Importance of anisotropic exchange interactions in honeycomb iridates. Minimal model for zigzag antiferromagnetic order in Na${}_2$IrO${}_3$

Abstract

In this work, we investigate the microscopic nature of the magnetism in honeycomb iridium-based systems by performing a systematic study of how the effective magnetic interactions in these compounds depend on various electronic microscopic parameters. We show that the minimal model describing the magnetism in A${}_2$IrO${}_3$ includes both isotropic and anisotropic Kitaev-type spin-exchange interactions between nearest and next-nearest neighbor Ir ions, and that the magnitude of the Kitaev interaction between next-nearest neighbor Ir magnetic moments is comparable with nearest neighbor interactions. We also find that, while the Heisenberg and the Kitaev interactions between nearest neighbors are correspondingly antiferro- and ferromagnetic, they both change sign for the next-nearest neighbors. Using classical Monte Carlo simulations we examine the magnetic phase diagram of the derived super-exchange model. Zigzag-type antiferromagnetic order is found to occupy a large part of the phase diagram of the model and, for ferromagnetic next-nearest neighbor Heisenberg interaction relevant for Na${}_2$IrO${}_3$, it can be stabilized even in the absence of third nearest neighbor coupling. Our results suggest that a natural physical origin of the zigzag phase experimentally observed in Na${}_2$IrO${}_3$ is due to the interplay of the Kitaev anisotropic interactions between nearest and next-nearest neighbors.

arXiv comment14 pages, 5 figures

References in corpus (26)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Novel Jeff = 1/2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr2IrO4
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Orbital order and fluctuations in Mott insulators
• Direct evidence of a zigzag spin chain structure in the honeycomb lattice: A neutron and x-ray diffraction investigation on single crystal $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Topological Insulators and Mott Physics from the Hubbard Interaction
• Crystal field splitting and correlation effect on the electronic structure of A2IrO3
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Na2IrO3 as a spin-orbit-assisted antiferromagnetic insulator with a 340 meV gap
• First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations
• Ab initio analysis of the tight-binding parameters and magnetic interactions in Na2IrO3
• Kitaev-Heisenberg-J2-J3 model for the iridates A2IrO3
• Critical properties of the Kitaev-Heisenberg model
• Spiral order in the honeycomb iridate Li2IrO3
• Spin-Orbital Locking, Emergent Pseudo-Spin, and Magnetic order in Honeycomb Lattice Iridates
• Magnetic ordering phenomena of interacting quantum spin Hall models
• Interplay of many-body and single-particle interactions in iridates and rhodates
• Spin and Orbital Contributions to Magnetically Ordered Moments in 5d Layered Perovskite Sr2IrO4

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