Hole-compensated Fe³⁺ impurities in quartz glasses: a contribution to subkelvin thermodynamics

This paper studies the contribution of [FeO₄]⁰ impurity substitution centres to subkelvin thermodynamic properties of quartz glasses. In the scenario considered an Fe³⁺ ion substitutes for a Si⁴⁺ ion in the metallic sublattice of quartz, and one of the neighbouring oxygen ions captures a hole, which compensates the local charge defect. The Fe³⁺ cation and the O^- anion, on which the hole is localized, form a bound small polaron. In this configuration the Fe³⁺ cation is subject to a crystal field with an approximate C₃ symmetry axis along the Fe³⁺-O^- direction. This axis plays a quantization role for the Fe³⁺ electronic spin. The hole is assumed to be tunnelling between two neighbouring oxygen ions, switching the quantization axis between two directions and therefore entangling the spin states. Due to this coupling between spin and spatial degrees of freedom an [FeO₄]⁰ centre may be considered as a paramagnetic tunnelling system (PTS). An explicit form derived for a single-PTS low-energy spectrum, together with the model parameter distribution function introduced, allows for a complete thermodynamic description of the [FeO₄]⁰-based PTS ensemble. In particular, a contribution to the ac dielectric constant, derived as a function of magnetic field and temperature, allows a semiquantitative fit to recent experimental data for the iron-contaminated multicomponent glass BaO-Al₂O₃-SiO₂. Taking into account a spin interaction between Fe³⁺ and O^- ions also allows us to account for the anomalous magnetothermal behaviour of the low-temperature specific heat, recently reported for the glasses BaO-Al₂O₃-SiO₂ and Duran and earlier for Pyrex.