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NMR and third sound studies of helium-3/helium-4 mixtures on a nuclepore substrate

Peter Sheldon

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

Nuclear magnetic resonance (NMR) and third sound measurements are reported for thin $\\sp3$He-$\\sp4$He mixture films, varying both the $\\sp3$He and $\\sp4$He thickness, and NMR measurements are reported for two dilute bulk mixtures. All measurements were made for temperatures 27 $\\le T \\le$ 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 $\\sp4$He coverage of $n\\sb4$ = 0.390 A$\\sp{-2}$ while varying the submonolayer $\\sp3$He coverages, 0.006 $\\le n\\sb3 \\le$ 0.063 A$\\sp{-2}$. 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 $\\sim\\ \\pi$ phase shift near T = 200 mK. The magnetization and longitudinal relaxation times of two dilute bulk mixtures of concentration X = 1 $\\times$ 10$\\sp{-5}$ and 2 $\\times$ 10$\\sp{-5}$, where X = $N\\sb3/(N\\sb3$ + $N\\sb4$) and $N\\sb{i}$ is the number of $\\sp{i}He$ atoms, are studied to look for the existence of a theoretically predicted "substrate state". The substrate state is a state where the $\\sp3$He is expected to preferentially sit between the substrate and liquid $\\sp4$He (in a two-dimensional state), rather than be dissolved in the bulk (in a three-dimensional state). The measurements show no evidence of the $\\sp3$He occupying a two-dimensional state, and are consistent with expected three-dimensional behavior. Very thin films of varying $\\sp4$He coverage, 0.148 $\\le n\\sb4 \\le$ 0.227 A$\\sp{-2}$, and with a fixed $\\sp3$He coverage, $n\\sb3$ = 0.006 A$\\sp{-2}$ were studied, looking for localization of the $\\sp3$He atoms in the random potential of the energetically inhomogenous $\\sp4$He 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.

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Dilute helium mixtures at low temperatures : properties and cooling methods

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•Jan 1, 2009•0 citations
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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.
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.
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.
In order to minimize the possibility of spin flips due to interactions with and on the walls of a sample cell, spin-polarized hydrogen (H\ensuremath{\downarrow}) is studied in a 4He^{4}\mathrm{He}4He sample cell, i.e., a sample cell which has been coated with a film of superfluid 4He^{4}\mathrm{He}4He. At low temperatures it is expected that the most dense H\ensuremath{\downarrow} sample will first form in the physisorbed state on the 4He^{4}\mathrm{He}4He film. In this paper we examine in detail the hydrodynamic consequences of this layered film configuration. We derive the expression for third sound in the general case that the films are compressible and both films have undergone superfluid transitions. In this case two propagating modes will be seen which will provide an uneqivocal demonstration of a superfluid transition in the H\ensuremath{\downarrow} film. We specialize to various limiting cases: incompressible films, saturated and unsaturated films, and the normal fluid H\ensuremath{\downarrow} blanket. In our discussion we stress the point that even if the H\ensuremath{\downarrow} has not gone superfluid it will still shift the 4He^{4}\mathrm{He}4He third-sound speed, that this shift is a direct measure of the H\ensuremath{\downarrow} film areal density, and that the magnitude of this shift is expected to be well within the precision of present-day third-sound experimental techniques. Thus third sound is expected to be a primary diagnostic tool in the study of H\ensuremath{\downarrow} films.
Possible acoustic modes in a superfluid 2D gas of hydrogen atoms adsorbed on the surface of liquid helium at T ≲ 0.1 K are considered depending on the oscillation frequency and times of energy and momentum transfers both between 2D subsystems of hydrogen atoms and ripplons and into the bulk liquid or substrate. Analogues of the usual and second sounds are realized in 2D hydrogen at high frequencies. In the case of weak coupling with the bulk liquid and substrate, ripplons provide an addition to the normal hydrogen component, which leads to a change in the speed of the second sound. In the most interesting range of low frequencies, an analogue of the fourth sound is realized, when ripplons and the normal hydrogen component are immobile and only the superfluid hydrogen component moves. In this case, when the rate of heat transfer into the bulk liquid is much lower than the sound frequency, oscillations of the temperature of hydrogen can be observed in phase with density oscillations. Methods for exciting acoustic modes are discussed.
This thesis describes experimental work on dilute mixtures of ³He in 4He, mainly at millikelvin temperatures. The isotopic helium mixture has the unique property of remaining a miscible liquid down to the absolute zero temperature. In the mK regime, it consists of two very different components: perfectly superfluid 4He, and a weakly interacting degenerate Fermi liquid of ³He, predicted by theory to undergo transition to the superfluid state at an extremely low temperature. To discover that transition, new ways of cooling helium mixtures need to be developed, as it is not likely that the conventional method of nuclear demagnetization of copper can be improved to reach helium temperatures notably below the temperatures of order 0.1 mK attained so far. \n Adiabatic melting of 4He in the presence of liquid ³He is probably the most promising method of cooling helium mixtures to microkelvin temperatures. It produces helium mixture colder than the initial temperature as a direct consequence of the mixing of the isotopes. The starting configuration is attainable by pressurizing liquid helium mixture to its solidification pressure at a temperature below some tens of mK, as only 4He then enters the solid phase. This thesis describes an experiment in which the method of adiabatic melting was, for the first time, realized at sub-millikelvin temperatures, where the superfluidity of the pure ³He phase enables, in principle, a drastic decrease of temperature. In the experiments, cooling from initial temperatures between 0.3 and 0.9 mK was detected, temperature reduction remaining below a factor of two for recognized reasons of a technical rather than fundamental nature. \n A capacitive differential pressure transducer, constructed for the experiment, was used for high accuracy measurements of the temperature dependence of the melting pressure of helium mixtures with several ³He concentrations. The melting pressure is suitable for thermometry and carries information on the interactions of ³He particles in the mixture. Also, the response of a quartz tuning fork immersed in helium was studied. Its sensitivity to the properties of the surrounding fluid was utilized to determine the saturation concentration of dilute ³He across the entire accessible pressure range. The tuning fork was found to exhibit a complex pattern of anomalies attributed to resonant modes of second sound, or concentration waves, inside its cylindrical container.