Optical Detection of a Phonon Bottleneck in Nd-Doped Lanthanum Ethyl Sulfate

The spin-lattice relaxation times of ${\mathrm{Nd}}^{142}$ and natural Nd doped into lanthanum ethyl sulfate (LaES) have been measured by an optical technique as a function of crystal size, concentration, and temperature. The measurements were performed with a microwave pump frequency of about 23 GHz with the steady magnetic field parallel to the $c$ axis of the crystals. A phonon bottleneck independent of crystal size was observed for the ${\mathrm{Nd}}^{142}$-doped LaES. Holstein's theory of resonant trapping is reviewed and is shown to be inapplicable to the observed bottleneck. However, for rare-earth salts with direct-process relaxation times of approximately ${10}^{-5\mathrm{}}$ sec or shorter, resonant trapping can appreciably lengthen the effective lifetime of the excited spin states. The observed bottleneck is explained with a simple kinetic theory and by assuming a large phonon reflection coefficient at the boundaries of the crystal. From this formulation, the lifetime of 23-GHz phonons in Nd-doped LaES is deduced to be 32 μsec at liquid-helium temperatures.