Dynamics of resonant phonons in ruby and alexandrite: A pair-state model.

Abstract

Measurements of the escape time (lifetime), \ensuremath{\tau}, of 29 and 37 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons from an optically excited volume in ruby (${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$:${\mathrm{Cr}}^{3+}$) and alexandrite (${\mathrm{BeAl}}_{2}$${\mathrm{O}}_{4}$:${\mathrm{Cr}}^{3+}$), respectively, are presented and compared with a model which takes into account Raman scattering of the phonons by the exchange-coupled ${\mathrm{Cr}}^{3+}$ pair states. The model differs from previous attempts to describe the dynamics of 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons in ruby in that the Raman scattering is calculated from specific pair-state wave functions and energy levels. The resulting single-parameter model produces excellent fits to the experimental data for both ruby and alexandrite, despite the fact that the dynamical processes which lead to the phonon escape are quite different in the two systems. The pair-state model presented here also predicts that the Raman scattering is dominated by pairs which have one ion in the $^{4}\mathrm{A}_{2}$(\ifmmode\pm\else\textpm\fi{}(1/2) states. Measurements of \ensuremath{\tau} as a function of temperature in a magnetic field confirm this prediction.