Universal scaling of the Anomalous Hall voltage of magnetic layer with the adjacent conducting layer

Abstract

The anomalous Hall voltage of magnetic heterostructures plays a key role as the indicator for the magnetization state and its interplay with a variety of spintronic effects. In this letter, we report the observation, mechanism, and impact of the universal, dramatic scaling of the anomalous Hall voltage of magnetic heterostructures with the thickness and resistivity of the nonmagnetic conducting layers (e.g., normal metal) by combining transport experiments, analytical derivation, and finite-element analyses. We identify that the mechanism is the serial resistor effect of the magnetic and non-magnetic layers within the magnetic heterostructures and irrelevant to any Fermi surface variation or angular momentum injection from the nonmagnetic layer to the magnetic layer. We also show that the accuracy of the harmonic Hall voltage analyses of magnetic heterostructures are unaffected by the under-measuring of the anomalous Hall voltage and other transverse voltages due to the serial resistor effect. These findings provide crucial information for understanding a variety of spintronic phenomena involving the anomalous Hall and other transverse voltages.