Spin interactions controlled by spin-orbit coupling in chromium trihalide 2D ferromagnets

Chromium trihalides (CrX₃, X = Cl, Br, I) provide an excellent material platform for exploring exotic two-dimensional (2D) spin orders. Three CrX₃ compounds have the same crystal structure and have the same Hamiltonian, but their different p-orbital ligand atoms X lead to different strength of spin-orbit coupling (SOC, λ), the key ingredient responsible for magnetic anisotropy. Here we present measured values of the spin interaction constants Heisenberg (J), Kitaev (K), and off-diagonal symmetric (Γ) exchange interactions in CrX₃ determined using field-angle dependent ferromagnetic resonance (FMR) spectroscopy and exact diagonalization. Furthermore, we investigate the correlation between those values and λ. The unique magnetic anisotropic feature originating from Kitaev interaction obtained from the FMR spectra directly shows the strong dependence on λ. K and Γ and their respective resulting two magnon band gaps ΔK and ΔΓ exhibit a strong λ² dependence, while J has a linear dependence on λ. This shows that the SOC strength λ of X plays a central role in the 2D magnetism of CrX₃.