Evidence for magnetic fractional excitations in a Kitaev quantum-spin-liquid candidate $α$-RuCl$_3$

$α$-RuCl$_3$ has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on $α$-RuCl$_3$ single crystals to explore the scattering continuum around the $Γ$ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that while the spin-wave excitations around the M point vanish above the transition temperature $T_{\rm N}$, the pure magnetic continuous excitations around the $Γ$ point are robust against temperature. Furthermore, by calculating the dynamical spin-spin correlation function using the cluster perturbation theory, we derive magnetic dispersion spectra based on the $K$-$Γ$ model, which involves with a ferromagnetic Kitaev interaction of -7.2 meV and an off-diagonal interaction of 5.6 meV. We find this model can reproduce not only the spin-wave excitation spectra around the M point, but also the non-spin-wave continuous magnetic excitations around the $Γ$ point. These results provide evidence for the existence of fractional excitations around the $Γ$ point originating from the Kitaev QSL state, and further support the validity of the $K$-$Γ$ model as the effective minimal spin model to describe $α$-RuCl$_3$.