Phonon avalanches in paramagnetic impurities with spin S=1/2 -: art. no. 066606

We theoretically study the dynamics of transverse-and-longitudinal acoustic waves propagating parallel to an external magnetic field in a crystal containing ion impurities with an effective spin S=1/2. Corresponding evolution equations describing the coherent pulse evolution are derived. These equations are used to study the phonon avalanches arising due to decay of an initially unstable state of the spin systems for different geometries of interaction. It is found that the coherent dynamics of acoustic pulses propagated in one direction is described by a pair of integrable systems of evolution equations. The picosecond acoustic pulses governed by these systems are "a few-cycle" pulses. By using a modified set of equations of the inverse scattering transform, it is found that the strong interaction of three or two components of the acoustic waves with the spin system is asymptotically described by the quasi-self-similar solutions. Physical applications of the obtained results are discussed.