Theory of indirect hyperfine interactions of oxygen-aluminum defects in ionic crystals

Abstract

Aluminum hyperfine interactions of the ${\mathrm{Al}}^{3+}$–${\mathrm{O}}^{\mathrm{-}}$-trapped-hole center in a number of oxides containing Al ions either as a constituent (${\mathrm{Al}}_2$ ${\mathrm{O}}_3$:${\mathrm{Mg}}^{2+}$, Na β-alumina) or as an impurity (${\mathrm{GeO}}_2$, ${\mathrm{SiO}}_2$) are analyzed with use of a semiempirical model of the exchange polarization mechanism of transferred hyperfine interactions. The theory quantitatively predicts the observed strong dependence of the negative isotropic hyperfine constant on the ${\mathrm{O}}^{\mathrm{-}}$-${\mathrm{Al}}^{3+}$ distance and, from estimates of the electrostatic-crystal-field energy at ${\mathrm{O}}^{\mathrm{-}}$, indicates a reasonable outward expansion (∼10%) of the ${\mathrm{Al}}^{3+}$ ions next to the ${\mathrm{O}}^{\mathrm{-}}$ hole center. The theory also accounts well for the observation that the anisotropic hyperfine constants in these centers vary only slightly despite the large variation in the corresponding isotropic splittings.