Decay of persistent spin helix due to the spin relaxation at boundaries

We study electron spin relaxation in one-dimensional structures of finite length in the presence of Bychkov-Rashba spin-orbit coupling and boundary spin relaxation. Using a spin kinetic equation approach, we formulate boundary conditions for the case of a partial spin polarization loss at the boundaries. These boundary conditions are used to derive corresponding boundary conditions for a spin drift-diffusion equation. The latter is solved analytically for the case of relaxation of a homogeneous spin polarization in one-dimensional finite-length structures. It is found that the spin relaxation consists of three stages (in some cases, two)-an initial D'yakonov-Perel' relaxation is followed by spin helix formation and its subsequent decay. Analytical expressions for the decay time are found. We support our analytical results by results of Monte Carlo simulations. DOI: 10.1103/PhysRevB.87.035430