Theoretical investigation of the magnetic dynamics in $α$-RuCl$_3$

Abstract

We study the spin-wave excitations in $α$-RuCl$_3$ by the spin-wave theory. Starting from the five-orbital Hubbard model and the perturbation theory, we derive an effective isospin-$1/2$ model in the large Hubbard ($U$) limit. Based on the energy-band structure calculated from the first-principle method, we find that the effective model can be further reduced to the $K$-$Γ$ model containing a ferromagnetic nearest-neighbor (NN) Kitaev interaction ($K$) and a NN off-diagonal exchange interaction ($Γ$). With the spin-wave theory, we find that the $K$-$Γ$ model can give magnetic excitations which is consistent with the recent neutron scattering experiments.

12 pages, 7 figures