Relationship between Faraday Rotation and Hall Effect in Amorphous Rare-Earth—Transition-Metal Alloys

The Faraday rotation and spontaneous Hall effect were investigated in amorphous thin films with compositions ${\left(\mathrm{GdFe}\right)}_{1-x}{M}_x$ ($M=\mathrm{B}\mathrm{i},\mathrm{S}\mathrm{n},\mathrm{A}\mathrm{u}$). Bismuth and tin are found to increase the Faraday rotation, ${\varphi }_{\mathrm{F}}$, the Hall resistivity, ${\rho }_{\mathrm{H}}$, and the sample resistivity, $\rho$, while Au decreases ${\varphi }_{\mathrm{F}}$, ${\rho }_{\mathrm{H}}$, and $\rho$ as compared to values observed for GdFe. Specifically, ${\varphi }_{\mathrm{F}}$ is proportional to the Hall angle ($\frac{{\rho }_{\mathrm{H}}}{\rho }$). A model first proposed by Voigt is developed to account for this proportionality.