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The evolution of the electron spin dynamics as consequence of carrierdelocalization in $n$-type GaAs is investigated by the recently developedextended pump-probe Kerr/Faraday rotation spectroscopy. We find that isolatedelectrons localized on donors demonstrate a prominent difference between thelongitudinal and transverse spin relaxation rates in magnetic field, which isalmost absent in the metallic phase. The inhomogeneous transverse dephasingtime $T_2^*$ of the spin ensemble strongly increases upon electrondelocalization as a result of motional narrowing that can be induced byincreasing either the donor concentration or the temperature. An unexpectedrelation between $T_2^*$ and the longitudinal spin relaxation time $T_1$ isfound, namely that their product is about constant, as explained by themagnetic field effect on the spin diffusion. We observe a two-stagelongitudinal spin relaxation which suggests the establishment of spintemperature in the system of exchange-coupled donor-bound electrons.

Electron charge and spin delocalization revealed in the optically probed longitudinal and transverse spin dynamics in $n$-GaAs