Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI$_3$

Abstract

We lay the foundation for determining the microscopic spin interactions in the two-dimensional (2D) ferromagnets by combining our angle-dependent ferromagnetic resonance (FMR) experiments on high quality CrI$_3$ single crystals with theoretical modeling based on symmetries. In the 2D limit, ferromagnetism is stabilized by magnetic anisotropy. We find the largest anisotropy arises from Kitaev interactions of strength $K~\sim-5.2$ meV, larger than the Heisenberg exchange $J~\sim-0.2$ meV. We further discover that the symmetric off-diagonal anisotropy $\Gamma\sim-67.5$ $\mu$eV, though small, plays the crucial role of opening a gap in the magnon spectrum and stabilizing ferromagnetism in the 2D limit. The resolution of the FMR data is sufficient to reveal a $\mu$eV-scale quadrupolar contribution in the $S=3/2$ magnet. Our identification of the interactions underlying ferromagnetism and exchange anisotropies opens paths towards 2D ferromagnets with higher T_\rm{C} and magnetically frustrated quantum spin liquids based on Kitaev physics.Comment: 5 pages, 4 figure