Assessing the Reliability of Anomalous Hall Conductivity Extraction in GdAlSi

Abstract

We examine the different methods of extracting the anomalous Hall conductivity using SrRuO$_3$ and GdAlSi. For SrRuO$_3$, where the ordinary Hall background is well defined and the magnetoconductance is small, subtracting the ordinary Hall contribution either before or after conversion from resistivity to conductivity yields nearly identical anomalous Hall conductivities. In GdAlSi, in contrast, the transverse response does not exhibit clear saturation, and both low- and high-field regions can appear approximately linear. We show that different interpretations of these linear regions as the ordinary Hall background, together with the treatment of the measured longitudinal resistance in the resistivity-to-conductivity conversion, can produce completely different estimates of the anomalous Hall conductivity. We also examine whether the nonlinear Hall response can instead be described within an ordinary Hall framework without invoking an anomalous contribution. Our analysis provides practical cautions for extracting excess Hall contributions in quantum materials.