Nuclear Magnetism of Normal 3He and 3He-4He Mixtures in Aerogel

We report NMR experiments at 8 T on ³ He and ³ He- ⁴ He mixtures filling the pores of 95% porous aerogel, for temperatures T 6 mK. Magnetization measurements of pure ³ He reveal a localized layer approximately one monolayer thick. The longitudinal relaxation includes a component logarithmic in time, which is apparently associated with a fraction of the localized ³ He atoms. When the localized ³ He is displaced by adding ⁴ He the logarithmic relaxation disappears and T ₁ for the dominant exponential relaxation increases. Measurements of the spin diffusion coefficient with the aerogel filled with dilute solution in equilibrium with bulk phase-separated mixture provide an unambiguous determination of the spin mean free path,_s = 58 nm     

Impurity Scattering Effect on Superfluidity of 3He in Aerogel

The impurity scattering effect on superfluid ³ He in aerogel is studied on the basis of the standard impurity theory within the weak coupling limit. We discuss the superfluid transition temperature and the superfluid density in the dirty Fermi liquid. The results are compared with recent experiments on the superfluidity of ³ He in aerogel. The low pressure data of the observed superfluid density are shown to be in better agreement with the results for the A-phase than for the B-phase. The B-phase results show considerable disagreement with the low pressure data.     

3He-4He Mixtures in 95% Porous Aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures in 95% porous aerogel found a phase diagram similar to that in 98% porous aerogel. The coexistence boundary on the ³ He rich side resides very close to, but nevertheless is detached from the superfluid transition line. Together with the findings in 98%, 87%, and 99.5% porous aerogel, this result supports the interpretation that the phase separation of ³ He- ⁴ He mixture in aerogel is induced by the capillary condensation of ⁴ He films from neighboring silica strands into ⁴ He rich domains.     

Acoustical Experiments on Superfluid 3He-4He Mixtures in Aerogel

This report discusses our results on the superfluidity of ³ He- ⁴ He mixtures in a 98% porosity silica aerogel. We have used low frequency sound to probe helium mixtures confined to aerogel, and have observed both the slow mode of superfluid ³ He in aerogel, which is manifested only below T_c, and an additional sound mode present only in the mixture. We attribute this novel sound mode to the slow-mode in the ⁴ He rich phase of the dilute ³ He- ⁴ He mixture. This mode exhibits positive frequency shifts below T_c in aerogel, while above T_c the mode is observed at a temperature independent frequency until close to T where it shifts to zero frequency.     

Capillary Condensation of Phase Separated Liquid 3He-4He Mixtures in Aerogel

We have studied details of the phase separation of ³ He- ⁴ He mixtures in aerogel for ⁴ He concentrations between 13 - 36% and at pressures of 0 and 22 bar. Simultaneous measurements of the ⁴ He concentration (measured with a parallel-plate capacitor) and of the tortuosity of the ⁴ He-rich phase (using the period of the torsional oscillator) provide evidence for the diversity of configurations of the ³ He- ⁴ He interface as a consequence of capillary condensation. Thus, for the same ⁴ He content within the aerogel, the ⁴ He-rich phase can have different interconnectivities determined by preparation history.     

Towards Superfluidity of 3He Diluted by 4He

Search for the superfluid state of dilute ³He dissolved to ⁴He is one of the major remaining problems of low temperature physics. We describe our two experiments designed to pursue the lowest achieved temperature in such mixtures essentially below the values reported before.     

Vibrating Quartz Crystal Studies of Wall-Film Superfluidity in Liquid 3He/4He Mixtures Near the Tricritical Concentration

We are using a thin quartz crystal immersed in the liquid, vibrating in shear modes at 24.8 and 94.0 MHz, to investigate the onset and growth of superfluidity in a thin film at the crystal surface in liquid ³He/⁴He mixtures having ³He mole fractions x near the tricritical value x=0.675. A parallel-plate capacitor in the cell monitors the phase-separation transition. Preliminary measurements of frequency shifts at x=0. 644 and x=0.705 show a relatively abrupt onset of wall-film superfluidity in the bulk normal region of the phase diagram at temperatures in good agreement with earlier studies of wall-film superfluidity by other methods.     

Superfluidity of solid4He

Using a procedure suggested by Leggett, an upper bound to the superfluid fraction in ground state solid ⁴ He slightly above the melting density is obtained numerically. The value obtained is 0.3±0.1. To judge the usefulness of this upper bound, we examine the conditions under which a symmetrized product of single-particle functions times a Jastrow function exhibits ODLRO, a necessary and sufficient condition for superfluid flow. It is found that ifU _ij (U _ij=? φ _i (x)φ _j (x) dx, and φ _i (x) is a single-particle wave function centered on the pointi) satisfies σ′_i U _ij>x, wherex varies from unity for long rangeU _ij (i.e.,U _ij decreases slowly enough asR _i?R_j increases) to a value of 12/7 for nearest-neighbor overlap only in the hcp lattice, then there is ODLRO, but not otherwise. Therefore, if the accepted single-particle functions are the true ones, then there is no ODLRO in solid ⁴ He, since the overlap is too small. We have explored the possibility of adding a flat tail, of magnitude λ′(VN)^?1/2 to the accepted single-particle functions. It is shown that if λ → 1 [λ ² =(λ′) ² +2(vNV ^?1)^1/2, andv=(? φ_i(x)dx)²], the system wave function becomes a pure Jastrow function, whereas if λ²?1??2×10 ^?1 , we have in effect the case where λ′=0; furthermore, there is ODLRO if λ ² ?1～?2×10 ^?1 . It is also concluded that the superfluid fraction upper bound of 0.3±0.1 obtained here as well as one suggested by Leggett are not very useful. We have not attempted to establish if there is some value of λ satisfying the above inequality such that the ground-state energy is lower than the value it takes for λ′=0.     

Observation of 4He Superfluidity in 1.8 nm-Pores

No Heading Superfluid properties of ⁴He adsorbed in uniform straight pore 1.8 nm in diameter were studied using a torsional oscillator. In the pore, the first one or two layers of adsorbed. ⁴He are solid, therefore the pore diameter is effectively reduced to about 1.1 or 0.4 nm. In order to investigate whether ⁴He becomes superfluid in such a narrow pore, we performed the oscillator experiments for two cases: ⁴He is adsorbed (1) on the bare substrate and (2) on the pore completely filled with N₂ atoms. In the latter case, only superfluid film coating the surface of the substrate grain can be detected. Compared with this case, an additional superfluid signal originating from ⁴He in the pore is observed for the bare substrate. This strongly suggests that ⁴He in the pore is superfluid.PACS numbers: 67.40.–w, 67.70.+n     

Pulsed Nonlinear Sound in Superfluid 4He and 4He-3He Mixtures

Sound modes in ⁴ He and ⁴ He- ³ He mixtures which arise out of the two-fluid equations are made up up a vector convective flow and scalar temperature changes. A method for modeling nonlinear pulses of sound with geometric approximations to the vector and scalar components has recently been applied towards understanding nonlinear second sound near the lambda point. ⁶ The same method may be used, in general, for modeling linear and nonlinear sounds in Helium II. We demonstrate with a model for nonlinear second sound pulses in ³ He- ⁴ He mixtures and compare the results to experimental observations.     

Adiabatic Fountain Resonance for 4He and 3He-4He Mixtures

We report an analysis of a superfluid Helmholtz resonance in the case of helium confined in a superleak. The resonance of the superfluid is achieved under nearly adiabatic conditions. Equations are derived for the resonance frequency, the temperature oscillations of the superleak and the phase relation of this signal relative to an ac heat input. The resonance frequency yields the superfluid fraction of the confined helium. Data are analyzed as function of frequency and temperature and yield parameters such as the dissipation and thermal conductivity which determine the resonance line shape. Estimates are made of the thermodynamic parameters in the resonance equation by using derivatives along the pressure-temperature-concentration lambda surface. These parameters are compared with results from the analysis of the resonance.     

Local Superfluidity in 4He and para-H2 Clusters

No Heading We present a new definition of local superfluidity around impurities in quantum fluids that provides a consistent analysis of the response of the inhomogeneous fluid density to the impurity rotations. This definition is based on the local decomposition of the moments of inertia of the fluid, which can be estimated from the projected area of exchange-coupled Feynman paths in path integral Monte Carlo calculations. Application to helium droplets doped with a planar phthalocyanine molecule shows that the first solvation layers parallel to the molecular plane consist of localized helium atoms that are totally inert to superfluid response, while the second solvation layers and capping regions at the end of the molecule exhibit partial and anisotropic superfluidity. Application to weakly bound complexes of the linear OCS molecule with para-hydrogen molecules shows evidence for the existence of molecular supersolids. We find that five H₂ molecules constitute a single ring around OCS which possesses both a solid-like pair correlation function and a complete superfluid response to rotation around the molecular axis below T ~ 1 K.PACS numbers: 36.40.–c, 36.40.Mr, 67.40.–w. 67.40. Yv     

Phase Separation Line for Solid Mixtures of 3He in 4He

The excess pressure due to the phase separation of solid mixtures of ³He in ⁴He held at a constant volume was measured and used for constructing the phase separation diagram of this system. We obtained high-quality homogeneous samples of the solid mixtures after several cycles of cooling down and heating up the two-phase crystal. This gave reliable and reproducible experimental data without hysteresis efects. We compared the phase diagram line obtained with various theoretical approaches, which describe the phase separation of the helium isotope mixtures. The regular solution model can not describe the experimental data well and neither can the asymmetrical Mullin's model. Good agreement is observed only with the theory of Edwards and Balibar which takes into account the difference between the crystal symmetry (hcp and bcc) of the coexisting phases.     

Distribution of 3He–4He Mixtures in a Bi-Porous System

We have investigated the distribution of ³He–⁴He mixtures in a system comprised of two porous materials: aerogel and silver sinter. The particle number density, and thus the ³He–⁴He concentration, was measured directly in the aerogel sample. We discuss both the observed history dependence for the low temperature equilibrium ⁴He fraction in aerogel and the temperature evolution of the ⁴He fraction.     

Melting and Crystallization of 3He Inclusions in Two-phase Solid 3He-4He Mixtures

The peculiar features of the phase diagram for the ³ He- ⁴ He system make it possible to melt the ³ He inclusions formed during phase separation of the mixture by further cooling and to crystallize them in subsequent heating. The kinetics of these processes is studied on a sample with a molar volume of 20.54 cm ³ /mole (P=31.7 bar) using pressure measurements. The time dependence of the crystal pressure P(t) is measured on cooling at a rate of 10 mK/h followed by heating. The dependence P(t) has two distinct rises in pressure, the first rise being associated with the phase separation of the mixture and the second one with the melting of the ³ He inclusions formed. It is shown that the melting of the ³ He inclusions is almost complete after the fast cooling and the observed pressure jump is in good agreement with the corresponding change in the molar volume. The repeated crystallization of the inclusions is found to give rise to a large pressure gradient near the boundary of the inclusions, suppressing quantum diffusion considerably. This may result in an incomplete crystallization of the inclusions. The experimentally observed difference between the initial and final pressure in the sample corresponds to the fact that approximately 20% of the ³ He remains in the liquid state.     

Rotating Superfluid 3He in Aerogel

Rotational effects on textures of superfluid ³He in aerogel with 98% porosity at a pressure 3.0 MPa were investigated by cw-NMR measurement at 700 kHz (H ₀=22 mT) under rotation up to 2π rad/s. At rest, the superfluidtransition to the A phase occurred at T ^aerogel _c =2.07 mK and the A phase was supercooled down to T ^aerogel _A→B==1.73～1.80 mK and became the B phase in the cooling process. In the warming process, the B phase was superheated up to T ^aerogel _c . In the B phase, a new peak appeared in the NMR spectrum by rotating the sample. The intensity of this peak increased as the rotation speed increased almost linealy to Ω and started to be saturated for Ω≥Ω _c. We attributed the new peak to the textural change caused by the counter flow and the onset of the saturation at Ω _c to the onset of vortex nucleation in aerogel. On deceleration, the peak intensity decreased and disappeared at Ω=Ω _v. Further decreasing Ω, the peak intensity increased even at Ω=0. The counterflow peak observed at Ω=0 indicates the existence of persistent current induced by pinned vortices in aerogel. In the A phase, we did not find any noticeable change in the NMR spectrum under the rotation speed up to 2π rad/s, or by cooling through T _c with or without rotation. We concluded that the ${\hat \ell }$ texture in the A phase was strongly pinned to aerogel. No spin wave satellite signal localized at a soft, core vortex was observed in contrast to the bulk A phase.     

Structure Factors of 3He-4He Mixtures

We briefly summarize the present understanding of the dynamic structure factors of liquid ³He-⁴He mixtures in the phonon-maxon-roton region and then present a new calculation using the memory function formalism. Results agree well with experimental data.     

Quasi-2D Flows of 3He – 4He Mixtures

Transport in degenerate ³ He- ⁴ He mixtures in quasi-2D flow channels is discussed. The quasiparticle mean free path combines particle-wall and particle-particle collisions including the interference between them. The temperature, concentration, and polarization dependences of the transport coefficients allow easy extraction of the correlation parameters of random surface roughness from transport data.     

Temperature and Concentration Relaxation in Phase-separated Superfluid 3He–4He Mixtures

The kinetics of the temperature and concentration variations in the superfluid ³He–⁴He mixtures with initial concentration of 9.8% ³He, and heated from below, was studied experimentally under the pressure of 0.38 bar over a temperature range of 150–400 mK. It is found that in contrast to homogeneous liquids, the temperature and concentration relaxation in phase-separated mixtures can be described by a superposition of two exponential processes in which the time constants of temperature and concentration variations coincide. If the initial mixture was homogeneous and phase separation was triggered by a heat flow, the temperature and concentration vary non-monotonically and exhibit anomalous features at the moment of phase separation. In this case the phase transition starts in the metastable superfluid, formed out of a quite supersaturated mixture where the nucleation of the new phase may be caused by quantized vortices. The results are analyzed in terms of two possible mechanisms of relaxation–the acoustic mechanism with the second sound velocity and the diffusive one connected with dissipative flows of impurity and thermal excitations. It is shown that the measured relaxation times agree with a prediction of the theory.