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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 CrI$_3$ single crystals with theoretical modeling based on symmetries. We discover that the Kitaev interaction is the strongest in this material with $K sim -5.2$ meV, 25 times larger than the Heisenberg exchange $J sim -0.2$ meV, and responsible for opening the $sim$5 meV gap at the Dirac points in the spin-wave dispersion. Furthermore, we find that the symmetric off-diagonal anisotropy $Gamma sim -67.5$ $mu$eV, though small, is crucial for opening a $sim$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 $T_text{C}$ as well as magnetically frustrated quantum spin liquids based on Kitaev physics.
Magnetic anisotropy is crucially important for the stabilization of two-dimensional (2D) magnetism, which is rare in nature but highly desirable in spintronics and for advancing fundamental knowledge. Recent works on CrI$_3$ and CrGeTe$_3$ monolayers
The family of atomically thin magnets holds great promise for a number of prospective applications in magneto-optoelectronics, with CrI$_3$ arguably being its most prototypical member. However, the formation of defects in this system remains unexplor
The spin transfer effect in ferromagnet-quantum dot (insulator)-ferromagnet Aharonov-Bohm (AB) ring system with Rashba spin-orbit (SO) interactions is investigated by means of Keldysh nonequilibrium Green function method. It is found that both the ma
We investigate the impact of mechanical strains and a perpendicular electric field on the electronic and magnetic ground-state properties of two-dimensional monolayer CrI$_3$ using density functional theory. We propose a minimal spin model Hamiltonia
The magnetic properties in two-dimensional van der Waals materials depend sensitively on structure. CrI3, as an example, has been recently demonstrated to exhibit distinct magnetic properties depending on the layer thickness and stacking order. Bulk