Incommensurate Counterrotating Magnetic Order Stabilized by Kitaev Interactions in the Layered Honeycomb $\alpha$-Li${}_2$IrO${}_3$

Abstract

The layered honeycomb magnet $\alpha$-Li${}_2$IrO${}_3$ has been theoretically proposed as a candidate to display novel magnetic behaviour associated with Kitaev interactions between spin-orbit entangled $j_{\mathrm{eff}}=1/2$ magnetic moments on a honeycomb lattice. Here we report single crystal magnetic resonant x-ray diffraction combined with powder magnetic neutron diffraction to reveal an incommensurate magnetic order in the honeycomb layers with Ir magnetic moments counter-rotating on nearest-neighbour sites. This type of magnetic structure has not been reported experimentally before in honeycomb magnets and cannot be explained by a spin Hamiltonian with dominant isotropic (Heisenberg) couplings. The magnetic structure shares many key features with the magnetic order in the structural polytypes $\beta$ and $\gamma$-Li${}_2$IrO${}_3$, understood theoretically to be stabilized by dominant Kitaev interactions between Ir moments located on the vertices of three-dimensional hyperhoneycomb and stripyhoneycomb lattices, respectively. Based on this analogy and a theoretical soft-spin analysis of magnetic ground states for candidate spin Hamiltonians, we propose that Kitaev interactions also dominate in $\alpha$-Li${}_2$IrO${}_3$, indicative of universal Kitaev physics across all three members of the harmonic honeycomb family of Li${}_2$IrO${}_3$ polytypes.

13 pages, 8 figures

References in corpus (9)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• 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
• Spiral order in the honeycomb iridate Li2IrO3
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• Unified theory of spiral magnetism in the harmonic-honeycomb iridates α, β, γ Li2IrO3

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