Spin waves and spin diffusion in Fermi liquids: Bounds on effective diffusion coefficients

We investigate the accuracy of the usual relaxation-time approximations, involving the spin-diffusion lifetime D, which are generally made in analyses of spin waves and the Leggett-Rice effect in Fermi liquids. By employing the variational methods of Ah-Sam, Ho/jgaard-Jensen, and Smith and of Egilsson and Pethick, we are able to determine upper and lower bounds on the effective diffusion coefficient resulting from spin-wave phenomena which are accurate in the whole Fermi-liquid regime (TTF). Our results indicate that the usual approximations break down for T7 mK in He3, but are accurate to within 2% in 5% -43He mixtures. Our results are consistent with values of F1a-0.6 at 0 bar, -0.4 at 27 bars in He3, but these have considerable uncertainties.