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

## TL;DR

This study combines experimental and theoretical methods to identify the dominant Kitaev interaction in CrI$_3$, revealing its role in magnetic anisotropy and stability of ferromagnetism in 2D materials.

## Contribution

It provides the first quantitative determination of the Kitaev interaction strength and other anisotropies in CrI$_3$ using angle-dependent FMR and symmetry-based modeling.

## Key findings

- Kitaev interaction is the strongest spin interaction in CrI$_3$
- Kitaev interaction opens a 5 meV gap at Dirac points
- Symmetric off-diagonal anisotropy stabilizes 2D ferromagnetism

## Abstract

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.