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Bulletin of the American Physical Society

The properties of {sub 3}He adsorbed on {sup 4}He films

R. B. Hallock

Published Apr 1, 1993• 0 citations
OpenAlex

Abstract

The {sup 3}He-{sup 4}He mixture film provides a remarkable opportunity to study the behavior of the uncharged 2D {sup 3}He Fermi fluid which resides on the {sup 4}He. Variation of the {sup 4}He film thickness allows one to vary the strength of the substrate field experienced by the {sup 3}He. Changes in the coverage of the {sup 3}He allow one to vary the strength of the {sup 3}He-{sup 3}He interaction and thereby study the evolution of the {sup 3}He system from the nearly ideal dilute 2D gas regime to the interacting 2D regime to the advent of 3D behavior. Recent experimental work, primarily by NMR techniques, on Nucleopore substrates for 30 {le} T {le} 600mK has resulted in a detailed picture of the energetics of the states available to the {sup 3}He, the stepwise evolution of the magnetization, spin relaxation and measurement of the diffusion of the {sup 3}He as a function of coverage and temperature. The state of current knowledge of the mixture film system will be discussed including connection to theoretical progress and the prospects for future work in this area.

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The {sup 3}He-{sup 4}He mixture film provides a remarkable opportunity to study the behavior of the uncharged 2D {sup 3}He Fermi fluid which resides on the {sup 4}He. Variation of the {sup 4}He film thickness allows one to vary the strength of the substrate field experienced by the {sup 3}He. Changes in the coverage of the {sup 3}He allow one to vary the strength of the {sup 3}He-{sup 3}He interaction and thereby study the evolution of the {sup 3}He system from the nearly ideal dilute 2D gas regime to the interacting 2D regime to the advent of 3D behavior. Recent experimental work, primarily by NMR techniques, on Nucleopore substrates for 30 {le} T {le} 600mK has resulted in a detailed picture of the energetics of the states available to the {sup 3}He, the stepwise evolution of the magnetization, spin relaxation and measurement of the diffusion of the {sup 3}He as a function of coverage and temperature. The state of current knowledge of the mixture film system will be discussed including connection to theoretical progress and the prospects for future work in this area.
Nuclear magnetic susceptibility measurements of the 3He^{3}\mathrm{He}3He in dilute 3He^{3}\mathrm{He}3He-4He^{4}\mathrm{He}4He mixture films are presented. At low 3He^{3}\mathrm{He}3He coverages (d3<0.1{d}_{3}<0.1d3​<0.1 layer), the 3He^{3}\mathrm{He}3He behaves approximately as a 2D ideal Fermi gas. For larger submonolayer 3He^{3}\mathrm{He}3He coverages, the low-temperature susceptibility is enhanced, increasing with increasing amounts of 3He^{3}\mathrm{He}3He, contrary to the 2D ideal Fermi-gas model. No evidence for a phase transition in the 3He^{3}\mathrm{He}3He is seen.
Nuclear magnetic resonance (NMR) and third sound measurements are reported for thin sp3\\sp3sp3He-sp4\\sp4sp4He mixture films, varying both the sp3\\sp3sp3He and sp4\\sp4sp4He thickness, and NMR measurements are reported for two dilute bulk mixtures. All measurements were made for temperatures 27 leTle\\le T \\leleTle 500 mK in a sample cell which contains both an NMR coil and a third sound resonator. The porous polycarbonite substrate Nuclepore is used for both its large surface area and its regularity of pore size and orientation. Films were studied with a fixed sp4\\sp4sp4He coverage of nsb4n\\sb4nsb4 = 0.390 Asp−2\\sp{-2}sp−2 while varying the submonolayer sp3\\sp3sp3He coverages, 0.006 lensb3le\\le n\\sb3 \\lelensb3le 0.063 Asp−2\\sp{-2}sp−2. Measurements of the magnetization, relaxation times and diffusion coefficient show evidence of a weakly interacting 2D Fermi gas. Evaporation from the film and thermal activation into higher energy states in the film allow us to obtain the energetics of the system from the magnetization and spin lattice relaxation time, respectively. Third sound measurements of the frequency and damping also show evidence of evaporation and thermal activation, and the energetics are obtained through these measurements also. The energetics from third sound compare quite well to those obtained through NMR methods. Third sound measurement of the phase between the drive current and film thickness fluctuation show an interesting simpi\\sim\\ \\pisimpi phase shift near T = 200 mK. The magnetization and longitudinal relaxation times of two dilute bulk mixtures of concentration X = 1 times\\timestimes 10sp−5\\sp{-5}sp−5 and 2 times\\timestimes 10sp−5\\sp{-5}sp−5, where X = Nsb3/(Nsb3N\\sb3/(N\\sb3Nsb3/(Nsb3 + Nsb4N\\sb4Nsb4) and NsbiN\\sb{i}Nsbi is the number of spiHe\\sp{i}HespiHe atoms, are studied to look for the existence of a theoretically predicted "substrate state". The substrate state is a state where the sp3\\sp3sp3He is expected to preferentially sit between the substrate and liquid sp4\\sp4sp4He (in a two-dimensional state), rather than be dissolved in the bulk (in a three-dimensional state). The measurements show no evidence of the sp3\\sp3sp3He occupying a two-dimensional state, and are consistent with expected three-dimensional behavior. Very thin films of varying sp4\\sp4sp4He coverage, 0.148 lensb4le\\le n\\sb4 \\lelensb4le 0.227 Asp−2\\sp{-2}sp−2, and with a fixed sp3\\sp3sp3He coverage, nsb3n\\sb3nsb3 = 0.006 Asp−2\\sp{-2}sp−2 were studied, looking for localization of the sp3\\sp3sp3He atoms in the random potential of the energetically inhomogenous sp4\\sp4sp4He surface. An enhancement to the expected low temperature magnetization and a four order of magnitude difference in the diffusion coefficient between the lowest and highest coverage are evidence of localization.
The experimental realization of a thin layer of spin-polarized hydrogen H↓ adsorbed on top of the surface of superfluid (4)He provides one of the best examples of a stable, nearly two-dimensional (2D) quantum Bose gas. We report a theoretical study of this system using quantum Monte Carlo methods in the limit of zero temperature. Using the full Hamiltonian of the system, composed of a superfluid (4)He slab and the adsorbed H↓ layer, we calculate the main properties of its ground state using accurate models for the pair interatomic potentials. Comparing the results for the layer with the ones obtained for a strictly 2D setup, we analyze the departure from the 2D character when the density increases. Only when the coverage is rather small the use of a purely 2D model is justified. The condensate fraction of the layer is significantly larger than in 2D at the same surface density, being as large as 60% at the largest coverage studied.
We examine the thermodynamics of a two-dimensional Fermi gas model describing adsorbed 3{}^{3}3Hein a thin superfluid 4{}^{4}4Hefilm. The 3{}^{3}3Hesystem is characterized by both a hydrodynamic effective mass and a set of discrete transverse single-particle states that model the effects of the interaction with the substrate that supports the film. We show that the magnetization steps seen in experiment are a simple manifestation of the T=0KT=0\mathrm{K}T=0K equation of state. We prove that perfectly horizontal magnetization steps rigorously disappear at any finite temperature. We show that the thermal stability of the steps is determined by the larger of $\ensuremath{\Delta}\ensuremath{\epsilon}/2,$ one-half of the level spacing, and ${\ensuremath{\mu}}_{m}{\mathcal{H}}_{0},$ the magnetic energy. We derive the conditions under which there exist points in the phase space (termed invariant points) through which all low-temperature isotherms pass exponentially close. The invariant points appear for magnetization versus 3{}^{3}3Hecoverage, chemical potential versus magnetization, magnetic susceptibility versus coverage, and speed of sound squared versus coverage. We compare our calculated invariant points for the magnetization versus coverage with experiment and find good agreement. We show that there exist small regions of thermodynamic phase space in which the temperature derivative of the pressure is negative. We explain these anomalous regions as the result of 3{}^{3}3Heatoms ``spilling over'' from a full Fermi sea to an empty Fermi sea upon the application of a small increase in temperature. Through a Maxwell relation, this behavior can also be seen as in the appearance of a local peak in low-temperature entropy isotherms versus coverage. In the limit of a two state model, we calculate the specific heat and show that a Schottky peak develops in the low 3{}^{3}3Hecoverage limit. We calculate the magnetic susceptibility and predict that it should exhibit a steplike structure versus 3{}^{3}3Hecoverage similar to that of the magnetization. We calculate the speed of sound and show that it should exhibit zero-temperature discontinuities at the points where new Fermi seas begin to be occupied. Both the steplike structure in the magnetic susceptibility and the discontinuity-type structure in the speed of sound persist to temperatures on the order of 100 mK, and are analyzed in terms of invariant points in their respective phase diagrams. We show explicitly that, in the Fermi gas limit, the zero-field magnetic susceptibility is simply proportional to the isothermal compressibility.
The nuclear magnetic susceptibility of 3He^{3}\mathrm{He}3He adsorbed on the surface of graphite, plated with a monolayer of solid 4He^{4}\mathrm{He}4He, has been measured at surface densities less than 0.055 \AA{} $^{\mathrm{\ensuremath{-}}2}$ and at temperatures down to 6 mK. A temperature-independent susceptibility is observed at low temperatures, which is strongly enhanced over the ideal-gas value, due to quasiparticle interactions. The inferred Landau-Fermi-liquid parameters allow a comparison with microscopic theories of interacting Fermi systems.