Transport properties of spin polarized3He-4He mixtures

We have calculated the viscosity, thermal conductivity, and longitudinal spin diffusion coefficient in³He-⁴He mixtures which are spin polarized. The calculation applies to all temperature regimes. We have also calculated the Onsager cross coefficient which arises because of the coupling between heat and longitudinal spin currents. The interaction between³He quasiparticles is taken to be a constant as a first approximation. We have also investigated the changes brought about by allowing the interaction to vary with the momentum of the quasiparticle.     

NMR studies of highly polarized liquid3He-4He mixtures

An efficient technique for maintaining large³He nuclear spin polarizations in liquid³He-⁴He mixtures has been developed and used to polarize samples contained in narrow tubes. Results obtained in a U-shaped cell and a coil-shaped cell are compared. A systematic study of the effects of dipolar fields within the sample on the characteristics of the observed long-lived magnetostatic modes is in progress. NMR signals obtained in the coil-shaped cell reveal phase separation and the existence of a highly polarized³He-rich region in the sample.Laboratoire de L'Ecole Normale Supérieure et de L'Université Pierre et Marie Curie, associé au CNRS (URA 18)     

3He-4He mixtures in aerogel

Superfluid density and heat capacity experiments on³He-⁴He mixtures in 98% porous aerogel show that in this system the coexistence boundary is detached from the superfluid transition line. The tricritical point is removed, and there is a superfluid phase on the³He rich side of the phase diagram. The presence of heat capacity peaks along the transition line down to a⁴He concentration of only 8% indicates the 3-dimensional nature of this transition.This work is supported by NSF under grants DMR-9008461 and DMR-9311918.     

3He-3He quasiparticle interaction in3He-4He mixtures under pressure

Based on our recent phase separation curve of³He-⁴He solution at elevated pressures, we propose new³He-³He quasiparticle interaction potentials, which reproduce the existing experimental results pretty well except for³He effective mass under pressure.     

NMR Studies on 3He-3He and 3He-4He tunneling motions in solid 3He-4He mixtures

Helium-3 nuclear spin relaxation times T ₁, T ₂, and T ₁have been measured for ³He-⁴He solid mixtures at the exchange plateau region (~0.5K). The ³He concentrations X ₃of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm³/mole in hcp phase. The spectral density function J() for dipolar field fluctuations was determined in the low-frequency branch from T ₁measurements and in the high-frequency branch from conventional T ₁measurements. It was found that J() is given by J() = cJ()|_3–4 + (1–c)J()|_3–3, where J()|_3–4 is the spectral density function due to the ³He-⁴He tunneling motions, and J()|_3–3 is that due to the ³He-³He tunneling motions. Using the Torrey theory, the correlation frequency of the ³He-⁴He tunneling motions was evaluated from T ₁data, and was found to be in good agreement with Landesman 's theory.Supported in part by the Japan Society for the Promotion of Science through a grant to Y.H.     

Vibrating superleak transducers in3He-4He mixtures

We generate second-sound resonances in a cylindrical cavity in³He-⁴He mixtures using vibrating Nuclepore filters. The properties of the cavity resonances are well described by the theory proposed by d'Humieres et al. The theory predicts the strength of cavity resonances as well as the phase shift between in- and out-of-phase components of the signal. By fitting these quantities we are able to get information about the compliance of the membrane, the distance of the membrane to the backplate, and the resistance to flow through the membrane. This enables us to predict the reflection coefficient of second-sound waves off the transducer. We also study the effect of a strong magentic field on the resonances.     

Two-phase sound in stratified3He-4He mixtures

The hydrodynamic boundary conditions at the normal liquid-superfluid interface in stratified³He-⁴He mixtures are formulated and applied to the propagation of low frequency two-phase sound. Coupling between the first- and second-sound modes occurs at low temperature because of the large increase of the Fermi-liquid transport coefficients. Starting with a normal homogeneous mixture, a coupling in a narrow range of temperature near the phase separation point is also predicted.     

The dielectric formalism for3He-4He mixtures

The microscopic theory of³He-⁴He mixtures with a Bose condensate is formulated in terms of the dielectric formalism. By expressing all correlation functions in terms of proper, irreducible contributions, one sets the stage for approximate calculations that will be consistent with various exact sum rules and Ward identities, just as in the case of pure⁴He. The present analysis includes a symmetry-breaking term that allows us to deal with the continuity equations properly, and is valid at finite temperature. As a specific application, we express the normal fluid density _N in terms of the static⁴He current-current correlation function. We also give the first formal proof that in the presence of a moving condensate, the³He atoms make no direct contribution to the superfluid flow.     

Compression of3He by refluxing4He: HEVAC effects in3He-4He mixtures

The effect of a refluxing ⁴ He gas facing a Rollin film on the concentration distribution of ³ He atoms is described. In some situations, a large concentration enhancement of the colder part can result. Possible applications are briefly discussed.Unité de recherche de l'Ecole Normale Supérieure et de l'Université Pierre et Marie Curie, associé au CNRS (URA 18).     

Critical and tricritical dynamics in3He-4He mixtures

A new formalism is presented to study the critical and tricritical dynamics of³He-⁴He mixtures near the superfluid transition for arbitrary concentration. In this fluid two conserved variables, the molar concentrationX and the entropys, are twofold coupled to a complex order parameter ψ first in the dynamic equations reversibly and second in the free energy dissipatively. However, at an intermediate concentrationX=X _D (which is 0.37 at the saturated vapor pressure) a linear combination ofX ands is found to be asymptotically decoupled from ψ both reversibly and dissipatively. There, dynamic renormalization group equations reduce to those of pure⁴He (or those of the F model) and some dynamic properties are common to those of pure⁴He. For example, atX≈X _D , the gradient ?(T?T _λ ) under heat flow goes to zero without³He mass flow, whereT _λ is the critical temperature, dependent onX, and the thermodiffusion ratio loses the singularity with the critical exponent α. Our dynamic renormalization group equations take into account the above two nonlinear couplings and can be used for any concentrations. Furthermore, using a linear response scheme, general relations are obtained among the kinetic coefficients. As a result the thermal conductivity on the λ line is found to be exactly proportional toX ^?1 at smallX. The coefficient in front ofX ^?1 can be expressed in terms of the diffusion constant of an isolated³He molecule in⁴He.     

Sound attenuation and3He-3He interaction in3He-4He liquid mixtures at saturated vapor pressure

The interaction potential between³He quasiparticles in³He-⁴He liquid mixtures is determined from the sound attenuation at saturated vapor pressure. Sound attenuation was measured in mixtures with³He mole fraction ranging from 0.0289 to 0.0573. The superfluid transition temperature of³He in mixtures and other properties were then estimated from the deduced interaction potential.     

Spin diffusion in dilute,polarized 3He-4He solutions

Spin dynamics for arbitrarily polarized and very dilute solutions of ³He in liquid ⁴He are described. We began at a very fundamental level by deriving a kinetic equation for arbitrarily polarized dilute quantum systems based on a method due to Boercker and Dufty. This approach allows more controlled approximations than our previous derivation based on the Kadanoff-Baym technique. Our previous work is here generalized to include T-matrix interactions rather than the Born approximation. Spin hydrodynamic equations are derived. The general equations are valid for both Fermi and Bose systems. By use of a well-known phenomenological potential to describe the ³He-³He T-matrix we calculate longitudinal and transverse spin diffusion coefficients D and D _¦ and the identical-particle spin-rotation parameter . We confirm that these two diffusion constants differ at low T with D approaching a constant as T 0, and D_¦~1/T². Estimates of errors made by our approximations are considered in detail. Good agreement is found in comparison with data from both Cornell University and the University of Massachusetts. We find that the s-wave approximation is inadequate and that mean-field corrections are important. Comparison is also made between theory and the recent UMass viscosity measurements.     

Nucleation of transitions in liquid 3He-4He mixtures

We present a complete set of data describing the nucleation both of superfluidity and phase separation at container walls in liquid ³He-⁴He mixtures. The appearance of superfluidity and the growth of phase-separated films are measured locally at the walls. A theoretical interpretation is given, important results of which are that the phase separation and superfluid transitions become uncoupled when the transitions are localized near the walls and that quantum fluctuations most probably strongly affect the nature of the superfluid nucleation transition at low temperature. Further, comparison of our results with data for transitions in pure ⁴He films demonstrates that a universality principle governs the transitions in both systems.Partly supported by NSF Grant No. DMR 75-21886.Laboratoire associé au CNRS.     

The solubility of spin-polarized3He in4He and the superfluidity of3He in3He-4He mixtures

We investigate the possibility of a large enhancement of the T = 0 finite solubility of³He in⁴He due to spin-polarization. The size of the effect depends on the fraction of³He atoms in the system. We present two different approaches for the limits of a small and a large number of³He atoms compared to the number of⁴He atoms. Since the possible³He superfluid phase transition depends on³He density, we calculate the consequences of this change in the solubility for its superfluid transition temperature. It is shown that for small fractions of³He, the transition temperature is enhanced mostly due to the enlargement of the up-spin Fermi sphere. In the opposite limit the transition temperature is enhanced as a result of the increased³He solubility.     

Sound attenuation in3He-4He liquid mixtures under pressure

The attenuation of sound was measured in³He-⁴He mixtures with³He concentrations ranging from 2.89 to 8.03% at pressures of 10 and 20 bar. The quasiparticle interaction potentials were then determined at each pressure by analyzing the sound attenuation data. The superfluid transition temperature of³He and other properties in the mixtures were then estimated from the interaction potentials.     

The velocity of second sound in3He-4He mixtures

The formula for the velocity of second sound in dilute³He-⁴He mixtures is derived, taking due account of both the effects of the interactions between the³He quasiparticles and their dispersion. The theory is compared to the recent experimental results of Greywall and Paalanen, and from this comparison it is possible to obtain both the inertial mass and the specific heat effective mass. Both masses are consistent with the mass in infinitely dilute solutions being (2.245±0.01)m ₃. Previous analyses of the velocity of second sound are critically discussed.     

Specific heat of3He-4He mixtures in Vycor glass

The specific heat of a ³ He- ⁴ He mixture filling a narrow pore is calculated in the temperature range 0.5–1 K, including the effect of van der Waals forces due to the walls, and is found to be compatible with the enhancement over the bulk liquid value experimentally observed for mixtures in Vycor glass.     

Vibrating-wire measurements in vacuum,liquid3He and liquid3He-4He mixtures

In order to overcome the 200µK - barrier in the refrigeration of liquid ³ He- ⁴ He mixtures we have constructed an experimental cell using only pure materials to minimize possible origins for heat leaks into the liquid. With this arrangement we were able to cool a saturated6.8%- mixture to a temperature of 150µK. A vibrating wire which was immersed in pure ³ He floating on top of the phase-separated mixture was used as a thermometer. This wire was calibrated in a second experiment with pure ³ He only in the cell. In superfluid ³ He-B at T0.15 mK the damping of the wire due to the quasiparticles becomes very small, and we observe typical characteristics of the vacuum damping of the wire which was extensively examined before filling any liquid into the cell.     

Superleak transducers of second sound in3He-4He mixtures

In a recent second-sound experiment in a dilute³He-⁴He mixture, Church et al.¹¹ were able to understand most of their data with the theory by d'Humières, Launay, and Libchaber.⁸ However, significant discrepancies exist at lower frequencies. We show that diffusive currents across the superleak are responsible for this deviation. What is more, we are able to determine the diffusion coefficientD from the low-frequency data.The equations governing the performance of oscillating superleak transducers and Peshkov transducers are derived in a systematic manner. This pertains to pure He-II as well as to mixtures. Mistakes in earlier works on dissipative effects of superleak transducers are corrected. Explicit formulas are given for the amplitude and linewidth of second sound, and the experimentally relevant parameters are discussed.     

Analysis of spin wave resonances in3He-4He mixtures

Spin waves have been reported previously in³He-⁴He mixtures using cw-NMR. The spin waves form standing waves in the rf coil used to detect the NMR signal. Only one resonance was observed, corresponding to ak vector of 1 mm^–1. This is in sharp contrast to similar experiments performed on pure³He, where several resonances were seen. An explanation is given of why this occurs and the resonant mode is identified. Furthermore, it is explained why there is an extra width to the resonance for temperatures below 2 mK. This is caused by radiation damping of the resonant mode. The theory is found to be in excellent agreement with the data. Further experiments are suggested, including details of an improved rf coil design, which should lead to information about the quasiparticle interaction.