Origin of the anomalous Hall effect in a disordered ferromagnetic Ho 1.25 Au 0.75 Si 1.55 single crystal

The anomalous Hall effect (AHE) serves as a pivotal transport phenomenon for deciphering the interplay between magnetic spin textures and topological bands in magnetic materials, with its origin attributed to intrinsic (momentum-space Berry curvature linked to Weyl or Dirac point) and extrinsic (spin-dependent scattering, i.e., skew scattering and side-jump) mechanisms. The complex magnetic structure and strong spin-orbit coupling effect of rare-earth magnetic materials make them an important platform for studying AHE. Here, we report a disordered ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ single crystal and investigate its magnetic and transport properties. In this single crystal, Ho-Au mixed occupancy on the $2c$ site and vacancies on the Si $2b$ sublattice give rise to pronounced chemical disorder. ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ belongs to the rare-earth ferromagnetic material with a magnetic ordering temperature of 8 K ( ${T}_{c}$ ) and easy magnetization along the $c$ axis. The magnetoresistance (MR) of ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ exhibits different behaviors at high and low temperatures in the $H\ensuremath{\parallel}ab$ and $I\ensuremath{\parallel}c$ configurations. At 3 K ($T\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{T}_{c}$), the MR remains negative as a result of the suppression of the scattering from spin fluctuations. With regard to the AHE, considering the scaling behavior between the anomalous Hall resistivity ${\ensuremath{\rho}}_{xz}^{A}$ and the longitudinal resistivity ${\ensuremath{\rho}}_{zz}$, the origin of the AHE in ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ can be described by the skew scattering mechanism. The dominance of skew scattering is likely driven by the structural disorder present in ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$: the Ho-Au mixed occupancy and Si vacancies create a random potential landscape and break local chemical periodicity, which are expected to enhance asymmetric carrier scattering. The anomalous Hall angle \ensuremath{\Theta}${}_{AH}$ and anomalous Hall factor ${S}_{H}$ of ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ are 0.49% and 0.03 ${\mathrm{V}}^{\ensuremath{-}1}$, respectively, at 3 K, and both decrease as the temperature rises. The small \ensuremath{\Theta}${}_{AH}$ and ${S}_{H}$ are attributed to the finite $s\text{\ensuremath{-}}f$ exchange coupling in this $4f$ localized-moment ferromagnet and to the enhanced scattering environment associated with Ho-Au mixed occupancy and Si vacancies. This work establishes disordered ${\mathrm{Ho}}_{1.25}{\mathrm{Au}}_{0.75}{\mathrm{Si}}_{1.55}$ as a platform for studying the role of structural disorder in skew-scatter-dominated AHE in rare-earth localized-moment ferromagnets.