Size effects in superfluidHe3films

Abstract

This paper addresses two related problems. One is the effect of small geometries on the superfluid phases of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and the other is the nature of the scattering of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ quasiparticles at surfaces. We perform measurements on 300-nm-thick films of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ created by confining the liquid between closely spaced Mylar sheets. The fluid is probed simultaneously by two methods. Nuclear magnetic resonance monitors the spin dynamics of the system, yielding information with which we identify the superfluid phase. In this case, the liquid signal must be separated from that of the adsorbed surface layer, with which it is averaged by spin exchange. The hydrodynamic response of the fluid is determined from the period and damping of a torsion pendulum, which generates oscillatory motion of the substrate. In the normal and superfluid phases alike, this response is strongly dependent on microscopic details of the quasiparticle interactions with the surface. We compare the superfluid measurements to the Ginzburg-Landau model in which the order parameter vanishes at the walls (the diffusive boundary condition). Results for the superfluid transition temperature, the superfluid density, and the NMR frequency shift are in good quantitative agreement with the theory. Also in accord with the theory, we find that the superfluid A phase is stabilized by the walls over a wide range of pressures and temperatures at which the B phase is stable in bulk. In contrast with the calculations, however, we do not observe the A-B phase boundary. The ${}_{}{}^3{}_{}{}^{}\mathrm{substrate}$ interface is modified in these experiments by the introduction of small quantities of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ plates out preferentially on the surfaces at low temperatures, an effect that persists until a layer several atoms deep has been built up. The boundary condition on the order parameter is observed to vary continuously with the surface ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ coverage, spanning almost the full range between the limits corresponding to diffusive and specular quasiparticle scattering.