  In this work, we investigate hole spin-flip transitions in a single
self-assembled InGaAs/GaAs quantum dot. We find the hole wave functions using
the 8-band $kp$ model and calculate phonon-assisted spin relaxation rates for
the ground-state Zeeman doublet. We systematically study the importance of
various admixture- and direct spin-phonon mechanisms giving rise to the
transition rates. We show that the biaxial and shear strain constitute dominant
spin-admixture coupling mechanisms. Then, we demonstrate that hole spin
lifetime can be increased if a quantum dot is covered by a strain-reducing
layer. Finally, we show that the spin relaxation can be described by an
effective model.
