Theoretical investigation of the magnetic dynamics in $\alpha$-RuCl$_3$

TL;DR

This paper provides a theoretical analysis of magnetic excitations in $ ext{RuCl}_3$, deriving an effective model from first principles and spin-wave theory, aligning well with experimental neutron scattering data.

Contribution

It introduces a derived effective $K$-$ extGamma$ model from first-principles calculations to explain magnetic excitations in $ ext{RuCl}_3$.

Findings

The effective model accurately reproduces neutron scattering results.

The $K$-$ extGamma$ model captures key magnetic interactions.

Spin-wave excitations are consistent with experimental observations.

Abstract

We study the spin-wave excitations in $\alpha$-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 $K$-$\Gamma$ model containing a ferromagnetic nearest-neighbor (NN) Kitaev interaction ($K$) and a NN off-diagonal exchange interaction ($\Gamma$). With the spin-wave theory, we find that the $K$-$\Gamma$ model can give magnetic excitations which is consistent with the recent neutron scattering experiments.