Determining Kitaev interaction in spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math> honeycomb Mott insulators
Jiefu Cen, Hae‐Young Kee
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 $\mathrm{Cr}{\mathrm{I}}_{3}$ 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 subdominant. 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.