Effect of Nuclear Quadrupole Interaction on the Relaxation in Amorphous Solids

TL;DR

This paper develops a theoretical model showing that nuclear quadrupole interactions influence magnetic field-dependent relaxation in amorphous solids, explaining recent experimental observations of dielectric constant variations at very low temperatures.

Contribution

The paper introduces a many-body relaxation theory for many-level tunneling systems affected by nuclear quadrupole interactions, linking these effects to magnetic field dependence in glasses.

Findings

Relaxation rate depends on magnetic field strength.

Nuclear quadrupole interactions explain magnetic field effects.

Theory aligns with experimental data on amorphous solids.

Abstract

Recently it has been experimentally demonstrated that certain glasses display an unexpected magnetic field dependence of the dielectric constant. In particular, the echo technique experiments have shown that the echo amplitude depends on the magnetic field. The analysis of these experiments results in the conclusion that the effect seems to be related to the nuclear degrees of freedom of tunneling systems. The interactions of a nuclear quadrupole electrical moment with the crystal field and of a nuclear magnetic moment with magnetic field transform the two-level tunneling systems inherent in amorphous dielectrics into many-level tunneling systems. The fact that these features show up at temperatures $T<100mK$, where the properties of amorphous materials are governed by the long-range $R^{-3}$ interaction between tunneling systems, suggests that this interaction is responsible for the magnetic field dependent relaxation. We have developed a theory of many-body relaxation in an ensemble of interacting many-level tunneling systems and show that the relaxation rate is controlled by the magnetic field. The results obtained correlate with the available experimental data. Our approach strongly supports the idea that the nuclear quadrupole interaction is just the key for understanding the unusual behavior of glasses in a magnetic field.