Mixing entropy of 3He-4He monolayers adsorbed on graphite

Calorimetric measurements on ³He-⁴He monolayers by Hickernell, McLean, and Vilches indicate that isotopic ordering takes place in both the low-density and registered lattice gas regimes. The low-density film heat capacity corresponds to imperfect 2D gas mixtures above T – 1 K. At lower temperatures the ⁴He fraction condenses to a 2D liquid, and the concurrent decrease in mixing entropy indicates concurrent isotopic separation. In the registered lattice gas mixtures the mixing entropy changes by a much smaller amount over the experimental region. It is argued that the observed changes are due to shortrange isotopic ordering tending towards segregation. From a detailed comparison with an Ising model, we estimate a transition temperature T _c 30 mK.Research supported by The National Science Foundation.     

Effects of 4He substitution on low temperature heat capacities of 2D 3He adsorbed on graphite

No Heading We measured heat capacities of the second layer ³He admixed with a small amount of ⁴He (= 0.9 nm^–2) on graphite preplated with a monolayer ⁴He. The aim of this study is to elucidate possible ⁴He substitution effects on a recently proposed new quantum phase existing at densities just below that (_4/7) for the 4/7 registered phase. This phase is supposed to be the hole (zero-point vacancy) doped Mott localized phase. The substitution gives rise to an excess heat capacity (C_ex) with unusual temperature and density dependencies which is most pronounced at a slightly lower density than _4/7. The C_ex stays relatively large even at _4/7, and suddenly disappears at a slightly higher density. One possible scenario, which is consistent with the present data, is that the C_ex comes from the isotopic mixing effect existing in a narrow density range around _4/7 and that there exists an excess particle phase just above _4/7 in addition to the hole doped phase below. The result may suggest finite fluidity or unexpectedly large band widths for the isotopic impurities in the 4/7 phase.PACS numbers: 67.70.+n, 67.55.–s, 71.10.Ay.     

Transport properties for a dilute solution of3He in two-dimensional liquid4He

The temperature variations of the diffusion coefficientD(T), thermal diffusion ratio k _T (T) and thermal conductivity (T) in a dilute solution of³He atom in two-dimensional liquid helium are evaluated explicitly by solving the kinetic equations via phonon-phonon, phonon-roton, roton-roton, impurityelementary excitation and impurity-impurity scatterings. In the low-temperature region, the main contributions toD(T) and (T) come from the interactions between phonons and impurities, while in the high-temperature region the interactions between impurities and whole elementary excitations contribute more strongly toD(T) and (T) than those of only elementary excitations. For a dilute solution, the thermal diffusion ratio k _T (T), neglecting the internal mass counterflow, is much smaller than the effective thermal diffusion ratio k _T ^* (T), which is a function of thermostatic properties. The effective thermal conductivity _eff is much larger than the thermal conductivity and has different temperature dependence from the thermal conductivity. The behaviors of the two-dimensional diffusion coefficient and thermal conductivity are much like the bulk case, where they exhibit exponential decay with increasing temperature, although they are much smaller than those of the bulk case.     

Superfluid onset in4He films adsorbed on pyrolytic graphite

Third-sound velocities and superfluid onsets have been studied for⁴He films adsorbed on pyrolytic graphite. The present onset data are compared with previous experiments on graphite substrates. The third-sound onset data are found to be significantly different from superfluid mass-flow and heat-flow data. A value of 3.19±0.52×10^–9 g cm^–2 K^–1 is obtained for the superfluid areal density at onset divided by the transition temperature. This value is consistent with the Kosterlitz-Thouless-Nelson picture of the phase transition in a two-dimensional superfluid.     

Thermal equilibration of fluids near the liquid-vapor critical point:3He and3He-4He mixtures

We study the temperature-equilibration process of fluids at constant volume in a thermal conductivity cell, where an initial temperature gradient relaxes to zero. The calculation is performed in the linear approximation for a pure fluid and a binary mixture. Near the critical point of the pure fluid, the adiabatic heating process, which takes place at constant volumeV, causes equilibration to proceed four times faster whenC _P /C _V 1 than for the process at constant pressureP. For the mixtures, the relaxation rate enhancement at constantV compared with constantP is restricted to a temperature region where the coupling between temperature and mass diffusion is small. The predictions are compared with experimental results for³He and for two³He-⁴He mixtures along their critical isochores. Finally, we discuss the thermal relaxation in the two-phase (liquid-gas) and one-phase (gas) regimes at the critical density, as measured with a conductivity and a calorimetry cell. The contrasting behavior for³He and a³He-⁴He mixture in these two regimes and under these different constraints is pointed out and discussed.     

Exchange and magnetic order in HCP 3He and adsorbed 3He with triangular lattice

A Schrödinger equation is derived which allows an improvement in the wave function of a quantum crystal inside the tunneling duct for exchange. This equation is used to derive a simple estimate of the exchange rate accurate enough to be used to compare various exchange mechanisms (two-body, three-body cyclic, etc.). We find that the ³ He bulk hcp crystal and ³ He surface triangular crystals have their exchange dominated by three-body cyclic exchange. Therefore the dominant part of the spin Hamiltonian will be Heisenberg nearest neighbor ferromagnetic. This result explains the ferro-magnetic tendency observed in adsorbed ³ He films. A ferromagnetic transition in hcp ³ He at the lowest pressures is predicted at 0.05±0.01 mK, corresponding to a Curie-Weiss constant of 0.075 \+ -0.015 mK.     

Apparent new phase of monolayer3He and4He films adsorbed on Grafoil as determined from heat capacity measurements

Heat capacity measurements in monolayer³He and⁴He films adsorbed on Grafoil at densities higher than the one corresponding to the substrate lattice registered phase show a series of sharp, narrow peaks at 1 K for densities between 0.072 and 0.077Å ^–2. The exact nature of the transition cannot be determined from this measurement alone, but several possibilities are discussed. It has been determined that the melting line of two-dimensional solid films starts atn=0.078Å ^–2 for both isotopes. Extensive heat capacity measurements at and above this density are presented for³He, and some new measurements for⁴He are shown to complement measurements reported elsewhere. The solid³He measurements are compared to predictions of recent models for melting in two dimensions.Work supported by National Science Foundation Grant # DMR72-03003A04.     

Ferromagnetic anomalies in two dimensional3He adsorbed on graphite

The second layer of solid³He adsorbed on graphite exhibits a pronounced exchange anomaly which is peaked sharply at a surface density of 0.075Å^–2. The much weaker exchange anomaly in the submonolayer solid film, first detected in heat capacity studies, has been investigated by measurements of the nuclear magnetic susceptibility to temperatures below 1mK and found to be ferromagnetic. We report the dependence of the effective exchange constant on surface density and propose a model in which both anomalies arise from similar two dimensional commensurate structures.     

High-resolution heat-capacity study of4He adsorbed on bare copper

In this paper the Heisenberg ferromagnet is considered in the quasi-Pauli representation. Bogoliubov's idea of associating with each change of spin projection a pair of creation and annihilation operators is, in some sense, rehabilitated. This treatment provides us with a quite satisfactory physical picture of the phenomena in ferromagnets. All the fundamental results for the isotropic ferromagnet at low temperatures, as well as in the vicinity of the Curie point, are reproduced in a mathematically simple and physically clear way. The basic statistical formulas for quasipaulions are also derived in this paper.     

Superfluidity of4He films adsorbed on hydrogen plated graphite

The superfluidity of⁴He on graphite with various preplatings of HD is under investigation using a torsional oscillator. Results for a bilayer of HD follow a similar pattern to those obtained earlier on pure⁴He films and are consistent with third sound measurements on graphite plated with a bilayer of hydrogen. In our case the first⁴He layer solidifies, consistent with behaviour observed in NMR studies of³He on a similarly prepared substrate. At a coverage of 11nm^–2 there is the onset of a region in which the transition temperature increases rapidly with coverage and the transition itself becomes sharper. At certain coverages pronounced signatures have been observed in the period shift and dissipation, which may indicate a further phase transition in the film at lower temperatures.     

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.     

Specific heat of adsorbed films of3He,4He,and isotopic helium mixtures near monolayer coverages

Specific heat results are presented for near-monolayer films of³He,⁴He, and isotopic He mixtures adsorbed on Vycor porous glass in the temperature range between 1 and 4°K. In the case of the pure He monolayers and submonolayers, the specific heats depend only onT ² , like a two-dimensional Debye elastic medium. A film of slightly greater than monolayer coverage needs an additional temperature-independent term. Monolayer coverages of mixtures are difficult to define, but all coverages used, some of which are submonolayer, need bothT ² andT-independent terms. The constant term may arise from atoms in the second layer forming a classical noninteracting system, which in the mixture case would indicate selective adsorption of⁴He in preference to³He at the substrate wall, in agreement with previous adsorption experiments on the same substrate.Work supported in part by the U.S. Atomic Energy Commission.     

Reaction-matrix theory of quantum solids and its application to3He and4He in body-centered cubic phases

The self-consistent reaction-matrix theory of quantum solids is applied to bcc³He and⁴He. The two-body correlation function is solved numerically in terms of partial waves. The results for ground-state energies, pressures, sound velocities, and phonon-dispersion curves are compared with those obtained by theS-wave correlation function. In both helium isotopes better agreement with experiments is obtained by the partial-wave analysis.On leave of absence from Institute of Physics, College of General Education, University of Tokyo, Tokyo, Japan.     

Desorption heat capacity of 3He adsorbed on solid neon

The desorption heat capacity of successive monolayers of ³He adsorbed on solid neon is measured and a rigid band model for the desorption is set up. The agreement between experiment and theory is good. The desorption energy varies between 55 and 25 K for the first layer as a function of coverage and is about 11 K for the second layer.This project was supported by the Swedish Natural Science Research Council.     

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.     

Onset of superfluidity in4He films adsorbed on a graphite-fiber substrate

A torsional oscillator technique has been employed to investigate the onset of superfluidity in⁴He adsorbed on graphite fibers. A low temperature capacitance pressure gauge has been used to characterize the layered growth of the film as mass is added to the experimental cell. At T=0.84 K the onset of superfluidity occurs after completion of three layers. A comparison with similar data for a Mylar substrate shows that the dissipation peaks are much sharper for the graphite-fiber substrate.     

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.     

Ground state of two-dimensional liquid 4He

The ground-state energy and liquid structure function of two-dimensional liquid ⁴He are calculated in the density range 0.028–0.075 Å^–2, using the Lennard-Jones 6–12 potential. The optimal Jastrow function is first determined by a self-consistent paired-phonon calculation and then the contributions of three-body factors the wave function are calculated. Tables of values are given at several densities for the radial distribution function, Jastrow function, and liquid structure function.Research supported by National Science Foundation Grants DMR 74-01237 A01 and DMR 78-09226.