Computational Study of the Magnetic Structure of Na$_2$IrO$_3$

TL;DR

This study uses first-principles calculations to determine the magnetic structure of Na$_2$IrO$_3$, revealing a zigzag antiferromagnetic order aligned along a specific direction, consistent with experimental data.

Contribution

The paper identifies the magnetic order direction in Na$_2$IrO$_3$ using first-principles methods and explains it via anisotropic interactions in an extended Kitaev-Heisenberg model.

Findings

Magnetic order is along g ≈ a + c direction.

Calculated spin gap is 10.4 meV.

Results align with experimental measurements.

Abstract

The magnetic structure of honeycomb iridate Na$_2$IrO$_3$ is of paramount importance to its exotic properties. The magnetic order is established experimentally to be zigzag antiferromagnetic. However, the previous assignment of ordered moment to the $\bm{a}$-axis is tentative. We examine the magnetic structure of Na$_{2}$IrO$_{3}$ using first-principles methods. Our calculations reveal that total energy is minimized when the zigzag antiferromagnetic order is magnetized along $\bm{g}\approx\bm{a}+\bm{c}$. Such a magnetic configuration is explained by adding anisotropic interactions to the nearest-neighbor Kitaev-Heisenberg model. Spin-wave spectrum is also calculated, where the calculated spin gap of $10.4$ meV can in principle be measured by future inelastic neutron scattering experiments. Finally we emphasize that our proposal is consistent with all known experimental evidence, including the most relevant resonant x-ray magnetic scattering measurements [X. Liu \emph{et al.} {Phys. Rev. B} \textbf{83}, 220403(R) (2011)].