We calculate the rates of phonon-assisted hyperfine spin flips during electron and hole tunneling between quantum dots in a self-assembled quantum dot molecule. We show that the hyperfine process dominates over the spin-orbit-induced spin relaxation in magnetic fields up to a few teslas for electrons, while for holes this crossover takes place at field magnitudes of a fraction of a tesla, upon the assumption of a large $d$-shell admixture to the valence band state, resulting in a strong transverse hyperfine coupling. The interplay of the two spin-flip mechanisms leads to a minimum of the spin-flip probability, which is, in principle, experimentally measurable and can be used as a test for the presence of substantial transverse hyperfine couplings in the valence band.

• Received 15 January 2021
• Revised 17 May 2021
• Accepted 7 July 2021

DOI:https://doi.org/10.1103/PhysRevB.104.045308