Spin helices in GaAs quantum wells: Interplay of electron density, spin diffusion, and spin lifetime

To establish a correlation between the spin diffusion, the spin lifetime, and the electron density, we study, employing time-resolved magneto-optical Kerr effect microscopy, the spin polarization evolution in low-dimensional GaAs semiconductors hosting two-dimensional electron gases. It is shown that for the establishment of the longest spin-lifetime, the variation of scattering rate with the electron density is of higher importance than the fulfilling of the persistent spin helix condition when the Rashba $\alpha$ and Dresselhaus $\beta$ parameters are balanced. More specifically, regardless of the $\alpha$ and $\beta$ linear dependencies on the electron density, the spin relaxation rate is determined by the spin diffusion coefficient that depends on electron density nonmonotonously. The longest experimental spin-lifetime occurs at an electron density, corresponding to the transition from Boltzmann to Fermi-Dirac statistics, which is several times higher than that when the persistent spin helix is expected. These facts highlight the role the electron density may play when considering applications for spintronic devices.