# Oscillations of Echo Amplitude in Glasses in a Magnetic Field Induced by Nuclear Dipole-Dipole Interaction

## TL;DR

This paper provides a theoretical analysis of how magnetic fields influence dipole echo amplitudes in glasses at very low temperatures, highlighting a universal behavior and matching experimental results without fitting parameters.

## Contribution

The study introduces a universal analytic function describing dipole echo amplitude dependence on magnetic fields, valid when nuclear dipole-dipole energy is much smaller than Zeeman energy.

## Key findings

- Nonmonotonic magnetic field dependence of echo amplitude
- Universal analytic function describes the effect
- Excellent agreement with experimental data

## Abstract

The effect of a magnetic field on the dipole echo amplitude in glasses (at temperatures of about 10 mK) induced by the dipole-dipole interaction of nuclear spins has been theoretically studied. It has been shown that a change in the positions of nuclear spins as a result of tunneling and their interaction with the external magnetic field E_H lead to a nonmonotonic magnetic field dependence of the dipole echo amplitude. The approximation that the nuclear dipole-dipole interaction energy E_d is much smaller than the Zeeman energy E_H has been found to be valid in the experimentally important cases. It has been shown that the dipole echo amplitude in this approximation may be described by a simple universal analytic function independent of the microscopic structure of the two-level systems. An excellent agreement of the theory with the experimental data has been obtained without fitting parameters (except for the unknown echo amplitude)