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 $H=J_2{\mathbf{S}}_1·{\mathbf{S}}_2+j_2{\left({\mathbf{S}}_1·{\mathbf{S}}_2\right)}^2$ with $J_2=83.6\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $j_2=-9.7\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, 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 $H=\Sigma J_{\mathrm{ij}}{\mathbf{s}}_{1i}·{\mathbf{s}}_{2j}$, 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 Néel and Curie-Weiss temperatures for ${\mathrm{Cr}}_2$ ${\mathrm{O}}_2$.