Spectral diffusion, phonon echoes, and saturation recovery in glasses at low temperatures

TLDR

Glasses below 1 K exhibit properties that can be explained by localized tunneling levels analogous to spin‑½ systems. The study demonstrates that spectral diffusion, caused by resonant‑frequency fluctuations, is key to interpreting recent ultrasonic experiments. The authors model the system with a time‑dependent coupling \(J_{ij}S_z^iS_z^j\) that incorporates a spin‑flipping rate \(T_1^{-1}\). The model predicts phase‑memory times for two‑ and three‑pulse phonon‑echo experiments at ~20 mK that qualitatively match Golding and Graebner’s data, a time‑dependent linewidth for saturation recovery near 100 mK, and, based on tunneling‑model parameters and specific‑heat comparisons, indicates that glasses may host two distinct types of tunneling levels.

Abstract

Many features of glasses below 1 K are explicable in terms of localized tunneling levels, for which a spin-$\frac{1}{2}$ analogy exists. Here we show that spectral diffusion, resulting from fluctuations in resonant frequency, is essential to our understanding of recent ultrasonic experiments. Our model involves a coupling among the levels of the form ${J}_{\mathrm{ij}}{S}_{z}^{i}{S}_{z}^{j}$, which acquires a time dependence when a spin-flipping rate ${T}_{1}^{\ensuremath{-}1}$ is introduced. For two- and three-pulse phonon-echo experiments near $T=20$ mK, we predict phase-memory times which agree qualitatively with the experimental results of Golding and Graebner. For saturation recovery, we predict a linewidth whose time dependence should be observable near $T=100$ mK. Estimates of tunneling-model parameters and comparison with specific-heat experiments suggest that glasses may contain two types of tunneling levels.