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∼−5.2 meV, 25 times larger than the Heisenberg exchange J∼−0.2 meV, and responsible for opening the ∼5 meV gap at the Dirac points in the spin-wave dispersion. Furthermore, we find that the symmetric off-diagonal anisotropy Γ∼−67.5μeV, though small, is crucial for opening a ∼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 μeV-scale quadrupolar contribution to the S=3/2 magnetism. Our identification of the underlying exchange anisotropies opens paths toward 2D ferromagnets with higher TC as well as magnetically frustrated quantum spin liquids based on Kitaev physics.
@article{arxiv.1902.00077,
title = {Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI$_3$},
author = {Inhee Lee and Franz G. Utermohlen and Kyusung Hwang and Daniel Weber and Chi Zhang and Johan van Tol and Joshua E. Goldberger and Nandini Trivedi and P. Chris Hammel},
journal= {arXiv preprint arXiv:1902.00077},
year = {2020}
}