On the theory of resonant susceptibility of dielectric glasses in magnetic field

TL;DR

This paper develops a theoretical framework for understanding how magnetic fields influence the dielectric susceptibility of insulating glasses at very low temperatures by affecting nuclear spins and quadrupole interactions.

Contribution

It introduces a new theoretical model linking magnetic field effects to nuclear quadrupole interactions and dielectric response in glasses at millikelvin temperatures.

Findings

Magnetic field suppresses nuclear quadrupole effects on permittivity.

Permittivity correction increases sharply when Zeeman splitting matches quadrupole interaction.

The model aligns with experimental observations of magnetic field dependence.

Abstract

The anomalous magnetic field dependence of dielectric properties of insulating glasses in the temperature interval $10mK<T<50mK$ is considered. In this temperature range, the dielectric permittivity is defined by the resonant contribution of tunneling systems. The external magnetic field regulates nuclear spins of tunneling atoms. This regulation suppresses a nuclear quadrupole interaction of these spins with lattice and, thus, affects the dielectric response of tunneling systems. It is demonstrated that in the absence of an external magnetic field the nuclear quadrupole interaction $b$ results in the correction to the permittivity $\delta\chi\sim| b| /T$ in the temperature range of interest. An application of a magnetic field results in a sharp increase of this correction approximately by a factor of two when the Zeeman splitting $m$ approaches the order of $| b| $. Further increase of the magnetic field results in a relatively smooth decrease in the correction until the Zeeman splitting approaches the temperature. This smooth dependence results from tunneling accompanied by a change of the nuclear spin projection. As the magnetic field surpasses the temperature, the correction vanishes. The results obtained in this paper are compared with experiment. A new mechanism of the low temperature nuclear spin-lattice relaxation in glasses is considered.