Brillouin Scattering from a Microwave-Phonon Bottleneck in MgO:Ni2+

Abstract

A large nonequilibrium distribution of microwave phonons arising from a phonon bottleneck has been observed in Ni-doped MgO using Brillouin light scattering; light scattering allows one to look directly at the phonons in a highly selective manner, and the intensity of the scattered light provides a direct measure of the effective temperatures of the phonons. With cw microwave saturation at 25.6 GHz of the $\ensuremath{\Delta}{m}_{s}=1$ spin transitions of the ${\mathrm{Ni}}^{2+}$ ion ($S=1$) at an ambient temperature of 2 \ifmmode^\circ\else\textdegree\fi{}K, the effective temperatures of slow-transverse acoustic phonons at 25.6 GHz propagating near a [110] crystal direction are increased to 270-4000 \ifmmode^\circ\else\textdegree\fi{}K, while the bulk of the lattice modes remain at the ambient temperature; the observed phonon heatings are in reasonable agreement with theoretical predictions based on a simple rate-equation formalism applied to the $S=1$ system. The measured bandwidth for the heated phonons is \ensuremath{\sim} 180 MHz, which is significantly less than the spin resonance (EPR) linewidth of \ensuremath{\sim} 500 MHz but in qualitative agreement with theory. After switching off the saturating microwaves, the phonon heating decays away in a characteristic nonlinear manner; the initial rapid drop in phonon excitation indicates an effective phonon lifetime \ensuremath{\sim} 5 \ensuremath{\mu}sec which is not intrinsic but determined by crystal geometry and surface condition. In accord with this relatively long lifetime, the excess phonon heating is observed to persist to ambient temperatures as high as 40 \ifmmode^\circ\else\textdegree\fi{}K. Under microwave saturation of the $\ensuremath{\Delta}{m}_{s}=1$ transitions at frequency $\ensuremath{\nu}$, significant heating of longitudinal phonons at $\ensuremath{\nu}$ and $2\ensuremath{\nu}$ has also been observed. The heating of the "forbidden" longitudinal phonons at $\ensuremath{\nu}$ is ascribed to mode conversion of other heated $\ensuremath{\nu}$ phonons into the longitudinal phonons at crystal boundaries, while the $2\ensuremath{\nu}$ phonon heating arises from $\ensuremath{\Delta}{m}_{s}=2$ transitions in the $S=1$ spin system. In addition, anomalously large heating (up to 40 000 \ifmmode^\circ\else\textdegree\fi{}K) of the slow-transverse phonons at $\ensuremath{\nu}$ has been observed in certain spatial regions of the crystals and is tentatively ascribed to a parametric process involving the $2\ensuremath{\nu}$ phonons.