Acoustic study of tunneling states in Kramers-ion-doped glasses: Wave propagation and phonon echoes.

Abstract

We report on an acoustic study of insulating glasses doped with dysprosium, gadolinium, and europium ions, which have Kramers degeneracy. The magnetic-ion content is varied between 1 and 10 at. %. The measurements are performed down to 10 mK, using acoustic frequencies up to 900 MHz and in magnetic fields up to 50 kG. There is an effect of the magnetic-ion concentration and the magnetic field on the sound velocity at low temperature. This effect is explained by assuming the existence of two kinds of low-energy excitations: the usual elastic tunneling states and some magnetic tunneling states, which are magnetic moments whose local anisotropy axis is almost perpendicular to the local magnetic field. These magnetic tunneling states have relaxation times shorter than the elastic ones by several orders of magnitude at low temperature. They couple strongly to the latter whose dynamics is then drastically changed. This one is directly observed in saturation-recovery and phonon-echo experiments. The relaxation time ${\mathit{T}}_{1}$ of the elastic tunneling states is strongly shortened by the magnetic ions, whereas their dephasing time ${\mathit{T}}_{2}$ remains almost unchanged. This effect implies a relaxation process much more efficient than the usual one-phonon process at low temperature.