First Principles calculations of the EFG tensors of Ba$_2$NaOsO$_6$, a Mott insulator with strong spin orbit coupling

Abstract

We present first principles calculations of the electrostatic properties of Ba2NaOsO6 (BNOO), a 5d 1 Mott insulator with strong spin orbit coupling (SOC) in its low temperature quantum phases. In light of recent NMR experiments showing that BNOO develops a local octahedral distortion that is accompanied by the emergence of an electric field gradient (EFG) and precedes the formation of long range magnetic order [

Evidence from first-principles calculations for orbital ordering in Ba2NaOsO6 : A Mott insulator with strong spin-orbit coupling

“…12 and calculations in Ref. 21. We note that these parameters are similar in magnitude to those of the SOC contributions we observe in the simulations presented below, which are between 1-2 eV.…”

“…Our numerical work is inspired by our recent NMR results revealing that this material exhibited a broken local point symmetry (BLPS) phase followed by a two-sublattice exotic canted ferromagnetic order (cFM). The local symmetry is broken by the orthorhombic Q2 distortion mode 21 . The question we addressed here is whether this distortion is accompanied by the emergence of orbital order.…”

“…The lattice structure with BLPS characterized by the orthorhombic Q2 distortion mode that was identified as being in the best agreement with NMR findings and referred to as Model A.3 in Ref. 21 was imposed.…”

“…This is in line with previous assertions that the SOC and Coulomb interactions in 5d perovskites are similar in magnitude. Projector augmented wave (PAW) 19,20 pseudopotentials (PPs) that include the p semi-core orbitals of the Os atom, which are essential for obtaining the observed electric field gradient (EFG) parameters 21 , were employed to increase the computational efficiency. A monoclinic unit cell with P2 symmetry is required to realize cFM order (see the Supplemental Information).…”

“…In the following subsections, we report our results for the orbital order, band structure, and density of states of BNOO when we impose magnetic order with [110] easy axes and the local orthorhombic distortion that best matched experiments 21 . In Table I, we summarize the converged orbital and spin magnetic moments.…”