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Multi-valley spin relaxation in $n$-type GaAs quantum wells with in-planeelectric field is investigated at high temperature by means of kinetic spinBloch equation approach. The spin relaxation time first increases and thendecreases with electric field, especially when the temperature is relativelylow. We show that $L$ valleys play the role of a ``drain'' of the total spinpolarization due to the large spin-orbit coupling in $L$ valleys and the strong$\Gamma$-$L$ inter-valley scattering, and thus can enhance spin relaxation ofthe total system effectively when the in-plane electric field is high. Underelectric field, spin precession resulting from the electric-field-inducedmagnetic field is observed. Meanwhile, due to the strong $\Gamma$-$L$inter-valley scattering as well as the strong inhomogeneous broadening in $L$valleys, electron spins in $L$ valleys possess almost the same damping rate andprecession frequency as those in $\Gamma$ valley. This feature still holds whena finite static magnetic field is applied in Voigt configuration, despite thatthe $g$-factor of $L$ valleys is much larger than that of $\Gamma$ valley.Moreover, it is shown that the property of spin precession of the whole systemis dominated by electrons in $\Gamma$ valley. Temperature, magnetic field, andimpurity can affect spin relaxation in low electric field regime. However, theyare shown to have marginal influence in high electric field regime.

Multi-valley spin relaxation in the presence of high in-plane electric fields in $n$-type GaAs quantum wells