Title: Ultra-low-current-density single-layer magnetic Weyl semimetal spin Hall nano-oscillators

Abstract: Topological quantum materials can exhibit unconventional surface states and anomalous transport properties. Still, their applications in spintronic devices are restricted as they require the growth of high-quality thin films with bulk-like properties. Here, we study 10--30 nm thick epitaxial ferromagnetic Co$_{\rm 2}$MnGa films with high structural order and very high values of the anomalous Hall conductivity, $\sigma_{\rm xy}=1.35\times10^{5}$ $\Omega^{-1} m^{-1}$ and the anomalous Hall angle, $\theta_{\rm H}=15.8\%$, both comparable to bulk values. We observe a dramatic crystalline orientation dependence of the Gilbert damping constant of a factor of two and a giant intrinsic spin Hall conductivity, $\mathit{\sigma_{\rm SHC}}=(6.08\pm 0.02)\times 10^{5}$ ($\hbar/2e$) $\Omega^{-1} m^{-1}$, an order of magnitude higher than literature values of multilayer Co$_{\rm 2}$MnGa stacks [1-3] and single-layer Ni, Co, Fe [4], and Ni$_{\rm 80}$Fe$_{\rm 20}$~[4,5]. As a consequence, spin-orbit-torque driven auto-oscillations of a 30 nm thick magnetic film are observed for the first time, at an ultralow threshold current density of $J_{th}=6.2\times10^{11}$ $Am^{-2}$. Theoretical calculations of the intrinsic spin Hall conductivity, originating from a strong Berry curvature, corroborate the results and yield values comparable to the experiment. Our results open up for the design of spintronic devices based on single layers of magnetic topological quantum materials.