Determining Kitaev interaction in spin-$S$ honeycomb Mott insulators

Abstract

The Kitaev interaction in a honeycomb lattice with higher-spin $S$ has been one of the central attractions, as it may offer quantum spin liquids. A microscopic theory showed that when the Hund's coupling at the transition metal generates $S>\frac{1}{2}$, the spin-orbit coupling at the heavy ligands provides a route to the Kitaev interaction. However, there have been debates over its strength compared to other symmetry-allowed interactions. Investigating the symmetry of the Hamiltonian for general $S$, we show the magnon energies at two momentum points related by a broken mirror symmetry reflect the Kitaev interaction when a magnetic field is in the mirror plane. Applying the symmetry analysis to CrI${}_3$ with $S=\frac{3}{2}$ together with the available angle-dependent ferromagnetic resonance data, we estimate the Kitaev interaction out of the full Hamiltonian and find that it is sub-dominant. Our theory can be tested by inelastic neutron scattering on candidate materials under the proposed magnetic field direction, which will advance the search for general $S$ Kitaev materials.

arXiv comment6 pages, 5 figures

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• Topological magnon gap engineering in van der Waals CrI${}_3$ ferromagnets
• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Sign Changes in Heat, Spin, and Orbital Magnon Transport Coefficients in Kitaev Ferromagnets
• Twice Hidden String Order and Competing Phases in the Spin-1/2 Kitaev-Gamma Ladder
• Intrinsic Spin Nernst Effect and Chiral Edge Modes in van der Waals Ferromagnetic Insulators: Dzyaloshinskii-Moriya vs. Kitaev Interactions
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Local spin-flip transitions induced by magnetic quantum impurities in two-dimensional magnets
• Spin-orbit coupling controlled two-dimensional magnetism in chromium trihalides