Dirac nodal lines and induced spin Hall effect in metallic rutile oxides

We have found Dirac nodal lines (DNLs) in the band structures of metallic rutile oxides IrO$_2$, OsO$_2$, and RuO$_2$ and revealed a large spin Hall conductivity contributed by these nodal lines, which explains a strong spin Hall effect (SHE) of IrO$_2$ discovered recently. Two types of DNLs exist. The first type forms DNL networks that extend in the whole Brillouin zone and appears only in the absence of spin-orbit coupling (SOC), which induces surface states on the boundary. Because of SOC-induced band anti-crossing, a large intrinsic SHE can be realized in these compounds. The second type appears at the Brillouin zone edges and is stable against SOC because of the protection of nonsymmorphic symmetry. Besides reporting new DNL materials, our work reveals the general relationship between DNLs and the SHE, indicating a way to apply Dirac nodal materials for spintronics.