Coherent-incoherent crossover of the intrinsic spin Hall effect in Pd

We report the coherent-incoherent crossover of the spin Hall effect in Pd. By measuring spin-orbit torques generated by oxygen-incorporated Pd films, we find two distinct regimes of the spin Hall effect; one in which the spin Hall conductivity is insensitive to the electric conductivity, and the other in which the spin Hall conductivity decreases with decreasing electric conductivity. The crossover between the two regimes is consistent with the prediction of the coherent-incoherent crossover of the spin Hall effect, which is analogous to that of the anomalous Hall effect. Unlike the anomalous Hall effect, for which the crossover has been observed for a wide class of ferromagnets, the crossover of the spin Hall effect has been confirmed only for Pt and Pt-based alloys. The observation of the crossover of the spin Hall effect for Pd supports the generality of this phenomenon, illustrating an important correspondence between the spin Hall effect and the anomalous Hall effect.