Leggett-Rice effect in a finite geometry

Abstract

The problem of restricted diffusion in the presence of the spin rotation effect is investigated theoretically. The concept of diffusion modes is applied to calculate the attenuation of the spin echo signal in a $\ensuremath{\theta}\ensuremath{-}180\ifmmode^\circ\else\textdegree\fi{}$ NMR sequence. First we study the diffusion modes in a one-dimensional geometry and show that there are in general two types of modes: bulk modes and edge modes. Then we show that the spin rotation effect tends to delocalize the modes and favor edge modes. An expression of the spin echo signal is given as a linear combination of diffusion modes. We study the refocusing of the echo signal and show that the spin rotation effect causes a phase shift. Approximate analytical expressions for the echo signal are given in the three limiting cases: free diffusion, motional narrowing, and localization. Finally, we show that the results of some experiments on spin diffusion anisotropy in spin-polarized ${}^{3}\mathrm{He}{\ensuremath{-}}^{4}\mathrm{He}$ mixtures are biased by restricted diffusion effects.