Spin and lattice dynamics of the two-dimensional van der Waals ferromagnet CrI3

Abstract Chromium tri-iodide (CrI₃) is a prototypical ferromagnetic van der Waals insulator with its genuinely two-dimensional (2D) long-range magnetic order below 45 K demonstrated recently. The underlying magnetic anisotropy has not been completely understood while both the Dzyaloshinskii-Moriya (DM) interaction and the Kitaev$$-\Gamma$$ type interaction have been considered as the relevant magnetic Hamiltonian. In addition, the relation between the crystal structure and the magnetic order needs to be further elucidated concerning their possible coupling in few-layer samples and in the topmost surface layers of bulk samples. Here, we investigate these issues via temperature- and magnetic field-dependent terahertz spectroscopy on bulk CrI₃ single crystals, focusing on the dynamics of ferromagnetic resonances (FMRs) and optical phonons in the terahertz (THz) region from 4 to 120 cm⁻¹ (from 0.5 to 15 meV). We narrow down the possible ranges of the interaction parameters such as the off-diagonal symmetric terms and the single-ion anisotropy. The accurate values of these parameters significantly constrain the magnitude of possible Kitaev$$-\Gamma$$ exchange interaction and the topological magnon gap. Moreover, the structure-magnetism relationship was critically analyzed based on the temperature- and field-dependences of two $${{\rm{E}}}_{{\rm{u}}}$$ in-plane optical phonon modes, which shows that the commonly believed structural phase diagram of CrI₃, derived from surface-preferential data, has to be seriously modified.