Transition from Intrinsic to Extrinsic Anomalous Hall Effect in the Ferromagnetic Weyl Semimetal PrAlGe$_{1-x}$Si$_x$

Abstract: Recent reports of a large anomalous Hall effect (AHE) in ferromagnetic Weyl semimetals (FM WSM) have led to a resurgence of interest in this enigmatic phenomenon. However, due to a lack of tunable materials, the interplay between the intrinsic mechanism caused by Berry curvature and extrinsic mechanisms due to scattering remains unclear in FM WSMs. In this contribution, we present a thorough investigation of both the extrinsic and intrinsic AHE in a new family of FM WSMs, PrAlGe${1-x}$Si$_x$, where $x$ can be tuned continuously. From DFT calculations, we show that the two end members, PrAlGe and PrAlSi, have different Fermi surfaces but similar Weyl node structures. Experimentally, we observe moderate changes in the anomalous Hall coefficient ($R_S$) but significant changes in the ordinary Hall coefficient ($R_0$) in PrAlGe${1-x}$Si$x$ as a function of $x$, confirming a change of Fermi surface. By comparing the magnitude of $R_0$ and $R_S$, we identify two regimes; $|R_0|<|R_S|$ when $x\le0.5$ and $|R_0|>|R_S|$ when $x>0.5$. Through a detailed scaling analysis, we discover a universal anomalous Hall conductivity (AHC) from intrinsic contribution when $x\le0.5$. Such universal AHC is absent when $x>0.5$. Thus, we point out the significance of the extrinsic mechanisms in FM WSMs and report the first observation of a transition from intrinsic to extrinsic AHE in PrAlGe${1-x}$Si$_x$.