Phonon Avalanche in Ce-Doped Lanthanum Magnesium Double Nitrate

We have studied the phonon avalanche in ${\mathrm{Ce}}^{3+}$-doped lanthanum magnesium double nitrate (LMN) by making observations on the spin system. A variety of experimental techniques involving pulsed microwaves and pulsed magnetic fields have been used. We have measured the phonon lifetime and made observations which are related to the form of the acoustic power spectrum generated by the avalanche. Consideration of the magnitudes involved suggests that a transition probability model is adequate to explain the results obtained with our LMN + Ce samples, and that the first half of the avalanche can be described by a function of the form $1-tanh\alpha (t-t_{\frac{1}{2}})$, where $t_{\frac{1}{2}}$ is the time at which the magnetization has fallen by ½. Deviations from this function in the tail of the avalanche are due to phonon decay and to cross relaxation. The form of the hole burnt out by the avalanche has been calculated on the transition-probability model and agrees well with observations. Brief discussion of the fully nonlinear case is given. This would only be applicable if the acoustic gain, the acoustic intensity, or $T_2$ were several times larger than the values which we have assumed here.