Anomalous spin diffusion in³He films: Expected behaviour in two-dimensional Fermi liquids

Abstract

It is shown that the recently observed and unexplained behaviour for spin diOE usion in 3 He ®lms can be understood in terms of the Fermi-liquid theory, provided that non-perturbative eOE ects characteristic of two dimensions are taken into account. It is conjectured that such a behaviour suggests the onset of a regime in which spin current is conserved.The theory of Fermi liquids in two dimensions has been at the centre of various discussions involving unexpected physics that have arisen in a broad range of interesting materials. Examples range from systems in the quantum Hall regime to copper oxide superconductors, including 3 He± 4 He quantum-¯uid mixtures. These latter provided grounds for the recent observation of unexpected behaviour, whose main cause will be argued in the following to be a consequence of the two-dimensionalit y of a general system of fermions. In a recent letter, Sheldon and Hallock (2000) presented experimental results for spin diOE usion in a thin ®lm of 3 He on top of a super¯uid 4 He ®lm. The result for the spin diOE usion coe cient D spin as a function of the 3 He coverage D 3 shows an upturn followed by a saturation and a downturn, as D 3 is increased. These features could not be reproduced by standard theoretical predictions (Miyake andMullin 1983, 1984). In the work reported by Sheldon and Hallock (2000), care has been taken to guarantee that the 3 He ®lm forms a two-dimensional (2D) system of interacting fermions, with little in¯uence from the 4 He super¯uid ®lm that is below. Hence one should be able to account for the observed features using theoretical results from a 2D Landau theory. It is argued in this letter that the theory of 2D Fermi liquids does account for the observed behaviour (regarding the existence of a peak in D spin as a function of D 3 ) provided that one includes non-perturbativ e eOE ects that are inherent in a Fermi liquid in two spatial dimensionsy (Engelbrecht and Randeria 1990). It is also pointed that the onset of regimes in the 2D Fermi liquid for which spin current is a conserved quantity (Farinas et al. 1999) is related to such a peaked behaviour; however, more experimental results are necessary to establish whether these regimes may be tuned or not.y Two dimensions means here that the quasiparticle's momenta are confined to a surface (the Fermi gas sits on a surface state adsorbed on superfluid 4 He); this leads to a one-dimensional Fermi surface.First some remarks on existing theoretical results are made, and an explanation is given for why the ®rst attempts to ®t the experimental data failed. Then the microscopic scenario that accounts for the physics underlying the peaked behaviour observed is devised and D spin is calculated; the result of this is plotted in ®gure 1 and compared with the experimental data. It should be stressed that the aim here is not to reproduce the experimental data fully, but to uncover the physics that lead to the observed peak. Indeed, although the accuracy of the theoretical ®tting is quite remarkable and consistent with t...