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Using a combination of density functional theory (DFT) and spin-wave theorymethods, we investigate the magnetic interactions and spin excitations insemiconducting VI$_3$. Exchange parameters of monolayer, bilayer, and bulkforms are evaluated by mapping the magnetic energies of various spinconfigurations, calculated using DFT+$U$, onto the Heisenberg model. Theintralayer couplings remain largely unchanged in three forms of VI$_3$, whilethe interlayer couplings show stronger dependence on the dimensionality of thematerials. We calculate the spin-wave spectra within a linear spin-wave theoryand discuss how various exchange parameters affect the magnon bands. Themagnon-magnon interaction is further incorporated, and the Curie temperature isestimated using a self-consistently renormalized spin-wave theory. Tounderstand the roles of constituent atoms on magnetocrystalline anisotropyenergy (MAE), we resolve MAE into sublattices and find that a strong negativeV-I inter-sublattice contribution is responsible for the relatively smalleasy-axis MAE in VI$_3$.

Magnetic interactions and spin excitations in van der Waals ferromagnet VI$_3$