Selection of direction of the ordered moments in Na${}_2$IrO${}_3$ and $\alpha -$RuCl${}_3$

Abstract

The magnetic orders in Na${}_2$IrO${}_3$ and $\alpha -$RuCl${}_3$, honeycomb systems with strong spin-orbit coupling and correlations, have been recently described by models with the dominant Kitaev interactions. In this work we discuss how the orientation of magnetic order parameter is selected in this class of models. We show that while the order-by-disorder mechanism in the models with solely Kitaev anisotropies always select cubic axes as easy axes for magnetic ordering, the additional effect of other small bond-dependent anisotropies, such as, e.g., $\Gamma$-terms, lead to a deviation of the order parameter from the cubic directions. We show that both the zigzag ground state and the face-diagonal orientation of magnetic moments in Na${}_2$IrO${}_3$ can be obtained within the $J_1-K_1-J_2-K_2-J_3$ model in the presence of perturbatively small $\Gamma$-terms. We also show that the zigzag phase found in the nearest neighbor Kitaev-Heisenberg model, relevant for $\alpha -$RuCl${}_3$, has some stability against the $\Gamma$-term.

10 pages, 6 figures

References in corpus (16)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Low-temperature crystal and magnetic structure of $\alpha$-RuCl3
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• Anisotropic Ru3+ 4d5 magnetism in the alpha-RuCl3 honeycomb system: susceptibility, specific heat and Zero field NMR
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $\beta$-Li2IrO3: full solution via magnetic resonant x-ray diffraction
• Importance of anisotropic exchange interactions in honeycomb iridates. Minimal model for zigzag antiferromagnetic order in Na${}_2$IrO${}_3$
• Spiral order in the honeycomb iridate Li2IrO3
• Order-by-disorder and spin-orbital liquids in a distorted Heisenberg-Kitaev model

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