Modeling of diffusion of injected electron spins in spin-orbit coupled microchannels

We report on a theoretical study of spin dynamics of an ensemble of spin-polarized electrons injected in a diffusive microchannel with linear Rashba and Dresselhaus spin-orbit coupling. We explore the dependence of the spin-precession and spin-diffusion lengths on the strengths of spin-orbit interaction and external magnetic fields, microchannel width, and orientation. Our results are based on numerical Monte Carlo simulations and on approximate analytical formulas, both treating the spin dynamics quantum-mechanically. We conclude that spin-diffusion lengths comparable or larger than the precession-length occur i) in the vicinity of the persistent spin helix regime for arbitrary channel width, and ii) in channels of similar or smaller width than the precession length, independent of the ratio of Rashba and Dresselhaus fields. For similar strengths of the Rashba and Dresselhaus fields, the steady-state spin-density oscillates or remains constant along the channel for channels parallel to the in-plane diagonal crystal directions. An oscillatory spin-polarization pattern tilted by 45$^{\circ}$ with respect to the channel axis is predicted for channels along the main cubic crystal directions. For typical experimental system parameters, magnetic fields of the order of Tesla are required to affect the spin-diffusion and spin-precession lengths.