Fascinating features of van der Waals magnetic materials have attracted much attention from theoretical and experimental researchers. Recently spin models for two-dimensional Mott insulators beyond the standard Heisenberg interaction have been developed. In particular, the bond-dependent spin ½ Kitaev model on honeycomb lattice is a rare example of exactly solvable model, which exhibits non-Abelian anyons under a magnetic field. Several candidate materials have been proposed and the Kitaev model with higher spins has been also studied. I will present a microscopic route to achieve higher spin Kitaev models in solid state materials [1], and its application to S=3/2 CrI₃ [2]. I will also discuss experimental strategies to extract the Kitaev and other bond-dependent Gamma interactions using the symmetry of a generic Hamiltonian.

 [1] Phys. Rev. Lett. 123, 037203 (2019)

[2]  Phys. Rev. Research 3, 013216 (2021)