Zero-temperature attenuation and transverse spin dynamics in fermi liquids. III. Low spin polarizations

Abstract

This is the third in a series of papers on microscopic theory of transverse dynamics in spin-polarized Fermi liquids. In the lowest order in polarization our exact general theory of Ref. 1 reproduces the conventional Landau-Silin-Leggett theory of Fermi liquids. The next term in polarization expansion contains a zero-temperature attenuation with the magnitude that does not depend on polarization. This attenuation results in a finite relaxation time in transverse spin dynamics at zero temperature and is responsible for anomalous temperature behavior of spin diffusion. The zero-temperature attenuation is determined by two angular harmonics of the derivatives of the mass operators and the irreducible vertex in off-shell directions, and cannot be expressed via standard Fermi liquid harmonics. At high polarizations, the parameters of transverse spin dynamics are calculated as an expansion in polarization. The expansion involves complex values of interaction function and energy on a set of isoenergetic surfaces with the radii between the Fermi momenta for up and down spins,p↓ andp↑. The results explain recent experimental data on spin diffusion in spin-polarized liquid3He↑ and3He↑-4He mixtures. The comparison with experimental data indicates that the superfluid transition temperature for3He in3He-4He mixtures may be much lower than the current estimates.