Surface Magnetism of Liquid 3He on 4He Pre-plated Graphite

No Heading The nuclear susceptibility of liquid ³He in Grafoil pre-plated by 2.5 and 3.5 layers of ⁴He has been studied with a cw NMR method at temperatures between 0.7 and 100 mK under various liquid pressures. The 3.5 layers of ⁴He pre-plating suppresses a formation of the first and second solid ³He layer, eliminating most of surface magnetization at saturated vapor pressure. However, with increasing liquid pressure, a magnetization obeying a Curie Weiss law gradually grows in the same way as in the previous experiment for pure liquid ³He. This magnetization, induced by pressurization, is attributable to the formation of solid ³He layer above the pre-plated ⁴He.PACS numbers: 67.80.Jd, 75.70 Cn, 67.70.+n.     

Measurement of the Solubility of 4He in Liquid 3He in the Fermi-Liquid Region

The phase separation temperatures of dilute solutions of ⁴He in liquid ³He in the Fermi-liquid region have been measured by detecting the ⁴He film formation sensitively. From the obtained solubility curve, the effective mass of ⁴He atom and the difference in binding energy of ⁴He in liquid ⁴He and in liquid ³He are proposed.     

Multiple positive ionic mobilities in normal liquid 3He contaminated with 4He

The positive ion in liquid ³He contaminated with 5 × 10^\s-4 parts of ⁴He is found at low temperatures to be able to exist in a number of discrete states with different mobilities. At a temperature of around 30 mK transitions from one species to another are observed. These transitions take place at a rate proportional to the ⁴He solubility. The different states may represent discrete values of ³He/⁴He ratio in the solid ion and immediately surrounding liquid.     

Kinetics of Liquid 3He Droplets in Solid 4He Matrix

Precise measurements of pressure in the crystal at constant volume were used to obtain the data on growth and dissolution kinetics of liquid ³ He droplets formed as a result of isotopic phase separation of solid ³ He- ⁴ He Mixtures. We studied several crystals with an initial ³ He concentration of 2.05% in the pressure range of 26–27 bar. It is shown that the growth of the liquid droplets during the stepwise cooling of the two-phase crystal is correctly described by the superposition of two exponential processes: diffusion decomposition with a small time constant and strain relaxation with a big time constant. The strain layer near the droplet boundaries is due to a great difference in molar volume between the droplets and the matrix, and leads to a plastic deformation of the matrix and to a non-equilibrium ³ He concentration in the matrix. Under such conditions quantum diffusion is significantly suppressed and ³ He atom transport occurs only as the strain is relaxed.     

Visualization of Bubble Nucleation in Boiling 3He

The heat transfer properties of ³He bubbles in the nucleate boiling state have been investigated in liquid ³He below 1.0 K by using the shadowgraph method. The temperature difference between the copper surface and liquid ³He temperature was also measured as a function of heat flux in steady state. The size and number of bubbles departing from the surface in a specific time were compared using photograph recorded by a high-speed video camera at various heat flux and liquid ³He temperature of 0.5, 0.7 and 1.0 K.     

4He in Liquid 3He below 0.1 K: Measurements of the Solubility and Prewetting Transition

We have measured the solubility of ⁴He in liquid ³He down to 0.04 K at various pressures. The solubility was obtained indirectly, from the thickness of the superfluid film in contact with unsaturated solutions. We determined the film thickness from the ratio of two parallel plate capacitors with different gaps, immersed in the unsaturated liquid. The technique is described in detail, with its advantages and drawbacks, including the effects of the edge capacitance and capillary condensation. For use in interpreting the data, the adsorption area and the van der Waals potential of the cell walls were found by measuring the thickness of ³He and ⁴He–³He films under their vapor pressure. By fitting the temperature dependence of the solubility to the predictions of Fermi liquid theory, we determined the ⁴He effective mass m*₄, the binding energy E ₄ and the partial volume v*₄, as a function of pressure. At 24 atm, a prewetting transition was observed in the ⁴He-rich film in contact with the liquid ³He. The transition, which is related to a similar phenomenon discovered by Tholen and Parpia at very low temperature, is explained by a simple model. An Appendix describes a new derivation of the thermodynamic functions of ³He-rich mixtures in Fermi liquid theory.     

Osmotic pressure of very dilute liquid mixtures of3He in4He

The osmotic pressure of very dilute liquid mixtures of³He in⁴He has been measured for the concentration range 0.08–0.6 mole%³He, and the temperature range 20–400 mK. The results are used to check the validity of different proposals for the³He–³He effective interaction.Work supported in part by the Gerald I. Swope Fund and the Batsheva de Rothschild Foundation.     

Thermodynamics of the liquid-solid interface in dilute solutions of3He in4He

We show that the (p, T, x) phase diagram of⁴He close to melting pressure (25.3 bars) with small concentrations of³He and at very low temperatures has several unanticipated and novel features. For pressures between 25.3 bars and a triple point pressurep*, estimated to be 25.8 bars, we find a dilute liquid solution of³He in equilibrium with solid⁴He. The concentration of the liquidx _c increases from zero to the dilute liquid solubility limitx ₀ as the pressure increases from the pure⁴He melting pressure atT=0 top*. We explore the possibility of self-cooling by lowering the pressure throughp*. We also consider the effects of a strong magnetic field, and show that it lowersx _c. An estimate of the kinetic growth coefficient is given. Finally, we discuss the possible adsorption of³He on the melting front and the consequent faceting enhancement of the solid⁴He.     

Superfluid Transition of a 4He Thin Film Pressurized by Bulk Liquid 3He

We measured transverse acoustic impedance Z of normal fluid ³He at 46.6 MHz on a surface coated with a thin ⁴He film. The real component of the impedance, Z′, in the coated samples deviates from Z′ in the pure ³He in the low temperature region. Z′ on the coated samples is almost identical with Z′ in the pure sample at high temperature and gradually deviates below a particular temperature T _onset . T _onset  is possibly the superfluid onset temperature of the ⁴He film pressurized by the bulk liquid ³He. The gradual decrease in Z′ means that the superfluid component in ⁴He film increases gradually, which is expected from the dynamic KT transition at high frequency. The thicker is the film, the higher is the T _onset . The range of T _onset we observed was between 40 and 160 mK. This is much lower than that at the saturated vapor pressure. Suppression of T _onset achieved by the applied pressure from bulk liquid ³He was presumably caused by the dissolved ³He in the film, thickening of the inert layers and/or by the strong correlation effect. The result shows that the specularity of ³He quasiparticle scattering is strongly affected by superfluidity of the ⁴He film.     

The preferential adsorption of 4He from 3He-4He mixtures onto Vycor glass

The preferential adsorption of ⁴He from liquid ³He-⁴He mixtures onto Vycor glass has been measured over a wide concentration range between 1 and 3 K. Over most of this temperature range the preferential adsorption extends beyond the second atomic layer, with a preferential binding energy of about 3.5 K/mole. Near 1 K and below, the thickness of the ⁴He layer increases rapidly as a precursor to the bulk liquid phase separation.     

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.     

NMR study of 3He bubbles in phase-separated solid 3He –4He mixtures

³ He droplets embedded in a solid ⁴ He matrix have been studied by NMR and pressure measurements. One feature of the experiment is that the mixture crystals, of ³ He concentration 1%, are grown under constant pressure conditions to minimise the formation of defects. A number of sample pressures below 34 bar have been studied. Isotopic phase separation and the melting of the bubbles are clearly observed. Measurements of T₁ , T₂ and magnetisation give detailed information on the structure of the droplets. At an initial sample pressure of 28.3 bar preliminary measurements of the T₁ of the liquid bubbles show a temperature dependence of the form (A+ B/T²)^–1. This indicates that the expected relaxation in the liquid is augmented by a constant contribution, probably from the surface of the droplets.     

Large Boundary Magnetism and Superfluidity of Liquid 3He in Nanometer-sized Porous Alumina

Continuous-wave NMR measurements were performed for liquid ³He in porous alumina with nominal pore size of 20 nm in diameter, at temperatures down to 0.3 mK. The signal is composed of two contributions: from the liquid and from the boundary solid layer of ³He on the alumina’s surface. The latter shows a well-known ferromagnetic tendency and signal intensities can be fitted to a Curie-Weiss law in the high temperature region. The obtained Weiss temperatures are 0.18 and 0.50 mK at 7.5 and 28 bar, respectively. ⁴He coverage (4 monolayers) completely eliminates boundary signal between 7.5 bar and 32.5 bar. The residual liquid signal shows frequency shift and broadening below superfluid transition temperatures depending on liquid pressures. The obtained P-T phase diagram well resembles that of bulk liquid ³He in spite of the very narrow pore-size comparable to the coherence length of superfluid ³He.      

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.     

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.     

Compressibility of 4He Liquid Confined in Nuclepore

Adding and removing ⁴ He from an experimental cell which contains the porous material Nuclepore results in capillary condensation, hysteresis and avalanches. The volume of liquid in the nearly cylindrical pores is monitored with a capacitance technique. For the situation when all of the pores are full, the initial removal of ⁴ He from the cell results in a slight non-hysteretic decrease in the capacitance, which we attribute to the isothermal compressibility of ⁴ He. As ⁴ He atoms are removed, the surface tension at the meniscus applies a negative pressure to the liquid in the filled pores, which results in a reduction of the density and a decrease in the capacitance. We present results for ⁴ He capillary condensed in 2000 Å pore diameter Nuclepore.     

The role of the attraction between liquid 3He and a solid substrate on the surface ferromagnetic instability of the 3He

After reviewing the properties of liquid ³He in contact with a substrate we calculate how much the van der Waals attraction to the wall additionally favors the surface ferromagnetic instability of the otherwise paramagnetic bulk liquid. We thus show that the observed Curie- Weiss-type susceptibility experimentally observed for liquid ³He in confined geometries in the millikelvin range undoubtedly has at least part of its source in the high-density fluid closest to the wall. The role of the solid ³He part sticking right on the wall is also discussed and further experiments (neutron ones in particular) are suggested.Laboratoire associé au C.N.R.S.     

Spin-dependent correlations in normal liquid 3He

Using a generalized Fermi hypernetted chain method on a Jastrow trial ground-state wave function, which includes a dependence on the z component of the nuclear spin, it is shown that spin correlations make a significant contribution to the ground-state energy of liquid ³He, accounting for much of the energy necessary to stabilize unpolarized liquid ³He relative to completely polarized ³He.Work supported in part by NSF grant DMR 7926447 and by the Deutsche Forschungsgemeinschaft.     

Ground-state properties of a3He impurity in liquid4He monolayers

We present the results of ground-state energies, radial distribution functions, liquid structure functions and effective interactions for a³He impurity in a⁴He background in two dimensions. The hypernetted-chain scheme for the system described by a Jastrow-type wavefunction is used, taking into account the triplet correlations and elementary diagrams up to fifth order. Solving the Euler-Lagrange equations for the two-body distribution functions, which contain triplet correlation and elementary diagrams, improves the results considerably. Furthermore, as a³He impurity is inserted into the⁴He background, the ground-state energy increases, but the equilibrium density decreases from 0.0350 Å^–2 to 0.0336 Å^–2. The radial distribution function is broadened, while its maximum is lowered and shifted to the right (the direction of increasing radial distance) due to its larger zero-point energy, with therefore less localization of the³He particle. The results are compared with Monte Carlo results and other studies.