Effect of Resonant Scattering by Paramagnetic Centers on the Propagation of Nonequilibrium Phonons

At low temperatures phonon anharmonic decay processes decrease enough to make it possible to get ballistic phonon propagation at frequencies up to 1011 – 1012 Hz. On the other hand, phonon scattering at resonant centres, if present, becomes more effective since the difference between the population of centre levels increases. It is known from experiments that the heat conductivity at low temperatures is reduced mainly by resonant scattering. And although resonant phonons in a crystal find themselves in a narrow band compared to the total spectra of acoustic vibrations, they play a crucial role in such process as paramagnetic relaxation. Even for low concentrations of resonant centres the lifetimes of the resonant phonons is reduced enough to make phonon propagation more diffusive than ballistic. It may result in phonon trapping being an example of the general problem of radiation trapping in resonant media (see 1,2).