Measurements of Torsional Oscillations and Thermal Conductivity in Solid 4He

Polycrystalline samples of hcp ⁴He of molar volume 19.5?cm³ with small amount of ³He impurities were grown in an annular container by the blocked-capillary method. Three concentrations of ³He, x ₃, were studied: isotopically purified ⁴He with the estimated x ₃≤10^?10, ‘well-grade’ helium with x ₃～3×10^?7 and a specially prepared mixture with x ₃=2.5×10^?6. The torsional oscillator response and thermal conductivity were investigated before and after annealing. The temperature and width of the torsional anomaly increase with increasing x ₃. Annealing resulted in an increased phonon mean free path but often in little change in the torsional oscillator response. While the magnitude of the torsional anomaly and phonon mean free path can be very different in different samples, no correlation was found between them; this implies that these two properties are controlled by different types of crystal defects. It seems plausible that the mean free path of thermal phonos at ～200?mK is controlled by vibrating dislocations while the magnitude of the frequency shift of torsional oscillations is governed by static defects such as pinned dislocations and grain boundaries.     

The Effect of 3He Impurities on Anomalous Oscillations in the Expansion of Solid 4He

The regular periodic intensity bursts recently observed in the expansion of solid ⁴He into vacuum have anomalies that have been attributed to a transition to some new solid phase induced by excess vacancies. Here it is shown that a small concentration of ³He, from 1% down to 0.1%, added to the ⁴He solid is sufficient to remove all the anomalies. The origin of the observed anomalies is discussed in the light of these new experiments.      

Anomalous Response of 4He Confined in Nanoporous Media to Torsional Oscillation

The existence of “Non-Classical Rotational Inertia (NCRI)” in solid ⁴He below 0.2?K has been controversial and interpreted by a number of different theories. We report on torsional oscillator measurements for ⁴He in a nanoporous Gelsil glass, which has a network of nanopores with 3.5?nm in diameter. In addition to the usual “low-T NCRI” with an onset temperature 0.15?K, we find a larger decrease in rotational moment of inertia in a broad range of temperature from 0.2 to 1.9?K. This “high-T inertial anomaly” is accompanied with multiple dissipation peaks, but has no dependence on torsional oscillation velocity unlike the low-T NCRI. Since the high-T anomaly is observed also in confined liquid states, it originates in amorphous solid ⁴He layer near the pore wall. Our result shows that different types of supersolid—like phenomena, i.e. inertial anomalies, can coexist in a single ⁴He sample, even with genuine superfluidity of liquid ⁴He.     

Response of a Mechanical Oscillator in Solid 4He

We present the first measurements of the response of a mechanical oscillator in solid ⁴He. We use a lithium niobate tuning fork operating in its fundamental resonance mode at a frequency of around 30 kHz. Measurements in solid ⁴He were performed close to the melting pressure. The tuning fork resonance shows substantial frequency shifts on cooling from around 1.5 K to below 10 mK. The response shows an abrupt change at the bcc-hcp transition. At low temperatures, below around 100 mK, the resonance splits into several overlapping resonances.     

Defects and Glassy Dynamics in Solid 4He: Perspectives and Current Status

We review the anomalous behavior of solid ⁴He at low temperatures with particular attention to the role of structural defects present in solid. The discussion centers around the possible role of two level systems and structural glassy components for inducing the observed anomalies. We propose that the origin of glassy behavior is due to the dynamics of defects like dislocations formed in ⁴He. Within the developed framework of glassy components in a solid, we give a summary of the results and predictions for the effects that cover the mechanical, thermodynamic, viscoelastic, and electro-elastic contributions of the glassy response of solid ⁴He. Our proposed glass model for solid ⁴He has several implications: (1) The anomalous properties of ⁴He can be accounted for by allowing defects to freeze out at lowest temperatures. The dynamics of solid ⁴He is governed by glasslike (glassy) relaxation processes and the distribution of relaxation times varies significantly between different torsional oscillator, shear modulus, and dielectric function experiments. (2) Any defect freeze-out will be accompanied by thermodynamic signatures consistent with entropy contributions from defects. It follows that such entropy contribution is much smaller than the required superfluid fraction, yet it is sufficient to account for excess entropy at lowest temperatures. (3) We predict a Cole-Cole type relation between the real and imaginary part of the response functions for rotational and planar shear that is occurring due to the dynamics of defects. Similar results apply for other response functions. (4) Using the framework of glassy dynamics, we predict low-frequency yet to be measured electro-elastic features in defect rich ⁴He crystals. These predictions allow one to directly test the ideas and very presence of glassy contributions in ⁴He.     

Simultaneous Measurement of Torsional Oscillation and Ultrasound Propagation in Solid 4He at Low Temperatures

Preliminary results of simultaneous measurements of 10 MHz longitudinal ultrasound propagation in solid ⁴He loaded onto torsional oscillator (TO) are reported. Temperature dependence of sound velocity and attenuation and that of amplitude and frequency of TO are measured. The properties of dislocation lines present in the solid samples are extracted from the ultrasound data and are compared with the shifts in TO frequency below 100 mK.     

Effects of 3He Impurity on the Non-classical Rotational Inertia of Solid 4He Studied by Double Resonance Torsional Oscillator

We have carried out systematic measurements of the ³He-impurity effect using a compound torsional pendulum, which allows probing “non-classical rotational inertia” (NCRI) of the identical solid ⁴He sample at two different frequencies at 495 Hz and 1172 Hz. The measurements have shown significant differences in the temperature dependence of the NCRI signal as well as the energy dissipation peak positions between the two frequencies. The NCRI fraction derived from the higher frequency mode is greater than that derived from the lower frequency mode at all temperatures. The normalized NCRI fraction shows that T ₅₀ (≡temperature at which NCRI fraction decreases to 50% of the maximum) is greater in the higher frequency mode by ～9, 18, 30 and 35 mK when the nominal ³He impurity added is 0.3, 6, 12 and 25 ppm, respectively. The systematic changes in the inverse quality factor (Q ^?1) were also measured at the same ³He-impurity concentrations.     

The Annealing Process in Solid 4He

We have used a torsional oscillator with square cross section and a resonance frequency of 185 Hz to confirm the nonclassical rotational inertia (NCRI) discovered by Kim and Chan (Nature 427:225, 2004; Science 305:1941, 2004). We have also found a strong correlation between the NCRI signal and a high dissipation Q ^?1 of 4×10^?6 of the oscillation above the transition temperature. Here, we present preliminary results of the annealing process in ⁴He at a pressure of 26 bar. When holding the temperature constant above 1 K we have observed a immediate rise in the period and a slow decay of the dissipation. The equilibrium value of Q ^?1 decreases with increasing temperature.     

Hysteretic Response of Torsionally Oscillated Solid 4He and Its Dependence on 3He Impurity Concentration

Measurements on hysteretic response of compound torsional oscillator containing annular-shaped solid ⁴He samples were carried out by varying the oscillator drive amplitude starting from high to low and then back up to the initial high value. Hysteresis in the oscillator frequency and amplitudes were observed only below an onset temperature. The hysteresis onset temperature (T _H ) did not depend on the oscillator frequency, width of the sample annulus, annealing and refreezing after melting. A systematic increase in T _H was observed as the ³He impurity concentration in solid ⁴He samples was increased. The dependence of T _H on ³He impurity concentration followed approximately that of the dissipation peak temperatures. Possible relationships of the observed hysteresis phenomena with models of solid ⁴He dynamics based on freezing of a vortex liquid and dislocation motion are discussed.     

Isochoric Compressibility of Solid 4He

We have performed experiments in which we inject atoms into hcp, solid ⁴He contained in a cell of fixed volume at pressures greater than the bulk melting pressure. We measure the change in pressure of the solid in response to the injection, which gives a measure of the isochoric compressibility. We show that at T??700?mK the solid undergoes very little growth and is incompressible. With decreasing temperature the compressibility rises, saturates near T??400 mK and may show weak evidence of a decrease near T??250 mK. Measurements at lower temperatures are necessary to fully test the predictions.     

Elastic Properties of Solid 4He

The shear modulus of solid ⁴He increases below 200 mK, with the same dependence on temperature, amplitude and ³He concentration as the frequency changes recently seen in torsional oscillator (TO) experiments. These have been interpreted as mass decoupling in a supersolid but the shear modulus behavior has a natural explanation in terms of dislocations. This paper summarizes early ultrasonic and elastic experiments which established the basic properties of dislocations in solid helium. It then describes the results of our experiments on the low temperature shear modulus of solid helium. The modulus changes can be explained in terms of dislocations which are mobile above 200 mK but are pinned by ³He impurities at low temperature. The changes we observe when we anneal or stress our crystals confirm that defects are involved. They also make it clear that the shear modulus measured at the lowest temperatures is the intrinsic value—it is the high temperature modulus which is reduced by defects. By measuring the shear modulus at different frequencies, we show that the amplitude dependence depends on stress in the crystal, rather than reflecting a superfluid-like critical velocity. The shear modulus changes shift to lower temperatures as the frequency decreases, showing that they arise from a crossover in a thermally activated relaxation process rather than from a true phase transition. The activation energy for this process is about 0.7 K but a wide distribution of energies is needed to fit the broad crossover. Although the shear modulus behavior can be explained in terms of dislocations, it is clearly related to the TO behavior. However, we made measurements on hcp ³He which show essentially the same modulus stiffening but there is no corresponding TO anomaly. This implies that the TO frequency changes are not simply due to mechanical stiffening of the oscillator—they only occur in the Bose solid. We conclude by pointing out some of the open questions involving the elastic and TO behavior of solid helium.     

Low Frequency Elastic Measurements on Solid ^{4}He in Vycor Using a Torsional Oscillator

Torsional oscillator (TO) experiments involving solid \(^{4}\) He confined in the nanoscale pores of Vycor glass showed anomalous frequency changes at temperatures below 200 mK. These were initially attributed to decoupling of some of the helium’s mass from the oscillator, the expected signature of a supersolid. However, these and similar anomalous effects seen with bulk \(^{4}\) He now appear to be artifacts arising from large shear modulus changes when mobile dislocations are pinned by \(^{3}\) He impurities. We have used a TO technique to directly measure the shear modulus of the solid \(^{4}\) He/Vycor system at a frequency (1.2 kHz) comparable to that used in previous TO experiments. The shear modulus increases gradually as the TO is cooled from 1 K to 20 mK. We attribute the gradual modulus change to the freezing out of thermally activated relaxation processes in the solid helium. The absence of rapid changes below 200 mK is expected since mobile dislocations could not exist in pores as small as those of Vycor. Our results support the interpretation of a recent TO experiment that showed no anomaly when elastic effects in bulk helium were eliminated by ensuring that there were no gaps around the Vycor sample.     

A Glassy Contribution to the Heat Capacity of hcp 4He Solids

We model the low-temperature specific heat of solid ⁴He in the hexagonal closed packed structure by invoking two-level tunneling states in addition to the usual phonon contribution of a Debye crystal for temperatures far below the Debye temperature, T<Θ _D /50. By introducing a cutoff energy in the two-level tunneling density of states, we can describe the excess specific heat observed in solid hcp ⁴He, as well as the low-temperature linear term in the specific heat. Agreement is found with recent measurements of the temperature behavior of both specific heat and pressure. These results suggest the presence of a very small fraction, at the parts-per-million (ppm) level, of two-level tunneling systems in solid ⁴He, irrespective of the existence of supersolidity.     

Charge Transport in Solid 4He

With the help of a new experimental technique strong anisotropy of the mobility of ions has been observed in hcp ⁴ He crystals. The mobility of positive ions in the direction of the six-fold axis is found to be 200 times higher than in the perpendicular direction. Activation energies of the mobility have been measured in both principal directions. They are equal to: 5.3K in the direction of the C₆-axis and 11K in the perpendicular direction. The behaviour of the ions' velocity in the strong electric field regime is also studied as a function of the orientation.     

The Quest for Bose-Einstein Condensation in Solid 4He

Ever since the seminal torsional oscillator (TO) measurements of Kim and Chan which suggested the existence of a phase transition in solid ⁴He, from normal to a ??supersolid?? state below a critical temperature T _c = 200 mK, there has been an unprecedented amount of excitement and research activity aimed at better understanding this phase. Despite much work, this remarkable phase has yet to be independently confirmed by conventional scattering techniques, such as neutron scattering. We have carried out a series of neutron scattering measurements, which we here review, aimed at observing Bose-Einstein condensation (BEC) in solid ⁴He at temperatures below T _c . In bulk liquid ⁴He, the appearance of BEC below T _?? signals the onset of superfluidity. The observation of a condensate fraction in the solid would provide an unambiguous confirmation for ??supersolidity??. Although, our measurements have not yet revealed a non-zero condensate fraction or algebraic off diagonal long-range order n ₀ in solid ⁴He down to 65 mK, i.e. n ₀=(0±0.3)%, our search for BEC and its corollaries continues with improved instrumentation.     

Dielectric Constant Measurements of Solid 4He

Careful measurements of the dielectric properties of solid ⁴He have been carried out down to 35 mK, considerably lower than the temperature range of previous studies. The sample was prepared from high purity gas with ³He concentrations of the order of 200 ppb and were formed by the blocked capillary method. The molar volume of the sample was 20.30 cm³. The dielectric constant of the samples was found to be independent of temperature down to 120 mK before showing a continuous increase with decreasing temperature and saturating below 50 mK. The total increase in ?? is 2 parts in 10^?5. The temperature dependence of ?? mimics the increase in the resonant frequency found in the torsional oscillator studies and also the increase found in the shear modulus measurements.     

Flow of Solid 4He Near Melting

Torsional oscillator measurements on solid ⁴He have demonstrated non-classical rotational inertia (NCRI), indicative of a supersolid phase transition. Recent experiments indicate that the NCRI fraction depends on isotopic purity and perhaps on details of crystal growth and annealing, suggesting that defects may be involved. Our recent experiments have shown that solid helium does not flow in response to pressure gradients at low temperatures. Close to the melting temperature we do observe mass flow, but it decreases rapidly with temperature. For solid helium in the pores of Vycor the flow appears to be thermally activated and disappears below about half the melting temperature. Flow in bulk helium is restricted to a much narrower temperature range. Very close to melting (within 20 mK) the flow completely eliminates pressure differences in less than a minute. At slightly lower temperatures we saw flow, but significant pressure differences remained even after annealing.