Measurements of Non-classical Rotational Inertia of Solid 4He at Two Frequencies

We have developed a double resonance compound torsional oscillator for studying non-classical rotational inertia (NCRI) of solid ⁴He at two different frequencies. The torsional oscillator consists of two beryllium copper torsion members, and two masses. The two masses rotate in phase in the first mode and out of phase in the second mode at resonance frequencies, 496 Hz and 1173 Hz, respectively. Samples of solid ⁴He (commercial grade with ³He impurity level less than 1 ppm) are grown with the blocked capillary method at pressures between 27 and 42 bar. Temperature dependences of NCRI signals at two different frequencies are observed in identical solid ⁴He at 37 bar.      

Elementary Excitations in Solid and Liquid 4He at the Melting Pressure

Recent discovery of a nonclassical rotational inertia (NCRI) in solid ⁴He below 0.2 K by Kim and Chan has revived great interest in the problem of supersolidity and initiated intensive study on the properties of solid ⁴He. A direct proof that the onset of NCRI corresponds to the supersolid transition would be the observation of a corresponding drop of the entropy of solid ⁴He below the transition temperature. We have measured the melting pressure of ultrapure ⁴He in the temperature range from 0.01 to 0.45 K with several single crystals grown at different pressures and with the accuracy of 0.5 μbar. In addition, supplementary measurements of the pressure in liquid ⁴He at constant volume have been performed, which allowed us to eliminate the contribution of the temperature-dependent properties of the pressure gauge from the measured melting pressure data. With the correction to the temperature-dependent sensitivity of the pressure gauge, the variation of the melting pressure of ⁴He below 320 mK obeys the pure T ⁴ law due to phonons with the accuracy of 0.5 μbar, and no sign of the transition is seen (Todoshchenko et al. in JETP Lett. 85:454, 2007). This sets the upper limit of ∼5⋅10⁻⁸ R for a possible excess entropy in high-quality ⁴He crystals below 320 mK. At higher temperatures the contribution from rotons in the superfluid ⁴He has been observed. The thermal expansion coefficient of the superfluid ⁴He has been measured in the range from 0.01 to 0.7 K with the accuracy of ∼10⁻⁷ 1/K, or by two orders of magnitude better than in previous measurements. The roton contributions to the melting pressure and to the pressure in liquid at a constant volume are consistent and yield the value of 6.8 K for the roton gap, which is very close to the values obtained with other methods. As no contribution due to weakly interacting vacancies to the melting pressure of ⁴He has been observed, the lower limit of about 5.5 K for their activation energy can be set.      

Contact Angle Singularity in 4He Crystals

Equilibrium shape of the interface between superfluid and crystalline ⁴He near the (0001) orientation is analyzed. We observe a singular dependence of the contact angle on the wall inclination with respect to the gravity. The energy of a step on the basal plane is measured. From the analysis of the meniscus profile the step-step interaction constant is estimated.      

Effect of the Magnetic Order on 3He Crystals

Solid ³He orders magnetically into two different phases below the Néel transition depending on the magnetic field (U2D2 or low field phase below 450 mT and CNAF or high field phase above 450 mT). We have performed measurements of the growth velocities and determined the step energies for different facets in both phases at B=0 T and B=2 T. It was found that the growth rate is much faster at B=2 T than at zero magnetic field. We conclude that the interface couples strongly to the crystal lattice at zero magnetic field while it seems to couple weakly at B=2 T. The ordering of the spins in the solid clearly affects the growth velocity of the crystals by an order of magnitude. Y.A. Parshin, permanently at the P.L. Kapitza Institute, Kosygina 2, Moscow 119334, Russia.     

Crystallization of 4He in Aerogels

Static behaviors of crystallization of ⁴He in porous materials, such as the increase of melting pressure, have been studied extensively, but nonequilibrium dynamics of the phase transition is hardly known. Our interest was in how ⁴He crystals grow in a 90.4% porosity aerogel. Aerogels are transparent and the dynamics in them can be studied visually. A Pomeranchuk-type variable-volume cell was used to study crystallization at a fixed temperature with a blocked capillary condition. By continuously compressing a chamber, the pressure rose above the bulk melting pressure and at a pressure 1.7 bar above the bulk melting pressure these crystals began to invade the aerogel. A clear crystal-superfluid interface was moved smoothly by the steady compression. No macroscopic facets were observed in the aerogel well below the bulk roughening transition temperature.      

On the Mechanism of the BCC-HCP Transformations in Small Lennard-Jones Crystals

The structure relaxation of the initially body-centered cubic clusters to the most favorable configurations has shown that the transition to the hexagonal close-packed structure starts at the cluster surface and propagates to the cluster center. The intermediate orthorhombic structure was found and forms in application to helium the regions with delocalized atoms, which are presumably important in connection with the phenomenon of ‘supersolidity’. The time to complete the transition depends on the cluster size and shape.      

Stacking Fault Energy in 4He Crystals

Recently observed non-classical rotational inertial (NCRI) in solid ⁴He is most probably related to defects which appear during the sample preparation. We have measured the energy of the stacking fault (SF) in an hcp ⁴He crystal at 0.2 K. The SF creates a groove with a dihedral angle of 155±5° on the crystal surface in a quasi-equilibrium with the liquid. The obtained value for the SF energy is (0.07±0.02) mJ/m², which is ～0.4 of the surface tension of the liquid–solid interface of ⁴He. Our findings suggest that the phenomenon of burst-like creation of new atomic layers might be accompanied by the creation of SFs.     

Fast Mode in Dense Aerogel Filled with Superfluid He II and Dilute Mixture of 3He in 4He

Longitudinal sound wave propagation in 90% porous silica aerogel filled with superfluid He II and dilute mixture of ³He in ⁴He has been studied using a low frequency resonance method. The observed fast mode was identified as a mode intermediate between the sound in the aerogel matrix and first sound. It was shown that the behavior of the fast mode in dense aerogel differs from both high porosity aerogel and rigid porous medium. We discuss the obtained results within the framework of theoretical models available.      

Transverse Resonances in Aerogel with Liquid 4He

We present preliminary studies of transverse resonances in a thin disk of aerogel filled with normal and superfluid ⁴ He in the temperature range 1.4 to 3 K. We observed a broad temperature independent mode in the normal phase and three narrow critical modes in the superfluid phase. The system was modeled by combining the equations of superfluid hydrodynamics of helium with those of elasticity of aerogel. Analytical solutions were obtained for a resonator of square profile and two types of boundary conditions at the transducers/aerogel interface. Comparison of the model solutions with the experimental data showed that the dynamics of the oscillation was dominated by compression rather than shear as in pure transverse sound. Recommendations for future improvements are made.     

Simultaneous Measurements of an Ultrasound and a Torsional Oscillator for 4He in a Nanoporous Glass

Previously, we carried out ultrasonic measurements for liquid ⁴He filled in a nanoporous glass (Gelsil), and observed an increase in the sound velocity due to decoupling of the superfluid component. At zero pressure, the superfluid transition temperature T _C is suppressed to 1.4 K from the bulk lambda point, 2.17 K. This behavior is the same as torsional oscillator measurements by Yamamoto et al. (Phys. Rev. Lett. 93:075302, 2004). However, the pressure dependence of T _C and the temperature dependence of the superfluid fraction are very different from the torsional oscillator measurements. In order to clarify the origin of the difference, we have developed a new technique of simultaneous measurement of an ultrasound and a torsional oscillator, and the system successfully works for a nanoporous glass. Here, we compare decoupling of the superfluid component for ⁴He films between an ultrasound and a torsional oscillator.     

3He Transverse Excited State Occupation in Thin 3He-4He Films

The discovery that ³ He was occupying transverse excited states at submonolayer coverages in ³ He-⁴ He mixture films on a Nuclepore substrate, was a surprise. In this note we discuss the relationship between theory and experiment in attempting to understand the physics of this behavior. We first discuss various single-atom-limit calculations of the level spacing between the ground-state and first excited state. We then introduce a free, quasi-particle picture for analyzing experimental magnetization step data and compare those results with the single-atom-limit calculations. The experiments clearly show excited state occupation at submonolayer coverages in contradistinction with the calculations. We then briefly discuss a microscopic, semi-phenomenological theory which, in agreement with experiment, yields ³ He occupation of the first excited state at submonolayer coverages. The mechanism is a model ³ He-³ He effective interaction due to one ripplon exchange. This effective interaction is density dependent and very long ranged. It strongly modifies the small-k properties of the ³ He self-energy and, in particular, causes the ground-state to first excited state level spacing to decrease with increasing ³ He areal density.     

Fluctuating Surfaces of Growing 4He Crystals in Aerogel

Crystal-superfluid interface of ⁴He in aerogel was shown to advance smoothly in a high temperature creep growth region above 0.6 K. In this report, we focused on the shape of the growing interface in the region and attempted to analyze the roughness of interfaces. The growth of rough interfaces is very common in nature and is known to often follow a scaling law; roughness usually increases with time and saturates in the later stage. We measured the roughness w(t) defined as the standard deviation of the interface height as a function of time t. It was found that w(t) in 98 % porosity aerogel initially increased with t and decreased after a particular time in the later stage. The abrupt reduction of roughness in the end of crystallization is unusual if it is intrinsic in the crystallization in aerogel.     

Nucleation and Avalanche of 4He Crystals in Aerogel

Dynamical transition of ⁴He crystals in aerogel was reported recently (Nomura et al. Phys. Rev. Lett. 101:175703, 2008). Bare aerogel, which was placed in the bulk ⁴He crystals, was used in the report. ⁴He crystals inside the aerogel grew via creep at high temperatures and via avalanche at low temperatures owing to the competition between thermal fluctuation and quenched disorder. Crystal-liquid interface advanced from the edge to inside of the aerogel. Crystal has a greater density than liquid so that the extra mass has to be transported in the crystallization process. It is not known how the mass is transported in the aerogel. To find a clue to this issue, we did an experiment with aerogel in a glass tube so that the aerogel had contact with the bulk on only one surface. In this case, a similar dynamical transition was observed at low temperatures. In the avalanche region, however, ⁴He crystals did not grow from the outer surface of the aerogel but nucleated at various sites inside the aerogel. This means that crystallization in aerogel does not occur by the forced invasion of ⁴He crystal but by a process of the bulk crystal once being melted and transported to increase the pressure of the liquid in the aerogel. Thus, a mass transport mechanisms for the crystallization has been revealed by this observation.     

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.     

Continuing Specific Heat Measurements of 3He in 3He - 4He Mixture Films

Additional data from our on-going experiments for the heat capacity of ³ He in ³ He- ⁴ He mixture films on a Nuclepore substrate are reported over the temperature range 90T165 mK, for ³ He coverages between 0.05 and 1.4 bulk-density atomic lagers, on a ⁴ He film of thickness 4.33 bulk-density atomic lagers. This is a two-dimensional Fermi liquid system, in which we can change the ³ He coverage and thus tune the Fermi temperature.     

Structural Defects in Czochralski-Grown CdWO4 Single Crystals

Structural imperfections (dislocations, pores, and twins) in CdWO₄ single crystals are investigated by microstructural analysis and x-ray diffraction. The radial dislocation distribution in the crystals is determined. The origin of pores and ways of eliminating them from CdWO₄ crystals are discussed.     

Thermally Stimulated Currents in MnGaInS4 Single Crystals

Thermally stimulated current measurements indicate that MnGaInS₄ single crystals contain fast trapping centers. The trap depths, concentrations, and capture cross sections are determined. The results obtained by the thermal cleaning method demonstrate that the band gap of MnGaInS₄ contains two trapping levels with exponential energy distributions: 0.05–0.20 and 0.16–0.25 eV.     

Specific Heat Measurements of 3He in 3He-4He Mixture Films

Preliminary data for the heat capacity of ³ He in ³ He- ⁴ He mixture films on a Nuclepore substrate are reported over the temperature range 90T165 mK, for ³ He coverages between 0.05 and 1.7 bulk-density atomic layers, and a ⁴ He film thickness of 4.33 bulk-density atomic layers. In this two-dimensional Fermi liquid system, a step structure appears in the specific heat as a function of ³ He coverage, similar to the step previously observed in the magnetization.     

Homogeneous Nucleation of 4He Crystals by Acoustic Waves

We have recently found experimental evidence for the homogeneous nucleation of crystals in metastable liquid ⁴He at high pressure. For this we combined the focusing of a high intensity spherical acoustic wave with a simple light scattering technique. We discuss the analysis used to distinguish between nucleation of bubbles in the negative pressure swings of the wave from nucleation of crystals in the positive swings. We also discuss the interest of our results and future developments of our experiment in the general context of the study of nucleation and instability limits in phase diagrams.