonation parameters on the applied magnetic field. We find that the magnetic detonation speed only slightly exceeds the sound speed in agreement with the experimental observations.