Evaluation of spin diffusion length and spin Hall angle of antiferromagnetic Weyl semimetal Mn$_3$Sn

Antiferromagnetic Weyl semimetal Mn$_3$Sn has shown to generate strong intrinsic anomalous Hall effect (AHE) at room temperature, due to large momentum-space Berry curvature from the time-reversal symmetry breaking electronic bands of the Kagome planes. This prompts us to investigate intrinsic spin Hall effect, a transverse phenomenon with identical origin as the intrinsic AHE. We report inverse spin Hall effect experiments in nanocrystalline Mn$_3$Sn nanowires at room temperature using spin absorption method which enables us to quantitatively derive both the spin diffusion length and the spin Hall angle in the same device. We observed clear absorption of the spin current in the Mn$_3$Sn nanowires when kept in contact with the spin transport channel of a lateral spin-valve device. We estimate spin diffusion length $lambda_{s(Mn_3Sn)}$ $sim$0.75 $pm$0.67 nm from the comparison of spin signal of an identical reference lateral spin valve without Mn$_3$Sn nanowire. From inverse spin Hall measurements, we evaluate spin Hall angle $theta_{SH}$ $sim$5.3 $pm$ 2.4 $%$ and spin Hall conductivity $sigma_{SH}$ $sim$46.9 $pm$ 3.4 ($hbar/e$) ($Omega$ cm)$^{-1}$. The estimated spin Hall conductivity agrees with both in sign and magnitude to the theoretically predicted intrinsic $sigma_{SH}^{int}$ $sim$36-96 ($hbar/e$) ($Omega$ cm)$^{-1}$. We also observed anomalous Hall effect at room temperature in nano-Hall bars prepared at the same time as the spin Hall devices. Large anomalous Hall conductivity along with adequate spin Hall conductivity makes Mn$_3$Sn a promising material for ultrafast and ultrahigh-density spintronics devices.