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.
The nuclear magnetic susceptibility of
3He adsorbed on the surface of graphite, plated with a monolayer of solid
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.
Continuous-wave nuclear magnetic resonance measurements have been performed on liquid
3He-
4He mixtures of 5.0% (at 0, 10, and 20 bars) and 9.5% (at 10 bars)
3He between 0.3 and 25 mK. In the collisionless regime the NMR line is observed to shift and have a maximum in width, effects attributable to spin-wave excitations in the mixture and the first direct evidence for the existence of collective excitations in the
3He-
4He Fermi systems. Analysis of the data yields the Fermi-liquid parameter
F1a for the 5%-
3He mixture.
Measurements of relative values of the nuclear magnetic susceptibility of
He3 vapor have been made by a pulsed resonance technique for several values of vapor density at 2 and 3.1\ifmmode^\circ\else\textdegree\fi{}K. The results of these measurements show that deviations from Curie's law are considerably smaller than those expected for a perfect Fermi gas. A theoretical expression is derived for the susceptibility at vapor densities sufficiently low that only binary collisions are important; a modification of the calculation of the second virial coefficient is used to evaluate the effect of direct interactions. The susceptibility is related to the difference between two virial coefficients, that of
He3 and that calculated for a hypothetical
He3 with zero spin. The theoretical results are in good quantitative agreement with the experimental data. They indicate that the perfect-Fermi-gas theory is not applicable to the calculation of the susceptibility of
He3 vapor at low density except at temperatures lower than 0.002\ifmmode^\circ\else\textdegree\fi{}K. Moreover, from the theoretical results it is concluded that deviations from Curie's law in the vapor are expected to be less than about 1% whenever higher order collisions do not contribute significantly to the interaction between
He3 atoms.
Dilute mixtures of
He3 in liquid
He4 are regarded as a set of
He3 atoms intereacting with elementary excitations of the
He4. The coupling between the
He3 and the
He4 is chosen phenomenologically and it is not weak but, for low temperatures, its main effects may be eliminated by means of two canonical transformations. The equations which determine the transformations describe the motion of a
He4 excitation in the presence of one or two
He3 atoms and, in the latter case, they resemble Faddeev's equations in the three-body problem. At low temperatures, there are few
He4 excitations and many of the properties of the mixture are determined by the effective
He3 Hamiltonian produced by the transformation. In this respect, the system behaves like a Fermi liquid. The
He3-
He3 potential is essentially momentum-independent and consists of the Van der Waals interaction together with an effectively repulsive potential induced by the
He4. It is suggested that a Fermi-liquid analysis is the best way of obtaining information about this potential, and the possible existence of a fermion superfluid phase transition is discussed from that point of view.
We examine the thermodynamics of a two-dimensional Fermi gas model describing adsorbed
3Hein a thin superfluid
4Hefilm. The
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=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
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
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
3Hecoverage limit. We calculate the magnetic susceptibility and predict that it should exhibit a steplike structure versus
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.