Spin-polarized 3He-4He solutions: Longitudinal spin diffusion and nonlinear spin dynamics.

Abstract

Pulsed-NMR techniques have been used to investigate longitudinal spin diffusion and nonlinear spin dynamics in dilute, spin-polarized $^{3}\mathrm{\ensuremath{-}}^{4}$He solutions between 4 and 400 mK. Solutions with $^{3}\mathrm{He}$ concentrations ${\mathit{x}}_{3}$=3.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ and 19.4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ were forcibly polarized to as much as 65% and 25%, respectively, with a 9.2-T magnetic field. A technique for measuring the coefficient of longitudinal spin diffusion ${\mathit{D}}_{\mathrm{?}}$ is described, and the results of the technique are compared with recent theoretical calculations. Throughout a temperature range that covers both degenerate and nondegenerate behaviors, theory and experiment are found to be in excellent quantitative agreement for ${\mathit{x}}_{3}$=3.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$, and in somewhat weaker agreement for ${\mathit{x}}_{3}$=19.4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$. The presence of strong molecular fields in this system is confirmed by the observation of multiple spin echoes, but it is found that they are not adequately described by recent theory. In addition, the observation of a novel, extremely long-lived oscillation with a lifetime on the order of 10 s is reported. These oscillations are found to have sensitive temperature and magnetic-field-gradient dependencies. A simple model which implies that this behavior is driven by a nonlinear instability is presented, and the results of numerical simulations based on this model are examined in an attempt to gain further insight into the spin dynamics of the system.