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Multivalley spin relaxation in $n$-type bulk GaAs in the presence of high electric fields

Multivalley spin relaxation in $n$-type bulk GaAs in the presence of high electric field is investigated from the microscopic kinetic spin Bloch equation approach with the $Γ$ and $L$ valleys included. We show that the spin relaxation time decreases monotonically with the electric field, which differs from the two-dimensional case and is recognized due to to the cubic form of the Dresselhauss spin-orbit coupling of the $Γ$ valley in bulk. In addition to the direct modulation of the spin relaxation time, the electric field also strongly influences the density and temperature dependences of the spin relaxation. In contrast to the monotonic decrease with increasing lattice temperature in the field-free condition, the spin relaxation time is shown to decrease more slowly under the influence of the electric field and even to increase monotonically in the case with small electron density and high electric field. We even predict a peak in weakly doped samples under moderate electric field due to the anomalous lattice-temperature dependence of the hot-electron temperature. As for the $L$ valleys, we show that instead of playing the role of a "drain" of the total spin polarization as in quantum well systems, in bulk they serve as a "momentum damping area", which prevents electrons from drifting to higher momentum states. This tends to suppress the inhomogeneous broadening and hence leads to an increase of the spin relaxation time.