Quantifying spin Hall angles from spin pumping: Experiments and Theory

Spin Hall effects intermix spin and charge currents even in nonmagnetic materials and, therefore, ultimately may allow the use of spin transport without the need for ferromagnets. We show how spin Hall effects can be quantified by integrating permalloy/normal metal (N) bilayers into a coplanar waveguide. A dc spin current in N can be generated by spin pumping in a controllable way by ferromagnetic resonance. The transverse dc voltage detected along the permalloy/N has contributions from both the anisotropic magnetoresistance (AMR) and the spin Hall effect, which can be distinguished by their symmetries. We developed a theory that accounts for both. In this way, we determine the spin Hall angle quantitatively for Pt, Au and Mo. This approach can readily be adapted to any conducting material with even very small spin Hall angles.