Stress- and temperature-dependent hysteresis of the shear modulus of solid helium

Abstract

The shear modulus of solid 4 He below 200 mK exhibits an unusual increase, the characteristics of which show remarkable similarities to those of the period reduction in torsional oscillator experiments. We systematically studied the drive strain and temperature dependence of the shear modulus at low temperatures. The hysteretic behavior depends strongly on the drive and cooling history, which can be associated with the thermally assisted Granato-Lucke dislocation theory. The phase diagram of the shear modulus is constructed on the basis of the emerging hysteretic behavior.An anomalous increase in the shear modulus at low temperatures was recently observed in solid helium [1]. The anomaly exhibits temperature, frequency, and 3 He concentration dependences resembling those of the nonclassical rotational inertia (NCRI) in torsional oscillator (TO) experiments [2,3]. These remarkable similarities have attracted theoretical and experimental attention [4,5]. For instance, a dislocation vibration model for the NCRI is proposed. The temperature dependence of the period of a torsional oscillator containing solid helium is derived from the variation in the average pinning length of dislocations in solid helium [6]. Other efforts to provide a non-supersolid explanation for the TO response were also motivated by the similarities between the two phenomena [4,5,7,8]. The Cornell group recently reported that the TO motion was controlled by the same microscopic excitation that is agitated by temperature and stress independently, which they suggested can be understood within the framework of a dissipation model in which the elastic properties change at low temperatures [9]. Nevertheless, the resonant period reduction found in some earlier TO measurements, including Ref.[9], can be ascribed to the change in the elastic properties of solid helium filling a torsion rod [10]. Thus, the similar response of TO to the drive and temperature agitation can be understood in terms of the dislocation pinning mechanism.The shear modulus increase can be interpreted as the pinning of dislocations by 3 He impurities according to the Granato-Lucke (GL) dislocation theory [11]. The original GL theory considers only the unpinning of dislocations by applied stress without a thermal-fluctuationinduced unbinding mechanism: a large stress reduces the number of pinning points by detaching 3 He impurities from dislocations, thus suppressing the shear modulus. Nevertheless, the effects of stress and temperature on the shear modulus are similar, so its temperature dependence can be explained by the variation in the dislocation loop length with progressive lengthening of freely vibrating dislocation segments due to thermal evaporation of 3 He impurities [1,6,12]. Moreover, the softening of the shear modulus is not a phase transition but a crossover of the thermally activated relaxation process from a stiff (pinned) state to a relaxed (unpinned) state.The discrepancy in the effects of the drive stress and temperature appears when the hysteretic behaviors dur...

Critical dislocation speed in helium-4 crystals

“…We call it "critical speed" for simplicity but it should be clear that there is no analogy with critical phenomena nor with the critical speed beyond which dissipation occurs in a superfluid flow. Our new results solve a running controversy about the frequency dependence of this motion, some authors [4] having observed that the transition temperature from a soft to a stiff state depends on frequency while some others have assumed [15,16] that there is no frequency dependence. Furthermore, our new observations appear important to understand the binding mechanism of 3 He impurities to dislocation and the damping of their motion in the low temperature regime where impurities bind to them.…”

“…The stress is calculated from the shear modulus µ at the transition temperature Tp for each applied strain, which is roughly the middle of the transition from stiff to soft. The three data points above 0.1 Pa are taken from Kang et al [16] in the region which they consider as a transition from fully pinned to partially pinned dislocations.…”

“…As concerns how 3 He binding affects the crystal stiffness, two different mechanisms have been considered. Iwasa [15] and Kang et al [16] proposed that the transition from a soft to a stiff state is only a consequence of the free length L of the dislocation evolving from a network pinning length L N to a smaller length, an impurity pinning length L i . Within the Granato-Lucke theory [17], at low frequency and if the dislocation damping is small, the temperature dependent shear modulus µ is given by…”

Search for supersolidity in solid 4 He using multiple-mode torsional oscillators

“…In terms of shear stress, 15 rad/s 2 correspond to 0.05 Pa, or a strain of 3 × 10 −9 , which, comparing to shear modulus measurement experiments (38), is below the 10 −7 critical strain reported, and is well into the fully pinned region for the 3 He atoms on the dislocations at 30 mK (39). We did not measure above 100 rad/s 2 because that made irreversible changes to the frequency; 100 rad/s 2 correspond to 0.3 Pa, which, according to a recent paper by Kim and coworkers (39), is in the hysteretic region for the dislocation behavior. At high enough accelerations even the frequency of the empty cell was altered, and the temperature of the cell could be affected.…”

Single spin asymmetry in forward pA collisions: Phenomenology at RHIC

“…For inclusive hadron productions at high-P h⊥ , SSA is computed from perturbative QCD where it becomes a probe of collinear twist-3 distributions. Recent measurements at RHIC considered collisions of polarized protons on nuclear targets and so a completely new interplay between spin physics and the physics of gluon saturation becomes a reality [4][5][6][7][8][9][10][11]. This is especially so, as gluon saturation is important in the forward region of the produced hadron where SSA is the largest.…”