Multilevel Tunnelling Systems and Fractal Clustering in the Low-Temperature Mixed Alkali-Silicate Glasses

TL;DR

This paper extends the standard two-level systems model to include multilevel tunneling systems, explaining magnetic effects and clustering phenomena in low-temperature mixed alkali-silicate glasses, aligning theory with experimental observations.

Contribution

The paper introduces an extension of the two-level systems model to multilevel tunneling systems, providing a better explanation for magnetic effects and fractal clustering in mixed glasses.

Findings

Multilevel tunneling systems improve agreement with experimental data.

Magnetic effects are explained by the extended model.

Fractal clustering is related to multilevel tunneling phenomena.

Abstract

The thermal and dielectric anomalies of window-type glasses at low temperatures ($T<$ 1 K) are rather successfully explained by the two-level systems (2LS) standard tunneling model (STM). However, the magnetic effects discovered in the multisilicate glasses in recent times, magnetic effects in the organic glasses and also some older data from mixed (SiO$_2$)$_{1-x}$(K$_2$O)$_x$ and (SiO$_2$)$_{1-x}$(Na$_2$O)$_x$ glasses indicate the need for a suitable extension of the 2LS-STM. We show that -- not only for the magnetic effects, but already for the mixed glasses in the absence of a field -- the right extension of the 2LS STM is provided by the (anomalous) multilevel tunnelling systems (A-TS) proposed by one of us for multicomponent amorphous solids. Though a secondary type of TS, different from the standard 2LS, was invoked long ago already, we clarify their physical origin and mathematical description and show that their contribution considerably improves the agreement with the experimental data.