Intrinsic spin Hall effect in topological semimetals with single Dirac nodal ring

The spin Hall effect (SHE) maintains a distinct, pivotal role within spintronics. In this study, we systematically investigate the intrinsic SHE of topological semimetals with a single Dirac nodal ring (DNR) in the half-Heusler ABC family of compounds (HfCoAs, HfCoP, HfNiAs, ZrCoP, TaCoGe, TiSiNi, NbCoSi). Taking HfCoAs as an example, we show that an ideal single DNR lies within the My mirror plane adjacent to the Fermi surface when spin-orbit coupling (SOC) is absent, as protected by combined space-time inversion (PT) symmetry and My mirror-reflection symmetry. With the inclusion of the SOC, the DNR is gapped out resulting in plenty of minimal band gap near the Fermi level, which yields a large spin Hall conductivity owing to the large spin Berry curvature hotspots around the nodal ring. Our research provides a comprehensive understanding of spin transport properties inherent in the simplest topological DNR semimetals, providing a solid foundation for exploring and engineering more complicated nodal line semimetals. This work may also offer practical applications in advancing spintronics device development with suitable SHE materials.