Ligand Spin-Orbit Coupling Primarily Determining Fundamental Spin Interactions in Chromium Trihalides

We use ferromagnetic resonance (FMR) spectroscopy to quantitatively determine the spin interactions in the chromium trihalides (CrX₃, X = Cl, Br, I) including the Heisenberg (J), Kitaev (K), and off-diagonal symmetric (Γ) exchange interactions in the Hamiltonian defined by crystal symmetries, and we investigate their correlations with spin-orbit coupling (SOC) strength of the p orbitals of the ligand atom X. Three CrX₃ compounds provide an excellent material platform for exploring and realizing exotic two-dimensional (2D) spin orders since they share the same crystal structure and have the same Hamiltonian, but the SOC strength imposed by the p orbital of the various ligands, X, is different. We find that most magnetic interactions and properties, such as K and Γ, their resulting two magnon band gaps, and the magnetocrystalline anisotropy and Curie temperature , are strongly correlated with the single-factor: SOC strength of the ligand p orbital, in contrast to Cr-Cr bond distance and Cr-X-Cr path angle, which can also have significant influence. This shows that the SOC of X plays a central role in the 2D magnetism of CrX₃, overwhelming the other two factors arising from crystal structure. We also calculate and predict the spin wave dispersions with our determined spin interaction constants for three CrX₃ and compare them.