[Paper Review] Mott Insulating Ground State and its Proximity to Spin-Orbit Insulators in Na$_{2}$IrO$_{3}$

Hosub Jin, Heung‐Sik Kim+3 more|ArXiv.org|Jul 4, 2009

Physics of Superconductivity and Magnetism3 citations

TL;DR

This study uses DFT+U+SOC calculations to demonstrate that Na2IrO3 exhibits a Mott insulating ground state with antiferromagnetic order, driven by strong spin-orbit coupling splitting the eg′ doublet near the Fermi level. The system lies close to a spin-orbit insulator phase, leading to strong in-plane magnetic anisotropy and magnetic frustration due to comparable nearest- and next-nearest-neighbor exchange couplings (J′/J = 0.47).

ABSTRACT

We present an anti-ferromagnetically ordered ground state of Na$_{2}$IrO$_{3}$ based on density-functional-theory calculations including both spin-orbit coupling and on-site Coulomb interaction $U$. We show that the splitting of $e_{g}'$ doublet states by the strong spin-orbit coupling is mainly responsible for the intriguing nature of its insulating gap and magnetic ground state. Due to its proximity to the spin-orbit insulator phase, the magnetic ordering as obtained with finite $U$ is found to exhibit a strong in-plane anisotropy. The phase diagram of Na$_{2}$IrO$_{3}$ suggests a possible interplay between spin-orbit insulator and Mott anti-ferromagnetic insulator phases.

Motivation & Objective

• To determine the electronic and magnetic ground state of Na2IrO3 by including both spin-orbit coupling (SOC) and on-site Coulomb interaction (U) in DFT calculations.
• To clarify the role of SOC in splitting eg′ doublet states and its impact on the insulating gap and magnetic ordering.
• To investigate the interplay between Mott insulating and spin-orbit insulating phases in Na2IrO3 via a phase diagram in λSO–U parameter space.
• To assess magnetic frustration by estimating exchange couplings J (nearest-neighbor) and J′ (next-nearest-neighbor) between Ir atoms.
• To explain the origin of strong in-plane anisotropy in the antiferromagnetic order, linked to proximity to the spin-orbit insulator phase.

Proposed method

• Performed DFT calculations using the OpenMX code with the linear-combination-of-pseudo-atomic-orbitals method and non-collinear formalism.
• Applied LDA+U+SOC approach with a relativistic j-dependent pseudopotential scheme to treat both on-site Coulomb repulsion (U) and spin-orbit coupling (λSO).
• Used a (14×14×14) k-point grid for Brillouin zone integration and full structural optimization with a 0.5×10−3 Hatree/Å force criterion.
• Constructed a minimal unit cell of Na2IrO3 based on the hexagonal structure of Na2RuO3, with IrO6 octahedra forming a honeycomb lattice.
• Calculated exchange couplings using a perturbative formalism: Jij = (1/2π)∫^EF dε [Ĝ↑ij Vj Ĝ↓ji Vi], where Ĝ is the Green’s function and V is the on-site exchange potential.
• Explored the λSO–U parameter space to map phase boundaries between paramagnetic metal, Mott insulator, and spin-orbit insulator phases.

Experimental results

Research questions

• RQ1 What is the true ground state of Na2IrO3 when both spin-orbit coupling and on-site Coulomb interaction are included in the electronic structure calculation?
• RQ2 How does spin-orbit coupling splitting of the eg′ doublet states influence the insulating gap and magnetic ordering in Na2IrO3?
• RQ3 What is the nature of the magnetic anisotropy observed in Na2IrO3, and how is it related to proximity to the spin-orbit insulator phase?
• RQ4 To what extent do nearest- and next-nearest-neighbor exchange interactions contribute to magnetic frustration in Na2IrO3?
• RQ5 Can a phase diagram in the λSO–U parameter space distinguish between Mott antiferromagnetic insulator and spin-orbit insulator phases in Na2IrO3?

Key findings

• The ground state of Na2IrO3 is an antiferromagnetic Mott insulator with U = 2.0–3.0 eV and λSO/λ0 = 1, confirmed by LDA+U+SOC calculations.
• The insulating gap arises primarily from strong spin-orbit coupling splitting the eg′ doublet states near the Fermi level, leading to spin-orbit entangled j_eff = 1/2 states.
• The magnetic ordering exhibits strong in-plane anisotropy due to proximity to the spin-orbit insulator phase, with moments quenched along the c-axis.
• The ratio of next-nearest-neighbor to nearest-neighbor exchange coupling is J′/J = 0.47, indicating significant magnetic frustration from competing exchange interactions.
• A phase diagram in λSO–U space reveals a boundary between Mott AFM insulator and SO insulator phases, with the real ground state lying within the Mott insulating region.
• The system remains time-reversal symmetric in the SO insulator phase due to Kramers degeneracy, while the Mott phase breaks symmetry via local magnetic moments.