${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ nuclear-spin dephasing in the ruby frozen core and ${\mathrm{Cr}}^{3+}$ spin-flip-time measurements

Nuclear-spin-echo decay has been measured in the ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ frozen core surrounding ${\mathrm{Cr}}^{3+}$ in ruby using optical Raman heterodyne detection. Bloembergen’s frozen-core model was directly verified by the observation of ∼1-msec dephasing times in the core compared with 60 μsec in the bulk. Observation of echoes in the ground and optically excited states of ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$ and ${}_{}{}^{53}{}_{}{}^{}\mathrm{Cr}$ allowed separation of direct and indirect ${\mathrm{Cr}}^{3+}$ spin-flip contributions to dephasing and hence measurement of the Cr-Cr spin-flip time. The direct dephasing time follows a square-law dependence on concentration, in accord with theory. Indirect dephasing has a square-root dependence on concentration, similar to that observed for optical echoes. Contrary to earlier studies, it is concluded that optical dephasing in ruby, in the concentration range 0.0034 to 0.05 wt. % ${\mathrm{Cr}}_2$${\mathrm{O}}_3$, is primarily due to magnetic fluctuations produced by ${\mathrm{Cr}}^{3+}$ spin flipping; i.e., that indirect rather than direct dephasing is dominant.