  We investigate hole spin relaxation in intrinsic and $p$-type bulk GaAs from
a fully microscopic kinetic spin Bloch equation approach. In contrast to the
previous study on hole spin dynamics, we explicitly include the intraband
coherence and the nonpolar hole-optical-phonon interaction, both of which are
demonstrated to be of great importance to the hole spin relaxation. The
relative contributions of the D'yakonov-Perel' and Elliott-Yafet mechanisms on
hole spin relaxation are also analyzed. In our calculation, the screening
constant, playing an important role in the hole spin relaxation, is treated
with the random phase approximation. In intrinsic GaAs, our result shows good
agreement with the experiment data at room temperature, where the hole spin
relaxation is demonstrated to be dominated by the Elliott-Yafet mechanism. We
also find that the hole spin relaxation strongly depends on the temperature and
predict a valley in the density dependence of the hole spin relaxation time at
low temperature due to the hole-electron scattering. In $p$-type GaAs, we
predict a peak in the spin relaxation time against the hole density at low
temperature, which originates from the distinct behaviors of the screening in
the degenerate and nondegenerate regimes. The competition between the screening
and the momentum exchange during scattering events can also lead to a valley in
the density dependence of the hole spin relaxation time in the low density
regime. At high temperature, the effect of the screening is suppressed due to
the small screening constant. Moreover, we predict a nonmonotonic dependence of
the hole spin relaxation time on temperature associated with the screening
together with the hole-phonon scattering. Finally, we find that the
D'yakonov-Perel' mechanism can markedly contribute to the .... (omitted due to
the limit of space)
