  The spin Hall effect (SHE) is an important spintronics phenomenon, which
allows transforming a charge current into a spin current and vice versa without
the use of magnetic materials or magnetic fields. To gain new insight into the
physics of the SHE and to identify materials with a substantial spin Hall
conductivities (SHC), we performed high-precision, high-throughput ab initio
electronic structure calculations of the intrinsic SHC for over 20,000
non-magnetic crystals. The calculations reveal a strong and unexpected relation
of the magnitude of the SHC with the crystalline symmetry, which we show exists
because large SHC is typically associated with mirror symmetry protected nodal
lines in the band structure. From the new developed database, we identify new
promising materials. This includes eleven materials with a SHC comparable or
even larger than that the up to now record Pt as well as materials with
different types of spin currents, which could allow for new types of
spin-obitronics devices.
