  In this work, the spin relaxation accompanying the spin diffusion in
symmetric Si/SiGe quantum wells without the D'yakonov-Perel' spin-relaxation
mechanism is calculated from a fully microscopic approach. The spin relaxation
is caused by the inhomogeneous broadening from the momentum-dependent spin
precessions in spatial domain under a magnetic field in the Voigt
configuration. In fact, this inhomogeneous broadening together with the
scattering lead to an irreversible spin relaxation along the spin diffusion.
The effects of scattering, magnetic field and electron density on spin
diffusion are investigated. Unlike the case of spin diffusion in the system
with the D'yakonov-Perel' spin-orbit coupling such as GaAs quantum wells where
the scattering can either enhance or reduce spin diffusion depending on whether
the system is in strong or weak scattering limit, the scattering in the present
system has no counter-effect on the inhomogeneous broadening and suppresses the
spin diffusion monotonically. The increase of magnetic field reduces the spin
diffusion, while the increase of electron density enhances the spin diffusion
when the electrons are degenerate but has marginal effect when the electrons
are nondegenerate.
