Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI3

We lay the foundation for determining the microscopic spin interactions in two-dimensional (2D) ferromagnets by combining angle-dependent ferromagnetic resonance (FMR) experiments on high quality CrI3 single crystals with theoretical modeling based on symmetries. We discover that the Kitaev interaction is the strongest in this material with K similar to -5.2 meV, 25 times larger than the Heisenberg exchange J similar to -0.2 meV, and responsible for opening the similar to 5 meV gap at the Dirac points in the spin-wave dispersion. Furthermore, we find that the symmetric off-diagonal anisotropy Gamma similar to -67.5 mu eV, though small, is crucial for opening a similar to 0.3 meV gap in the magnon spectrum at the zone center and stabilizing ferromagnetism in the 2D limit. The high resolution of the FMR data further reveals a mu eV-scale quadrupolar contribution to the S = 3/2 magnetism. Our identification of the underlying exchange anisotropies opens paths toward 2D ferromagnets with higher T-C as well as magnetically frustrated quantum spin liquids based on Kitaev physics.