Observation of the quasidiffusive propagation of phonons in Mg2SiO4:Ho3+ using time-resolved photo-phonon spectroscopy

The energy flux of phonons produced due to the nonradiative laser-induced transitions of Ho³⁺ impurity ions in forsterite from the ⁵ F ₅ states has been measured using a superconductor bolometer at a temperature of 2 K. The dependence of the flux on the laser wavelength, the time elapsed after the action of a laser pulse, and the phonon propagation path length is analyzed. It is found that the excitation of Ho³⁺ to some states leads to the diffusive propagation of emitted phonons in the spontaneous frequency decay mode (quasidiffusive mode of propagation): the time of arrival of a phonon pulse is almost a linear function of the path length, but it is several times longer than the longest ballistic time of flight (for transverse phonons). The diffusion coefficient and the nonradiative relaxation time are determined from the best fit to the experiment.