Systematic variation of spin-orbit coupling with d-orbital filling: Large inverse spin Hall effect in 3d transition metals

It is generally believed that spin-orbit coupling (SOC) follows Z(4) (atomic number) dependence and becomes significant only in heavy elements. Consequently, SOC in 3d transition metals should be negligible given their small Z. Using dynamic spin pumping of Y3Fe5O12-based structures, we uncover a systematic evolution of the spin Hall angle (theta(SH)) with d-orbital filling in a series of 3d metals, reminiscent of behavior observed in 5d metals. In particular, Cr and Ni show very large theta(SH) (half of that for Pt), indicating that d-orbital filling rather than Z plays a dominant role in the spin Hall effect (SHE) in 3d metals. This result enriches our understanding of SHE and broadens the scope of materials available for exploring the rich phenomena enabled by SOC as well as presenting a guidepost for testing theoretical models of spin-orbit coupling in transition metals.