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.
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