Castaing instabilities in longitudinal spin-diffusion experiments

Abstract

We analyze the anomalous long-lived NMR signals which have been observed in longitudinal spin-diffusion experiments with Fermi fluids. These signals have been attributed to the Castaing instability of the spin current in the Leggett equation. By considering an idealized experimental geometry in which diffusion occurs between two reservoirs of up and down spins connected via a thin tube, we are able to carry out a full stability analysis of the longitudinal spin current. We show that, in the absence of a field gradient, the instability of the spin current sets in when the spin-rotation parameter exceeds the critical value μM = π/2. In the unstable regime, we obtain spontaneous domain-wall structures as solutions to the steady-state Leggett equation, and discuss their formation from small perturbations. We find that the domain wall reduces the spin current through the tube, leading to an extraordinary increase of the lifetime of the magnetization in the reservoirs. We also show that a magnetic field gradient confines the instability, and that a large enough gradient stabilizes the longitudinal spin current.