We report a systematic study of the spin relaxation anisotropy between single electron Zeeman sublevels in three-dimensional cuboidal GaAs quantum dots (QDs). The QDs are subject to an in-plane magnetic field. As the field orientation varies, the relaxation rate oscillates periodically, showing 'magic' angles where the relaxation rate is suppressed by several orders of magnitude. This behavior is found in QDs with different shapes, heights, crystallographic orientations and external fields. The origin of these angles can be traced back to the symmetries of the spin admixing terms of the Hamiltonian. Our results evidence that cubic Dresselhaus terms play an important role in determining the spin relaxation anisotropy, which can induce deviations of the 'magic' angles from the crystallographic directions reported in recent experiments (P Scarlino et al 2014 Phys. Rev. Lett. 113 256802).This work was supported by UJI-Bancaixa Project No. P1-1B2011-01, MINECO Project No. CTQ2011-27324, and FPU Grant (C S)
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