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To establish a correlation between the spin diffusion, the spin lifetime, andthe electron density, we study, employing time-resolved magneto-optical Kerreffect microscopy, the spin polarization evolution in low-dimensional GaAssemiconductors hosting two-dimensional electron gases. It is shown that for theestablishment of the longest spin-lifetime, the variation of scattering ratewith the electron density is of higher importance than the fulfilling of thepersistent 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 relaxationrate is determined by the spin diffusion coefficient that depends on electrondensity nonmonotonously. The longest experimental spin-lifetime occurs at anelectron density, corresponding to the transition from Boltzmann to Fermi-Diracstatistics, which is several times higher than that when the persistent spinhelix is expected. These facts highlight the role the electron density may playwhen considering applications for spintronic devices.

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