single crystals from ferromagnetic resonance

We provide the detailed magnetic anisotropy structure of a CrI₃ single crystal obtained through the measurement of the angle dependence of ferromagnetic resonance. We present a microscopic spin model describing the anisotropic interactions in a monolayer in terms of the experimentally measured Heisenberg, Kitaev, symmetric-anisotropic and quadrupole interactions that incorporate the material’s crystal symmetries. Comparison of T_c calculated using spin wave theory with the experimentally known values reveals that CrI₃ is dominantly a Kitaev ferromagnet rather than Heisenberg. We also find that symmetric-anisotropic interaction stabilizes 2D ferromagnetic order by opening the magnon gap ~ 0.4 meV at the center of the Brillouin zone and we predict a Kitaev-interaction-induced ~ 5 meV magnon gap opening at the Dirac point. This work clarifies the complex anisotropic behaviour of spins in CrI₃, opening a route to develop 2D ferromagnets with higher T_c and explore novel 2D spin orders arising from Kitaev physics in van der Waals materials.