  We develop a theory of effects of electron-electron collisions on the
Dyakonov-Perel' spin relaxation in multi-valley quantum wells. It is shown that
the electron-electron scattering rate which governs the spin relaxation is
different from that in a single-valley system. The theory is applied to Si/SiGe
(001)-grown quantum wells where two valleys are simultaneously populated by
free carriers. The dependences of the spin relaxation rate on temperature,
electron concentration and valley-orbit splitting are calculated and discussed.
We demonstrate that in a wide range of temperatures the electron-electron
collisions can govern spin relaxation in high-quality Si/SiGe quantum wells.
