Optical and Electron-Spin-Resonance Studies of Fourth-Nearest-Neighbor Chromium Ion Pairs in Ruby

Abstract

The fine structure of the optical fluorescence spectrum arising from the fourth-nearest-neighbor chromium ion pair system in ruby is studied using high-resolution optical spectroscopy, ordinary electron-spin resonance, and optically detected electron-spin resonance. The ground-state energy levels of this system are found to be describable by a simple spin Hamiltonian of the form $\mathcal{H}=g\ensuremath{\beta}\mathbf{H}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}+\frac{J}{2}[S(S+1)\ensuremath{-}\frac{15}{2}]+{D}_{S}[S_{z}^{}{}_{}{}^{2}\ensuremath{-}\frac{1}{3}S(S+1)]+{E}_{S}[S_{x}^{}{}_{}{}^{2}\ensuremath{-}S_{y}^{}{}_{}{}^{2}]$ where the directions of the symmetry axes, ${D}_{S}$, and ${E}_{S}$ each depend on the spin $S$ in a predictable way, requiring only two adjustable parameters: ${D}_{c}$ (the usual second-order crystal-field term of axial symmetry) and ${D}_{E}$ (a similar term arising from the anisotropic exchange interaction). The value of ${D}_{c}$ is found to be -0.191\ifmmode\pm\else\textpm\fi{}0.005 ${\mathrm{cm}}^{\ensuremath{-}1}$, which is equal to that for the isolated ion. The value of ${D}_{E}$ is found to be -0.021\ifmmode\pm\else\textpm\fi{}0.005 ${\mathrm{cm}}^{\ensuremath{-}1}$. A phonon-assisted energy-transfer mechanism is postulated to account for the existence of the optically detected spin-resonance spectrum.