Not yet reviewed by Pith; the record is open.

We study theoretically antiferromagnet (AFM) based spin-Hall nano-oscillators (SHNOs) consisting of a nano-constriction (NC) in a thin-film uniaxial AFM. By solving the derived SW equation we evidence radially propagating spin waves (SWs) at THz frequencies similar to the Slonczewski SWs known at GHz frequencies for a ferromagnet-based SHNO. We predict a minimum threshold current for a specific NC radius accessible by the state-of-the-art nanotechnology. The exchange interaction enhanced spin pumping for AFMs leads to a strong thickness dependent threshold frequency. We show that the uniaxial AFMs generate ac electrical fields via spin pumping that are three orders of magnitude larger than reported for biaxial AFMs. Our work enhances the fundamental understanding of current-driven SWs in AFM-SHNOs and enables optimization of practical devices in terms of material choice, device geometry, and frequency tunability. The propagating SWs offer remote THz signal generation and an efficient means for synchronization of SHNOs when aiming at high power.