NMR Characterization of 3He Nanoclusters Embedded in hcp 4He

The properties of ³He nanoclusters in phase-separated solid ³He-⁴He mixture were investigated using pulse NMR. Samples of pressure between 2.64 and 3.71 MPa and NMR frequencies, 62.5, 125, and 250 kHz were used. Magnetization was measured in the temperature range between 0.6 to 10 mK. The solid-like fraction was obtained from the relative magnitudes of magnetization and it showed a sharp increase with pressure around 2.94 MPa accompanying an abrupt change in Weiss temperature. For samples of pressure between 2.94 and 3.15 MPa, the magnetization could be separated into two components with different spin-spin relaxation time T ^* ₂'s. The short and long T ^* ₂ components showed ferromagnetic and antiferromagnetic tendencies, respectively. The long component showed an anomalous decrease of magnetization below 1.05 mK.     

Ultrasonic attenuation in hcp 4He

The ultrasonic attenuation was measured for longitudinal sound waves in solid hcp ⁴He at frequencies of 5, 15, and 25 MHz from 0.25 to 3.5 K. Near melting, the attenuation is very small and in agreement with theoretical predictions. In most samples the attenuation rises gradually with falling temperature until a point is reached which approximately corresponds to the onset of a previously observed velocity anomaly. Then the attenuation rises more quickly and remains very large to the lowest temperatures measured. Two samples exhibit neither a steep rise in attenuation nor a velocity anomaly. A number of explanations for the large attenuation are considered.Research supported by grants from the National Research Council of Canada.     

Vortex Dynamics in hcp Solid 4He

The peculiar features noted in (Penzev et al. in Phys. Rev. Lett. 101: 065301, 2008) we conjecture are evidence of a vortex fluid state in solid He. We suggest to analyze this state by means of the dynamics of quantized vortices, as used for the tangle of vortices in superfluid turbulence. We introduce parameters of the vortex tangle dynamics, e.g., relaxation time for the drift of lines in parallel to the torsional oscillation axis. We briefly discuss the transition from the supposed vortex fluid state into the supposed supersolid state (Shimizu et al. in Phys. Rev. Lett., arXiv:0903.1326).     

Overview on Solid 4He and the Issue of Supersolidity

Here we provide an overview of the status of the field of solid ⁴He with a focus on the recent theoretical and experimental activities stimulated by the 2004 experiments of Kim and Chan. The overview attempts to place the experimental and theoretical work in context, to respect the historical flow of the field and discuss our present understanding of the question of supersolidity in ⁴He. The possibility of supersolidity in cold atoms and in other systems is also addressed. Special issues of the Journal of Low Temperature Physics (168(3/4), 2012; 169(3/4), 2012), in addition to this issue, have been devoted to this subject and this overview is meant to accompany those issues of the journal.     

Search for Supersolidity in 4He in Low-Frequency Sound Experiments

We present results of the search for supersolid ⁴He using low-frequency, low-level mechanical excitation of a solid sample grown and cooled at fixed volume. We have observed low frequency non-linear resonances that constitute anomalous features. These features, which appear below ∼0.8 K, are absent in ³He. The frequency, the amplitude at which the nonlinearity sets in, and the upper temperature limit of existence of these resonances depend markedly on the sample history.     

Experimental Apparatus to Search for Supersolidity in Monolayer ^4He on Graphite

We describe some details of a new experimental setup for torsional oscillator (TO) measurement of $^4$ He monolayers adsorbed on a graphite surface. This setup is designed to seek for the possible supersolid phase, in which crystalline order coexists with superfluidity, in two dimensional (2D) solid $^4$ He below 300 mK. Among such 2D solids, the commensurate phase in the second layer on graphite is the most hopeful candidate for the novel supersolid phase since it is the lowest-density quantum solid ever found. An exfoliated graphite substrate we used is ZYX which has at least ten times longer surface coherence length compared to Grafoil, an exfoliated graphite most commonly used in previous experiments. The first version of TO we made has the resonant frequency of 786.8 Hz and the Q value of $1.1\times 10^5$ at $T \le 10$  mK. The resonant frequency of this particular TO without any He samples ( $f_{\mathrm {cell}}$ ) showed unexpectedly large temperature variation and non-reproducibility below 1 K as well as sudden jumps when mechanical shocks are applied to the experimental apparatus. We found the stability of $f_{\mathrm {cell}}$ is highly correlated with the temperature stability of 1 K pot in dilution refrigerator.     

Quantized Vortex State in hcp Solid 4He

The quantized vortex state appearing in the recently discovered new states in hcp ⁴He since their discovery (Kim and Chan, Nature, 427:225–227, 2004; Science, 305:1941, 2004) is discussed. Special attention is given to evidence for the vortex state as the vortex fluid (VF) state (Anderson, Nat. Phys., 3:160–162, 2007; Phys. Rev. Lett., 100:215301, 2008; Penzev et al., Phys. Rev. Lett., 101:065301, 2008; Nemirovskii et al., arXiv:0907.0330, 2009) and its transition into the supersolid (SS) state (Shimizu et al., arXiv:0903.1326, 2009; Kubota et al., J. Low Temp. Phys., 158:572–577, 2010; J. Low Temp. Phys., 162:483–491, 2011). Its features are described. The historical explanations (Reatto and Chester, Phys. Rev., 155(1):88–100, 1967; Chester, Phys. Rev. A, 2(1):256–258, 1970; Andreev and Lifshitz, JETP Lett., 29:1107–1113, 1969; Leggett, Phys. Rev. Lett., 25(22), 1543–1546, 1970; Matsuda and Tsuneto, Prog. Theor. Phys., 46:411–436, 1970) for the SS state in quantum solids such as solid ⁴He were based on the idea of Bose Einstein Condensation (BEC) of the imperfections such as vacancies, interstitials and other possible excitations in the quantum solids which are expected because of the large zero-point motions. The SS state was proposed as a new state of matter in which real space ordering of the lattice structure of the solid coexists with the momentum space ordering of superfluidity. A new type of superconductors, since the discovery of the cuprate high T _c superconductors, HTSCs (Bednorz and Mueller, Z. Phys., 64:189, 1986), has been shown to share a feature with the vortex state, involving the VF and vortex solid states. The high T _c s of these materials are being discussed in connection to the large fluctuations associated with some other phase transitions like the antiferromagnetic transition in addition to that of the low dimensionality. The supersolidity in the hcp solid ⁴He, in contrast to the new superconductors which have multiple degrees of freedom of the Cooper pairs with spin as well as angular momentum freedom, has a unique feature of possessing possibly only the momentum fluctuations and vortex ring excitations associated with the possible low dimensional fluctuations of the subsystem(s). The high onset temperature of the VF state can be understood by considering thermally excited low D quantized vortices and it may be necessary to seek low dimensional sub-systems in hcp He which are hosts for vortices.     

Elementary excitations and a collective mode in hcp4He

We have measured the velocity and attenuation of sound at 10, 30, and 50 MHz in solid⁴He at higher purity, lower density, and lower acoustic power than have been measured previously. At 10 MHz the velocity varies asT ⁴, as would be expected for a very high quality crystal with remarkably low dislocation density. The temperature dependence of the attenuation reveals coupling to thermally activated excitations that are consistent with vacancies measured in other work. However, in our work the activation energy is 0.7 K so that their concentration is sufficiently high to require Bose statistics. At 30 and 50 MHz, an unexpected, additional resonant behavior was observed. We show that the resonance is consistent with the existence of a collective mode of the vacancies and with a finite population of ground state vacancies.     

Effects of 4He impurities on 3He nuclear spin-lattice relaxation in hcp solid 3He

Nuclear spin-lattice relaxation properties of hcp solid ³He with ⁴He impurities have been studied. At temperatures below the exchange plateau region, three kinds of relaxation time were observed. To analyze the data, a phenomenological four-bath model was developed, the four baths being the Zeeman bath, the phonon bath, an X-bath, and a Y-bath. The X-bath consists of the exchange bath and a part of the ⁴He-⁴He elastic interaction bath. The Y-bath is the main part of the elastic interaction bath. We measured the concentration dependence of the energy constants of all the baths, as well as the temperature and concentration dependences of the three kinds of relaxation time. The relaxation behavior corresponding to the process between the X-bath and the Y-bath could not be expressed by a single exponential function of time and the relaxation rate was strongly dependent on the concentration. This process may be related to the internal thermal equilibrium process within the elastic interaction bath. The impurity-dependent relaxation time between the X-bath and the phonon bath had a temperature dependence of T ^–n with n = 7.4±0.3.     

Fast Diffusion Process in Quenched hcp Dilute Solid 3He–4He Mixture

The study of phase structure of dilute ³He–⁴He solid mixtures of differing quality is performed by the spin echo NMR technique. The diffusion coefficient is determined for each coexistent phase. Two diffusion processes are observed in rapidly quenched (non-equilibrium) hcp samples: the first process has a diffusion coefficient corresponding to hcp phase and the second one has huge diffusion coefficient corresponding to liquid phase, which is evidence of liquid-like inclusions formation during fast crystal growing. It is established that these inclusions disappear in equilibrium crystals after careful annealing.     

Vacancy-induced transitions in hcp 3He

It is known from the work of Nagaoka that in hcp or fcc ³He a ferromagnetic alignment of nuclear spins does not give the lowest vacancy energy. We show that an ordered spin structure has a lower vacancy energy than either random or ferromagnetic structures. We study the possibility of vacancies inducing a transition to this spin structure, and of vacancies forming polarons. The latter is found to be more likely, and we estimate the fraction of vacancies forming polarons as a function of temperature. We briefly comment on the case of a vacancy in crystals of ⁴He with ³He impurity.Supported by the U.S. Department of Energy under Contract EY-76-C-02-1198.On leave from BARC, Bombay, India     

Subboundaries in hcp4He crystals studied by SR X-ray topography

The internal structure of hcp⁴He crystals was studied by SR (synchrotron radiation) X-ray topography. Subboundaries in the crystals appeared as black or white bands in the X-ray topographs. In one of the hcp⁴He crystals, the subboundaries turned out to be flat planes perpendicular to the basal plane. They were small-angle tilt boundaries which consisted of basal edge dislocations. The dislocation spacing in one of the subboundaries was determined to be 800 nm and the total density of the boundary dislocations to be 2.6 × 10⁵ cm^–2. The subboundaries in another hcp⁴He crystal were curved and/or branching, indicating that the crystal was strained.     

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.     

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.      

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.     

Heat capacity and pressure at phase separation and solidification of3He in hcp4He

We have measured heat capacity and pressure of 0.45% and 0.9%³He-⁴He mixtures at pressures between 25 bar and 33 bar and temperatures between 20 mK and 250 mK. The data show the latent heats and the pressure changes associated with the phase separation (or remixing) and with the liquification (or solidification) of the resulting droplets in the hcp matrix. Above about 31 bar, the phase separation and the liquid-solid phase transition are separately observable. From these data, as well as from the heat capacity of the liquid droplets, we conclude that the droplets are filled with almost pure³He showing bulk behavior and that only a part of the separated³He is liquified. The amount of the liquid depends on the history of the sample. The phase separation is reproducible and lasted for many hours. In the pressure range of the hcp-L₁-L₂ univariant the sample moves along the univariant for a limited temperature range.     

Transverse Ultrasound Measurements in 4He Single Crystals

Recently, Kim and Chan (Science 305:1941, 2004; Phys. Rev. Lett. 97:115302, 2006) have reported an anomalous decoupling transition of solid ⁴He in a torsional oscillator measurement, and interpret their results as evidence for non-classical rotational inertia and a possible supersolid phase of ⁴He. The detailed nature and properties of such a “supersolid” state in ⁴He are still far from being clear, although there are clues from experiments involving ³He impurities, different sample cell geometries, annealing effects and grain boundary flow. Defects produced during crystal growth or deformation (e.g. dislocations) may affect supersolidity, or even produce it, and they are expected to have significant impact on the elastic properties of the solid. The supersolid fraction could also decouple from the lattice and produce a decrease in the transverse sound speed. We have begun the experiments in this laboratory to study such effects, measuring the velocity and attenuation of transverse ultrasound at 10 MHz in ⁴He single crystals grown at constant pressure.      

4He Crystals on an Oscillating Plate

Shape and motion of ⁴He crystals in superfluid placed on a transversely oscillating plate were investigated visually. The plate was glued onto a piezo post which was driven in a shear mode electrically. The purpose of the experiment was to drive a ⁴He crystal by a piezoelectric device which can be used to drive ordinary solids by the inchworm method. Facets of a single ⁴He crystal 3 mm in width were destroyed by a single sawtooth pulse of 1 ms duration at 0.4 K. In case of a larger crystal 7.5 mm in width and 0.8 mm in height, only one side of the crystal moved toward the center of the crystal, while the other side never moved despite application of 100 pulses at 10 ms intervals. Therefore, the crystal grew vertically and its height varied from 0.8 mm to about 1.4 mm during the pulses. This anisotropic behavior had nothing to do with the direction of the sawtooth driver. Many of the observed behaviors were puzzling, but it can be said that the crystals responded to the oscillation sensitively and the sawtooth pulse induced a very anisotropic motion of the crystal surface.