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We study the effect of the coupling between the hole $s$ shell of one quantumdot and the $p$ shell in the other dot forming a quantum dot molecule on thespin relaxation between the sublevels of the hole $s$ state. Using an effectivemodel that captures the spin-orbit effects in the $p$ shell irrespective oftheir origin, we show that the strong spin mixing in the $p$ shell can betransferred to the $s$ shell of the other dot, leading to enhanced spinrelaxation in a certain energy range around the $s$-$p$ resonance if the dotsare misaligned and the magnetic field is tilted from the sample plane.

Spin-orbit-induced hole spin relaxation in a quantum dot molecule: the effect of $s$-$p$ coupling