Generalized Rotational Susceptibility Studies of Solid 4He

Using a novel SQUID-based torsional oscillator (TO) technique to achieve increased sensitivity and dynamic range, we studied TO’s containing solid ⁴He. Below ～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 ⁴He rotational dynamics, we implemented a new approach based upon the generalized rotational susceptibility $chi_{{}^{4}mathrm{He}}^{ - 1}(omega,T)$ . 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 $chi_{{}^{4}mathrm{He}}^{ -1}(omega,tau(T))$ with τ(T) representing a relaxation rate for inertially active microscopic excitations. In such models, the characteristic temperature T ^? at which df/dT and D pass simultaneously through a maximum occurs when the TO angular frequency ω and the relaxation rate are matched: ωτ(T ^?)=1. Then, by introducing the free inertial decay (FID) technique to solid ⁴He 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 τ(T,V) diverges smoothly everywhere without exhibiting a critical temperature or velocity, as expected in ωτ=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 ⁴He 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 ⁴He are associated with generation of the same microscopic excitations as those produced by direct shear strain.