Identifying Fundamental Spin Interactions in CrI₃, CrBr₃, and CrCl₃ through Ferromagnetic Resonance

Fundamental spin interactions in two-dimensional (2D) ferromagnets CrI₃, CrBr₃, and CrCl₃ were determined through analysis of angle dependent ferromagnetic resonance (FMR). Van der Waals 2D ferromagnets have attracted much attention since the advent of atomic monolayer ferromagnets. However, little was known about the fundamental spin interactions underlying 2D ferromagnetism and the origin of their magnetic anisotropy. A new spin model constrained by crystal symmetries based on three main spin interactions, Heisenberg, Kitaev, and off-diagonal symmetric exchange interactions describes these data well. Their precise strengths are determined experimentally obtained from FMR and Curie temperature. One key finding is that the Kitaev interaction is much stronger than other interactions in CrI₃. This surprising result is expected to provide important guidance for realizing novel 2D spin orders, such as magnetically frustrated quantum spin liquids. This Kitaev interaction opens a ~ 4 meV gap in the magnon band, which is corroborated by recent inelastic neutron scattering measurements. We extend our FMR studies to other chromium trihalides, such as CrBr₃ and CrCl₃, to gain a more general understanding of the spin exchange interactions associated with spin-orbit coupling.