Ballistic-diffusive crossover in spin propagation and precession

In the transient spin grating (TSG) technique, electron spins are optically oriented in a standing wave (``grating'') of spin polarization with wavevector $q$. TSG measures spin propagation through the time-dependence of the grating amplitude. We have shown$^1$ that for GaAs 2DEGs diffusive spin motion at low mobility $\mu$ crosses over at high $\mu$ to motion that is ballistic on length-scale of the grating---the mean free path exceeds $q^{-1}$. The ballistic regime is characterized by oscillations in the spin-grating amplitude with frequency $\omega\approx v_Fq$. In this talk we present data from TSG and time-resolved Kerr rotation measurements on $n$-doped GaAs quantum wells. We explore the crossover between ballistic and diffusive behavior as a function of temperature and of disorder. We also explore a second, distinct crossover in the spin dynamics that occurs as $v_Fq$ is tuned through the spin-orbit precession frequency, $\Omega_{SO}\approx0.2$ THz. \newline [1] C. P. Weber \textit{et al. Nature} \textbf{437} p. 1330 (2005).