Generalized Rotational Susceptibility Studies of Solid He-4

V. Gadagkar, E. J. Pratt, B. Hunt, M. Yamashita, M. J. Graf, A. V. Balatsky, J. C. Davis*

*Corresponding author for this work

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1 Citation (Scopus)


Using a novel SQUID-based torsional oscillator (TO) technique to achieve increased sensitivity and dynamic range, we studied TO's containing solid He-4. Below similar to 250 mK, the TO resonance frequency f increases and its dissipation D passes through a maximum as first reported by Kim and Chan. To achieve unbiased analysis of such He-4 rotational dynamics, we implemented a new approach based upon the generalized rotational susceptibility . Upon cooling, we found that equilibration times within f(T) and D(T) exhibit a complex synchronized ultraslow evolution toward equilibrium indicative of glassy freezing of crystal disorder conformations which strongly influence the rotational dynamics. We explored a more specific with tau(T) representing a relaxation rate for inertially active microscopic excitations. In such models, the characteristic temperature T (au) at which df/dT and D pass simultaneously through a maximum occurs when the TO angular frequency omega and the relaxation rate are matched: omega I"(T (au))=1. Then, by introducing the free inertial decay (FID) technique to solid He-4 TO studies, we carried out a comprehensive map of f(T,V) and D(T,V) where V is the maximum TO rim velocity. These data indicated that the same microscopic excitations controlling the TO motions are generated independently by thermal and mechanical stimulation of the crystal. Moreover, a measure for their relaxation times tau(T,V) diverges smoothly everywhere without exhibiting a critical temperature or velocity, as expected in omega I"=1 models. Finally, following the observations of Day and Beamish, we showed that the combined temperature-velocity dependence of the TO response is indistinguishable from the combined temperature-strain dependence of the He-4 shear modulus. Together, these observations imply that ultra-slow equilibration of crystal disorder conformations controls the rotational dynamics and, for any given disorder conformation, the anomalous rotational responses of solid He-4 are associated with generation of the same microscopic excitations as those produced by direct shear strain.

Original languageEnglish
Pages (from-to)180-196
Number of pages17
JournalJournal of Low Temperature Physics
Issue number3-4
Publication statusPublished - Nov 2012


  • Supersolid helium
  • Generalized rotational susceptibility
  • Superglass
  • Torsional oscillator


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