  Hole spin relaxation in [001] strained asymmetric Si/Si$_{0.7}$Ge$_{0.3}$
(Ge/Si$_{0.3}$Ge$_{0.7}$) quantum wells is investigated in the situation with
only the lowest hole subband being relevant. The effective Hamiltonian of the
lowest hole subband is obtained by the subband L\"owdin perturbation method in
the framework of the six-band Luttinger ${\bf k}\cdot{\bf p}$ model, with
sufficient basis functions included. The lowest hole subband in Si/SiGe quantum
wells is light-hole like with the Rashba spin-orbit coupling term depending on
momentum both linearly and cubically, while that in Ge/SiGe quantum wells is a
heavy hole state with the Rashba spin-orbit coupling term depending on momentum
only cubically. The hole spin relaxation is investigated by means of the fully
microscopic kinetic spin Bloch equation approach, with all the relevant
scatterings considered. It is found that the hole-phonon scattering is very
weak, which makes the hole-hole Coulomb scattering become very important. The
hole system in Si/SiGe quantum wells is generally in the strong scattering
limit, while that in Ge/SiGe quantum wells can be in either the strong or the
weak scattering limit. The Coulomb scattering leads to a peak in both the
temperature and hole density dependences of spin relaxation time in Si/SiGe
quantum wells, located around the crossover between the degenerate and
nondegenerate regimes. Nevertheless, the Coulomb scattering leads to not only a
peak but also a valley in the temperature dependence of spin relaxation time in
Ge/SiGe quantum wells.... (The remaining is omitted due to the limit of space).
