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

TL;DR

This study uses first principles calculations to analyze the electric field gradient tensors in Ba$_2$NaOsO$_6$, revealing structural distortions and their relation to experimental NMR findings in a spin-orbit coupled Mott insulator.

Contribution

It identifies the specific octahedral distortion mode in Ba$_2$NaOsO$_6$ that aligns with experimental data, enhancing understanding of its structural and magnetic properties.

Findings

The local orthorhombic Q2 distortion mode matches experimental observations.

The EFG is unaffected by different magnetic orderings.

Combines NMR data with first principles calculations for comprehensive insight.

Abstract

We present first principles calculations of the electrostatic properties of Ba$_2$NaOsO$_6$ (BNOO), a 5$d^1$ 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 [Lu et al., Nature Comm. 8, 14407 (2017), Liu et al., Phys. Rev. B. 97, 224103 (2018), Liu et al., Physica B. 536, 863 (2018)], we calculated BNOO's EFG tensor for several different model distortions. The local orthorhombic distortion that we identified as mostly strongly agreeing with experiment corresponds to a Q2 distortion mode of the Na-O octahedra, in agreement with conclusions given in [Liu et al., Phys. Rev. B. 97, 224103 (2018)]. Furthermore, we found that the EFG is insensitive to the type of underlying magnetic order. By combining NMR results with first principles modeling, we have thus forged a more complete understanding of BNOO's structural and magnetic properties, which could not be achieved based upon experiment or theory alone.