Intrinsic spin-Hall contribution to the anomalous Hall effect in amorphous GdFeCo ferrimagnet/heavy-metal bilayer systems

Abstract

We investigate the anomalous Hall effect (AHE) in GdFeCo/Pt, GdFeCo/SiN, and GdFeCo/Ta amorphous ferrimagnet/heavy-metal heterostructures for a wide temperature range including the magnetization compensation temperature. To take into account the peculiar temperature dependence of the magnetization in the ferrimagnet, the FeCo magnetization is extracted and used to normalize the anomalous Hall resistivity. From scaling law analysis, we find that AHE in GdFeCo/Pt and GdFeCo/Ta is mainly due to the intrinsic spin-Hall effect (SHE) occurring in the heavy-metal layers. Our results demonstrate the close correlation between the AHE and the SHE. Given that the AHE also originates in the heavy-metal layers, we also propose a circuit model that allows one to separate the AHE from the ferrimagnet layer and from the heavy-metal layer. In heterostructures of a poorly conductive magnetic layer and a heavy-metal layer, careful analysis is crucial to distinguish whether the AHE originates from the magnetic or the heavy-metal layer.