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

Aluminum hyperfine interactions of the Al³⁺--O^--trapped-hole center in a number of oxides containing Al ions either as a constituent (Al₂{O}₃$:${Mg}²⁺, Na β-alumina) or as an impurity ({GeO}₂$, ${SiO}₂$) 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 O^--Al³⁺ distance and, from estimates of the electrostatic-crystal-field energy at O^-, indicates a reasonable outward expansion ({~}10%) of the Al³⁺ ions next to the O^- 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.