  We have studied the effect of nonequilibrium longitudinal optical phonons on
hot-electron spin relaxation in $n$-type GaAs quantum wells. The longitudinal
optical phonons, due to the finite relaxation rate, are driven to
nonequilibrium states by electrons under an in-plane electric field. The
nonequilibrium phonons then in turn influence the electron spin relaxation
properties via modifying the electron heating and drifting. The spin relaxation
time is elongated due to the enhanced electron heating and thus the
electron-phonon scattering in the presence of nonequilibrium phonons. The
frequency of spin precession, which is roughly proportional to the electron
drift velocity, can be either increased (at low electric field and/or high
lattice temperature) or decreased (at high electric field and/or low lattice
temperature). The nonequilibrium phonon effect is more pronounced when the
electron density is high and the impurity density is low.
