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We investigate the antiferromagnetic insulating state of the recentlydiscovered double perovskites Sr$_2$XOsO$_6$ (X$=$Sc, Mg) by using ab-initiocalculations (based on Density Functional Theory and Dynamical Mean-FieldTheory) to elucidate the interplay between electronic correlations andspin-orbit coupling. The structural details of Sr$_2$XOsO$_6$ (X$=$Sc, Mg)induce band narrowing effects which enhance local electronic correlations. Thehalf-filled $5d^3$ orbitals of Os in Sr$_2$ScOsO$_6$ fall into a magneticallyordered correlated regime, which is slightly affected and reduced by thespin-orbit coupling. The electronic configuration $5d^2$ of Os inSr$_2$MgOsO$_6$ responses differently to electronic correlations promoting aless localized state than Sr$_2$ScOsO$_6$ at the same strength of electronicinteractions. We find that the inclusion of spin-orbit coupling drivesSr$_2$MgOsO$_6$ toward insulating behaviour and promotes a large tendency information of orbital magnetization antiparallel to the spin moment. Theformation of the AFM state is linked to the evidence of correlated Hubbardbands in the paramagnetic solution of Sr$_2$XOsO$_6$ (X$=$Sc, Mg).

The influence of Coulomb Correlations and Spin-Orbit Coupling in the electronic structure of double perovskites Sr$_2$XOsO$_6$ (X$=$Sc, Mg)