Heat Capacity Measurements of 3He-4He Mixture Films

We report heat capacity measurements from our on-going experiments on two-dimensional liquid ³He on superfluid ⁴He thin films absorbed on Nuclepore. The ³He coverage dependence of the heat capacity for 0.02–0.50 bulk-density layers of ³He with 3.10 bulk-density layers of ⁴He over the temperature range 40≤T≤200 mK is presented. We find the effective mass of ³He on 3.10 layers of ⁴He is greater than that on 4.33 layers of ⁴He, consistent with our previous magnetic susceptibility 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.     

Evaporative Cooling of 3He-4He Mixture Films

Heat transport by saturated ³He-⁴He films has been studied at temperatures 50..350 mK and the bulk concentration of ³He ranging from 0.1 ppm to 5%. The cooling of the film, when locally heated above 160 mK, is mainly via 2D flow of surface ³He from colder area followed by evaporation of ³He. At certain heating power the 2D flow becomes a bottleneck, the heated spot runs out of ³He and its temperature abruptly increases. The critical power is nearly proportional to the surface density of ³He. For higher ³He concentrations another distinct step in temperature has been observed at a lower heating power. It is attributed to the existence of an excited ³He surface state whose population starts at ³He surface density of 3.5×10¹⁴ cm^–2. The second state is located about 1.2 K higher in energy than the ground state and provides an additional channel for the 2D flow of ³He.     

The Two-Dimensional World of 3He in 3He-4He Mixture Films

For thin films of ⁴He at low temperatures the addition of sub-monolayer numbers of ³He atoms results in the ³He residing in a ground state at the free surface of the ⁴He film. For low ³He coverage the ³He are a nearly ideal two-dimensional Fermi system. With increasing numbers of ³He atoms the interactions among the ³He increase. The results from a number of experiments that reveal the remarkable properties of this rich, interacting, two-dimensional ³He system are described. These results include the magnetization, the energetics of the ³He atoms in quantum states, the diffusion of the ³He along the ⁴He film, and the ³He effective mass. The techniques employed include NMR, specific heat, quartz crystal microbalance and third sound. A clearer picture of the properties of the ³He is now emerging, and preliminary numbers for the ³He coverage dependence of the Fermi Liquid parameters are presented. Prospects for the observation of superfluidity of the ³He in this system are discussed.     

3He Spin Diffusion Measurements for 3He - 4He Mixture Films on Nuclepore

Preliminary ³ He spin diffusion results for ³ He - ⁴ He mixture films on Nuclepore are presented as a function of ³ He coverage for 0.1 T 0.3 K. We report measurements for a constant ⁴ He coverage of 4.41 bulk density atomic layers with ³ He coverages between 0.3 and 2.1 layers. The diffusion is observed to decrease with increasing amounts of ³ He, and some structure as a function of temperature is present.     

Superfluid Phase Transition of 3He-4He Mixture Films Adsorbed on Alumina Powder

The superfluid phase transition of ³ He- ⁴ He mixture films adsorbed on 500 Å alumina powder has been studied for mixture films whose superfluid thickness is less than a monolayer. The transitions are found to be controlled by the Kosterlitz-Thouless critical line, but a strong broadening of the transition is observed as the ³ He concentration is increased. Analyzing the broadening in terms of a KT vortex-pair theory modified for the the finite powder size yields a vortex core parameter which increases nearly linearly with added ³ He. Also observed in these measurements is a temperature-dependent and ³ He-dependent depletion of the superfluid density at low temperatures, which is thought to arise from the high-frequency ripplon/third sound excitations of the film.     

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.     

Separation of 3He from 3He-4He Mixture by means of Adsorption

No Heading A simple technique for purifying ³He from a ⁴He admixture is presented. The technique is based on different adsorption energies of ³He and ⁴He.PACS numbers: 81.20.Ym, 67.60.–g.     

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.     

Spin Diffusion Measurements in Spin-Polarised Liquid 3He-4He Mixtures

We report on investigations of spin diffusion in isotopic helium liquid mixtures using a multi-echo technique in applied magnetic field gradients. Samples (up to 1 cm ³ in volume) are obtained by liquefaction of optically polarised gas. NMR measurements are performed at saturated vapour pressure in a low magnetic field (2.2 mT). Signal-to-noise ratios stay high down to ³ He concentrations of order a few parts per thousand at 1K for instance. We demonstrate that the experimental accuracy of spin diffusion measurements is substantially improved using optically polarised mixtures. We have observed that the dynamics of the precession of the transverse magnetisation can be altered due to large dipolar fields at high magnetisation densities. Effects on spin-echo signals and implications for the extension of spin diffusion measurements with our technique are discussed.     

Observation of the Fermi Fluid in 3He-4He Mixture Films Formed in One-Dimensional 28 Å Pores

A ³He film formed in quite narrow pores is one of the possible model systems for a one-dimensional Fermi fluid. Here we report our new heat capacity resugts of ³He and ⁴He film adsorbed in a straight pore 28 Å in diameter down to 5 mK. The coverage and temperature dependence of the heat capacity indicates that a fluid phase appears between the second layer promotion and the complete filling of the pores. Since the heat capacity of ³He adsorbed on the bare substrate shows a large upturn due to the nuclear heat capacity of the localized ³He, it is difficugt to observe the true heat capacity of the fluid phase. By replacing the localized ³He, we can successfully suppress the upturn and observe the true heat capacity of the fluid phase.     

Models for Third Sound in Thin 3He-4He Films

Third sound speeds in³He-⁴He thin films are sensitive to the transverse single-particle state occupied by the³He. The third sound speed in the low coverage region with the³He occupying the transverse ground-state can be understood quantitatively. The onset of occupation of the first excited transverse state is signaled by a high coverage feature in the third sound speed. Three third sound models for the high coverage region, differing in their assumptions about the spatial distribution of the excited states, are introduced. Using the experimental third sound data, these models can also be used to infer the fractional population of the³He in the first excited state as a function of coverage. It is found that the third sound analyses each predict a larger fractional population in the first excited state at monolayer completion than a recent analysis of magnetization step data taken on the same system.     

Possible Existence of Dense Superfluid 3He-4He Mixture in Aerogel

While studying superfluid ³He of 2.4 MPa in 97.5 %-porosity aerogel with NMR/MRI techniques, we find that the T _C is reduced when more than adequate amount of ⁴He, which covers the surface of silica strands, is introduced. For a sample, whose T _C is reduced to as low as 0.9 mK, we find that the spin diffusion coefficient in the normal phase is increased by a factor of 1.56 both in high temperature region, where ³He-³He scattering dominates, and in low temperature region, where ³He-aerogel scattering dominates. This enhancement is attributed to a modification of Landau parameter $F_{0}^{a}$ from ?0.757 to ?0.62, which is a change towards less ferromagnetic direction. The modification of microscopic quantity could be explained if small amount of ⁴He has homogeneously mixed into liquid ³He in the aerogel.     

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.     

Onset of Convection in Superfluid 3He-4He Mixture Heated from Below

The thermal instability of ³He-⁴He mixtures caused by heating the liquid from below has been studied experimentally. The temperature gradients were measured which appeared in the mixture with initial concentration 9.8% of ³He below 0.5 K in the presence of different heat flows from the heater at the cell bottom. At a certain critical heat flow the effective thermal conductivity of the liquid was observed to increase sharply which was naturally attributed to the convective heat transfer. It is shown that the thermal convection develops at high temperature gradients. In this case the Rayleigh numbers exceed many orders of magnitude those for heating from above. Thus the convective instability develops in a system in which the light liquid is at the top and where no prerequisite for instability is seemingly available. The resugts obtained are analyzed in terms of the theory of convective instability in binary mixtures. It is suggested that the phase separation, of superfluid mixtures caused by a heat flow could be a destabilizing factor initiating convection. The vortex formation in superfluid helium and the related turbulent flows appearing at high temperature gradients can be another factor favourable for instability of the liquid.     

3He-3He and 4He-4He Cross Sections in Matter at Low Temperature

The Galitskii-Migdal-Feynman (GMF) formalism is applied to liquid ³He and (for the first time) to liquid ⁴He. The effective total, diffusion and viscosity cross sections, as well as the effective scattering length and the effective range, are calculated. For liquid ³He, it is found that S-wave scattering dominates for wave number k<0.5 Å^?1. At the Fermi momentum k _F, the effective partial cross section σ _? (and thus the total cross section σ _T) has a singularity (virtual state). This singularity may be interpreted as a signature of superfluidity or a quasi-bound state. For k>2 Å^?1, the effective total cross section is nearly constant. On the other hand, it is found in liquid ⁴He that S-wave scattering dominates for k<0.3 Å^?1, and a peak exists in σ _T arising from a peak in the effective D-wave cross section. This resonance corresponds to a quasi-bound state trapped by the ?=2 centrifugal barrier. The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the matter cross section at low temperatures. This effect is absent in the ³He gas. It is, therefore, a purely many-body effect in liquid ³He. With increasing energies, the matter results approach the vacuum results. This indicates that the high-energy behavior is dominated by the self-energy contribution; the many-body effects can be neglected.     

Second Sound Measurements Near the Tricritical Point in 3He-4He Mixtures

In this paper we discuss a pulsed second sound experiment, aimed at determining accurately the critical exponent , and the predicted logarithmic correction to scaling, for the superfluid density along a tricritical path in the ³ He- ⁴ He phase diagram. We present an accurate estimate for the limits for closest approach to the tricritical point, as set by gravitationally induced sample inhomogeneities and finite size effects, and discuss some of the complications associated with measurements close to the tricritical point.     

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.     

Vibrating Wire Measurements in 3He-4He Mixtures in the Ballistic Quasiparticle Regime

We present our first high resolution vibrating wire resonator data on dilute ³ He- ⁴ He mixtures at ultra low temperatures. Measurements were performed at saturated vapor pressure with ³ He concentrations below the phase separation limit. The behavior of the damping at very low temperatures does not follow the modified slip correction analysis previously applied to extend the validity of the hydrodynamic treatment.