We establish the effect of electronic correlations and strong-spin-orbit coupling on the emergence of the insulating state and the quadrupolar order in the magnetically frustrated 5d double perovskite Ba2MgReO6
(BMRO). BMRO exhibits a transition to a tetragonally distorted paramagnetic phase below Tq ∼ 33 K and a transition to a non-collinear magnetically ordered state below Tm ∼ 18 K. Using density functional theory in combination with dynamical mean-field theory (DFT+DMFT) we demonstrate that BMRO should be classified as
normal Mott insulator where the spin-orbit coupling is not crucial for the formation of the insulating state. Our calculations further reveal a subtle interplay between the electronic quadrupolar order and the Jahn-Teller distortion, where the primary instability is of electronic origin but the coupling to the structural distortion determines the specific character of the emerging order. Furthermore, we explore the multipolar energy surface with and without Jahn-Teller distortion using a recently developed method for performing DFT(+U) calculations with constained local multipoles.