Microwave dielectric echoes in Naβ-alumina

Abstract

Microwave dielectric echoes have been observed in Na $\beta$-alumina at temperatures between 18 and 75 mK. The results provide further evidence for the existence of low-energy two-level tunneling systems (TLS). The TLS electric dipole moment $p$ and density of states $\overline{P}$ were determined to be $p=4.8\mathrm{}\pm 0.8 D$ and $\overline{P}=1.5\mathrm{}\times {10}^{32}$ ${\mathrm{erg}}^{-1\mathrm{}}$ ${\mathrm{cm}}^{-3\mathrm{}}$, respectively. The nonexponential time-dependent echo decay provides evidence for spectral diffusion. Previously proposed models incorporating spectral diffusion processes in echo decay are shown to approximate the observed time-decay rates at a given temperature. However, the observed dependence of the echo decay on temperature was much weaker than predicted by spectral diffusion models.