Abstract
Electron spin lifetimes are investigated in bulk wurtzite $n$-GaN up to very high doping densities by time-resolved Kerr-rotation spectroscopy. The doping densities range from $5\ifmmode\times\else\texttimes\fi{}{10}^{15}$ to $1.5\ifmmode\times\else\texttimes\fi{}{10}^{19}$ cm${}^{\ensuremath{-}3}$, corresponding to Fermi temperatures as high as 1200 K. The spin lifetime shows a maximum at the onset of degeneracy. The additional determination of momentum scattering times allows for a direct comparison with an analytical expression of the spin relaxation tensor in wurtzite semiconductors for a degenerate electron gas following Dyakonov-Perel theory. We find good agreement with the experiment up to the highest densities without any fitting parameter. The only known theoretical value ${\ensuremath{\alpha}}_{e}=$ 9.0 meV \AA{} of the $k$-linear contribution to spin-orbit coupling in the conduction band is shown to be valid up to the highest doping densities.
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