A hidden constant in the anomalous Hall effect of a high-purity magnet MnSi

Measurements of the Hall conductivity in MnSi can provide incisive tests of theories of the anomalous Hall (AH) effect, because both the mean-free-path and magnetoresistance (MR) are unusually large for a ferromagnet. The large MR provides an accurate way to separate the AH conductivity $sigma_{xy}^A$ from the ordinary Hall conductivity $sigma_{xy}^N$. Below the Curie temperature $T_C$, $sigma_{xy}^A$ is linearly proportional to $ M$ (magnetization) with a proportionality constant $S_H$ that is independent of both $T$ and $H$. In particular, $S_H$ remains a constant while $sigma_{xy}^N$ changes by a factor of 100 between 5 K and $T_C$. We discuss implications of the hidden constancy in $S_H$.