Domain Walls Due to Anisotropic Diffusion in 3.8% ³He-⁴He Solutions

Abstract

Nonlinear anisotropic spin diffusion is considered in ³He-⁴He solutions at the ³He concentration 3.8% where spin-rotation effects are absent. For large anisotropy D _∥ $\gg$ D _⊥ it is shown that a long-lived domain wall solution exists in which transverse magnetization is confined in a tube between two reservoirs of up and down spins, as in a longitudinal spin diffusion experiment. This is possible when D _∥ $\gg$ D _⊥ because diffusion of the transverse magnetization away from the domain wall is balanced by longitudinal diffusion toward the wall. Furthermore, the spin current between the up- and down-spin reservoirs is reduced because the spins must diffuse through the domain wall via transverse diffusion. The decay rate of the wall due to small external and demagnetizing field gradients is also calculated.