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Spin-orbit coupling has been reported to be responsible for the insulatingnature of the 5d$^1$ osmate double perovskite Ba$_2$NaOsO$_6$ (BNOO). However,whether spin-orbit coupling indeed drives the metal-to-insulator transition(MIT) in this compound is an open question. In this work we investigate theimpact of relativistic effects on the electronic properties of BNOO via densityfunctional theory plus dynamical mean-field theory calculations in theparamagnetic regime, where the insulating phase is experimentally observed. Thecorrelated subspace is modeled with spinor projectors of the projectoraugumented wave method (PAW) employed in the Vienna Ab Initio SimulationPackage (VASP), suitably interfaced with the TRIQS package. The inclusion ofPAW spinor projectors in TRIQS enables the treatment of spin-orbit couplingeffects fully ab-initio within the dynamical mean-field theory framework. Inthe present work, we show that spin-orbit coupling, although assisting the MITin BNOO, is not the main driving force for its gapped spectra, placing thismaterial in the Mott insulator regime. Relativistic effects primarily impactthe correlated states' character, excitations, and magnetic ground-stateproperties.

The Mott transition in the 5d$^1$ compound Ba$_2$NaOsO$_6:$ a DFT+DMFT study with PAW spinor projectors