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

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