Determining Kitaev interaction in spin-S honeycomb Mott insulators

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>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 CrI₃ with S=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.