Energy Levels of Chromium Ion Pairs in Ruby

Abstract

The lower energy levels of a number of transitions due to second-, third-, and fourth-nearest-neighbor chromium ion pairs in ruby are located by measuring the temperature dependence of optical absorption. Energy-level diagrams are constructed, from which many of the observed lines are identified. The measurements are consistent with earlier results for the ground states of first-, third-, and fourth-nearest-neighbor pairs. The ground-state levels of the second-nearest-neighbor pairs are describable by the isotropic exchange interaction $H={J}_{2}{\mathbf{S}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{2}+{j}_{2}{({\mathbf{S}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{2})}^{2}$ with ${J}_{2}=83.6$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and ${j}_{2}=\ensuremath{-}9.7$ ${\mathrm{cm}}^{\ensuremath{-}1}$, where ${S}_{1}$ and ${S}_{2}$ are the total spins of each of the two chromium ions. Description of the optically excited states requires a more general expression for the exchange interaction, of the form $H=\ensuremath{\Sigma}{J}_{\mathrm{ij}}{\mathbf{s}}_{1i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{s}}_{2j}$, where ${s}_{1i}$ and ${s}_{2j}$ are the spins of electrons occupying the various one-electron orbitals on ions 1 and 2. The ground-state coupling parameters for the first four nearest-neighbor types are used to estimate the N\'eel and Curie-Weiss temperatures for ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{2}$.