We model the electron and hole spin dynamics in an undoped double quantum dot structure, considering the carrier tunneling between quantum dots. Taking into account also the presence of an in-plane or tilted magnetic field, we provide the simulation of magneto-optical experiments, like the time resolved Kerr rotation measurement, which are performed currently on such structures to probe the temporal spin dynamics. With our model, we reproduce the experimentally observed effect of the extension of the spin polarization life time caused by the spatial charge separation, which may occur in structures of this type. Moreover, we provide a number of qualitative predictions concerning the necessary conditions for observation of this effect as well as about possible channels of its suppression, including the spin-orbit coupling, which leads to tunneling of carriers accompanied by a spin-flip. We consider also the impact of the magnetic field tilting, which results in an interesting spin polarization dynamics.

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