The spin Hall effect (SHE) and the inverse spin Hall effect (ISHE) have been widely utilized to interconvert the charge and spin current. In them, the charge current, spin current and spin polarization are orthogonal to each other 1. Based on the general tensor requirement of the spin-charge conversion, additional possibilities can be introduced when the order parameter, the magnetization of a ferromagnet, is involved 2. We herein report the spin-charge conversion in perpendicular magnetized Ti(3 nm)/Co(0.6 nm)/Pd(2 nm)/Co(0.4 nm)/Pd(2 nm)4 multilayers, simplified as Co/Pd multilayers, with the spin pumping measurements. We unambiguously observed the anomalous inverse spin Hall effect (AISHE) in Co/Pd multilayers, where the charge current is collinear with the spin polarization. And both the sign and magnitude of AISHE can be linearly regulated by the out-of-plane magnetization of Co/Pd multilayers. Further, the observed amplitude ratio of AISHE/ISHE in spin pumping measurements is independent of the applied microwave frequency, indicating that it is a material specific parameter.

References
1 J. E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999). 2 X. R. Wang, Commun. Phys. 4, 55 (2021).